Numerical Investigation of the Local Scour for Tripod Pile Foundation

Numerical Investigation of the Local Scour for Tripod Pile Foundation

Waqed H. Hassan | Zahraa Mohammad Fadhe* | Rifqa F. Thiab | Karrar Mahdi
Civil Engineering Department, Faculty of Engineering, University of Warith Al-Anbiyaa, Kerbala 56001, Iraq
Civil Engineering Department, Faculty of Engineering, University of Kerbala, Kerbala 56001, Iraq
Corresponding Author Email: Waqed.hammed@uowa.edu.iq

OPEN ACCESS

Abstract: 

This work investigates numerically a local scour moves in irregular waves around tripods. It is constructed and proven to use the numerical model of the seabed-tripod-fluid with an RNG k turbulence model. The present numerical model then examines the flow velocity distribution and scour characteristics. After that, the suggested computational model Flow-3D is a useful tool for analyzing and forecasting the maximum scour development and the flow field in random waves around tripods. The scour values affecting the foundations of the tripod must be studied and calculated, as this phenomenon directly and negatively affects the structure of the structure and its design life. The lower diagonal braces and the main column act as blockages, increasing the flow accelerations underneath them.  This increases the number of particles that are moved, which in turn creates strong scouring in the area. The numerical model has a good agreement with the experimental model, with a maximum percentage of error of 10% between the experimental and numerical models. In addition, Based on dimensional analysis parameters, an empirical equation has been devised to forecast scour depth with flow depth, median size ratio, Keulegan-Carpenter (Kc), Froud number flow, and wave velocity that the results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50) and the scour depth attains its steady-current value for Vw < 0.75. As the Froude number rises, the maximum scour depth will be large.

Keywords: 

local scour, tripod foundation, Flow-3D​, waves

1. Introduction

New energy sources have been used by mankind since they become industrialized. The main energy sources have traditionally been timber, coal, oil, and gas, but advances in the science of new energies, such as nuclear energy, have emerged [1, 2]. Clean and renewable energy such as offshore wind has grown significantly during the past few decades. There are numerous different types of foundations regarding offshore wind turbines (OWTs), comprising the tripod, jacket, gravity foundation, suction anchor (or bucket), and monopile [3, 4]. When the water depth is less than 30 meters, Offshore wind farms usually employ the monopile type [4]. Engineers must deal with the wind’s scouring phenomenon turbine foundations when planning and designing wind turbines for an offshore environment [5]. Waves and currents generate scour, this is the erosion of soil near a submerged foundation and at its location [6]. To predict the regional scour depth at a bridge pier, Jalal et al. [7-10] developed an original gene expression algorithm using artificial neural networks. Three monopiles, one main column, and several diagonal braces connecting the monopiles to the main column make up the tripod foundation, which has more complicated shapes than a single pile. The design of the foundation may have an impact on scour depth and scour development since the foundation’s form affects the flow field [11, 12]. Stahlmann [4] conducted several field investigations. He discovered that the main column is where the greatest scour depth occurred. Under the main column is where the maximum scour depth occurs in all experiments. The estimated findings show that higher wave heights correspond to higher flow velocities, indicating that a deeper scour depth is correlated with finer silt granularity [13] recommends as the design value for a single pile. These findings support the assertion that a tripod may cause the seabed to scour more severely than a single pile. The geography of the scour is significantly more influenced by the KC value (Keulegan–Carpenter number)

The capability of computer hardware and software has made computational fluid dynamics (CFD) quite popular to predict the behavior of fluid flow in industrial and environmental applications has increased significantly in recent years [14].

Finding an acceptable piece of land for the turbine’s construction and designing the turbine pile precisely for the local conditions are the biggest challenges. Another concern related to working in a marine environment is the effect of sea waves and currents on turbine piles and foundations. The earth surrounding the turbine’s pile is scoured by the waves, which also render the pile unstable.

In this research, the main objective is to investigate numerically a local scour around tripods in random waves. It is constructed and proven to use the tripod numerical model. The present numerical model is then used to examine the flow velocity distribution and scour characteristics.

2. Numerical Model

To simulate the scouring process around the tripod foundation, the CFD code Flow-3D was employed. By using the fractional area/volume method, it may highlight the intricate boundaries of the solution domain (FAVOR).

This model was tested and validated utilizing data derived experimentally from Schendel et al. [15] and Sumer and Fredsøe [6]. 200 runs were performed at different values of parameters.

2.1 Momentum equations

The incompressible viscous fluid motion is described by the three RANS equations listed below [16]:

(1)

\frac{\partial u}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial u}{\partial x}+v{{A}_{y}}\frac{\partial u}{\partial y}+w{{A}_{z}}\frac{\partial u}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial x}+{{G}_{x}}+fx

(2)

\frac{\partial v}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial v}{\partial x}+v{{A}_{y}}\frac{\partial v}{\partial y}+w{{A}_{z}}\frac{\partial v}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial y}+{{G}_{y}}+\text{f}y

 (3)

\frac{\partial w}{\partial t}+\frac{1}{{{V}_{F}}}\left( u{{A}_{x}}\frac{\partial w}{\partial x}+v{{A}_{y}}\frac{\partial w}{\partial y}+w{{A}_{z}}\frac{\partial w}{\partial z} \right)=-\frac{1}{\rho }\frac{\partial p}{\partial z}+{{G}_{z}}+\text{fz}

where, respectively, u, v, and w represent the x, y, and z flow velocity components; volume fraction (VF), area fraction (Ai; I=x, y, z), water density (f), viscous force (fi), and body force (Gi) are all used in the formula.

2.2 Model of turbulence

Several turbulence models would be combined to solve the momentum equations. A two-equation model of turbulence is the RNG k-model, which has a high efficiency and accuracy in computing the near-wall flow field. Therefore, the flow field surrounding tripods was captured using the RNG k-model.

2.3 Model of sediment scour

2.3.1 Induction and deposition

Eq. (4) can be used to determine the particle entrainment lift velocity [17].

(4)

{{u}_{lift,i}}={{\alpha }_{i}}{{n}_{s}}d_{*}^{0.3}{{\left( \theta -{{\theta }_{cr}} \right)}^{1.5}}\sqrt{\frac{\parallel g\parallel {{d}_{i}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{{{\rho }_{f}}}}

α𝛼i   is the Induction parameter, ns the normal vector is parallel to the seafloor, and for the present numerical model, ns=(0,0,1), θ𝜃cr is the essential Shields variable, g is the accelerated by gravity, di is the size of the particles, ρi is species density in beds, and d∗ The diameter of particles without dimensions; these values can be obtained in Eq. (5).

(5)

{{d}_{*}}={{d}_{i}}{{\left( \frac{\parallel g\parallel {{\rho }_{f}}\left( {{\rho }_{i}}-{{\rho }_{f}} \right)}{\mu _{f}^{2}} \right)}^{1/3}}

μ𝜇f is this equation a dynamic viscosity of the fluid. cr was determined from an equation based on Soulsby [18].

(6)

{{\theta }_{cr}}=\frac{0.3}{1+1.2{{d}_{*}}}+0.055\left[ 1-\text{exp}\left( -0.02{{d}_{*}} \right) \right]

The equation was used to determine how quickly sand particles set Eq. (7):

(7)

{{\mathbf{u}}_{\text{nsettling},i}}=\frac{{{v}_{f}}}{{{d}_{i}}}\left[ {{\left( {{10.36}^{2}}+1.049d_{*}^{3} \right)}^{0.5}}-10.36 \right]

vf  stands for fluid kinematic viscosity.

2.3.2 Transportation for bed loads

Van Rijn [19] states that the speed of bed load conveyance was determined as:

(8)

{{~}_{\text{bedload},i}}=\frac{{{q}_{b,i}}}{{{\delta }_{i}}{{c}_{b,i}}{{f}_{b}}}

fb  is the essential particle packing percentage, qb, i is the bed load transportation rate, and cb, I the percentage of sand by volume i. These variables can be found in Eq. (9), Eq. (10), fb, δ𝛿i the bed load thickness.

(9)

{{q}_{b,i}}=8{{\left[ \parallel g\parallel \left( \frac{{{\rho }_{i}}-{{\rho }_{f}}}{{{\rho }_{f}}} \right)d_{i}^{3} \right]}^{\frac{1}{2}}}

(10)

{{\delta }_{i}}=0.3d_{*}^{0.7}{{\left( \frac{\theta }{{{\theta }_{cr}}}-1 \right)}^{0.5}}{{d}_{i}}

In this paper, after the calibration of numerous trials, the selection of parameters for sediment scour is crucial. Maximum packing fraction is 0.64 with a shields number of 0.05, entrainment coefficient of 0.018, the mass density of 2650, bed load coefficient of 12, and entrainment coefficient of 0.01.

3. Model Setup

To investigate the scour characteristics near tripods in random waves, the seabed-tripod-fluid numerical model was created as shown in Figure 1. The tripod basis, a seabed, and fluid and porous medium were all components of the model. The seabed was 240 meters long, 40 meters wide, and three meters high. It had a median diameter of d50 and was composed of uniformly fine sand. The 2.5-meter main column diameter D. The base of the main column was three dimensions above the original seabed. The center of the seafloor was where the tripod was, 130 meters from the offshore and 110 meters from the onshore. To prevent wave reflection, the porous media were positioned above the seabed on the onshore side.

image013.png

Figure 1. An illustration of the numerical model for the seabed-tripod-fluid

3.1 Generation of meshes

Figure 2 displays the model’s mesh for the Flow-3D software grid. The current model made use of two different mesh types: global mesh grid and nested mesh grid. A mesh grid with the following measurements was created by the global hexahedra mesh grid: 240m length, 40m width, and 32m height. Around the tripod, a finer nested mesh grid was made, with dimensions of 0 to 32m on the z-axis, 10 to 30 m on the x-axis, and 25 to 15 m on the y-axis. This improved the calculation’s precision and mesh quality.

image014.png

Figure 2. The mesh block sketch

3.2 Conditional boundaries

To increase calculation efficiency, the top side, The model’s two x-z plane sides, as well as the symmetry boundaries, were all specified. For u, v, w=0, the bottom boundary wall was picked. The offshore end of the wave boundary was put upstream. For the wave border, random waves were generated using the wave spectrum from the Joint North Sea Wave Project (JONSWAP). Boundary conditions are shown in Figure 3.

image015.png

Figure 3. Boundary conditions of the typical problem

The wave spectrum peak enhancement factor (=3.3 for this work) and can be used to express the unidirectional JONSWAP frequency spectrum.

3.3 Mesh sensitivity

Before doing additional research into scour traits and scour depth forecasting, mesh sensitivity analysis is essential. Three different mesh grid sizes were selected for this section: Mesh 1 has a 0.45 by 0.45 nested fine mesh and a 0.6 by 0.6 global mesh size. Mesh 2 has a 0.4 global mesh size and a 0.35 nested fine mesh size, while Mesh 3 has a 0.25 global mesh size and a nested fine mesh size of 0.15. Comparing the relative fine mesh size (such as Mesh 2 or Mesh 3) to the relatively coarse mesh size (such as Mesh 1), a larger scour depth was seen; this shows that a finer mesh size can more precisely represent the scouring and flow field action around a tripod. Significantly, a lower mesh size necessitates a time commitment and a more difficult computer configuration. Depending on the sensitivity of the mesh guideline utilized by Pang et al., when Mesh 2 is applied, the findings converge and the mesh size is independent [20]. In the next sections, scouring the area surrounding the tripod was calculated using Mesh 2 to ensure accuracy and reduce computation time. The working segment generates a total of 14, 800,324 cells.

3.4 Model validation

Comparisons between the predicted outcomes from the current model and to confirm that the current numerical model is accurate and suitably modified, experimental data from Sumer and Fredsøe [6] and Schendel et al. [15] were used. For the experimental results of Run 05, Run 15, and Run 22 from Sumer and Fredsøe [6], the experimental A9, A13, A17, A25, A26, and A27 results from Schendel et al. [15], and the numerical results from the current model are shown in Figure 4. The present model had d50=0.051cm, the height of the water wave(h)=10m, and wave velocity=0.854 m.s-1.

image016.png

Figure 4. Cell size effect

image017.png

Figure 5. Comparison of the present study’s maximum scour depth with that authored by Sumer and Fredsøe [6] and Schendel et al. [15]

According to Figure 5, the highest discrepancy between the numerical results and experimental data is about 10%, showing that overall, there is good agreement between them. The ability of the current numerical model to accurately depict the scour process and forecast the maximum scour depth (S) near foundations is demonstrated by this. Errors in the simulation were reduced by using the calibrated values of the parameter. Considering these results, a suggested simulated scouring utilizing a Flow-3D numerical model is confirmed as a superior way for precisely forecasting the maximum scour depth near a tripod foundation in random waves.

3.5 Dimensional analysis

The variables found in this study as having the greatest impacts, variables related to flow, fluid, bed sediment, flume shape, and duration all had an impact on local scouring depth (t). Hence, scour depth (S) can be seen as a function of these factors, shown as:

(11)

S=f\left(\rho, v, V, h, g, \rho s, d_{50}, \sigma g, V_w, D, d, T_v, t\right)

With the aid of dimensional analysis, the 14-dimensional parameters in Eq. (11) were reduced to 6 dimensionless variables using Buckingham’s -theorem. D, V, and were therefore set as repetition parameters and others as constants, allowing for the ignoring of their influence. Eq. (12) thus illustrates the relationship between the effect of the non-dimensional components on the depth of scour surrounding a tripod base.

(12)

\frac{S}{D}=f\left(\frac{h}{D}, \frac{d 50}{D}, \frac{V}{V W}, F r, K c\right)

where, SD𝑆𝐷 are scoured depth ratio, VVw𝑉𝑉𝑤 is flow wave velocity, d50D𝑑50𝐷 median size ratio, $Fr representstheFroudnumber,and𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠𝑡ℎ𝑒𝐹𝑟𝑜𝑢𝑑𝑛𝑢𝑚𝑏𝑒𝑟,𝑎𝑛𝑑Kc$ is the Keulegan-Carpenter.

4. Result and Discussion

4.1 Development of scour

Similar to how the physical model was used, this numerical model was also used. The numerical model’s boundary conditions and other crucial variables that directly influence the outcomes were applied (flow depth, median particle size (d50), and wave velocity). After the initial 0-300 s, the scour rate reduced as the scour holes grew quickly. The scour depths steadied for about 1800 seconds before reaching an asymptotic value. The findings of scour depth with time are displayed in Figure 6.

4.2 Features of scour

Early on (t=400s), the scour hole began to appear beneath the main column and then began to extend along the diagonal bracing connecting to the wall-facing pile. Gradually, the geography of the scour; of these results is similar to the experimental observations of Stahlmann [4] and Aminoroayaie Yamini et al. [1]. As the waves reached the tripod, there was an enhanced flow acceleration underneath the main column and the lower diagonal braces as a result of the obstructing effects of the structural elements. More particles are mobilized and transported due to the enhanced near-bed flow velocity, it also increases bed shear stress, turbulence, and scour at the site. In comparison to a single pile, the main column and structural components of the tripod have a significant impact on the flow velocity distribution and, consequently, the scour process and morphology. The main column and seabed are separated by a gap, therefore the flow across the gap may aid in scouring. The scour hole first emerged beneath the main column and subsequently expanded along the lower structural components, both Aminoroayaie Yamini et al. [1] and Stahlmann [4] made this claim. Around the tripod, there are several different scour morphologies and the flow velocity distribution as shown in Figures 7 and 8.

image023.png

Figure 6. Results of scour depth with time

image024.png

image025.png

image026.png

image027.png

Figure 7. The sequence results of scour depth around tripod development (reached to steady state) simulation time

image028.png

image029.png

image030.png

image031.png

Figure 8. Random waves of flow velocity distribution around a tripod

4.3 Wave velocity’s (Vw) impact on scour depth

In this study’s section, we looked at how variations in wave current velocity affected the scouring depth. Bed scour pattern modification could result from an increase or decrease in waves. As a result, the backflow area produced within the pile would become stronger, which would increase the depth of the sediment scour. The quantity of current turbulence is the primary cause of the relationship between wave height and bed scour value. The current velocity has increased the extent to which the turbulence energy has changed and increased in strength now present. It should be mentioned that in this instance, the Jon swap spectrum random waves are chosen. The scour depth attains its steady-current value for Vw<0.75, Figure 9 (a) shows that effect. When (V) represents the mean velocity=0.5 m.s-1.

image032.png

(a)

image033.png

(b)

image034.png

(c)

image035.png

(d)

Figure 9. Main effects on maximum scour depth (Smax) as a function of column diameter (D)

4.4 Impact of a median particle (d50) on scour depth

In this section of the study, we looked into how variations in particle size affected how the bed profile changed. The values of various particle diameters are defined in the numerical model for each run numerical modeling, and the conditions under which changes in particle diameter have an impact on the bed scour profile are derived. Based on Figure 9 (b), the findings of the numerical modeling show that as particle diameter increases the maximum scour depth caused by wave contact decreases. When (d50) is the diameter of Sediment (d50). The Shatt Al-Arab soil near Basra, Iraq, was used to produce a variety of varied diameters.

4.5 Impact of wave height and flow depth (h) on scour depth

One of the main elements affecting the scour profile brought on by the interaction of the wave and current with the piles of the wind turbines is the height of the wave surrounding the turbine pile causing more turbulence to develop there. The velocity towards the bottom and the bed both vary as the turbulence around the pile is increased, modifying the scour profile close to the pile. According to the results of the numerical modeling, the depth of scour will increase as water depth and wave height in random waves increase as shown in Figure 9 (c).

4.6 Froude number’s (Fr) impact on scour depth

No matter what the spacing ratio, the Figure 9 shows that the Froude number rises, and the maximum scour depth often rises as well increases in Figure 9 (d). Additionally, it is crucial to keep in mind that only a small portion of the findings regarding the spacing ratios with the smallest values. Due to the velocity acceleration in the presence of a larger Froude number, the range of edge scour downstream is greater than that of upstream. Moreover, the scouring phenomena occur in the region farthest from the tripod, perhaps as a result of the turbulence brought on by the collision of the tripod’s pile. Generally, as the Froude number rises, so does the deposition height and scour depth.

4.7 Keulegan-Carpenter (KC) number

The geography of the scour is significantly more influenced by the KC value. Greater KC causes a deeper equilibrium scour because an increase in KC lengthens the horseshoe vortex’s duration and intensifies it as shown in Figure 10.

The result can be attributed to the fact that wave superposition reduced the crucial KC for the initiation of the scour, particularly under small KC conditions. The primary variable in the equation used to calculate This is the depth of the scouring hole at the bed. The following expression is used to calculate the Keulegan-Carpenter number:

Kc=Vw∗TpD𝐾𝑐=𝑉𝑤∗𝑇𝑝𝐷                          (13)

where, the wave period is Tp and the wave velocity is shown by Vw.

image037.png

Figure 10. Relationship between the relative maximum scour depth and KC

5. Conclusion

(1) The existing seabed-tripod-fluid numerical model is capable of faithfully reproducing the scour process and the flow field around tripods, suggesting that it may be used to predict the scour around tripods in random waves.

(2) Their results obtained in this research at various flow velocities and flow depths demonstrated that the maximum scour depth rate depended on wave height with rising velocities and decreasing particle sizes (d50).

(3) A diagonal brace and the main column act as blockages, increasing the flow accelerations underneath them. This raises the magnitude of the disturbance and the shear stress on the seafloor, which in turn causes a greater number of particles to be mobilized and conveyed, as a result, causes more severe scour at the location.

(4) The Froude number and the scouring process are closely related. In general, as the Froude number rises, so does the maximum scour depth and scour range. The highest maximum scour depth always coincides with the bigger Froude number with the shortest spacing ratio.

Since the issue is that there aren’t many experiments or studies that are relevant to this subject, therefore we had to rely on the monopile criteria. Therefore, to gain a deeper knowledge of the scouring effect surrounding the tripod in random waves, further numerical research exploring numerous soil, foundation, and construction elements as well as upcoming physical model tests will be beneficial.

Nomenclature

CFDComputational fluid dynamics
FAVORFractional Area/Volume Obstacle Representation
VOFVolume of Fluid
RNGRenormalized Group
OWTsOffshore wind turbines
Greek Symbols
ε, ωDissipation rate of the turbulent kinetic energy, m2s-3
Subscripts
d50Median particle size
VfVolume fraction
GTTurbulent energy of buoyancy
KTTurbulent velocity
PTKinetic energy of the turbulence
ΑiInduction parameter
nsInduction parameter
ΘΘcrThe essential Shields variable
DiDiameter of sediment
d∗The diameter of particles without dimensions
µfDynamic viscosity of the fluid
qb,iThe bed load transportation rate
Cs,iSand particle’s concentration of mass
DDiameter of pile
DfDiffusivity
DDiameter of main column
FrFroud number
KcKeulegan–Carpenter number
GAcceleration of gravity g
HFlow depth
VwWave Velocity
VMean Velocity
TpWave Period
SScour depth

  References

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[2] Hassan, W.H., Hashim, F.S. (2020). The effect of climate change on the maximum temperature in Southwest Iraq using HadCM3 and CanESM2 modelling. SN Applied Sciences, 2(9): 1494. https://doi.org/10.1007/s42452-020-03302-z

[3] Fazeres-Ferradosa, T., Rosa-Santos, P., Taveira-Pinto, F., Pavlou, D., Gao, F.P., Carvalho, H., Oliveira-Pinto, S. (2020). Preface: Advanced research on offshore structures and foundation design part 2. In Proceedings of the Institution of Civil Engineers-Maritime Engineering. Thomas Telford Ltd, 173(4): 96-99. https://doi.org/10.1680/jmaen.2020.173.4.96

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Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

Estimating maximum initial wave amplitude of subaerial landslide tsunamis: A three-dimensional modelling approach

해저 산사태 쓰나미의 최대 초기 파동 진폭 추정: 3차원 모델링 접근법

Ramtin Sabeti a, Mohammad Heidarzadeh ab

aDepartment of Architecture and Civil Engineering, University of Bath, Bath BA27AY, UK
bHydroCoast Consulting Engineers Ltd, Bath, UK

https://doi.org/10.1016/j.ocemod.2024.102360

Highlights

  • •Landslide travel distance is considered for the first time in a predictive equation.
  • •Predictive equation derived from databases using 3D physical and numerical modeling.
  • •The equation was successfully tested on the 2018 Anak Krakatau tsunami event.
  • •The developed equation using three-dimensional data exhibits a 91 % fitting quality.

Abstract

Landslide tsunamis, responsible for thousands of deaths and significant damage in recent years, necessitate the allocation of sufficient time and resources for studying these extreme natural hazards. This study offers a step change in the field by conducting a large number of three-dimensional numerical experiments, validated by physical tests, to develop a predictive equation for the maximum initial amplitude of tsunamis generated by subaerial landslides. We first conducted a few 3D physical experiments in a wave basin which were then applied for the validation of a 3D numerical model based on the Flow3D-HYDRO package. Consequently, we delivered 100 simulations using the validated model by varying parameters such as landslide volume, water depth, slope angle and travel distance. This large database was subsequently employed to develop a predictive equation for the maximum initial tsunami amplitude. For the first time, we considered travel distance as an independent parameter for developing the predictive equation, which can significantly improve the predication accuracy. The predictive equation was tested for the case of the 2018 Anak Krakatau subaerial landslide tsunami and produced satisfactory results.

Keywords

Tsunami, Subaerial landslide, Physical modelling, Numerical simulation, FLOW-3D HYDRO

1. Introduction and literature review

The Anak Krakatau landslide tsunami on 22nd December 2018 was a stark reminder of the dangers posed by subaerial landslide tsunamis (Ren et al., 2020; Mulia et al. 2020a; Borrero et al., 2020; Heidarzadeh et al., 2020; Grilli et al., 2021). The collapse of the volcano’s southwest side into the ocean triggered a tsunami that struck the Sunda Strait, leading to approximately 450 fatalities (Syamsidik et al., 2020; Mulia et al., 2020b) (Fig. 1). As shown in Fig. 1, landslide tsunamis (both submarine and subaerial) have been responsible for thousands of deaths and significant damage to coastal communities worldwide. These incidents underscored the critical need for advanced research into landslide-generated waves to aid in hazard prediction and mitigation. This is further emphasized by recent events such as the 28th of November 2020 landslide tsunami in the southern coast mountains of British Columbia (Canada), where an 18 million m3 rockslide generated a massive tsunami, with over 100 m wave run-up, causing significant environmental and infrastructural damage (Geertsema et al., 2022).

Fig 1

Physical modelling and numerical simulation are crucial tools in the study of landslide-induced waves due to their ability to replicate and analyse the complex dynamics of landslide events (Kim et al., 2020). In two-dimensional (2D) modelling, the discrepancy between dimensions can lead to an artificial overestimation of wave amplification (e.g., Heller and Spinneken, 2015). This limitation is overcome with 3D modelling, which enables the scaled-down representation of landslide-generated waves while avoiding the simplifications inherent in 2D approaches (Erosi et al., 2019). Another advantage of 3D modelling in studying landslide-generated waves is its ability to accurately depict the complex dynamics of wave propagation, including lateral and radial spreading from the slide impact zone, a feature unattainable with 2D models (Heller and Spinneken, 2015).

Physical experiments in tsunami research, as presented by authors such as Romano et al. (2020), McFall and Fritz (2016), and Heller and Spinneken (2015), have supported 3D modelling works through validation and calibration of the numerical models to capture the complexities of wave generation and propagation. Numerical modelling has increasingly complemented experimental approach in tsunami research due to the latter’s time and resource-intensive nature, particularly for 3D models (Li et al., 2019; Kim et al., 2021). Various numerical approaches have been employed, from Eulerian and Lagrangian frameworks to depth-averaged and Navier–Stokes models, enhancing our understanding of tsunami dynamics (Si et al., 2018; Grilli et al., 2019; Heidarzadeh et al., 2017, 2020; Iorio et al., 2021; Zhang et al., 2021; Kirby et al., 2022; Wang et al., 2021, 2022; Hu et al., 2022). The sophisticated numerical techniques, including the Particle Finite Element Method and the Immersed Boundary Method, have also shown promising results in modelling highly dynamic landslide scenarios (Mulligan et al., 2020; Chen et al., 2020). Among these methods and techniques, FLOW-3D HYDRO stands out in simulating landslide-generated tsunami waves due to its sophisticated technical features such as offering Tru Volume of Fluid (VOF) method for precise free surface tracking (e.g., Sabeti and Heidarzadeh 2022a). TruVOF distinguishes itself through a split Lagrangian approach, adeptly reducing cumulative volume errors in wave simulations by dynamically updating cell volume fractions and areas with each time step. Its intelligent adaptation of time step size ensures precise capture of evolving free surfaces, offering unparalleled accuracy in modelling complex fluid interfaces and behaviour (Flow Science, 2023).

Predictive equations play a crucial role in assessing the potential hazards associated with landslide-generated tsunami waves due to their ability to provide risk assessment and warnings. These equations can offer swift and reasonable evaluations of potential tsunami impacts in the absence of detailed numerical simulations, which can be time-consuming and expensive to produce. Among multiple factors and parameters within a landslide tsunami generation, the initial maximum wave amplitude (Fig. 1) stands out due to its critical role. While it is most likely that the initial wave generated by a landslide will have the highest amplitude, it is crucial to clarify that the term “initial maximum wave amplitude” refers to the highest amplitude within the first set of impulse waves. This parameter is essential in determining the tsunami’s impact severity, with higher amplitudes signalling a greater destructive potential (Sabeti and Heidarzadeh 2022a). Additionally, it plays a significant role in tsunami modelling, aiding in the prediction of wave propagation and the assessment of potential impacts.

In this study, we initially validate the FLOW-3D HYDRO model through a series of physical experiments conducted in a 3D wave tank at University of Bath (UK). Upon confirmation of the model’s accuracy, we use it to systematically vary parameters namely landslide volume, water depth, slope angle, and travel distance, creating an extensive database. Alongside this, we perform a sensitivity analysis on these variables to discern their impacts on the initial maximum wave amplitude. The generated database was consequently applied to derive a non-dimensional predictive equation aimed at estimating the initial maximum wave amplitude in real-world landslide tsunami events.

Two innovations of this study are: (i) The predictive equation of this study is based on a large number of 3D experiments whereas most of the previous equations were based on 2D results, and (ii) For the first time, the travel distance is included in the predictive equation as an independent parameter. To evaluate the performance of our predictive equation, we applied it to a previous real-world subaerial landslide tsunami, i.e., the Anak Krakatau 2018 event. Furthermore, we compare the performance of our predictive equation with other existing equations.

2. Data and methods

The methodology applied in this research is a combination of physical and numerical modelling. Limited physical modelling was performed in a 3D wave basin at the University of Bath (UK) to provide data for calibration and validation of the numerical model. After calibration and validation, the numerical model was employed to model a large number of landslide tsunami scenarios which allowed us to develop a database for deriving a predictive equation.

2.1. Physical experiments

To validate our numerical model, we conducted a series of physical experiments including two sets in a 3D wave basin at University of Bath, measuring 2.50 m in length (WL), 2.60 m in width (WW), and 0.60 m in height (WH) (Fig. 2a). Conducting two distinct sets of experiments (Table 1), each with different setups (travel distance, location, and water depth), provided a robust framework for validation of the numerical model. For wave measurement, we employed a twin wire wave gauge from HR Wallingford (https://equipit.hrwallingford.com). In these experiments, we used a concrete prism solid block, the dimensions of which are outlined in Table 2. In our experiments, we employed a concrete prism solid block with a density of 2600 kg/m3, chosen for its similarity to the natural density of landslides, akin to those observed with the 2018 Anak Krakatau tsunami, where the landslide composition is predominantly solid rather than granular. The block’s form has also been endorsed in prior studies (Watts, 1998; Najafi-Jilani and Ataie-Ashtiani, 2008) as a suitable surrogate for modelling landslide-induced waves. A key aspect of our methodology was addressing scale effects, following the guidelines proposed by Heller et al. (2008) as it is described in Table 1. To enhance the reliability and accuracy of our experimental data, we conducted each physical experiment three times which revealed all three experimental waveforms were identical. This repetition was aimed at minimizing potential errors and inconsistencies in laboratory measurements.

Fig 2

Table 1. The locations and other information of the laboratory setups for making landslide-generated waves in the physical wave basin. This table details the specific parameters for each setup, including slope range (α), slide volume (V), kinematic viscosity (ν), water depth (h), travel distance (D), surface tension coefficient of water (σ), Reynolds number (R), Weber number (W), and the precise coordinates of the wave gauges (WG).

Labα(°)V (m³)h (m)D (m)WG’s Location(ν) (m²/s)(σ) (N/m)Acceptable range for avoiding scale effects*Observed values of W and R ⁎⁎
Lab 1452.60 × 10−30.2470.070X1=1.090 m1.01 × 10−60.073R > 3.0 × 105R1 = 3.80 × 105
Y1=1.210 m
W1 = 8.19 × 105
Z1=0.050mW >5.0 × 103
Lab 2452.60 × 10−30.2460.045X2=1.030 m1.01 × 10−60.073R2 = 3.78 × 105
Y2=1.210 mW2 = 8.13 × 105
Z2=0.050 m

⁎

The acceptable ranges for avoiding scale effects are based on the study by Heller et al. (2008).⁎⁎

The Reynolds number (R) is given by g0.5h1.5/ν, with ν denoting the kinematic viscosity. The Weber number (W) is W = ρgh2/σ, where σ represents surface tension coefficient and ρ = 1000kg/m3 is the density of water. In our experiments, conducted at a water temperature of approximately 20 °C, the kinematic viscosity (ν) and the surface tension coefficient of water (σ) are 1.01 × 10−6 m²/s and 0.073 N/m, respectively (Kestin et al., 1978).

Table 2. Specifications of the solid block used in physical experiments for generating subaerial landslides in the laboratory.

Solid-block attributesProperty metricsGeometric shape
Slide width (bs)0.26 mImage, table 2
Slide length (ls)0.20 m
Slide thickness (s)0.10 m
Slide volume (V)2.60 × 10−3 m3
Specific gravity, (γs)2.60
Slide weight (ms)6.86 kg

2.2. Numerical simulations applying FLOW-3D hydro

The detailed theoretical framework encompassing the governing equations, the computational methodologies employed, and the specific techniques used for tracking the water surface in these simulations are thoroughly detailed in the study by Sabeti et al. (2024). Here, we briefly explain some of the numerical details. We defined a uniform mesh for our flow domain, carefully crafted with a fine spatial resolution of 0.005 m (i.e., grid size). The dimensions of the numerical model directly matched those of our wave basin used in the physical experiment, being 2.60 m wide, 0.60 m deep, and 2.50 m long (Fig. 2). This design ensures comprehensive coverage of the study area. The output intervals of the numerical model are set at 0.02 s. This timing is consistent with the sampling rates of wave gauges used in laboratory settings. The friction coefficient in the FLOW-3D HYDRO is designated as 0.45. This value corresponds to the Coulombic friction measurements obtained in the laboratory, ensuring that the simulation accurately reflects real-world physical interactions.

In order to simulate the landslide motion, we applied coupled motion objects in FLOW-3D-HYDRO where the dynamics are predominantly driven by gravity and surface friction. This methodology stands in contrast to other models that necessitate explicit inputs of force and torque. This approach ensures that the simulation more accurately reflects the natural movement of landslides, which is heavily reliant on gravitational force and the interaction between sliding surfaces. The stability of the numerical simulations is governed by the Courant Number criterion (Courant et al., 1928), which dictates the maximum time step (Δt) for a given mesh size (Δx) and flow speed (U). According to Courant et al. (1928), this number is required to stay below one to ensure stability of numerical simulations. In our simulations, the Courant number is always maintained below one.

In alignment with the parameters of physical experiments, we set the fluid within the mesh to water, characterized by a density of 1000 kg/m³ at a temperature of 20 °C. Furthermore, we defined the top, front, and back surfaces of the mesh as symmetry planes. The remaining surfaces are designated as wall types, incorporating no-slip conditions to accurately simulate the interaction between the fluid and the boundaries. In terms of selection of an appropriate turbulence model, we selected the k–ω model that showed a better performance than other turbulence methods (e.g., Renormalization-Group) in a previous study (Sabeti et al., 2024). The simulations are conducted using a PC Intel® Core™ i7-10510U CPU with a frequency of 1.80 GHz, and a 16 GB RAM. On this PC, completion of a 3-s simulation required approximately 12.5 h.

2.3. Validation

The FLOW-3D HYDRO numerical model was validated using the two physical experiments (Fig. 3) outlined in Table 1. The level of agreement between observations (Oi) and simulations (Si) is examined using the following equation:(1)�=|��−����|×100where ε represents the mismatch error, Oi denotes the observed laboratory values, and Si represents the simulated values from the FLOW-3D HYDRO model. The results of this validation process revealed that our model could replicate the waves generated in the physical experiments with a reasonable degree of mismatch (ε): 14 % for Lab 1 and 8 % for Lab 2 experiments, respectively (Fig. 3). These values indicate that while the model is not perfect, it provides a sufficiently close approximation of the real-world phenomena.

Fig 3

In terms of mesh efficiency, we varied the mesh size to study sensitivity of the numerical results to mesh size. First, by halving the mesh size and then by doubling it, we repeated the modelling by keeping other parameters unchanged. This analysis guided that a mesh size of ∆x = 0.005 m is the most effective for the setup of this study. The total number of computational cells applying mesh size of 0.005 m is 9.269 × 106.

2.4. The dataset

The validated numerical model was employed to conduct 100 simulations, incorporating variations in four key landslide parameters namely water depth, slope angle, slide volume, and travel distance. This methodical approach was essential for a thorough sensitivity analysis of these variables, and for the creation of a detailed database to develop a predictive equation for maximum initial tsunami amplitude. Within the model, 15 distinct slide volumes were established, ranging from 0.10 × 10−3 m3 to 6.25 × 10−3 m3 (Table 3). The slope angle varied between 35° and 55°, and water depth ranged from 0.24 m to 0.27 m. The travel distance of the landslides was varied, spanning from 0.04 m to 0.07 m. Detailed configurations of each simulation, along with the maximum initial wave amplitudes and dominant wave periods are provided in Table 4.

Table 3. Geometrical information of the 15 solid blocks used in numerical modelling for generating landslide tsunamis. Parameters are: ls, slide length; bs, slide width; s, slide thickness; γs, specific gravity; and V, slide volume.

Solid blockls (m)bs (m)s (m)V (m3)γs
Block-10.3100.2600.1556.25 × 10−32.60
Block-20.3000.2600.1505.85 × 10−32.60
Block-30.2800.2600.1405.10 × 10−32.60
Block-40.2600.2600.1304.39 × 10−32.60
Block-50.2400.2600.1203.74 × 10−32.60
Block-60.2200.2600.1103.15 × 10−32.60
Block-70.2000.2600.1002.60 × 10−32.60
Block-80.1800.2600.0902.11 × 10−32.60
Block-90.1600.2600.0801.66 × 10−32.60
Block-100.1400.2600.0701.27 × 10−32.60
Block-110.1200.2600.0600.93 × 10−32.60
Block-120.1000.2600.0500.65 × 10−32.60
Block-130.0800.2600.0400.41 × 10−32.60
Block-140.0600.2600.0300.23 × 10−32.60
Block-150.0400.2600.0200.10 × 10−32.60

Table 4. The numerical simulation for the 100 tests performed in this study for subaerial solid-block landslide-generated waves. Parameters are aM, maximum wave amplitude; α, slope angle; h, water depth; D, travel distance; and T, dominant wave period. The location of the wave gauge is X=1.030 m, Y=1.210 m, and Z=0.050 m. The properties of various solid blocks are presented in Table 3.

Test-Block Noα (°)h (m)D (m)T(s)aM (m)
1Block-7450.2460.0290.5100.0153
2Block-7450.2460.0300.5050.0154
3Block-7450.2460.0310.5050.0156
4Block-7450.2460.0320.5050.0158
5Block-7450.2460.0330.5050.0159
6Block-7450.2460.0340.5050.0160
7Block-7450.2460.0350.5050.0162
8Block-7450.2460.0360.5050.0166
9Block-7450.2460.0370.5050.0167
10Block-7450.2460.0380.5050.0172
11Block-7450.2460.0390.5050.0178
12Block-7450.2460.0400.5050.0179
13Block-7450.2460.0410.5050.0181
14Block-7450.2460.0420.5050.0183
15Block-7450.2460.0430.5050.0190
16Block-7450.2460.0440.5050.0197
17Block-7450.2460.0450.5050.0199
18Block-7450.2460.0460.5050.0201
19Block-7450.2460.0470.5050.0191
20Block-7450.2460.0480.5050.0217
21Block-7450.2460.0490.5050.0220
22Block-7450.2460.0500.5050.0226
23Block-7450.2460.0510.5050.0236
24Block-7450.2460.0520.5050.0239
25Block-7450.2460.0530.5100.0240
26Block-7450.2460.0540.5050.0241
27Block-7450.2460.0550.5050.0246
28Block-7450.2460.0560.5050.0247
29Block-7450.2460.0570.5050.0248
30Block-7450.2460.0580.5050.0249
31Block-7450.2460.0590.5050.0251
32Block-7450.2460.0600.5050.0257
33Block-1450.2460.0450.5050.0319
34Block-2450.2460.0450.5050.0294
35Block-3450.2460.0450.5050.0282
36Block-4450.2460.0450.5050.0262
37Block-5450.2460.0450.5050.0243
38Block-6450.2460.0450.5050.0223
39Block-7450.2460.0450.5050.0196
40Block-8450.2460.0450.5050.0197
41Block-9450.2460.0450.5050.0198
42Block-10450.2460.0450.5050.0184
43Block-11450.2460.0450.5050.0173
44Block-12450.2460.0450.5050.0165
45Block-13450.2460.0450.4040.0153
46Block-14450.2460.0450.4040.0124
47Block-15450.2460.0450.5050.0066
48Block-7450.2020.0450.4040.0220
49Block-7450.2040.0450.4040.0219
50Block-7450.2060.0450.4040.0218
51Block-7450.2080.0450.4040.0217
52Block-7450.2100.0450.4040.0216
53Block-7450.2120.0450.4040.0215
54Block-7450.2140.0450.5050.0214
55Block-7450.2160.0450.5050.0214
56Block-7450.2180.0450.5050.0213
57Block-7450.2200.0450.5050.0212
58Block-7450.2220.0450.5050.0211
59Block-7450.2240.0450.5050.0208
60Block-7450.2260.0450.5050.0203
61Block-7450.2280.0450.5050.0202
62Block-7450.2300.0450.5050.0201
63Block-7450.2320.0450.5050.0201
64Block-7450.2340.0450.5050.0200
65Block-7450.2360.0450.5050.0199
66Block-7450.2380.0450.4040.0196
67Block-7450.2400.0450.4040.0194
68Block-7450.2420.0450.4040.0193
69Block-7450.2440.0450.4040.0192
70Block-7450.2460.0450.5050.0190
71Block-7450.2480.0450.5050.0189
72Block-7450.2500.0450.5050.0187
73Block-7450.2520.0450.5050.0187
74Block-7450.2540.0450.5050.0186
75Block-7450.2560.0450.5050.0184
76Block-7450.2580.0450.5050.0182
77Block-7450.2590.0450.5050.0183
78Block-7450.2600.0450.5050.0191
79Block-7450.2610.0450.5050.0192
80Block-7450.2620.0450.5050.0194
81Block-7450.2630.0450.5050.0195
82Block-7450.2640.0450.5050.0195
83Block-7450.2650.0450.5050.0197
84Block-7450.2660.0450.5050.0197
85Block-7450.2670.0450.5050.0198
86Block-7450.2700.0450.5050.0199
87Block-7300.2460.0450.5050.0101
88Block-7350.2460.0450.5050.0107
89Block-7360.2460.0450.5050.0111
90Block-7370.2460.0450.5050.0116
91Block-7380.2460.0450.5050.0117
92Block-7390.2460.0450.5050.0119
93Block-7400.2460.0450.5050.0121
94Block-7410.2460.0450.5050.0127
95Block-7420.2460.0450.4040.0154
96Block-7430.2460.0450.4040.0157
97Block-7440.2460.0450.4040.0162
98Block-7450.2460.0450.5050.0197
99Block-7500.2460.0450.5050.0221
100Block-7550.2460.0450.5050.0233

In all these 100 simulations, the wave gauge was consistently positioned at coordinates X=1.09 m, Y=1.21 m, and Z=0.05 m. The dominant wave period for each simulation was determined using the Fast Fourier Transform (FFT) function in MATLAB (MathWorks, 2023). Furthermore, the classification of wave types was carried out using a wave categorization graph according to Sorensen (2010), as shown in Fig. 4a. The results indicate that the majority of the simulated waves are on the border between intermediate and deep-water waves, and they are categorized as Stokes waves (Fig. 4a). Four sample waveforms from our 100 numerical experiments are provided in Fig. 4b.

Fig 4

The dataset in Table 4 was used to derive a new predictive equation that incorporates travel distance for the first time to estimate the initial maximum tsunami amplitude. In developing this equation, a genetic algorithm optimization technique was implemented using MATLAB (MathWorks 2023). This advanced approach entailed the use of genetic algorithms (GAs), an evolutionary algorithm type inspired by natural selection processes (MathWorks, 2023). This technique is iterative, involving selection, crossover, and mutation processes to evolve solutions over several generations. The goal was to identify the optimal coefficients and powers for each landslide parameter in the predictive equation, ensuring a robust and reliable model for estimating maximum wave amplitudes. Genetic Algorithms excel at optimizing complex models by navigating through extensive combinations of coefficients and exponents. GAs effectively identify highly suitable solutions for the non-linear and complex relationships between inputs (e.g., slide volume, slope angle, travel distance, water depth) and the output (i.e., maximum initial wave amplitude, aM). MATLAB’s computational environment enhances this process, providing robust tools for GA to adapt and evolve solutions iteratively, ensuring the precision of the predictive model (Onnen et al., 1997). This approach leverages MATLAB’s capabilities to fine-tune parameters dynamically, achieving an optimal equation that accurately estimates aM. It is important to highlight that the nondimensionalized version of this dataset is employed to develop a predictive equation which enables the equation to reproduce the maximum initial wave amplitude (aM) for various subaerial landslide cases, independent of their dimensional differences (e.g., Heler and Hager 2014; Heller and Spinneken 2015; Sabeti and Heidarzadeh 2022b). For this nondimensionalization, we employed the water depth (h) to nondimensionalize the slide volume (V/h3) and travel distance (D/h). The slide thickness (s) was applied to nondimensionalize the water depth (h/s).

2.5. Landslide velocity

In discussing the critical role of landslide velocity for simulating landslide-generated waves, we focus on the mechanisms of landslide motion and the techniques used to record landslide velocity in our simulations (Fig. 5). Also, we examine how these methods were applied in two distinct scenarios: Lab 1 and Lab 2 (see Table 1 for their details). Regarding the process of landslide movement, a slide starts from a stationary state, gaining momentum under the influence of gravity and this acceleration continues until the landslide collides with water, leading to a significant reduction in its speed before eventually coming to a stop (Fig. 5) (e.g., Panizzo et al. 2005).

Fig 5

To measure the landslide’s velocity in our simulations, we attached a probe at the centre of the slide, which supplied a time series of the velocity data. The slide’s velocity (vs) peaks at the moment it enters the water (Fig. 5), a point referred to as the impact time (tImp). Following this initial impact, the slides continue their underwater movement, eventually coming to a complete halt (tStop). Given the results in Fig. 5, it can be seen that Lab 1, with its longer travel distance (0.070 m), exhibits a higher peak velocity of 1.89 m/s. This increase in velocity is attributed to the extended travel distance allowing more time for the slide to accelerate under gravity. Whereas Lab 2, featuring a shorter travel distance (0.045 m), records a lower peak velocity of 1.78 m/s. This difference underscores how travel distance significantly influences the dynamics of landslide motion. After reaching the peak, both profiles show a sharp decrease in velocity, marking the transition to submarine motion until the slides come to a complete stop (tStop). There are noticeable differences observable in Fig. 5 between the Lab-1 and Lab-2 simulations, including the peaks at 0.3 s . These variations might stem from the placement of the wave gauge, which differs slightly in each scenario, as well as the water depth’s minor discrepancies and, the travel distance.

2.6. Effect of air entrainment

In this section we examine whether it is required to consider air entrainment for our modelling or not as the FLOW-3D HYDRO package is capable of modelling air entrainment. The process of air entrainment in water during a landslide tsunami and its subsequent transport involve two key components: the quantification of air entrainment at the water surface, and the simulation of the air’s transport within the fluid (Hirt, 2003). FLOW-3D HYDRO employs the air entrainment model to compute the volume of air entrained at the water’s surface utilizing three approaches: a constant density model, a variable density model accounting for bulking, and a buoyancy model that adds the Drift-FLUX mechanism to variable density conditions (Flow Science, 2023). The calculation of the entrainment rate is based on the following equation:(2)�������=������[2(��−�����−2�/���)]1/2where parameters are: Vair, volume of air; Cair, entrainment rate coefficient; As, surface area of fluid; ρ, fluid density; k, turbulent kinetic energy; gn, gravity normal to surface; Lt, turbulent length scale; and σ, surface tension coefficient. The value of k is directly computed from the Reynolds-averaged Navier-Stokes (RANS) (k–w) calculations in our model.

In this study, we selected the variable density + Drift-FLUX model, which effectively captures the dynamics of phase separation and automatically activates the constant density and variable density models. This method simplifies the air-water mixture, treating it as a single, homogeneous fluid within each computational cell. For the phase volume fractions f1and f2​, the velocities are expressed in terms of the mixture and relative velocities, denoted as u and ur, respectively, as follows:(3)��1��+�.(�1�)=��1��+�.(�1�)−�.(�1�2��)=0(4)��2��+�.(�2�)=��2��+�.(�2�)−�.(�1�2��)=0

The outcomes from this simulation are displayed in Fig. 6, which indicates that the influence of air entrainment on the generated wave amplitude is approximately 2 %. A value of 0.02 for the entrained air volume fraction means that, in the simulated fluid, approximately 2 % of the volume is composed of entrained air. In other words, for every unit volume of the fluid-air mixture at that location, 2 % is air and the remaining 98 % is water. The configuration of Test-17 (Table 4) was employed for this simulation. While the effect of air entrainment is anticipated to be more significant in models of granular landslide-generated waves (Fritz, 2002), in our simulations we opted not to incorporate this module due to its negligible impact on the results.

Fig 6

3. Results

In this section, we begin by presenting a sequence of our 3D simulations capturing different time steps to illustrate the generation process of landslide-generated waves. Subsequently, we derive a new predictive equation to estimate the maximum initial wave amplitude of landslide-generated waves and assess its performance.

3.1. Wave generation and propagation

To demonstrate the wave generation process in our simulation, we reference Test-17 from Table 4, where we employed Block-7 (Tables 3, 4). In this configuration, the slope angle was set to 45°, with a water depth of 0.246 m and a travel distance at 0.045 m (Fig. 7). At 0.220 s, the initial impact of the moving slide on the water is depicted, marking the onset of the wave generation process (Fig. 7a). Disturbances are localized to the immediate area of impact, with the rest of the water surface remaining undisturbed. At this time, a maximum water particle velocity of 1.0 m/s – 1.2 m/s is seen around the impact zone (Fig. 7d). Moving to 0.320 s, the development of the wave becomes apparent as energy transfer from the landslide to the water creates outwardly radiating waves with maximum water particle velocity of up to around 1.6 m/s – 1.8 m/s (Fig. 7b, e). By the time 0.670 s, the wave has fully developed and is propagating away from the impact point exhibiting maximum water particle velocity of up to 2.0 m/s – 2.1 m/s. Concentric wave fronts are visible, moving outwards in all directions, with a colour gradient signifying the highest wave amplitude near the point of landslide entry, diminishing with distance (Fig. 7c, f).

Fig 7

3.2. Influence of landslide parameters on tsunami amplitude

In this section, we investigate the effects of various landslide parameters namely slide volume (V), water depth (h), slipe angle (α) and travel distance (D) on the maximum initial wave amplitude (aM). Fig. 8 presents the outcome of these analyses. According to Fig. 8, the slide volume, slope angle, and travel distance exhibit a direct relationship with the wave amplitude, meaning that as these parameters increase, so does the amplitude. Conversely, water depth is inversely related to the maximum initial wave amplitude, suggesting that the deeper the water depth, the smaller the maximum wave amplitude will be (Fig. 8b).

Fig 8

Fig. 8a highlights the pronounced impact of slide volume on the aM, demonstrating a direct correlation between the two variables. For instance, in the range of slide volumes we modelled (Fig. 8a), The smallest slide volume tested, measuring 0.10 × 10−3 m3, generated a low initial wave amplitude (aM= 0.0066 m) (Table 4). In contrast, the largest volume tested, 6.25 × 10−3 m3, resulted in a significantly higher initial wave amplitude (aM= 0.0319 m) (Table 4). The extremities of these results emphasize the slide volume’s paramount impact on wave amplitude, further elucidated by their positions as the smallest and largest aM values across all conducted tests (Table 4). This is corroborated by findings from the literature (e.g., Murty, 2003), which align with the observed trend in our simulations.

The slope angle’s influence on aM was smooth. A steady increase of wave amplitude was observed as the slope angle increased (Fig. 8c). In examining travel distance, an anomaly was identified. At a travel distance of 0.047 m, there was an unexpected dip in aM, which deviates from the general increasing trend associated with longer travel distances. This singular instance could potentially be attributed to a numerical error. Beyond this point, the expected pattern of increasing aM with longer travel distances resumes, suggesting that the anomaly at 0.047 m is an outlier in an otherwise consistent trend, and thus this single data point was overlooked while deriving the predictive equation. Regarding the inverse relationship between water depth and wave amplitude, our result (Fig. 8b) is consistent with previous reports by Fritz et al. (2003), (2004), and Watts et al. (2005).

The insights from Fig. 8 informed the architecture of the predictive equation in the next Section, with slide volume, travel distance, and slope angle being multiplicatively linked to wave amplitude underscoring their direct correlations with wave amplitude. Conversely, water depth is incorporated as a divisor, representing its inverse relationship with wave amplitude. This structure encapsulates the dynamics between the landslide parameters and their influence on the maximum initial wave amplitude as discussed in more detail in the next Section.

3.3. Predictive equation

Building on our sensitivity analysis of landslide parameters, as detailed in Section 3.2, and utilizing our nondimensional dataset, we have derived a new predictive equation as follows:(5)��/ℎ=0.015(tan�)0.10(�ℎ3)0.90(�ℎ)0.10(ℎ�)−0.11where, V is sliding volume, h is water depth, α is slope angle, and s is landslide thickness. It is important to note that this equation is valid only for subaerial solid-block landslide tsunamis as all our experiments were for this type of waves. The performance of this equation in predicting simulation data is demonstrated by the satisfactory alignment of data points around a 45° line, indicating its accuracy and reliability with regard to the experimental dataset (Fig. 9). The quality of fit between the dataset and Eq. (5) is 91 % indicating that Eq. (5) represents the dataset very well. Table 5 presents Eq. (5) alongside four other similar equations previously published. Two significant distinctions between our Eq. (5) and these others are: (i) Eq. (5) is derived from 3D experiments, whereas the other four equations are based on 2D experiments. (ii) Unlike the other equations, our Eq. (5) incorporates travel distance as an independent parameter.

Fig 9

Table 5. Performance comparison among our newly-developed equation and existing equations for estimating the maximum initial amplitude (aM) of the 2018 Anak Krakatau subaerial landslide tsunami. Parameters: aM, initial maximum wave amplitude; h, water depth; vs, landslide velocity; V, slide volume; bs, slide width; ls, slide length; s, slide thickness; α, slope angle; and ����, volume of the final immersed landslide. We considered ����= V as the slide volume.

EventPredictive equationsAuthor (year)Observed aM (m) ⁎⁎Calculated aM (m)Error, ε (%) ⁎⁎⁎⁎
2018 Anak Krakatau tsunami (Subaerial landslide) *��/ℎ=1.32���ℎNoda (1970)1341340
��/ℎ=0.667(0.5(���ℎ)2)0.334(���)0.754(���)0.506(�ℎ)1.631Bolin et al. (2014) ⁎⁎⁎13459424334
��/ℎ=0.25(������ℎ2)0.8Robbe-Saule et al. (2021)1343177
��/ℎ=0.4545(tan�)0.062(�ℎ3)0.296(ℎ�)−0.235Sabeti and Heidarzadeh (2022b)1341266
��/ℎ=0.015(tan�)0.10(�ℎ3)0.911(�ℎ)0.10(ℎ�)−0.11This study1341302.9

⁎

Geometrical and kinematic parameters of the 2018 Anak Krakatau subaerial landslide based on Heidarzadeh et al. (2020), Grilli et al. (2019) and Grilli et al. (2021): V=2.11 × 107 m3, h= 50 m; s= 114 m; α= 45°; ls=1250 m; bs= 2700 m; vs=44.9 m/s; D= 2500 m; aM= 100 m −150 m.⁎⁎

aM= An average value of aM = 134 m is considered in this study.⁎⁎⁎

The equation of Bolin et al. (2014) is based on the reformatted one reported by Lindstrøm (2016).⁎⁎⁎⁎

Error is calculated using Eq. (1), where the calculated aM is assumed as the simulated value.

Additionally, we evaluated the performance of this equation using the real-world data from the 2018 Anak Krakatau subaerial landslide tsunami. Based on previous studies (Heidarzadeh et al., 2020; Grilli et al., 2019, 2021), we were able to provide a list of parameters for the subaerial landslide and associated tsunami for the 2018 Anak Krakatau event (see footnote of Table 5). We note that the data of the 2018 Anak Krakatau event was not used while deriving Eq. (5). The results indicate that Eq. (5) predicts the initial amplitude of the 2018 Anak Krakatau tsunami as being 130 m indicating an error of 2.9 % compared to the reported average amplitude of 134 m for this event. This performance indicates an improvement compared to the previous equation reported by Sabeti and Heidarzadeh (2022a) (Table 5). In contrast, the equations from Robbe-Saule et al. (2021) and Bolin et al. (2014) demonstrate higher discrepancies of 4200 % and 77 %, respectively (Table 5). Although Noda’s (1970) equation reproduces the tsunami amplitude of 134 m accurately (Table 5), it is crucial to consider its limitations, notably not accounting for parameters such as slope angle and travel distance.

It is essential to recognize that both travel distance and slope angle significantly affect wave amplitude. In our model, captured in Eq. (5), we integrate the slope angle (α) through the tangent function, i.e., tan α. This choice diverges from traditional physical interpretations that often employ the cosine or sine function (e.g., Heller and Hager, 2014; Watts et al., 2003). We opted for the tangent function because it more effectively reflects the direct impact of slope steepness on wave generation, yielding superior estimations compared to conventional methods.

The significance of this study lies in its application of both physical and numerical 3D experiments and the derivation of a predictive equation based on 3D results. Prior research, e.g. Heller et al. (2016), has reported notable discrepancies between 2D and 3D wave amplitudes, highlighting the important role of 3D experiments. It is worth noting that the suitability of applying an equation derived from either 2D or 3D data depends on the specific geometry and characteristics inherent in the problem being addressed. For instance, in the case of a long, narrow dam reservoir, an equation derived from 2D data would likely be more suitable. In such contexts, the primary dynamics of interest such as flow patterns and potential wave propagation are predominantly two-dimensional, occurring along the length and depth of the reservoir. This simplification to 2D for narrow dam reservoirs allows for more accurate modelling of these dynamics.

This study specifically investigates waves initiated by landslides, focusing on those characterized as solid blocks instead of granular flows, with slope angles confined to a range of 25° to 60°. We acknowledge the additional complexities encountered in real-world scenarios, such as dynamic density and velocity of landslides, which could affect the estimations. The developed equation in this study is specifically designed to predict the maximum initial amplitude of tsunamis for the aforementioned specified ranges and types of landslides.

4. Conclusions

Both physical and numerical experiments were undertaken in a 3D wave basin to study solid-block landslide-generated waves and to formulate a predictive equation for their maximum initial wave amplitude. At the beginning, two physical experiments were performed to validate and calibrate a 3D numerical model, which was subsequently utilized to generate 100 experiments by varying different landslide parameters. The generated database was then used to derive a predictive equation for the maximum initial wave amplitude of landslide tsunamis. The main features and outcomes are:

  • •The predictive equation of this study is exclusively derived from 3D data and exhibits a fitting quality of 91 % when applied to the database.
  • •For the first time, landslide travel distance was considered in the predictive equation. This inclusion provides more accuracy and flexibility for applying the equation.
  • •To further evaluate the performance of the predictive equation, it was applied to a real-world subaerial landslide tsunami (i.e., the 2018 Anak Krakatau event) and delivered satisfactory performance.

CRediT authorship contribution statement

Ramtin Sabeti: Conceptualization, Methodology, Validation, Software, Visualization, Writing – review & editing. Mohammad Heidarzadeh: Methodology, Data curation, Software, Writing – review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding

RS is supported by the Leverhulme Trust Grant No. RPG-2022-306. MH is funded by open funding of State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, grant number SKHL2101. We acknowledge University of Bath Institutional Open Access Fund. MH is also funded by the Great Britain Sasakawa Foundation grant no. 6217 (awarded in 2023).

Acknowledgements

Authors are sincerely grateful to the laboratory technician team, particularly Mr William Bazeley, at the Faculty of Engineering, University of Bath for their support during the laboratory physical modelling of this research. We appreciate the valuable insights provided by Mr. Brian Fox (Senior CFD Engineer at Flow Science, Inc.) regarding air entrainment modelling in FLOW-3D HYDRO. We acknowledge University of Bath Institutional Open Access Fund.

Data availability

  • All data used in this study are given in the body of the article.

References

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Fig. 3. (a–c) Snapshots of the CtFD simulation of laser-beam irradiation: (a) Top, (b) longitudinal vertical cross-sectional, and (c) transversal vertical cross-sectional views. (d) z-position of the solid/liquid interface during melting and solidification.

Solute segregation in a rapidly solidified Hastelloy-X Ni-based superalloy during laser powder bed fusion investigated by phase-field simulations and computational thermal-fluid dynamics

Masayuki Okugawa ab, Kenji Saito a, Haruki Yoshima a, Katsuhiko Sawaizumi a, Sukeharu Nomoto c, Makoto Watanabe c, Takayoshi Nakano ab, Yuichiro Koizumi abShow moreAdd to MendeleyShareCite

https://doi.org/10.1016/j.addma.2024.104079

Get rights and content Under a Creative Commons license open access

Abstract

Solute segregation significantly affects material properties and is a critical issue in the laser powder-bed fusion (LPBF) additive manufacturing (AM) of Ni-based superalloys. To the best of our knowledge, this is the first study to demonstrate a computational thermal-fluid dynamics (CtFD) simulation coupled multi-phase-field (MPF) simulation with a multicomponent-composition model of Ni-based superalloy to predict solute segregation under solidification conditions in LPBF. The MPF simulation of the Hastelloy-X superalloy reproduced the experimentally observed submicron-sized cell structure. Significant solute segregations were formed within interdendritic regions during solidification at high cooling rates of up to 108 K s-1, a characteristic feature of LPBF. Solute segregation caused a decrease in the solidus temperature (TS), with a reduction of up to 30.4 K, which increases the risk of liquation cracks during LPBF. In addition, the segregation triggers the formation of carbide phases, which increases the susceptibility to ductility dip cracking. Conversely, we found that the decrease in TS is suppressed at the melt-pool boundary regions, where re-remelting occurs during the stacking of the layer above. Controlling the re-remelting behavior is deemed to be crucial for designing crack-free alloys. Thus, we demonstrated that solute segregation at the various interfacial regions of Ni-based multicomponent alloys can be predicted by the conventional MPF simulation. The design of crack-free Ni-based superalloys can be expedited by MPF simulations of a broad range of element combinations and their concentrations in multicomponent Ni-based superalloys.

Graphical abstract

Keywords

Laser powder-bed fusion, Hastelloy-X Nickel-based superalloy, solute element segregation, computational thermal-fluid dynamics simulation, phase-field method

1. Introduction

Additive manufacturing (AM) technologies have attracted considerable attention as they allow us to easily build three-dimensional (3D) parts with complex geometries. Among the wide range of available AM techniques, laser powder-bed fusion (LPBF) has emerged as a preferred technique for metal AM [1], [2], [3], [4], [5]. In LPBF, metal products are built layer-by-layer by scanning laser, which fuse metal powder particles into bulk solids.

Significant attempts have been made to integrate LPBF techniques within the aerospace industry, with a particular focus on weldable Ni-based superalloys, such as IN718 [6], [7], [8], IN625 [9], [10], and Hastelloy-X (HX) [11], [12], [13], [14]. Non-weldable alloys, such as IN738LC [15], [16] and CMSX-4 [1], [17] are also suitable for their sufficient creep resistance under higher temperature conditions. However, non-weldable alloys are difficult to build using LPBF because of their susceptibility to cracking during the process. In general, a macro solute-segregation during solidification is suppressed by the rapid cooling conditions (up to 108 K s-1) unique to the LPBF process [18]. However, the solute segregation still occurs in the interdendritic regions that are smaller than the micrometer scale [5], [19], [20], [21]; these regions are suggested to be related to the hot cracks in LPBF-fabricated parts. Therefore, an understanding of solute segregation is essential for the fabrication of reliable LPBF-fabricated parts while avoiding cracks.

The multiphase-field (MPF) method has gained popularity for modeling the microstructure evolution and solute segregation under rapid cooling conditions [5], [20], [21], [22], [23], [24], [25], [26], [27], [28]. Moreover, quantifiable predictions have been achieved by combining the MPF method with temperature distribution analysis methods such as the finite-element method (FEM) [20] and computational thermal-fluid dynamics (CtFD) simulations [28]. These aforementioned studies have used binary-approximated multicomponent systems, such as Ni–Nb binary alloys, to simulate IN718 alloys. While MPF simulations using binary alloy systems can effectively reproduce microstructure formations and segregation behaviors, the binary approximation might be affected by the chemical interactions between the removed solute elements in the target multicomponent alloy. The limit of absolute stability predicted by the Mullins-Sekerka theory [29] is also crucial because the limit velocity is close to the solidification rate in the LPBF process and is different in multicomponent and binary-approximated systems. The difference between the solidus and liquidus temperatures, ΔT0, directly determines the absolute stability according to the Mullins-Sekerka theory. For example, the ΔT0 values of IN718 and its binary-approximated Ni–5 wt.%Nb alloy are 134 K [28] and 71 K [30], respectively. The solidification rate compared to the limit of absolute stability, i.e., the relative non-equilibrium of solidification, changes by simplification of the system. It is therefore important to use the composition of the actual multicomponent system in such simulations. However, to the best of our knowledge, there is no MPF simulation using a multicomponent model coupled with a temperature analysis simulation to predict solute segregation in a Ni-based superalloy.

In this study, we demonstrate that the conventional MPF model can reproduce experimentally observed dendritic structures by performing a phase-field simulation using the temperature distribution obtained by a CtFD simulation of a multicomponent Ni-based alloy (conventional solid-solution hardening-type HX). The MPF simulation revealed that the segregation behavior of solute elements largely depends on the regions of the melt pool, such as the cell boundary, the interior of the melt-pool boundary, and heat-affected regions. The sensitivities of the various interfaces to liquation and solidification cracks are compared based on the predicted concentration distributions. Moreover, the feasibility of using the conventional MPF model for LPBF is discussed in terms of the absolute stability limit.

2. Methods

2.1. Laser-beam irradiation experiments

Rolled and recrystallized HX ingots with dimensions of 20 × 50 × 10 mm were used as the specimens for laser-irradiation experiments. The specimens were irradiated with a laser beam scanned along straight lines of 10 mm in length using a laser AM machine (EOS 290 M, EOS) equipped with a 400 W Yb-fiber laser. Irradiation was performed with a beam power of P = 300 W and a scanning speed of V = 600 mm s-1, which are the conditions generally used in the LPBF fabrication of Ni-based superalloy [8]. The corresponding line energy was 0.5 J mm-1. The samples were cut perpendicular to the beam-scanning direction for cross-sectional observation using a field-emission scanning electron microscope (FE-SEM, JEOL JSM 6500). Crystal orientation analysis was performed by electron backscatter diffraction (EBSD). The sizes of each crystal grain and their aspect ratios were evaluated by analyzing the EBSD data.

2.2. CtFD simulation

CtFD simulations of the laser-beam irradiation of HX were performed using a 3D thermo-fluid analysis software (Flow Science FLOW-3D® with Flow-3D Weld module). A Gaussian heat source model was used, in which the irradiation intensity distribution of the beam is regarded as a symmetrical Gaussian distribution over the entire beam. The distribution of the beam irradiation intensity is expressed by the following equation.(1)q̇=2ηPπR2exp−2r2R2.

Here, P is the power, R is the effective beam radius, r is the actual beam radius, and η is the beam absorption rate of the substrate. To improve the accuracy of the model, η was calculated by assuming multiple reflections using the Fresnel equation:(2)�=1−121+1−�cos�21+1+�cos�2+�2−2�cos�+2cos2��2+2�cos�+2cos2�.

ε is the Fresnel coefficient and θ is the incident angle of the laser. A local laser melt causes the vaporization of the material and results in a high vapor pressure. This vapor pressure acts as a recoil pressure on the surface, pushing the weld pool down. The recoil pressure is reproduced using the following equation.(3)precoil=Ap0exp∆HLVRTV1−TVT.

Here, p0 is the atmospheric pressure, ∆HLV is the latent heat of vaporization, R is the gas constant, and TV is the boiling point at the saturated vapor pressure. A is a ratio coefficient that is generally assumed to be 0.54, indicating that the recoil pressure due to evaporation is 54% of the vapor pressure at equilibrium on the liquid surface.

Table 1 shows the parameters used in the simulations. Most parameters were evaluated using an alloy physical property calculation software (Sente software JMatPro v11). The values in a previously published study [31] were used for the emissivity and the Stefan–Boltzmann constant, and the values for pure Ni [32] were used for the heat of vaporization and vaporization temperatures. The Fresnel coefficient, which determines the beam absorption efficiency, was used as a fitting parameter to reproduce the morphology of the experimentally observed melt region, and a Fresnel coefficient of 0.12 was used in this study.

Table 1. Parameters used in the CtFD simulations.

ParameterSymbolValueReference
Density at 298.15 Kρ8.24 g cm-3[⁎]
Liquidus temperatureTL1628.15 K[⁎]
Solidus temperatureTS1533.15 K[⁎]
Viscosity at TLη6.8 g m-1 s-1[⁎]
Specific heat at 298.15 KCP0.439 J g-1 K-1[⁎]
Thermal conductivity at 298.15 Kλ10.3 W m-1 K-1[⁎]
Surface tension at TLγL1.85 J m-2[⁎]
Temperature coefficient of surface tensiondγL/dT–2.5 × 10−4 J m-2 K-1[⁎]
EmissivityΕ0.27[31]
Stefan–Boltzmann constantσ5.67 × 10-8 W m-2 K-4[31]
Heat of fusionΔHSL2.76 × 102 J g-1[32]
Heat of vaporizationΔHLV4.29 × 103 J g-1[32]
Vaporization temperatureTV3110 K[32]

⁎

Calculated using JMatPro v11.

The dimensions of the computational domain of the numerical model were 4.0 mm in the beam-scanning direction, 0.4 mm in width, and 0.3 mm in height. A uniform mesh size of 10 μm was applied throughout the computational domain. The boundary condition of continuity was applied to all boundaries except for the top surface. The temperature was initially set to 300 K. P and V were set to their experimental values, i.e., 300 W and 600 mm s-1, respectively. Solidification conditions based on the temperature gradient, G, the solidification rate, R, and the cooling rate were evaluated, and the obtained temperature distribution was used in the MPF simulations.

2.3. MPF simulation

Two-dimensional MPF simulations weakly coupled with the CtFD simulation were performed using the Microstructure Evolution Simulation Software (MICRESS) [33], [34], [35], [36], [37] with the TQ-Interface for Thermo-Calc [38]. A simplified HX alloy composition of Ni-21.4Cr-17.6Fe-0.46Mn-8.80Mo-0.39Si-0.50W-1.10Co-0.08 C (mass %) was used in this study. The Gibbs free energy and diffusion coefficient of the system were calculated using the TCNI9 thermodynamic database [39] and the MOBNi5 mobility database [40]. Τhe equilibrium phase diagram calculated using Thermo-Calc indicates that the face-centered cubic (FCC) and σ phases appear as the equilibrium solid phases [19]. However, according to the time-temperature-transformation (TTT) diagram [41], the phases are formed after the sample is maintained for tens of hours in a temperature range of 1073 to 1173 K. Therefore, only the liquid and FCC phases were assumed to appear in the MPF simulations. The simulation domain was 5 × 100 μm, and the grid size Δx and interface width were set to 0.025 and 0.1 µm, respectively. The interfacial mobility between the solid and liquid phases was set to 1.0 × 10-8 m4 J-1 s-1. Initially, one crystalline nucleus with a [100] crystal orientation was placed at the left bottom of the simulation domain, with the liquid phase occupying the remainder of the domain. The model was solidified under the temperature field distribution obtained by the CtFD simulation. The concentration distribution and crystal orientation of the solidified model were examined. The primary dendrite arm space (PDAS) was compared to the experimental PDAS measured by the cross-sectional SEM observation.

In an actual LPBF process, solidified layers are remelted and resolidified during the stacking of the one layer above, thereby greatly affecting solute element distributions in those regions. Therefore, remelting and resolidification simulations were performed to examine the effect of remelting on solute segregation. The solidified model was remelted and resolidified by applying a time-dependent temperature field shifted by 60 μm in the height direction, assuming reheating during the stacking of the upper layer (i.e., the upper 40 μm region of the simulation box was remelted and resolidified). The changes in the composition distribution and formed microstructure were investigated.

3. Results

3.1. Experimental observation of melt pool

Fig. 1 shows a cross-sectional optical microscopy image and corresponding inverse pole figure (IPF) orientation maps obtained from the laser-melted region of HX. The dashed line indicates the fusion line. A deep melted region was formed by keyhole-mode melting due to the vaporization of the metal and resultant recoil pressure. Epitaxial growth from the unmelted region was observed. Columnar crystal grains with an average diameter of 5.46 ± 0.32 μm and an aspect ratio of 3.61 ± 0.13 appeared at the melt regions (Figs. 1b–1d). In addition, crystal grains growing in the z direction could be observed in the lower center.

Fig. 1

Fig. 2a shows a cross-sectional backscattering electron image (BEI) obtained from the laser-melted region indicated by the black square in Fig. 1a. The bright particles with a diameter of approximately 2 μm observed outside the melt pool. It is well known that M6C, M23C6, σ, and μ precipitate phases are formed in Hastelloy-X [41]. These precipitates mainly consisted of Mo, Cr, Fe, and Ni; The μ and M6C phases are rich in Mo, while the σ and M23C6 phases are rich in Cr. The SEM energy dispersive X-ray spectroscopy analysis suggested that the bright particles are the stable precipitates as shown in Fig. S2 and Table S1. Conversely, there are no carbides in the melt pool. This suggests that the cooling rate is extremely high during LPBF, which prevents the formation of a stable carbide during solidification. Figs. 2b–2f show magnified BEI images at different height positions indicated in Fig. 2a. Bright regions are observed between the cells, which become fragmentary at the center of the melt pool, as indicated by the yellow arrow heads in Figs. 2e and 2f.

Fig. 2

3.2. CtFD simulation

Figs. 3a–3c show snapshots of the CtFD simulation of HX at 2.72 ms, with the temperature indicated in color. A melt pool with an elongated teardrop shape formed and keyhole-mode melting was observed at the front of the melt region. The cooling rate, temperature gradient (G), and solidification rate (R) were evaluated from the temporal change in the temperature distribution of the CtFD simulation results. The z-position of the solid/liquid interface during the melting and solidification processes is shown in Fig. 3d. The interface goes down rapidly during melting and then rises during solidification. The MPF simulation of the microstructure formation during solidification was performed using the temperature distribution. Moreover, the microstructure formation process during the fabrication of the upper layer was investigated by remelting and resolidifying the solidified layer using the same temperature distribution with a 60 μm upward shift, corresponding to the layer thickness commonly used in the LPBF of Ni-based superalloys.

Fig. 3

Figs. 4a–4c show the changes in the cooling rate, temperature gradient, and solidification rate in the center line of the melt pool parallel to the z direction. To output the solidification conditions at the solid/liquid interface in the melt pool, only the data of the mesh where the solid phase ratio was close to 0.5 were plotted. Solidification occurred where the cooling rate was in the range of 2.1 × 105–1.6 × 106 K s-1, G was in the range of 3.6 × 105–1.9 × 107 K m-1, and R was in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The cooling rate was the highest near the fusion line and decreased as the interface approached the center of the melt region (Fig. 4a). G also exhibited the highest value in the regions near the fusion line and decreased throughout the solid/liquid interface toward the center of the melt pool (Fig. 4b). R had the lowest value near the fusion line and increased as the interface approached the center of the melt region (Fig. 4c).

Fig. 4

3.3. MPF simulations coupled with CtFD simulation

MPF simulations of solidification, remelting, and resolidification were performed using the temperature-time distribution obtained by the CtFD simulation. Fig. 5 shows the MPF solidified models colored by phase and Mo concentration. All the computational domains show the FCC phase after the solidification (Fig. 5a). Dendrites grew parallel to the heat flow direction, and solute segregations were observed in the interdendritic regions. At the bottom of the melt pool (Fig. 5d), planar interface growth occurred before the formation of primary dendrites. The bottom of the melt pool is the turning point of the solid/liquid interface from the downward motion in melting to the upward motion in solidification. Thus, the solidification rate at the boundary is zero, and is extremely low immediately above the molt-pool boundary. Here, the lower limit of the solidification rate (R) for dendritic growth can be represented by the constitutional supercooling criterion [29], Vcs = (G × DL) / ΔT, and planar interface growth occurs at R < Vcs. DL and ΔT denote the diffusion coefficient in the liquid and the equilibrium freezing range, respectively. The results suggest that planar interface growth occurs at the bottom of the melt pool, resulting in a dark region with a different solute element distribution. Some of the primary dendrites were diminished by competition with other dendrites. In addition, secondary dendrite arms could be seen in the upper regions (Fig. 5c), where solidification occurred at a lower cooling rate. The fragmentation of the solute segregation near the secondary dendrite arms is similar to that observed in the experimental melt pool shown in Figs. 2e and 2f, and the secondary dendrite arms are suggested to have appeared at the center of the melt region. Fig. 6 shows the PDASs measured from the MPF simulation models, compared to the experimental PDASs measured by the cross-sectional SEM observation of the laser-melted regions (Fig. 2). The PDAS obtained by the MPF simulation become larger as the solidification progress. Ghosh et al. [21] evident by the phase-field method that the PDAS decreases as the cooling rate increases under the rapid cooling conditions obtained by the finite element analysis. In this study, the cooling rate was decreased as the interface approached the center of the melt region (Fig. 4a), and the trends in PDAS changes with respect to cooling rate is same as the reported trend [21]. The simulated trends of the PDAS with the position in the melt pool agreed well with the experimental trends. However, all PDASs in the simulation were larger than those observed in the experiment at the same positions. Ode et al. [42] reported that PDAS differences between 2D and 3D MPF simulations can be represented by PDAS2D = 1.12 × PDAS3D owing to differences in the effects of the interfacial energy and diffusivity. We also performed 2D and 3D MPF simulations under the solidification conditions of G = 1.94 × 107 K m-1 and R = 0.82 m s-1 (Fig. S1), and found that the PDAS from the 2D MPF simulation was 1.26 times larger than that from the 3D simulation. Therefore, the cell structure obtained by the CtFD simulation coupled with the 2D MPF simulation agreed well with the experimental results over the entire melt pool region considering the dimensional effects.

Fig. 5
Fig. 6

Fig. 7b1 and 7c1 show the concentration profiles of the solidified model along the growth direction indicated by dashed lines in Fig. 7a. The differences in concentrations from the alloy composition are also shown in Fig. 7b2 and 7c2. Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. The solute segregation behavior agrees with the experimentally observation [43] and the prediction by the Scheil-Gulliver simulation [19]. Segregation occurred to the highest degree in Mo, while the ratio of segregation to the alloy composition was remarkable in C. The concentration fluctuations correlated with the position in the melt pool and decreased at the center of the melt pool, which was suggested to correspond to the lower cooling rate in this region. Conversely, droplets that appeared between secondary dendrite arms in the upper regions of the simulation domain exhibited a locally high segregation of solute elements, with the same amount of segregation as that at the bottom of the melt pool.

Fig. 7

3.4. Remelting and resolidification simulation

The solidified model was subjected to remelting and resolidification conditions by shifting the temperature profile upward by 60 µm to reveal the effect of reheating on the solute segregation behavior. Figs. 8a and 8b shows the simulation domains of the HX model after resolidification, colored by phase and Mo concentration. The magnified MPF models during the resolidification of the regions indicated by rectangles in Figs. 8a and 8b are also shown as Figs. 8c and 8d. Dendrites grew from the bottom of the remelted region, with the segregation of solute elements occurring in the interdendritic regions. The entire domain become the FCC phase after the resolidification, as shown in Fig. 8a. The bottom of the remelted regions exhibited a different microstructure, and Mo was depressed at the remelted regions, rather than the interdendritic regions. The different solute segregation behavior [44] and the microstructure formation [45] at the melt pool boundary is also observed in LPBF manufactured 316 L stainless steel. We found that this microstructure was formed by further remelting during the resolidification process, which is shown in Fig. 9. Here, the solidified HX model was heated, and the interdendritic regions were preferentially melted while concentration fluctuations were maintained (Fig. 9a1 and 9a2). Subsequently, planer interface growth occurs near the melt pool boundary where the solidification rate is almost zero, and the dendrites outside of the boundary are grown epitaxially (Fig. 9b1 and 9b2). However, these remelted again because of the temperature rise (Fig. 9c1 and 9c2, and the temperature-time profile shown in Fig. 9e). The remelted regions then cooled and solidified with the abnormal solute segregations (Fig. 9d1 and 9d2). Then, dendrite grows from amplified fluctuations under the solidification rate larger than the criterion of constitutional supercooling (Fig. 9d1, 9d2, and Fig. 8d). It has been reported [46], [47] that temperature rising owning to latent heat affects microstructure formation: phase-field simulations of a Ni–Al binary alloy suggest that the release of latent heat during solidification increases the average temperature of the system [46] and strongly influences the solidification conditions [47]. In this study, the release of latent heat during solidification is considered in CtFD simulations for calculating the temperature distribution, and the temperature increase is suggested to have also occurred due to the release of latent heat.

Fig. 8
Fig. 9

Fig. 10b1 and 10c1 show the solute element concentration line profiles of the resolidified model along the growth direction indicated by dashed lines in Fig. 10a. Fig. 10b2 and 10c2 show the corresponding differences in concentration from the alloy composition. The segregation behavior of solute elements at the interdendritic regions (Fig. 10b1 and 10b2) was the same as that in the solidified model (Figs. 7b1 and 7b2). Here, Cr, Mo, C, Mn, and W were segregated to the interdendritic regions, while Si, Fe, and Co were depressed. However, the concentration fluctuations at the interdendritic regions were larger than those in the solidified model. Moreover, the segregation of the outside of the melt pool, i.e., the heat-affected zone, was remarkable throughout remelting and resolidification. Different segregation behaviors were observed in the re-remelted region: Mo, Si, Mn, and W were segregated, while Ni, Fe, and Co were depressed. These solute segregations caused by remelting are expected to heavily influence the crack behavior.

Fig. 10

4. Discussion

4.1. Effect of segregation of solute elements on liquation cracking susceptibility

Strong solute segregation was observed between the interdendritic regions of the solidified alloy (Fig. 7). In addition, the solute segregation behavior was significantly affected by remelting and resolidification and varied across the alloy. Solute segregation can be categorized by the regions shown in Fig. 11a1–11a4, namely the cell boundary (Fig. 11a1), interior of the melt-pool boundary (Fig. 11a2), re-remelted regions (Fig. 11a3), and heat-affected regions (Fig. 11a4). The concentration profiles of these regions are shown in Fig. 11b1–11b4. Solute segregation was the highest in the cell boundary region. The solute segregation in the heat-affected region was almost the same as that in the cell boundary region, but seemed to have been attenuated by reheating during remelting and resolidification. The interior of the melt-pool boundary region also had the same tendency for solute segregation. However, the amount of Cr segregation was smaller than that of Mo. A decrease in the Cr concentration was also mitigated, and the concentration remained the same as that in the alloy composition. Fig. 11c1–11c4 show the chemical potentials of the solute elements for the FCC phase at 1073 K calculated using the compositions of those interfacial regions. All the interfacial regions showed non-constant chemical potentials for each element along the perpendicular direction, but the fluctuations of the chemical potentials differed by the type of interfaces. In particular, the fluctuation of the chemical potential of C at the cell boundary region was the largest, suggesting it can be relaxed easily by heat treatment. On the other hand, the fluctuations of the other elements in all the regions were small. The solute segregations are most likely to remain after the heat treatment and are supposed to affect the cracking susceptibilities.

Fig. 11

The solidus temperatures TS, the difference between the liquidus and solidus temperatures (i.e., the brittle temperature range (BTR)), and the fractions of the equilibrium precipitate phases at 1073 K of the interfacial regions were calculated as the liquation, solidification, and ductility dip cracking susceptibilities, respectively. At the cell boundary (Fig. 12a1), interior of the melt-pool boundary (Fig. 12a1), and heat-affected regions (Fig. 12a1), the internal and interfacial regions exhibited higher and lower TS compared to that of the alloy composition, respectively. The lowest Ts was obtained with the composition at the cell boundary region, which is the largest solute-segregated region. It has been suggested that strong segregations of solute elements in LPBF lead to liquation cracks [16]. This study also supports this suggestion, and liquation cracks are more likely to occur at the interfacial regions indicated by predicting the solute segregation behavior using the MPF model. Additionally, the BTRs of the cell boundary, interior of the melt-pool boundary, and heat-affected regions were wider at the interdendritic regions, and solidification cracks were also likely to occur in these regions. Moreover, within the solute segregation regions, the fraction of the precipitate phases in these interfacial regions was larger than that calculated using the alloy composition (Fig. 12c1, 12c2, and 12c4). This indicates that ductility dip cracking is also likely to occur at the cell boundary, interior of the melt-pool boundary, and in heat-affected regions. Contrarily, we found that the re-remelted region exhibited a higher TS and smaller BTR even in the interfacial region (Fig. 12a3 and 12b3), where the solute segregation behavior was different from that of the other regions. In addition, the re-remelting region exhibited less precipitation compared with the other segregated regions (Fig. 12c3). The re-remelting caused by the latent heat can attenuate solute segregation, prevent Ts from decreasing, decrease the BTR, and decrease the amount of precipitate phases. Alloys with a large amount of latent heat are expected to increase the re-remelting region, thereby decreasing the susceptibility to liquation and ductility dip cracks due to solute element segregation. This can be a guide for designing alloys for the LPBF process. As mentioned in Section 3.4, the microstructure [45] and the solute segregation behavior [44] at the melt pool boundary of LPBF-manufactured 316 L stainless steel are observed, and they are different from that of the interdendritic regions. Experimental observations of the solute segregation behavior in the LPBF-fabricated Ni-based alloys are currently underway.

Fig. 12

4.2. Applicability of the conventional MPF simulation to microstructure formation under LPBF

As the solidification growth rate increases, segregation coefficients approach 1, and the fluctuation of the solid/liquid interface is suppressed by the interfacial tension. The interface growth occurs in a flat fashion instead of having a cellular morphology at a velocity above the absolute stability limit, Ras, predicted by the Mullins-Sekerka theory [29]: Ras = (ΔT0 DL) / (k Γ) where ΔT0, DL, k, and Γ are the difference between the liquidus and solidus temperatures, equilibrium segregation coefficient, the diffusivity of liquid, and the Gibbs-Thomson coefficient, respectively.

The Ras of HX was calculated using the equation and the thermodynamic parameters obtained by the TCNI9 thermodynamic database [39]. The calculated Ras of HX was 3.9 m s-1 and is ten times larger than that of the Ni–Nb alloy (approximately 0.4 m s-1) [20]. The HX alloy was solidified under R values in the range of 8.2 × 10−2–6.3 × 10−1 m s-1. The theoretically calculated criterion is larger than the evaluated R, and is in agreement with the experiment in which dendritic growth is observed in the melt pool (Fig. 5). In contrast, Karayagiz et al. [20] reported that the R of the Ni–Nb binary alloy under LPBF was as high as approximately 2 m s-1, and planar interface growth was observed to be predominant under the high-growth-rate conditions. These experimentally observed microstructures agree well with the prediction by the Mullins-Sekerka theory about the relationship between the morphology and solidification rates.

In this study, the solidification microstructure formed by the laser-beam irradiation of an HX multicomponent Ni-based superalloy was reproduced by a conventional MPF simulation, in which the system was assumed to be in a quasi-equilibrium condition. Boussinot et al. [24] also suggested that the conventional phase-field model can be applied to simulate the microstructure of an IN718 multicomponent Ni-based superalloy in LPBF. In contrast, Kagayaski et al. [20] suggested that the conventional MPF simulation cannot be applied to the solidification of the Ni-Nb binary alloy system and that the finite interface dissipation model proposed by Steinbach et al. [48], [49] is necessary to simulate the high solidification rates observed in LPBF. The difference in the applicability of the conventional MPF method to HX and Ni–Nb binary alloys is presumed to arise from the differences in the non-equilibrium degree of these systems under the high solidification rates of LPBF. The results suggest that Ras can be used as a simple index to apply the conventional MPF model for solidification in LPBF. Solidification becomes a non-equilibrium process as the solidification rate approaches the limit of absolute stability, Ras. In this study, the solidification of the HX multicomponent system occurred under a relatively low solidification rate compared to Ras, and the microstructure of the conventional MPF model was successfully reproduced in the physical experiment. However, note that the limit of absolute stability predicted by the Mullins-Sekerka theory was originally proposed for solidification in a binary alloy system, and further investigation is required to consider its applicability to multicomponent alloy systems. Moreover, the fast solidification, such as in the LPBF process, causes segregation coefficient approaching a value of 1 [20], [21], [25] corresponds to a diffusion length that is on the order of the atomic interface thickness. When the segregation coefficient approaches 1, solute undercooling disappears; hence, there is no driving force to amplify fluctuations regardless of whether interfacial tension is present. This phenomenon should be further investigated in future studies.

5. Conclusions

We simulated solute segregation in a multicomponent HX alloy under the LPBF process by an MPF simulation using the temperature distributions obtained by a CtFD simulation. We set the parameters of the CtFD simulation to match the melt pool shape formed in the laser-irradiation experiment and found that solidification occurred under high cooling rates of up to 1.6 × 106 K s-1.

MPF simulations using the temperature distributions from CtFD simulation could reproduce the experimentally observed PDAS and revealed that significant solute segregation occurred at the interdendritic regions. Equilibrium thermodynamic calculations using the alloy compositions of the segregated regions when considering crack sensitivities suggested a decrease in the solidus temperature and an increase in the amount of carbide precipitation, thereby increasing the susceptibility to liquation and ductility dip cracks in these regions. Notably, these changes were suppressed at the melt-pool boundary region, where re-remelting occurred during the stacking of the layer above. This effect can be used to achieve a novel in-process segregation attenuation.

Our study revealed that a conventional MPF simulation weakly coupled with a CtFD simulation can be used to study the solidification of multicomponent alloys in LPBF, contrary to the cases of binary alloys investigated in previous studies. We discussed the applicability of the conventional MPF model to the LPBF process in terms of the limit of absolute stability, Ras, and suggested that alloys with a high limit velocity, i.e., multicomponent alloys, can be simulated using the conventional MPF model even under the high solidification velocity conditions of LPBF.

CRediT authorship contribution statement

Masayuki Okugawa: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Takayoshi Nakano: Writing – review & editing, Validation, Supervision, Funding acquisition. Yuichiro Koizumi: Writing – review & editing, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Sukeharu Nomoto: Writing – review & editing, Validation, Investigation. Makoto Watanabe: Writing – review & editing, Validation, Supervision, Funding acquisition. Katsuhiko Sawaizumi: Validation, Software, Investigation, Formal analysis, Data curation. Kenji Saito: Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Haruki Yoshima: Visualization, Validation, Software, Investigation, Formal analysis, Data curation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper

Acknowledgments

This work was partly supported by the Cabinet Office, Government of Japan, Cross-ministerial Strategic Innovation Promotion Program (SIP), “Materials Integration for Revolutionary Design System of Structural Materials,” (funding agency: The Japan Science and Technology Agency), by JSPS KAKENHI Grant Numbers 21H05018 and 21H05193, and by CREST Nanomechanics: Elucidation of macroscale mechanical properties based on understanding nanoscale dynamics for innovative mechanical materials (Grant Number: JPMJCR2194) from the Japan Science and Technology Agency (JST). The authors would like to thank Mr. H. Kawabata and Mr. K. Kimura for their technical support with the sample preparations and laser beam irradiation experiments.

Appendix A. Supplementary material

Download : Download Word document (654KB)

Supplementary material.

Data availability

Data will be made available on request.

References

Schematic diagram of HP-LPBF melting process.

Modeling and numerical studies of high-precision laser powder bed fusion

Yi Wei ;Genyu Chen;Nengru Tao;Wei Zhou
https://doi.org/10.1063/5.0191504

In order to comprehensively reveal the evolutionary dynamics of the molten pool and the state of motion of the fluid during the high-precision laser powder bed fusion (HP-LPBF) process, this study aims to deeply investigate the specific manifestations of the multiphase flow, solidification phenomena, and heat transfer during the process by means of numerical simulation methods. Numerical simulation models of SS316L single-layer HP-LPBF formation with single and double tracks were constructed using the discrete element method and the computational fluid dynamics method. The effects of various factors such as Marangoni convection, surface tension, vapor recoil, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool have been paid attention to during the model construction process. The results show that the molten pool exhibits a “comet” shape, in which the temperature gradient at the front end of the pool is significantly larger than that at the tail end, with the highest temperature gradient up to 1.69 × 108 K/s. It is also found that the depth of the second track is larger than that of the first one, and the process parameter window has been determined preliminarily. In addition, the application of HP-LPBF technology helps to reduce the surface roughness and minimize the forming size.

Topics

Heat transfer, Nonequilibrium thermodynamics, Solidification process, Computer simulation, Discrete element method, Lasers, Mass transfer, Fluid mechanics, Computational fluid dynamics, Multiphase flows

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I. INTRODUCTION

Laser powder bed fusion (LPBF) has become a research hotspot in the field of additive manufacturing of metals due to its advantages of high-dimensional accuracy, good surface quality, high density, and high material utilization.1,2 With the rapid development of electronics, medical, automotive, biotechnology, energy, communication, and optics, the demand for microfabrication technology is increasing day by day.3 High-precision laser powder bed fusion (HP-LPBF) is one of the key manufacturing technologies for tiny parts in the fields of electronics, medical, automotive, biotechnology, energy, communication, and optics because of its process characteristics such as small focal spot diameter, small powder particle size, and thin powder layup layer thickness.4–13 Compared with LPBF, HP-LPBF has the significant advantages of smaller focal spot diameter, smaller powder particle size, and thinner layer thickness. These advantages make HP-LPBF perform better in producing micro-fine parts, high surface quality, and parts with excellent mechanical properties.

HP-LPBF is in the exploratory stage, and researchers have already done some exploratory studies on the focal spot diameter, the amount of defocusing, and the powder particle size. In order to explore the influence of changing the laser focal spot diameter on the LPBF process characteristics of the law, Wildman et al.14 studied five groups of different focal spot diameter LPBF forming 316L stainless steel (SS316L) processing effect, the smallest focal spot diameter of 26 μm, and the results confirm that changing the focal spot diameter can be achieved to achieve the energy control, so as to control the quality of forming. Subsequently, Mclouth et al.15 proposed the laser out-of-focus amount (focal spot diameter) parameter, which characterizes the distance between the forming plane and the laser focal plane. The laser energy density was controlled by varying the defocusing amount while keeping the laser parameters constant. Sample preparation at different focal positions was investigated, and their microstructures were characterized. The results show that the samples at the focal plane have finer microstructure than those away from the focal plane, which is the effect of higher power density and smaller focal spot diameter. In order to explore the influence of changing the powder particle size on the characteristics of the LPBF process, Qian et al.16 carried out single-track scanning simulations on powder beds with average powder particle sizes of 70 and 40 μm, respectively, and the results showed that the melt tracks sizes were close to each other under the same process parameters for the two particle-size distributions and that the molten pool of powder beds with small particles was more elongated and the edges of the melt tracks were relatively flat. In order to explore the superiority of HP-LPBF technology, Xu et al.17 conducted a comparative analysis of HP-LPBF and conventional LPBF of SS316L. The results showed that the average surface roughness of the top surface after forming by HP-LPBF could reach 3.40 μm. Once again, it was verified that HP-LPBF had higher forming quality than conventional LPBF. On this basis, Wei et al.6 comparatively analyzed the effects of different laser focal spot diameters on different powder particle sizes formed by LPBF. The results showed that the smaller the laser focal spot diameter, the fewer the defects on the top and side surfaces. The above research results confirm that reducing the laser focal spot diameter can obtain higher energy density and thus better forming quality.

LPBF involves a variety of complex systems and mechanisms, and the final quality of the part is influenced by a large number of process parameters.18–24 Some research results have shown that there are more than 50 factors affecting the quality of the specimen. The influencing factors are mainly categorized into three main groups: (1) laser parameters, (2) powder parameters, and (3) equipment parameters, which interact with each other to determine the final specimen quality. With the continuous development of technologies such as computational materials science and computational fluid dynamics (CFD), the method of studying the influence of different factors on the forming quality of LPBF forming process has been shifted from time-consuming and laborious experimental characterization to the use of numerical simulation methods. As a result, more and more researchers are adopting this approach for their studies. Currently, numerical simulation studies on LPBF are mainly focused on the exploration of molten pool, temperature distribution, and residual stresses.

  1. Finite element simulation based on continuum mechanics and free surface fluid flow modeling based on fluid dynamics are two common approaches to study the behavior of LPBF molten pool.25–28 Finite element simulation focuses on the temperature and thermal stress fields, treats the powder bed as a continuum, and determines the molten pool size by plotting the elemental temperature above the melting point. In contrast, fluid dynamics modeling can simulate the 2D or 3D morphology of the metal powder pile and obtain the powder size and distribution by certain algorithms.29 The flow in the molten pool is mainly affected by recoil pressure and the Marangoni effect. By simulating the molten pool formation, it is possible to predict defects, molten pool shape, and flow characteristics, as well as the effect of process parameters on the molten pool geometry.30–34 In addition, other researchers have been conducted to optimize the laser processing parameters through different simulation methods and experimental data.35–46 Crystal growth during solidification is studied to further understand the effect of laser parameters on dendritic morphology and solute segregation.47–54 A multi-scale system has been developed to describe the fused deposition process during 3D printing, which is combined with the conductive heat transfer model and the dendritic solidification model.55,56
  2. Relevant scholars have adopted various different methods for simulation, such as sequential coupling theory,57 Lagrangian and Eulerian thermal models,58 birth–death element method,25 and finite element method,59 in order to reveal the physical phenomena of the laser melting process and optimize the process parameters. Luo et al.60 compared the LPBF temperature field and molten pool under double ellipsoidal and Gaussian heat sources by ANSYS APDL and found that the diffusion of the laser energy in the powder significantly affects the molten pool size and the temperature field.
  3. The thermal stresses obtained from the simulation correlate with the actual cracks,61 and local preheating can effectively reduce the residual stresses.62 A three-dimensional thermodynamic finite element model investigated the temperature and stress variations during laser-assisted fabrication and found that powder-to-solid conversion increases the temperature gradient, stresses, and warpage.63 Other scholars have predicted residual stresses and part deflection for LPBF specimens and investigated the effects of deposition pattern, heat, laser power, and scanning strategy on residual stresses, noting that high-temperature gradients lead to higher residual stresses.64–67 

In short, the process of LPBF forming SS316L is extremely complex and usually involves drastic multi-scale physicochemical changes that will only take place on a very small scale. Existing literature employs DEM-based mesoscopic-scale numerical simulations to investigate the effects of process parameters on the molten pool dynamics of LPBF-formed SS316L. However, a few studies have been reported on the key mechanisms of heating and solidification, spatter, and convective behavior of the molten pool of HP-LPBF-formed SS316L with small laser focal spot diameters. In this paper, the geometrical properties of coarse and fine powder particles under three-dimensional conditions were first calculated using DEM. Then, numerical simulation models for single-track and double-track cases in the single-layer HP-LPBF forming SS316L process were developed at mesoscopic scale using the CFD method. The flow genesis of the melt in the single-track and double-track molten pools is discussed, and their 3D morphology and dimensional characteristics are discussed. In addition, the effects of laser process parameters, powder particle size, and laser focal spot diameter on the temperature field, characterization information, and defects in the molten pool are discussed.

II. MODELING

A. 3D powder bed modeling

HP-LPBF is an advanced processing technique for preparing target parts layer by layer stacking, the process of which involves repetitive spreading and melting of powders. In this process, both the powder spreading and the morphology of the powder bed are closely related to the results of the subsequent melting process, while the melted surface also affects the uniform distribution of the next layer of powder. For this reason, this chapter focuses on the modeling of the physical action during the powder spreading process and the theory of DEM to establish the numerical model of the powder bed, so as to lay a solid foundation for the accuracy of volume of fluid (VOF) and CFD.

1. DEM

DEM is a numerical technique for calculating the interaction of a large number of particles, which calculates the forces and motions of the spheres by considering each powder sphere as an independent unit. The motion of the powder particles follows the laws of classical Newtonian mechanics, including translational and rotational,38,68–70 which are expressed as follows:����¨=���+∑��ij,

(1)����¨=∑�(�ij×�ij),

(2)

where �� is the mass of unit particle i in kg, ��¨ is the advective acceleration in m/s2, And g is the gravitational acceleration in m/s2. �ij is the force in contact with the neighboring particle � in N. �� is the rotational inertia of the unit particle � in kg · m2. ��¨ is the unit particle � angular acceleration in rad/s2. �ij is the vector pointing from unit particle � to the contact point of neighboring particle �⁠.

Equations (1) and (2) can be used to calculate the velocity and angular velocity variations of powder particles to determine their positions and velocities. A three-dimensional powder bed model of SS316L was developed using DEM. The powder particles are assumed to be perfect spheres, and the substrate and walls are assumed to be rigid. To describe the contact between the powder particles and between the particles and the substrate, a non-slip Hertz–Mindlin nonlinear spring-damping model71 was used with the following expression:�hz=��������+��[(�����ij−�eff����)−(�����+�eff����)],

(3)

where �hz is the force calculated using the Hertzian in M. �� and �� are the radius of unit particles � and � in m, respectively. �� is the overlap size of the two powder particles in m. ��⁠, �� are the elastic constants in the normal and tangential directions, respectively. �ij is the unit vector connecting the centerlines of the two powder particles. �eff is the effective mass of the two powder particles in kg. �� and �� are the viscoelastic damping constants in the normal and tangential directions, respectively. �� and �� are the components of the relative velocities of the two powder particles. ��� is the displacement vector between two spherical particles. The schematic diagram of overlapping powder particles is shown in Fig. 1.

FIG. 1.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of overlapping powder particles.

Because the particle size of the powder used for HP-LPBF is much smaller than 100 μm, the effect of van der Waals forces must be considered. Therefore, the cohesive force �jkr of the Hertz–Mindlin model was used instead of van der Waals forces,72 with the following expression:�jkr=−4��0�*�1.5+4�*3�*�3,

(4)1�*=(1−��2)��+(1−��2)��,

(5)1�*=1��+1��,

(6)

where �* is the equivalent Young’s modulus in GPa; �* is the equivalent particle radius in m; �0 is the surface energy of the powder particles in J/m2; α is the contact radius in m; �� and �� are the Young’s modulus of the unit particles � and �⁠, respectively, in GPa; and �� and �� are the Poisson’s ratio of the unit particles � and �⁠, respectively.

2. Model building

Figure 2 shows a 3D powder bed model generated using DEM with a coarse powder geometry of 1000 × 400 × 30 μm3. The powder layer thickness is 30 μm, and the powder bed porosity is 40%. The average particle size of this spherical powder is 31.7 μm and is normally distributed in the range of 15–53 μm. The geometry of the fine powder was 1000 × 400 × 20 μm3, with a layer thickness of 20 μm, and the powder bed porosity of 40%. The average particle size of this spherical powder is 11.5 μm and is normally distributed in the range of 5–25 μm. After the 3D powder bed model is generated, it needs to be imported into the CFD simulation software for calculation, and the imported geometric model is shown in Fig. 3. This geometric model is mainly composed of three parts: protective gas, powder bed, and substrate. Under the premise of ensuring the accuracy of the calculation, the mesh size is set to 3 μm, and the total number of coarse powder meshes is 1 704 940. The total number of fine powder meshes is 3 982 250.

FIG. 2.

VIEW LARGEDOWNLOAD SLIDE

Three-dimensional powder bed model: (a) coarse powder, (b) fine powder.

FIG. 3.

VIEW LARGEDOWNLOAD SLIDE

Geometric modeling of the powder bed computational domain: (a) coarse powder, (b) fine powder.

B. Modeling of fluid mechanics simulation

In order to solve the flow, melting, and solidification problems involved in HP-LPBF molten pool, the study must follow the three governing equations of conservation of mass, conservation of energy, and conservation of momentum.73 The VOF method, which is the most widely used in fluid dynamics, is used to solve the molten pool dynamics model.

1. VOF

VOF is a method for tracking the free interface between the gas and liquid phases on the molten pool surface. The core idea of the method is to define a volume fraction function F within each grid, indicating the proportion of the grid space occupied by the material, 0 ≤ F ≤ 1 in Fig. 4. Specifically, when F = 0, the grid is empty and belongs to the gas-phase region; when F = 1, the grid is completely filled with material and belongs to the liquid-phase region; and when 0 < F < 1, the grid contains free surfaces and belongs to the mixed region. The direction normal to the free surface is the direction of the fastest change in the volume fraction F (the direction of the gradient of the volume fraction), and the direction of the gradient of the volume fraction can be calculated from the values of the volume fractions in the neighboring grids.74 The equations controlling the VOF are expressed as follows:𝛻����+�⋅(��→)=0,

(7)

where t is the time in s and �→ is the liquid velocity in m/s.

FIG. 4.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of VOF.

The material parameters of the mixing zone are altered due to the inclusion of both the gas and liquid phases. Therefore, in order to represent the density of the mixing zone, the average density �¯ is used, which is expressed as follows:72�¯=(1−�1)�gas+�1�metal,

(8)

where �1 is the proportion of liquid phase, �gas is the density of protective gas in kg/m3, and �metal is the density of metal in kg/m3.

2. Control equations and boundary conditions

Figure 5 is a schematic diagram of the HP-LPBF melting process. First, the laser light strikes a localized area of the material and rapidly heats up the area. Next, the energy absorbed in the region is diffused through a variety of pathways (heat conduction, heat convection, and surface radiation), and this process triggers complex phase transition phenomena (melting, evaporation, and solidification). In metals undergoing melting, the driving forces include surface tension and the Marangoni effect, recoil due to evaporation, and buoyancy due to gravity and uneven density. The above physical phenomena interact with each other and do not occur independently.

FIG. 5.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of HP-LPBF melting process.

  1. Laser heat sourceThe Gaussian surface heat source model is used as the laser heat source model with the following expression:�=2�0����2exp(−2�12��2),(9)where � is the heat flow density in W/m2, �0 is the absorption rate of SS316L, �� is the radius of the laser focal spot in m, and �1 is the radial distance from the center of the laser focal spot in m. The laser focal spot can be used for a wide range of applications.
  2. Energy absorptionThe formula for calculating the laser absorption �0 of SS316L is as follows:�0=0.365(�0[1+�0(�−20)]/�)0.5,(10)where �0 is the direct current resistivity of SS316L at 20 °C in Ω m, �0 is the resistance temperature coefficient in ppm/°C, � is the temperature in °C, and � is the laser wavelength in m.
  3. Heat transferThe basic principle of heat transfer is conservation of energy, which is expressed as follows:𝛻𝛻𝛻�(��)��+�·(��→�)=�·(�0����)+��,(11)where � is the density of liquid phase SS316L in kg/m3, �� is the specific heat capacity of SS316L in J/(kg K), 𝛻� is the gradient operator, t is the time in s, T is the temperature in K, 𝛻�� is the temperature gradient, �→ is the velocity vector, �0 is the coefficient of thermal conduction of SS316L in W/(m K), and  �� is the thermal energy dissipation term in the molten pool.
  4. Molten pool flowThe following three conditions need to be satisfied for the molten pool to flow:
    • Conservation of mass with the following expression:𝛻�·(��→)=0.(12)
    • Conservation of momentum (Navier–Stokes equation) with the following expression:𝛻𝛻𝛻𝛻���→��+�(�→·�)�→=�·[−pI+�(��→+(��→)�)]+�,(13)where � is the pressure in Pa exerted on the liquid phase SS316L microelement, � is the unit matrix, � is the fluid viscosity in N s/m2, and � is the volumetric force (gravity, atmospheric pressure, surface tension, vapor recoil, and the Marangoni effect).
    • Conservation of energy, see Eq. (11)
  5. Surface tension and the Marangoni effectThe effect of temperature on the surface tension coefficient is considered and set as a linear relationship with the following expression:�=�0−��dT(�−��),(14)where � is the surface tension of the molten pool at temperature T in N/m, �� is the melting temperature of SS316L in K, �0 is the surface tension of the molten pool at temperature �� in Pa, and σdσ/ dT is the surface tension temperature coefficient in N/(m K).In general, surface tension decreases with increasing temperature. A temperature gradient causes a gradient in surface tension that drives the liquid to flow, known as the Marangoni effect.
  6. Metal vapor recoilAt higher input energy densities, the maximum temperature of the molten pool surface reaches the evaporation temperature of the material, and a gasification recoil pressure occurs vertically downward toward the molten pool surface, which will be the dominant driving force for the molten pool flow.75 The expression is as follows:��=0.54�� exp ���−���0���,(15)where �� is the gasification recoil pressure in Pa, �� is the ambient pressure in kPa, �� is the latent heat of evaporation in J/kg, �0 is the gas constant in J/(mol K), T is the surface temperature of the molten pool in K, and Te is the evaporation temperature in K.
  7. Solid–liquid–gas phase transitionWhen the laser hits the powder layer, the powder goes through three stages: heating, melting, and solidification. During the solidification phase, mutual transformations between solid, liquid, and gaseous states occur. At this point, the latent heat of phase transition absorbed or released during the phase transition needs to be considered.68 The phase transition is represented based on the relationship between energy and temperature with the following expression:�=�����,(�<��),�(��)+�−����−����,(��<�<��)�(��)+(�−��)����,(��<�),,(16)where �� and �� are solid and liquid phase density, respectively, of SS316L in kg/m3. �� and �� unit volume of solid and liquid phase-specific heat capacity, respectively, of SS316L in J/(kg K). �� and ��⁠, respectively, are the solidification temperature and melting temperature of SS316L in K. �� is the latent heat of the phase transition of SS316L melting in J/kg.

3. Assumptions

The CFD model was computed using the commercial software package FLOW-3D.76 In order to simplify the calculation and solution process while ensuring the accuracy of the results, the model makes the following assumptions:

  1. It is assumed that the effects of thermal stress and material solid-phase thermal expansion on the calculation results are negligible.
  2. The molten pool flow is assumed to be a Newtonian incompressible laminar flow, while the effects of liquid thermal expansion and density on the results are neglected.
  3. It is assumed that the surface tension can be simplified to an equivalent pressure acting on the free surface of the molten pool, and the effect of chemical composition on the results is negligible.
  4. Neglecting the effect of the gas flow field on the molten pool.
  5. The mass loss due to evaporation of the liquid metal is not considered.
  6. The influence of the plasma effect of the molten metal on the calculation results is neglected.

It is worth noting that the formulation of assumptions requires a trade-off between accuracy and computational efficiency. In the above models, some physical phenomena that have a small effect or high difficulty on the calculation results are simplified or ignored. Such simplifications make numerical simulations more efficient and computationally tractable, while still yielding accurate results.

4. Initial conditions

The preheating temperature of the substrate was set to 393 K, at which time all materials were in the solid state and the flow rate was zero.

5. Material parameters

The material used is SS316L and the relevant parameters required for numerical simulations are shown in Table I.46,77,78

TABLE I.

SS316L-related parameters.

PropertySymbolValue
Density of solid metal (kg/m3) �metal 7980 
Solid phase line temperature (K) �� 1658 
Liquid phase line temperature (K) �� 1723 
Vaporization temperature (K) �� 3090 
Latent heat of melting (⁠ J/kg⁠) �� 2.60×105 
Latent heat of evaporation (⁠ J/kg⁠) �� 7.45×106 
Surface tension of liquid phase (N /m⁠) � 1.60 
Liquid metal viscosity (kg/m s) �� 6×10−3 
Gaseous metal viscosity (kg/m s) �gas 1.85×10−5 
Temperature coefficient of surface tension (N/m K) ��/�T 0.80×10−3 
Molar mass (⁠ kg/mol⁠) M 0.05 593 
Emissivity � 0.26 
Laser absorption �0 0.35 
Ambient pressure (kPa) �� 101 325 
Ambient temperature (K) �0 300 
Stefan–Boltzmann constant (W/m2 K4) � 5.67×10−8 
Thermal conductivity of metals (⁠ W/m K⁠) � 24.55 
Density of protective gas (kg/m3) �gas 1.25 
Coefficient of thermal expansion (/K) �� 16×10−6 
Generalized gas constant (⁠ J/mol K⁠) R 8.314 

III. RESULTS AND DISCUSSION

With the objective of studying in depth the evolutionary patterns of single-track and double-track molten pool development, detailed observations were made for certain specific locations in the model, as shown in Fig. 6. In this figure, P1 and P2 represent the longitudinal tangents to the centers of the two melt tracks in the XZ plane, while L1 is the transverse profile in the YZ plane. The scanning direction is positive and negative along the X axis. Points A and B are the locations of the centers of the molten pool of the first and second melt tracks, respectively (x = 1.995 × 10−4, y = 5 × 10−7, and z = −4.85 × 10−5).

FIG. 6.

VIEW LARGEDOWNLOAD SLIDE

Schematic diagram of observation position.

A. Single-track simulation

A series of single-track molten pool simulation experiments were carried out in order to investigate the influence law of laser power as well as scanning speed on the HP-LPBF process. Figure 7 demonstrates the evolution of the 3D morphology and temperature field of the single-track molten pool in the time period of 50–500 μs under a laser power of 100 W and a scanning speed of 800 mm/s. The powder bed is in the natural cooling state. When t = 50 μs, the powder is heated by the laser heat and rapidly melts and settles to form the initial molten pool. This process is accompanied by partial melting of the substrate and solidification together with the melted powder. The molten pool rapidly expands with increasing width, depth, length, and temperature, as shown in Fig. 7(a). When t = 150 μs, the molten pool expands more obviously, and the temperature starts to transfer to the surrounding area, forming a heat-affected zone. At this point, the width of the molten pool tends to stabilize, and the temperature in the center of the molten pool has reached its peak and remains largely stable. However, the phenomenon of molten pool spatter was also observed in this process, as shown in Fig. 7(b). As time advances, when t = 300 μs, solidification begins to occur at the tail of the molten pool, and tiny ripples are produced on the solidified surface. This is due to the fact that the melt flows toward the region with large temperature gradient under the influence of Marangoni convection and solidifies together with the melt at the end of the bath. At this point, the temperature gradient at the front of the bath is significantly larger than at the end. While the width of the molten pool was gradually reduced, the shape of the molten pool was gradually changed to a “comet” shape. In addition, a slight depression was observed at the top of the bath because the peak temperature at the surface of the bath reached the evaporation temperature, which resulted in a recoil pressure perpendicular to the surface of the bath downward, creating a depressed region. As the laser focal spot moves and is paired with the Marangoni convection of the melt, these recessed areas will be filled in as shown in Fig. 7(c). It has been shown that the depressed regions are the result of the coupled effect of Marangoni convection, recoil pressure, and surface tension.79 By t = 500 μs, the width and height of the molten pool stabilize and show a “comet” shape in Fig. 7(d).

FIG. 7.

VIEW LARGEDOWNLOAD SLIDE

Single-track molten pool process: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠.

Figure 8 depicts the velocity vector diagram of the P1 profile in a single-track molten pool, the length of the arrows represents the magnitude of the velocity, and the maximum velocity is about 2.36 m/s. When t = 50 μs, the molten pool takes shape, and the velocities at the two ends of the pool are the largest. The variation of the velocities at the front end is especially more significant in Fig. 8(a). As the time advances to t = 150 μs, the molten pool expands rapidly, in which the velocity at the tail increases and changes more significantly, while the velocity at the front is relatively small. At this stage, the melt moves backward from the center of the molten pool, which in turn expands the molten pool area. The melt at the back end of the molten pool center flows backward along the edge of the molten pool surface and then converges along the edge of the molten pool to the bottom center, rising to form a closed loop. Similarly, a similar closed loop is formed at the front end of the center of the bath, but with a shorter path. However, a large portion of the melt in the center of the closed loop formed at the front end of the bath is in a nearly stationary state. The main cause of this melt flow phenomenon is the effect of temperature gradient and surface tension (the Marangoni effect), as shown in Figs. 8(b) and 8(e). This dynamic behavior of the melt tends to form an “elliptical” pool. At t = 300 μs, the tendency of the above two melt flows to close the loop is more prominent and faster in Fig. 8(c). When t = 500 μs, the velocity vector of the molten pool shows a stable trend, and the closed loop of melt flow also remains stable. With the gradual laser focal spot movement, the melt is gradually solidified at its tail, and finally, a continuous and stable single track is formed in Fig. 8(d).

FIG. 8.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of single-track molten pool velocity in XZ longitudinal section: (a) t = 50  ��⁠, (b) t = 150  ��⁠, (c) t = 300  ��⁠, (d) t = 500  ��⁠, (e) molten pool flow.

In order to explore in depth the transient evolution of the molten pool, the evolution of the single-track temperature field and the melt flow was monitored in the YZ cross section. Figure 9(a) shows the state of the powder bed at the initial moment. When t = 250 μs, the laser focal spot acts on the powder bed and the powder starts to melt and gradually collects in the molten pool. At this time, the substrate will also start to melt, and the melt flow mainly moves in the downward and outward directions and the velocity is maximum at the edges in Fig. 9(b). When t = 300 μs, the width and depth of the molten pool increase due to the recoil pressure. At this time, the melt flows more slowly at the center, but the direction of motion is still downward in Fig. 9(c). When t = 350 μs, the width and depth of the molten pool further increase, at which time the intensity of the melt flow reaches its peak and the direction of motion remains the same in Fig. 9(d). When t = 400 μs, the melt starts to move upward, and the surrounding powder or molten material gradually fills up, causing the surface of the molten pool to begin to flatten. At this time, the maximum velocity of the melt is at the center of the bath, while the velocity at the edge is close to zero, and the edge of the melt starts to solidify in Fig. 9(e). When t = 450 μs, the melt continues to move upward, forming a convex surface of the melt track. However, the melt movement slows down, as shown in Fig. 9(f). When t = 500 μs, the melt further moves upward and its speed gradually becomes smaller. At the same time, the melt solidifies further, as shown in Fig. 9(g). When t = 550 μs, the melt track is basically formed into a single track with a similar “mountain” shape. At this stage, the velocity is close to zero only at the center of the molten pool, and the flow behavior of the melt is poor in Fig. 9(h). At t = 600 μs, the melt stops moving and solidification is rapidly completed. Up to this point, a single track is formed in Fig. 9(i). During the laser action on the powder bed, the substrate melts and combines with the molten state powder. The powder-to-powder fusion is like the convergence of water droplets, which are rapidly fused by surface tension. However, the fusion between the molten state powder and the substrate occurs driven by surface tension, and the molten powder around the molten pool is pulled toward the substrate (a wetting effect occurs), which ultimately results in the formation of a monolithic whole.38,80,81

FIG. 9.

VIEW LARGEDOWNLOAD SLIDE

Evolution of single-track molten pool temperature and melt flow in the YZ cross section: (a) t = 0  ��⁠, (b) t = 250  ��⁠, (c) t = 300  ��⁠, (d) t = 350  ��⁠, (e) t = 400  ��⁠, (f) t = 450  ��⁠, (g) t = 500  ��⁠, (h) t = 550  ��⁠, (i) t = 600  ��⁠.

The wetting ability between the liquid metal and the solid substrate in the molten pool directly affects the degree of balling of the melt,82,83 and the wetting ability can be measured by the contact angle of a single track in Fig. 10. A smaller value of contact angle represents better wettability. The contact angle α can be calculated by�=�1−�22,

(17)

where �1 and �2 are the contact angles of the left and right regions, respectively.

FIG. 10.

VIEW LARGEDOWNLOAD SLIDE

Schematic of contact angle.

Relevant studies have confirmed that the wettability is better at a contact angle α around or below 40°.84 After measurement, a single-track contact angle α of about 33° was obtained under this process parameter, which further confirms the good wettability.

B. Double-track simulation

In order to deeply investigate the influence of hatch spacing on the characteristics of the HP-LPBF process, a series of double-track molten pool simulation experiments were systematically carried out. Figure 11 shows in detail the dynamic changes of the 3D morphology and temperature field of the double-track molten pool in the time period of 2050–2500 μs under the conditions of laser power of 100 W, scanning speed of 800 mm/s, and hatch spacing of 0.06 mm. By comparing the study with Fig. 7, it is observed that the basic characteristics of the 3D morphology and temperature field of the second track are similar to those of the first track. However, there are subtle differences between them. The first track exhibits a basically symmetric shape, but the second track morphology shows a slight deviation influenced by the difference in thermal diffusion rate between the solidified metal and the powder. Otherwise, the other characteristic information is almost the same as that of the first track. Figure 12 shows the velocity vector plot of the P2 profile in the double-track molten pool, with a maximum velocity of about 2.63 m/s. The melt dynamics at both ends of the pool are more stable at t = 2050 μs, where the maximum rate of the second track is only 1/3 of that of the first one. Other than that, the rest of the information is almost no significant difference from the characteristic information of the first track. Figure 13 demonstrates a detailed observation of the double-track temperature field and melts flow in the YZ cross section, and a comparative study with Fig. 9 reveals that the width of the second track is slightly wider. In addition, after the melt direction shifts from bottom to top, the first track undergoes four time periods (50 μs) to reach full solidification, while the second track takes five time periods. This is due to the presence of significant heat buildup in the powder bed after the forming of the first track, resulting in a longer dynamic time of the melt and an increased molten pool lifetime. In conclusion, the level of specimen forming can be significantly optimized by adjusting the laser power and hatch spacing.

FIG. 11.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool process: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 12.

VIEW LARGEDOWNLOAD SLIDE

Vector plot of double-track molten pool velocity in XZ longitudinal section: (a) t = 2050  ��⁠, (b) t = 2150  ��⁠, (c) t = 2300  ��⁠, (d) t = 2500  ��⁠.

FIG. 13.

VIEW LARGEDOWNLOAD SLIDE

Evolution of double-track molten pool temperature and melt flow in the YZ cross section: (a) t = 2250  ��⁠, (b) t = 2300  ��⁠, (c) t = 2350  ��⁠, (d) t = 2400  ��⁠, (e) t = 2450  ��⁠, (f) t = 2500  ��⁠, (g) t = 2550  ��⁠, (h) t = 2600  ��⁠, (i) t = 2650  ��⁠.

In order to quantitatively detect the molten pool dimensions as well as the remolten region dimensions, the molten pool characterization information in Fig. 14 is constructed by drawing the boundary on the YZ cross section based on the isothermal surface of the liquid phase line. It can be observed that the heights of the first track and second track are basically the same, but the depth of the second track increases relative to the first track. The molten pool width is mainly positively correlated with the laser power as well as the scanning speed (the laser line energy density �⁠). However, the remelted zone width is negatively correlated with the hatch spacing (the overlapping ratio). Overall, the forming quality of the specimens can be directly influenced by adjusting the laser power, scanning speed, and hatch spacing.

FIG. 14.

VIEW LARGEDOWNLOAD SLIDE

Double-track molten pool characterization information on YZ cross section.

In order to study the variation rule of the temperature in the center of the molten pool with time, Fig. 15 demonstrates the temperature variation curves with time for two reference points, A and B. Among them, the red dotted line indicates the liquid phase line temperature of SS316L. From the figure, it can be seen that the maximum temperature at the center of the molten pool in the first track is lower than that in the second track, which is mainly due to the heat accumulation generated after passing through the first track. The maximum temperature gradient was calculated to be 1.69 × 108 K/s. When the laser scanned the first track, the temperature in the center of the molten pool of the second track increased slightly. Similarly, when the laser scanned the second track, a similar situation existed in the first track. Since the temperature gradient in the second track is larger than that in the first track, the residence time of the liquid phase in the molten pool of the first track is longer than that of the second track.

FIG. 15.

VIEW LARGEDOWNLOAD SLIDE

Temperature profiles as a function of time for two reference points A and B.

C. Simulation analysis of molten pool under different process parameters

In order to deeply investigate the effects of various process parameters on the mesoscopic-scale temperature field, molten pool characteristic information and defects of HP-LPBF, numerical simulation experiments on mesoscopic-scale laser power, scanning speed, and hatch spacing of double-track molten pools were carried out.

1. Laser power

Figure 16 shows the effects of different laser power on the morphology and temperature field of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. When P = 50 W, a smaller molten pool is formed due to the lower heat generated by the Gaussian light source per unit time. This leads to a smaller track width, which results in adjacent track not lapping properly and the presence of a large number of unmelted powder particles, resulting in an increase in the number of defects, such as pores in the specimen. The surface of the track is relatively flat, and the depth is small. In addition, the temperature gradient before and after the molten pool was large, and the depression location appeared at the biased front end in Fig. 16(a). When P = 100 W, the surface of the track is flat and smooth with excellent lap. Due to the Marangoni effect, the velocity field of the molten pool is in the form of “vortex,” and the melt has good fluidity, and the maximum velocity reaches 2.15 m/s in Fig. 16(b). When P = 200 W, the heat generated by the Gaussian light source per unit time is too large, resulting in the melt rapidly reaching the evaporation temperature, generating a huge recoil pressure, forming a large molten pool, and the surface of the track is obviously raised. The melt movement is intense, especially the closed loop at the center end of the molten pool. At this time, the depth and width of the molten pool are large, leading to the expansion of the remolten region and the increased chance of the appearance of porosity defects in Fig. 16(c). The results show that at low laser power, the surface tension in the molten pool is dominant. At high laser power, recoil pressure is its main role.

FIG. 16.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different laser powers: (a) P = 50 W, (b) P = 100 W, (c) P = 200 W.

Table II shows the effect of different laser powers on the characteristic information of the double-track molten pool at a scanning speed of 800 mm/s and a hatch spacing of 0.06 mm. The negative overlapping ratio in the table indicates that the melt tracks are not lapped, and 26/29 indicates the melt depth of the first track/second track. It can be seen that with the increase in laser power, the melt depth, melt width, melt height, and remelted zone show a gradual increase. At the same time, the overlapping ratio also increases. Especially in the process of laser power from 50 to 200 W, the melting depth and melting width increased the most, which increased nearly 2 and 1.5 times, respectively. Meanwhile, the overlapping ratio also increases with the increase in laser power, which indicates that the melting and fusion of materials are better at high laser power. On the other hand, the dimensions of the molten pool did not change uniformly with the change of laser power. Specifically, the depth-to-width ratio of the molten pool increased from about 0.30 to 0.39 during the increase from 50 to 120 W, which further indicates that the effective heat transfer in the vertical direction is greater than that in the horizontal direction with the increase in laser power. This dimensional response to laser power is mainly affected by the recoil pressure and also by the difference in the densification degree between the powder layer and the metal substrate. In addition, according to the experimental results, the contact angle shows a tendency to increase and then decrease during the process of laser power increase, and always stays within the range of less than 33°. Therefore, in practical applications, it is necessary to select the appropriate laser power according to the specific needs in order to achieve the best processing results.

TABLE II.

Double-track molten pool characterization information at different laser powers.

Laser power (W)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
50 16 54 11 / −10 23 
100 26/29 74 14 18 23.33 33 
200 37/45 116 21 52 93.33 28 

2. Scanning speed

Figure 17 demonstrates the effect of different scanning speeds on the morphology and temperature field of the double-track molten pool at a laser power of 100 W and a hatch spacing of 0.06 mm. With the gradual increase in scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. When � = 200 mm/s, the slow scanning speed causes the material to absorb too much heat, which is very easy to trigger the overburning phenomenon. At this point, the molten pool is larger and the surface morphology is uneven. This situation is consistent with the previously discussed scenario with high laser power in Fig. 17(a). However, when � = 1600 mm/s, the scanning speed is too fast, resulting in the material not being able to absorb sufficient heat, which triggers the powder particles that fail to melt completely to have a direct effect on the bonding of the melt to the substrate. At this time, the molten pool volume is relatively small and the neighboring melt track cannot lap properly. This result is consistent with the previously discussed case of low laser power in Fig. 17(b). Overall, the ratio of the laser power to the scanning speed (the line energy density �⁠) has a direct effect on the temperature field and surface morphology of the molten pool.

FIG. 17.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different scanning speed: (a)  � = 200 mm/s, (b)  � = 1600 mm/s.

Table III shows the effects of different scanning speed on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and hatch spacing of 0.06 mm. It can be seen that the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. With the increase in scanning speed, the melt depth, melt width, melt height, remelted zone, and overlapping ratio show a gradual decreasing trend. Among them, the melt depth and melt width decreased faster, while the melt height and remolten region decreased relatively slowly. In addition, when the scanning speed was increased from 200 to 800 mm/s, the decreasing speeds of melt depth and melt width were significantly accelerated, while the decreasing speeds of overlapping ratio were relatively slow. When the scanning speed was further increased to 1600 mm/s, the decreasing speeds of melt depth and melt width were further accelerated, and the un-lapped condition of the melt channel also appeared. In addition, the contact angle increases and then decreases with the scanning speed, and both are lower than 33°. Therefore, when selecting the scanning speed, it is necessary to make reasonable trade-offs according to the specific situation, and take into account the factors of melt depth, melt width, melt height, remolten region, and overlapping ratio, in order to achieve the best processing results.

TABLE III.

Double-track molten pool characterization information at different scanning speeds.

Scanning speed (mm/s)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
200 55/68 182 19/32 124 203.33 22 
1600 13 50 11 / −16.67 31 

3. Hatch spacing

Figure 18 shows the effect of different hatch spacing on the morphology and temperature field of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. The surface morphology and temperature field of the first track and second track are basically the same, but slightly different. The first track shows a basically symmetric morphology along the scanning direction, while the second track shows a slight offset due to the difference in the heat transfer rate between the solidified material and the powder particles. When the hatch spacing is too small, the overlapping ratio increases and the probability of defects caused by remelting phenomenon grows. When the hatch spacing is too large, the neighboring melt track cannot overlap properly, and the powder particles are not completely melted, leading to an increase in the number of holes. In conclusion, the ratio of the line energy density � to the hatch spacing (the volume energy density E) has a significant effect on the temperature field and surface morphology of the molten pool.

FIG. 18.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool under different hatch spacings: (a) H = 0.03 mm, (b) H = 0.12 mm.

Table IV shows the effects of different hatch spacing on the characteristic information of the double-track molten pool under the condition of laser power of 100 W and scanning speed of 800 mm/s. It can be seen that the hatch spacing has little effect on the melt depth, melt width, and melt height, but has some effect on the remolten region. With the gradual expansion of hatch spacing, the remolten region shows a gradual decrease. At the same time, the overlapping ratio also decreased with the increase in hatch spacing. In addition, it is observed that the contact angle shows a tendency to increase and then remain stable when the hatch spacing increases, which has a more limited effect on it. Therefore, trade-offs and decisions need to be made on a case-by-case basis when selecting the hatch spacing.

TABLE IV.

Double-track molten pool characterization information at different hatch spacings.

Hatch spacing (mm)Depth (μm)Width (μm)Height (μm)Remolten region (μm)Overlapping ratio (%)Contact angle (°)
0.03 25/27 82 14 59 173.33 30 
0.12 26 78 14 / −35 33 

In summary, the laser power, scanning speed, and hatch spacing have a significant effect on the formation of the molten pool, and the correct selection of these three process parameters is crucial to ensure the forming quality. In addition, the melt depth of the second track is slightly larger than that of the first track at higher line energy density � and volume energy density E. This is mainly due to the fact that a large amount of heat accumulation is generated after the first track, forming a larger molten pool volume, which leads to an increase in the melt depth.

D. Simulation analysis of molten pool with powder particle size and laser focal spot diameter

Figure 19 demonstrates the effect of different powder particle sizes and laser focal spot diameters on the morphology and temperature field of the double-track molten pool under a laser power of 100 W, a scanning speed of 800 mm/s, and a hatch spacing of 0.06 mm. In the process of melting coarse powder with small laser focal spot diameter, the laser energy cannot completely melt the larger powder particles, resulting in their partial melting and further generating excessive pore defects. The larger powder particles tend to generate zigzag molten pool edges, which cause an increase in the roughness of the melt track surface. In addition, the molten pool is also prone to generate the present spatter phenomenon, which can directly affect the quality of forming. The volume of the formed molten pool is relatively small, while the melt depth, melt width, and melt height are all smaller relative to the fine powder in Fig. 19(a). In the process of melting fine powders with a large laser focal spot diameter, the laser energy is able to melt the fine powder particles sufficiently, even to the point of overmelting. This results in a large number of fine spatters being generated at the edge of the molten pool, which causes porosity defects in the melt track in Fig. 19(b). In addition, the maximum velocity of the molten pool is larger for large powder particle sizes compared to small powder particle sizes, which indicates that the temperature gradient in the molten pool is larger for large powder particle sizes and the melt motion is more intense. However, the size of the laser focal spot diameter has a relatively small effect on the melt motion. However, a larger focal spot diameter induces a larger melt volume with greater depth, width, and height. In conclusion, a small powder size helps to reduce the surface roughness of the specimen, and a small laser spot diameter reduces the minimum forming size of a single track.

FIG. 19.

VIEW LARGEDOWNLOAD SLIDE

Simulation results of double-track molten pool with different powder particle size and laser focal spot diameter: (a) focal spot = 25 μm, coarse powder, (b) focal spot = 80 μm, fine powder.

Table V shows the maximum temperature gradient at the reference point for different powder sizes and laser focal spot diameters. As can be seen from the table, the maximum temperature gradient is lower than that of HP-LPBF for both coarse powders with a small laser spot diameter and fine powders with a large spot diameter, a phenomenon that leads to an increase in the heat transfer rate of HP-LPBF, which in turn leads to a corresponding increase in the cooling rate and, ultimately, to the formation of finer microstructures.

TABLE V.

Maximum temperature gradient at the reference point for different powder particle sizes and laser focal spot diameters.

Laser power (W)Scanning speed (mm/s)Hatch spacing (mm)Average powder size (μm)Laser focal spot diameter (μm)Maximum temperature gradient (×107 K/s)
100 800 0.06 31.7 25 7.89 
11.5 80 7.11 

IV. CONCLUSIONS

In this study, the geometrical characteristics of 3D coarse and fine powder particles were first calculated using DEM and then numerical simulations of single track and double track in the process of forming SS316L from monolayer HP-LPBF at mesoscopic scale were developed using CFD method. The effects of Marangoni convection, surface tension, recoil pressure, gravity, thermal convection, thermal radiation, and evaporative heat dissipation on the heat and mass transfer in the molten pool were considered in this model. The effects of laser power, scanning speed, and hatch spacing on the dynamics of the single-track and double-track molten pools, as well as on other characteristic information, were investigated. The effects of the powder particle size on the molten pool were investigated comparatively with the laser focal spot diameter. The main conclusions are as follows:

  1. The results show that the temperature gradient at the front of the molten pool is significantly larger than that at the tail, and the molten pool exhibits a “comet” morphology. At the top of the molten pool, there is a slightly concave region, which is the result of the coupling of Marangoni convection, recoil pressure, and surface tension. The melt flow forms two closed loops, which are mainly influenced by temperature gradients and surface tension. This special dynamic behavior of the melt tends to form an “elliptical” molten pool and an almost “mountain” shape in single-track forming.
  2. The basic characteristics of the three-dimensional morphology and temperature field of the second track are similar to those of the first track, but there are subtle differences. The first track exhibits a basically symmetrical shape; however, due to the difference in thermal diffusion rates between the solidified metal and the powder, a slight asymmetry in the molten pool morphology of the second track occurs. After forming through the first track, there is a significant heat buildup in the powder bed, resulting in a longer dynamic time of the melt, which increases the life of the molten pool. The heights of the first track and second track remained essentially the same, but the depth of the second track was greater relative to the first track. In addition, the maximum temperature gradient was 1.69 × 108 K/s during HP-LPBF forming.
  3. At low laser power, the surface tension in the molten pool plays a dominant role. At high laser power, recoil pressure becomes the main influencing factor. With the increase of laser power, the effective heat transfer in the vertical direction is superior to that in the horizontal direction. With the gradual increase of scanning speed, the surface morphology of the molten pool evolves from circular to elliptical. In addition, the scanning speed has a significant effect on the melt depth, melt width, melt height, remolten region, and overlapping ratio. Too large or too small hatch spacing will lead to remelting or non-lap phenomenon, which in turn causes the formation of defects.
  4. When using a small laser focal spot diameter, it is difficult to completely melt large powder particle sizes, resulting in partial melting and excessive porosity generation. At the same time, large powder particles produce curved edges of the molten pool, resulting in increased surface roughness of the melt track. In addition, spatter occurs, which directly affects the forming quality. At small focal spot diameters, the molten pool volume is relatively small, and the melt depth, the melt width, and the melt height are correspondingly small. Taken together, the small powder particle size helps to reduce surface roughness, while the small spot diameter reduces the forming size.

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Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Effects of ramp slope and discharge on hydraulic performance of submerged hump weirs

Arash Ahmadi a, Amir H. Azimi b

Abstract

험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 경사는 자유 및 침수 흐름 조건 모두에서 험프 웨어의 성능에 영향을 미치는 설계 매개변수입니다.

침수된 험프보의 유출 특성 및 수위 변화에 대한 램프 경사 및 유출의 영향을 조사하기 위해 일련의 수치 시뮬레이션이 수행되었습니다. 1V:1H에서 1V:5H까지의 5개 램프 경사를 다양한 업스트림 방전에서 테스트했습니다.

수치모델의 검증을 위해 수치결과를 실험실 데이터와 비교하였다. 수면수위 예측과 유출계수의 시뮬레이션 불일치는 각각 전체 범위의 ±10%와 ±5% 이내였습니다.

모듈 한계 및 방전 감소 계수의 변화에 대한 램프 경사의 영향을 연구했습니다. 험프보의 경사로 경사가 증가함에 따라 상대적으로 높은 침수율에서 모듈러 한계가 발생함을 알 수 있었다.

침수 시작은 방류 수위를 작은 증분으로 조심스럽게 증가시켜 모델링되었으며 그 결과는 모듈 한계의 고전적인 정의와 비교되었습니다. 램프 경사와 방전이 증가함에 따라 모듈러 한계가 증가하는 것으로 밝혀졌지만, 모듈러 한계의 고전적인 정의는 모듈러 한계가 방전과 무관하다는 것을 나타냅니다.

Hump weir 하류의 속도와 와류장은 램프 경사에 의해 제어되는 와류 구조 형성을 나타냅니다. 에너지 손실은 수치 출력으로부터 계산되었으며 정규화된 에너지 손실은 침수에 따라 선형적으로 감소하는 것으로 나타났습니다.

Hump weirs are amongst conventional hydraulic structures for water level control and discharge measurement. The slope in the upstream and downstream ramps is a design parameter that affects the performance of Hump weirs in both free and submerged flow conditions. A series of numerical simulations was performed to investigate the effects of ramp slope and discharge on discharge characteristics and water level variations of submerged Hump weirs. Five ramp slopes ranging from 1V:1H to 1V:5H were tested at different upstream discharges. The numerical results were compared with the laboratory data for verifications of the numerical model. The simulation discrepancies in prediction of water surface level and discharge coefficient were within ±10 % and ±5 % of the full range, respectively. The effects of ramp slope on variations of modular limit and discharge reduction factor were studied. It was found that the modular limit occurred at relatively higher submergence ratios as the ramp slope in Hump weirs increased. The onset of submergence was modeled by carefully increasing tailwater level with small increments and the results were compared with the classic definition of modular limit. It was found that the modular limit increases with increasing the ramp slope and discharge while the classic definition of modular limit indicated that the modular limit is independent of the discharge. The velocity and vortex fields in the downstream of Hump weirs indicated the formation vortex structure, which is controlled by the ramp slope. The energy losses were calculated from the numerical outputs, and it was found that the normalized energy losses decreased linearly with submergence.

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Introduction

Weirs have been utilized predominantly for discharge measurement, flow diversion, and water level control in open channels, irrigation canal, and natural streams due to their simplicity of operation and accuracy. Several research studies have been conducted to determine the head-discharge relationship in weirs as one of the most common hydraulic structures for flow measurement (Rajaratnam and Muralidhar, 1969 [[1], [2], [3]]; Vatankhah, 2010, [[4], [5], [6]]; b [[7], [8], [9]]; Azimi and Seyed Hakim, 2019; Salehi et al., 2019; Salehi and Azimi, 2019, [10]. Weirs in general are classified into two major categories named as sharp-crested weirs and weirs of finite-crest length (Rajaratnam and Muralidhar, 1969; [11]. Sharp-crested weirs are typically used for flow measurement in small irrigation canals and laboratory flumes. In contrast, weirs of finite crest length are more suitable for water level control and flow diversion in rivers and natural streams [7,[12], [13], [14]].

The head-discharge relationship in sharp-crested weirs is developed by employing energy equation between two sections in the upstream and downstream of the weir and integration of the velocity profile at the crest of the weir as:

where Qf is the free flow discharge, B is the channel width, g is the acceleration due to gravity, ho is the water head in free-flow condition, and Cd is the discharge coefficient. Rehbock [15] proposed a linear correlation between discharge coefficient and the ratio of water head, ho, and the weir height, P as Cd = 0.605 + 0.08 (ho/P).

Upstream and/or downstream ramp(s) can be added to sharp-crested weirs to enhance the structural stability of the weir. A sharp-crested weir with upstream and/or downstream ramp(s) are known as triangular weirs in the literature. Triangular weirs with both upstream and downstream ramps are also known as Hump weirs and are first introduced in the experimental study of Bazin [16]. The ramps are constructed upstream and downstream of sharp-crested weirs to enhance the weir’s structural integrity and improve the hydraulic performance of the weir. In free-flow condition, the discharge coefficient of Hump weirs increases with increasing downstream ramp slope but decreases as upstream ramp slope increases (Azimi et al., 2013).

The hydraulic performance of weirs is evaluated in both free and submerged flow conditions. In free flow condition, water freely flows over weirs since the downstream water level is lower than that of the crest level of the weir. Channel blockage or flood in the downstream of weirs can raise the tailwater level, t. As tailwater passes the crest elevation in sharp-crested weirs, the upstream flow decelerates due to the excess pressure force in the downstream and the upstream water level increases. The onset of water level raise due to tailwater raise is called the modular limit. Once the tailwater level passes the modular limit, the weir is submerged. In sharp-crested weirs, the submerged flow regime may occur even before the tailwater reaches the crest elevation [8,14], whereas, in weirs of finite crest length, the upstream water level remains unchanged even if the tailwater raises above the crest elevation and it normally causes submergence once the tailwater level passes the critical depth at the crest of the weir [7,17]. The degree of submergence can be estimated by careful observation of the water surface profile. Observations of water surface at different submergence levels indicated two distinct flow patterns in submerged sharp-crested weirs that was initially classified as impinging jet and surface flow regimes [14]. [8] analyzed the variations of water surface profiles over submerged sharp-crested weirs with different submergence ratios and defined four distinct regimes of impinging jet, surface jump, surface wave, and surface jet.

[18] characterized the onset of submergence by defining the modular limit as a stage when the free flow head increases by +1 mm due to tailwater rise. The definition of modular limit is somewhat arbitrary, and it is difficult to identify for large discharges because the upstream water surface begins to fluctuate. This definition did not consider the effects of channel and weir geometries. The experimental data in triangular weirs and weirs finite-crest length with upstream and downstream ramp(s) revealed that the modular limit varied with the ratio of the free-flow head to the total streamwise length of the weir [17]. Weirs of finite crest length with upstream and downstream ramps are known as embankment weirs in literature [1,19,20] and Azimi et al., 2013) [19]. conducted two series of laboratory experiments to study the hydraulics of submerged embankment weirs with the upstream and downstream ramps of 1V:1H and 1V:2H. Empirical correlations were proposed to directly estimate the flow discharge in submerged embankment weirs for t/h > 0.7 where h is the water head in submerged flow condition. He found that the free flow discharge is a function of upstream water head, but the submerged discharge is a function of submergence level, t/h [21]. studied the hydraulics of four embankment weirs with different weir heights ranging from 0.09 m to 0.36 m. It was found that submerged embankments with a higher ho/P, where P is the height of the weir, have a smaller discharge reduction due to submergence. Effects of crest length in embankment weirs with both upstream and downstream ramps of 1V:2H was studied in both free and submerged flow conditions [1]. It was found that the modular limit in submerged embankment weirs decreased linearly with the relative crest length, Ho/(Ho + L), where Ho is the total head and L is the crest length.

In submerged flow condition, the performance of weirs is quantified by the discharge reduction factor, ψ, which is a ratio of the submerged discharge, Qs, to the corresponding free-flow discharge, Qf, based on the upstream head, h [12]. In submerged-flow conditions, flow discharge can be estimated as:��=���

[1] proposed a formula to predict ψ that could be used for embankment weirs with different crest lengths ranging from 0 to 0.3 m as:�=(1−��)�where n is an exponent varying from 4 to 7 and Yt is the normalized submergence defined as:��=�ℎ−[0.85−(0.5��+�)]1−[0.85−(0.5��+�)]where H is the total upstream head in submerged-flow conditions [7]. proposed a simpler formula to predict ψ for weirs of finite-crest length as:�=[1−(�ℎ)�]�where m and n are exponents varying for different types of weirs. Hakim and Azimi (2017) employed regression analysis to propose values of n = 0.25 and m = 0.28 (ho/L)−2.425 for triangular weirs.

The discharge capacity of weirs decreases in submerged flow condition and the onset of submergence occurs at the modular limit. Therefore, the determination of modular limit in weirs with different geometries is critical to understanding the sensitivity of a particular weir model with tailwater level variations. The available definition of modular limit as when head water raises by +1 mm due to tailwater rise does not consider the effects of channel and weir geometries. Therefore, a new and more accurate definition of modular limit is proposed in this study to consider the effect of other geometry and approaching flow parameters. The second objective of this study is to evaluate the effects of upstream and downstream ramps and ramps slopes on the hydraulic performance of submerged Hump weirs. The flow patterns, velocity distributions, and energy dissipation rates were extracted from validated numerical data to better understand the discharge reduction mechanism in Hump weirs in both free and submerged flow conditions.

Section snippets

Governing equations

Numerical simulation has been employed as an efficient and effective method to analyze free surface flow problems and in particular investigating on the hydraulics of flow over weirs [22]. The weir models were developed in numerical domain and the water pressure and velocity field were simulated by employing the FLOW-3D solver (Flow Science, Inc., Santa Fe, USA). The numerical results were validated with the laboratory measurements and the effects of ramps slopes on the performance of Hump

Verification of numerical model

The experimental observations of Bazin [16,17] were used for model validation in free and submerged flow conditions, respectively. The weir height in the study of Bazin was P = 0.5 m and two ramp slopes of 1V:1H and 1V:2H were tested. The bed and sides of the channel were made of glass, and the roughness distribution of the bed and walls were uniform. The Hump weir models in the study of Seyed Hakim and Azimi (2017) had a weir height of 0.076 m and ramp slopes of 1V:2H in both upstream and

Conclusions

A series of numerical simulations was performed to study the hydraulics and velocity pattern downstream of a Hump weir with symmetrical ramp slopes. Effects of ramp slope and discharge on formation of modular limit and in submerged flow condition were tested by conducting a series of numerical simulations on Hump weirs with ramp slopes varying from 1V:1H to 1V:5H. A comparison between numerical results and experimental data indicated that the proposed numerical model is accurate with a mean

Author contributions

Arash Ahmadi: Software, Validation, Visualization, Writing – original draft. Amir Azimi: Conceptualization, Funding acquisition, Investigation, Project administration, Supervision, Writing – review & editing

Uncited References

[30]; [31]; [32]; [33].

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (33)

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Lab-on-a-Chip 시스템의 혈류 역학에 대한 검토: 엔지니어링 관점

Review on Blood Flow Dynamics in Lab-on-a-Chip Systems: An Engineering Perspective

  • Bin-Jie Lai
  • , 
  • Li-Tao Zhu
  • , 
  • Zhe Chen*
  • , 
  • Bo Ouyang*
  • , and 
  • Zheng-Hong Luo*

Abstract

다양한 수송 메커니즘 하에서, “LOC(lab-on-a-chip)” 시스템에서 유동 전단 속도 조건과 밀접한 관련이 있는 혈류 역학은 다양한 수송 현상을 초래하는 것으로 밝혀졌습니다.

본 연구는 적혈구의 동적 혈액 점도 및 탄성 거동과 같은 점탄성 특성의 역할을 통해 LOC 시스템의 혈류 패턴을 조사합니다. 모세관 및 전기삼투압의 주요 매개변수를 통해 LOC 시스템의 혈액 수송 현상에 대한 연구는 실험적, 이론적 및 수많은 수치적 접근 방식을 통해 제공됩니다.

전기 삼투압 점탄성 흐름에 의해 유발되는 교란은 특히 향후 연구 기회를 위해 혈액 및 기타 점탄성 유체를 취급하는 LOC 장치의 혼합 및 분리 기능 향상에 논의되고 적용됩니다. 또한, 본 연구는 보다 정확하고 단순화된 혈류 모델에 대한 요구와 전기역학 효과 하에서 점탄성 유체 흐름에 대한 수치 연구에 대한 강조와 같은 LOC 시스템 하에서 혈류 역학의 수치 모델링의 문제를 식별합니다.

전기역학 현상을 연구하는 동안 제타 전위 조건에 대한 보다 실용적인 가정도 강조됩니다. 본 연구는 모세관 및 전기삼투압에 의해 구동되는 미세유체 시스템의 혈류 역학에 대한 포괄적이고 학제적인 관점을 제공하는 것을 목표로 한다.

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KEYWORDS: 

1. Introduction

1.1. Microfluidic Flow in Lab-on-a-Chip (LOC) Systems

Over the past several decades, the ability to control and utilize fluid flow patterns at microscales has gained considerable interest across a myriad of scientific and engineering disciplines, leading to growing interest in scientific research of microfluidics. 

(1) Microfluidics, an interdisciplinary field that straddles physics, engineering, and biotechnology, is dedicated to the behavior, precise control, and manipulation of fluids geometrically constrained to a small, typically submillimeter, scale. 

(2) The engineering community has increasingly focused on microfluidics, exploring different driving forces to enhance working fluid transport, with the aim of accurately and efficiently describing, controlling, designing, and applying microfluidic flow principles and transport phenomena, particularly for miniaturized applications. 

(3) This attention has chiefly been fueled by the potential to revolutionize diagnostic and therapeutic techniques in the biomedical and pharmaceutical sectorsUnder various driving forces in microfluidic flows, intriguing transport phenomena have bolstered confidence in sustainable and efficient applications in fields such as pharmaceutical, biochemical, and environmental science. The “lab-on-a-chip” (LOC) system harnesses microfluidic flow to enable fluid processing and the execution of laboratory tasks on a chip-sized scale. LOC systems have played a vital role in the miniaturization of laboratory operations such as mixing, chemical reaction, separation, flow control, and detection on small devices, where a wide variety of fluids is adapted. Biological fluid flow like blood and other viscoelastic fluids are notably studied among the many working fluids commonly utilized by LOC systems, owing to the optimization in small fluid sample volumed, rapid response times, precise control, and easy manipulation of flow patterns offered by the system under various driving forces. 

(4)The driving forces in blood flow can be categorized as passive or active transport mechanisms and, in some cases, both. Under various transport mechanisms, the unique design of microchannels enables different functionalities in driving, mixing, separating, and diagnosing blood and drug delivery in the blood. 

(5) Understanding and manipulating these driving forces are crucial for optimizing the performance of a LOC system. Such knowledge presents the opportunity to achieve higher efficiency and reliability in addressing cellular level challenges in medical diagnostics, forensic studies, cancer detection, and other fundamental research areas, for applications of point-of-care (POC) devices. 

(6)

1.2. Engineering Approach of Microfluidic Transport Phenomena in LOC Systems

Different transport mechanisms exhibit unique properties at submillimeter length scales in microfluidic devices, leading to significant transport phenomena that differ from those of macroscale flows. An in-depth understanding of these unique transport phenomena under microfluidic systems is often required in fluidic mechanics to fully harness the potential functionality of a LOC system to obtain systematically designed and precisely controlled transport of microfluids under their respective driving force. Fluid mechanics is considered a vital component in chemical engineering, enabling the analysis of fluid behaviors in various unit designs, ranging from large-scale reactors to separation units. Transport phenomena in fluid mechanics provide a conceptual framework for analytically and descriptively explaining why and how experimental results and physiological phenomena occur. The Navier–Stokes (N–S) equation, along with other governing equations, is often adapted to accurately describe fluid dynamics by accounting for pressure, surface properties, velocity, and temperature variations over space and time. In addition, limiting factors and nonidealities for these governing equations should be considered to impose corrections for empirical consistency before physical models are assembled for more accurate controls and efficiency. Microfluidic flow systems often deviate from ideal conditions, requiring adjustments to the standard governing equations. These deviations could arise from factors such as viscous effects, surface interactions, and non-Newtonian fluid properties from different microfluid types and geometrical layouts of microchannels. Addressing these nonidealities supports the refining of theoretical models and prediction accuracy for microfluidic flow behaviors.

The analytical calculation of coupled nonlinear governing equations, which describes the material and energy balances of systems under ideal conditions, often requires considerable computational efforts. However, advancements in computation capabilities, cost reduction, and improved accuracy have made numerical simulations using different numerical and modeling methods a powerful tool for effectively solving these complex coupled equations and modeling various transport phenomena. Computational fluid dynamics (CFD) is a numerical technique used to investigate the spatial and temporal distribution of various flow parameters. It serves as a critical approach to provide insights and reasoning for decision-making regarding the optimal designs involving fluid dynamics, even prior to complex physical model prototyping and experimental procedures. The integration of experimental data, theoretical analysis, and reliable numerical simulations from CFD enables systematic variation of analytical parameters through quantitative analysis, where adjustment to delivery of blood flow and other working fluids in LOC systems can be achieved.

Numerical methods such as the Finite-Difference Method (FDM), Finite-Element-Method (FEM), and Finite-Volume Method (FVM) are heavily employed in CFD and offer diverse approaches to achieve discretization of Eulerian flow equations through filling a mesh of the flow domain. A more in-depth review of numerical methods in CFD and its application for blood flow simulation is provided in Section 2.2.2.

1.3. Scope of the Review

In this Review, we explore and characterize the blood flow phenomena within the LOC systems, utilizing both physiological and engineering modeling approaches. Similar approaches will be taken to discuss capillary-driven flow and electric-osmotic flow (EOF) under electrokinetic phenomena as a passive and active transport scheme, respectively, for blood transport in LOC systems. Such an analysis aims to bridge the gap between physical (experimental) and engineering (analytical) perspectives in studying and manipulating blood flow delivery by different driving forces in LOC systems. Moreover, the Review hopes to benefit the interests of not only blood flow control in LOC devices but also the transport of viscoelastic fluids, which are less studied in the literature compared to that of Newtonian fluids, in LOC systems.

Section 2 examines the complex interplay between viscoelastic properties of blood and blood flow patterns under shear flow in LOC systems, while engineering numerical modeling approaches for blood flow are presented for assistance. Sections 3 and 4 look into the theoretical principles, numerical governing equations, and modeling methodologies for capillary driven flow and EOF in LOC systems as well as their impact on blood flow dynamics through the quantification of key parameters of the two driving forces. Section 5 concludes the characterized blood flow transport processes in LOC systems under these two forces. Additionally, prospective areas of research in improving the functionality of LOC devices employing blood and other viscoelastic fluids and potentially justifying mechanisms underlying microfluidic flow patterns outside of LOC systems are presented. Finally, the challenges encountered in the numerical studies of blood flow under LOC systems are acknowledged, paving the way for further research.

2. Blood Flow Phenomena

ARTICLE SECTIONS

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2.1. Physiological Blood Flow Behavior

Blood, an essential physiological fluid in the human body, serves the vital role of transporting oxygen and nutrients throughout the body. Additionally, blood is responsible for suspending various blood cells including erythrocytes (red blood cells or RBCs), leukocytes (white blood cells), and thrombocytes (blood platelets) in a plasma medium.Among the cells mentioned above, red blood cells (RBCs) comprise approximately 40–45% of the volume of healthy blood. 

(7) An RBC possesses an inherent elastic property with a biconcave shape of an average diameter of 8 μm and a thickness of 2 μm. This biconcave shape maximizes the surface-to-volume ratio, allowing RBCs to endure significant distortion while maintaining their functionality. 

(8,9) Additionally, the biconcave shape optimizes gas exchange, facilitating efficient uptake of oxygen due to the increased surface area. The inherent elasticity of RBCs allows them to undergo substantial distortion from their original biconcave shape and exhibits high flexibility, particularly in narrow channels.RBC deformability enables the cell to deform from a biconcave shape to a parachute-like configuration, despite minor differences in RBC shape dynamics under shear flow between initial cell locations. As shown in Figure 1(a), RBCs initiating with different resting shapes and orientations displaying display a similar deformation pattern 

(10) in terms of its shape. Shear flow induces an inward bending of the cell at the rear position of the rim to the final bending position, 

(11) resulting in an alignment toward the same position of the flow direction.

Figure 1. Images of varying deformation of RBCs and different dynamic blood flow behaviors. (a) The deforming shape behavior of RBCs at four different initiating positions under the same experimental conditions of a flow from left to right, (10) (b) RBC aggregation, (13) (c) CFL region. (18) Reproduced with permission from ref (10). Copyright 2011 Elsevier. Reproduced with permission from ref (13). Copyright 2022 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/. Reproduced with permission from ref (18). Copyright 2019 Elsevier.

The flexible property of RBCs enables them to navigate through narrow capillaries and traverse a complex network of blood vessels. The deformability of RBCs depends on various factors, including the channel geometry, RBC concentration, and the elastic properties of the RBC membrane. 

(12) Both flexibility and deformability are vital in the process of oxygen exchange among blood and tissues throughout the body, allowing cells to flow in vessels even smaller than the original cell size prior to deforming.As RBCs serve as major components in blood, their collective dynamics also hugely affect blood rheology. RBCs exhibit an aggregation phenomenon due to cell to cell interactions, such as adhesion forces, among populated cells, inducing unique blood flow patterns and rheological behaviors in microfluidic systems. For blood flow in large vessels between a diameter of 1 and 3 cm, where shear rates are not high, a constant viscosity and Newtonian behavior for blood can be assumed. However, under low shear rate conditions (0.1 s

–1) in smaller vessels such as the arteries and venules, which are within a diameter of 0.2 mm to 1 cm, blood exhibits non-Newtonian properties, such as shear-thinning viscosity and viscoelasticity due to RBC aggregation and deformability. The nonlinear viscoelastic property of blood gives rise to a complex relationship between viscosity and shear rate, primarily influenced by the highly elastic behavior of RBCs. A wide range of research on the transient behavior of the RBC shape and aggregation characteristics under varied flow circumstances has been conducted, aiming to obtain a better understanding of the interaction between blood flow shear forces from confined flows.

For a better understanding of the unique blood flow structures and rheological behaviors in microfluidic systems, some blood flow patterns are introduced in the following section.

2.1.1. RBC Aggregation

RBC aggregation is a vital phenomenon to be considered when designing LOC devices due to its impact on the viscosity of the bulk flow. Under conditions of low shear rate, such as in stagnant or low flow rate regions, RBCs tend to aggregate, forming structures known as rouleaux, resembling stacks of coins as shown in Figure 1(b). 

(13) The aggregation of RBCs increases the viscosity at the aggregated region, 

(14) hence slowing down the overall blood flow. However, when exposed to high shear rates, RBC aggregates disaggregate. As shear rates continue to increase, RBCs tend to deform, elongating and aligning themselves with the direction of the flow. 

(15) Such a dynamic shift in behavior from the cells in response to the shear rate forms the basis of the viscoelastic properties observed in whole blood. In essence, the viscosity of the blood varies according to the shear rate conditions, which are related to the velocity gradient of the system. It is significant to take the intricate relationship between shear rate conditions and the change of blood viscosity due to RBC aggregation into account since various flow driving conditions may induce varied effects on the degree of aggregation.

2.1.2. Fåhræus-Lindqvist Effect

The Fåhræus–Lindqvist (FL) effect describes the gradual decrease in the apparent viscosity of blood as the channel diameter decreases. 

(16) This effect is attributed to the migration of RBCs toward the central region in the microchannel, where the flow rate is higher, due to the presence of higher pressure and asymmetric distribution of shear forces. This migration of RBCs, typically observed at blood vessels less than 0.3 mm, toward the higher flow rate region contributes to the change in blood viscosity, which becomes dependent on the channel size. Simultaneously, the increase of the RBC concentration in the central region of the microchannel results in the formation of a less viscous region close to the microchannel wall. This region called the Cell-Free Layer (CFL), is primarily composed of plasma. 

(17) The combination of the FL effect and the following CFL formation provides a unique phenomenon that is often utilized in passive and active plasma separation mechanisms, involving branched and constriction channels for various applications in plasma separation using microfluidic systems.

2.1.3. Cell-Free Layer Formation

In microfluidic blood flow, RBCs form aggregates at the microchannel core and result in a region that is mostly devoid of RBCs near the microchannel walls, as shown in Figure 1(c). 

(18) The region is known as the cell-free layer (CFL). The CFL region is often known to possess a lower viscosity compared to other regions within the blood flow due to the lower viscosity value of plasma when compared to that of the aggregated RBCs. Therefore, a thicker CFL region composed of plasma correlates to a reduced apparent whole blood viscosity. 

(19) A thicker CFL region is often established following the RBC aggregation at the microchannel core under conditions of decreasing the tube diameter. Apart from the dependence on the RBC concentration in the microchannel core, the CFL thickness is also affected by the volume concentration of RBCs, or hematocrit, in whole blood, as well as the deformability of RBCs. Given the influence CFL thickness has on blood flow rheological parameters such as blood flow rate, which is strongly dependent on whole blood viscosity, investigating CFL thickness under shear flow is crucial for LOC systems accounting for blood flow.

2.1.4. Plasma Skimming in Bifurcation Networks

The uneven arrangement of RBCs in bifurcating microchannels, commonly termed skimming bifurcation, arises from the axial migration of RBCs within flowing streams. This uneven distribution contributes to variations in viscosity across differing sizes of bifurcating channels but offers a stabilizing effect. Notably, higher flow rates in microchannels are associated with increased hematocrit levels, resulting in higher viscosity compared with those with lower flow rates. Parametric investigations on bifurcation angle, 

(20) thickness of the CFL, 

(21) and RBC dynamics, including aggregation and deformation, 

(22) may alter the varying viscosity of blood and its flow behavior within microchannels.

2.2. Modeling on Blood Flow Dynamics

2.2.1. Blood Properties and Mathematical Models of Blood Rheology

Under different shear rate conditions in blood flow, the elastic characteristics and dynamic changes of the RBC induce a complex velocity and stress relationship, resulting in the incompatibility of blood flow characterization through standard presumptions of constant viscosity used for Newtonian fluid flow. Blood flow is categorized as a viscoelastic non-Newtonian fluid flow where constitutive equations governing this type of flow take into consideration the nonlinear viscometric properties of blood. To mathematically characterize the evolving blood viscosity and the relationship between the elasticity of RBC and the shear blood flow, respectively, across space and time of the system, a stress tensor (τ) defined by constitutive models is often coupled in the Navier–Stokes equation to account for the collective impact of the constant dynamic viscosity (η) and the elasticity from RBCs on blood flow.The dynamic viscosity of blood is heavily dependent on the shear stress applied to the cell and various parameters from the blood such as hematocrit value, plasma viscosity, mechanical properties of the RBC membrane, and red blood cell aggregation rate. The apparent blood viscosity is considered convenient for the characterization of the relationship between the evolving blood viscosity and shear rate, which can be defined by Casson’s law, as shown in eq 1.

𝜇=𝜏0𝛾˙+2𝜂𝜏0𝛾˙⎯⎯⎯⎯⎯⎯⎯√+𝜂�=�0�˙+2��0�˙+�

(1)where τ

0 is the yield stress–stress required to initiate blood flow motion, η is the Casson rheological constant, and γ̇ is the shear rate. The value of Casson’s law parameters under blood with normal hematocrit level can be defined as τ

0 = 0.0056 Pa and η = 0.0035 Pa·s. 

(23) With the known property of blood and Casson’s law parameters, an approximation can be made to the dynamic viscosity under various flow condition domains. The Power Law model is often employed to characterize the dynamic viscosity in relation to the shear rate, since precise solutions exist for specific geometries and flow circumstances, acting as a fundamental standard for definition. The Carreau and Carreau–Yasuda models can be advantageous over the Power Law model due to their ability to evaluate the dynamic viscosity at low to zero shear rate conditions. However, none of the above-mentioned models consider the memory or other elastic behavior of blood and its RBCs. Some other commonly used mathematical models and their constants for the non-Newtonian viscosity property characterization of blood are listed in Table 1 below. 

(24−26)Table 1. Comparison of Various Non-Newtonian Models for Blood Viscosity 

(24−26)

ModelNon-Newtonian ViscosityParameters
Power Law(2)n = 0.61, k = 0.42
Carreau(3)μ0 = 0.056 Pa·s, μ∞ = 0.00345 Pa·s, λ = 3.1736 s, m = 2.406, a = 0.254
Walburn–Schneck(4)C1 = 0.000797 Pa·s, C2 = 0.0608 Pa·s, C3 = 0.00499, C4 = 14.585 g–1, TPMA = 25 g/L
Carreau–Yasuda(5)μ0 = 0.056 Pa·s, μ∞ = 0.00345 Pa·s, λ = 1.902 s, n = 0.22, a = 1.25
Quemada(6)μp = 0.0012 Pa·s, k∞ = 2.07, k0 = 4.33, γ̇c = 1.88 s–1

The blood rheology is commonly known to be influenced by two key physiological factors, namely, the hematocrit value (H

t) and the fibrinogen concentration (c

f), with an average value of 42% and 0.252 gd·L

–1, respectively. Particularly in low shear conditions, the presence of varying fibrinogen concentrations affects the tendency for aggregation and rouleaux formation, while the occurrence of aggregation is contingent upon specific levels of hematocrit. 

(27) The study from Apostolidis et al. 

(28) modifies the Casson model through emphasizing its reliance on hematocrit and fibrinogen concentration parameter values, owing to the extensive knowledge of the two physiological blood parameters.The viscoelastic response of blood is heavily dependent on the elasticity of the RBC, which is defined by the relationship between the deformation and stress relaxation from RBCs under a specific location of shear flow as a function of the velocity field. The stress tensor is usually characterized by constitutive equations such as the Upper-Convected Maxwell Model 

(29) and the Oldroyd-B model 

(30) to track the molecule effects under shear from different driving forces. The prominent non-Newtonian features, such as shear thinning and yield stress, have played a vital role in the characterization of blood rheology, particularly with respect to the evaluation of yield stress under low shear conditions. The nature of stress measurement in blood, typically on the order of 1 mPa, is challenging due to its low magnitude. The occurrence of the CFL complicates the measurement further due to the significant decrease in apparent viscosity near the wall over time and a consequential disparity in viscosity compared to the bulk region.In addition to shear thinning viscosity and yield stress, the formation of aggregation (rouleaux) from RBCs under low shear rates also contributes to the viscoelasticity under transient flow 

(31) and thixotropy 

(32) of whole blood. Given the difficulty in evaluating viscoelastic behavior of blood under low strain magnitudes and limitations in generalized Newtonian models, the utilization of viscoelastic models is advocated to encompass elasticity and delineate non-shear components within the stress tensor. Extending from the Oldroyd-B model, Anand et al. 

(33) developed a viscoelastic model framework for adapting elasticity within blood samples and predicting non-shear stress components. However, to also address the thixotropic effects, the model developed by Horner et al. 

(34) serves as a more comprehensive approach than the viscoelastic model from Anand et al. Thixotropy 

(32) typically occurs from the structural change of the rouleaux, where low shear rate conditions induce rouleaux formation. Correspondingly, elasticity increases, while elasticity is more representative of the isolated RBCs, under high shear rate conditions. The model of Horner et al. 

(34) considers the contribution of rouleaux to shear stress, taking into account factors such as the characteristic time for Brownian aggregation, shear-induced aggregation, and shear-induced breakage. Subsequent advancements in the model from Horner et al. often revolve around refining the three aforementioned key terms for a more substantial characterization of rouleaux dynamics. Notably, this has led to the recently developed mHAWB model 

(35) and other model iterations to enhance the accuracy of elastic and viscoelastic contributions to blood rheology, including the recently improved model suggested by Armstrong et al. 

(36)

2.2.2. Numerical Methods (FDM, FEM, FVM)

Numerical simulation has become increasingly more significant in analyzing the geometry, boundary layers of flow, and nonlinearity of hyperbolic viscoelastic flow constitutive equations. CFD is a powerful and efficient tool utilizing numerical methods to solve the governing hydrodynamic equations, such as the Navier–Stokes (N–S) equation, continuity equation, and energy conservation equation, for qualitative evaluation of fluid motion dynamics under different parameters. CFD overcomes the challenge of analytically solving nonlinear forms of differential equations by employing numerical methods such as the Finite-Difference Method (FDM), Finite-Element Method (FEM), and Finite-Volume Method (FVM) to discretize and solve the partial differential equations (PDEs), allowing for qualitative reproduction of transport phenomena and experimental observations. Different numerical methods are chosen to cope with various transport systems for optimization of the accuracy of the result and control of error during the discretization process.FDM is a straightforward approach to discretizing PDEs, replacing the continuum representation of equations with a set of finite-difference equations, which is typically applied to structured grids for efficient implementation in CFD programs. 

(37) However, FDM is often limited to simple geometries such as rectangular or block-shaped geometries and struggles with curved boundaries. In contrast, FEM divides the fluid domain into small finite grids or elements, approximating PDEs through a local description of physics. 

(38) All elements contribute to a large, sparse matrix solver. However, FEM may not always provide accurate results for systems involving significant deformation and aggregation of particles like RBCs due to large distortion of grids. 

(39) FVM evaluates PDEs following the conservation laws and discretizes the selected flow domain into small but finite size control volumes, with each grid at the center of a finite volume. 

(40) The divergence theorem allows the conversion of volume integrals of PDEs with divergence terms into surface integrals of surface fluxes across cell boundaries. Due to its conservation property, FVM offers efficient outcomes when dealing with PDEs that embody mass, momentum, and energy conservation principles. Furthermore, widely accessible software packages like the OpenFOAM toolbox 

(41) include a viscoelastic solver, making it an attractive option for viscoelastic fluid flow modeling. 

(42)

2.2.3. Modeling Methods of Blood Flow Dynamics

The complexity in the blood flow simulation arises from deformability and aggregation that RBCs exhibit during their interaction with neighboring cells under different shear rate conditions induced by blood flow. Numerical models coupled with simulation programs have been applied as a groundbreaking method to predict such unique rheological behavior exhibited by RBCs and whole blood. The conventional approach of a single-phase flow simulation is often applied to blood flow simulations within large vessels possessing a moderate shear rate. However, such a method assumes the properties of plasma, RBCs and other cellular components to be evenly distributed as average density and viscosity in blood, resulting in the inability to simulate the mechanical dynamics, such as RBC aggregation under high-shear flow field, inherent in RBCs. To accurately describe the asymmetric distribution of RBC and blood flow, multiphase flow simulation, where numerical simulations of blood flows are often modeled as two immiscible phases, RBCs and blood plasma, is proposed. A common assumption is that RBCs exhibit non-Newtonian behavior while the plasma is treated as a continuous Newtonian phase.Numerous multiphase numerical models have been proposed to simulate the influence of RBCs on blood flow dynamics by different assumptions. In large-scale simulations (above the millimeter range), continuum-based methods are wildly used due to their lower computational demands. 

(43) Eulerian multiphase flow simulations offer the solution of a set of conservation equations for each separate phase and couple the phases through common pressure and interphase exchange coefficients. Xu et al. 

(44) utilized the combined finite-discrete element method (FDEM) to replicate the dynamic behavior and distortion of RBCs subjected to fluidic forces, utilizing the Johnson–Kendall–Roberts model 

(45) to define the adhesive forces of cell-to-cell interactions. The iterative direct-forcing immersed boundary method (IBM) is commonly employed in simulations of the fluid–cell interface of blood. This method effectively captures the intricacies of the thin and flexible RBC membranes within various external flow fields. 

(46) The study by Xu et al. 

(44) also adopts this approach to bridge the fluid dynamics and RBC deformation through IBM. Yoon and You utilized the Maxwell model to define the viscosity of the RBC membrane. 

(47) It was discovered that the Maxwell model could represent the stress relaxation and unloading processes of the cell. Furthermore, the reduced flexibility of an RBC under particular situations such as infection is specified, which was unattainable by the Kelvin–Voigt model 

(48) when compared to the Maxwell model in the literature. The Yeoh hyperplastic material model was also adapted to predict the nonlinear elasticity property of RBCs with FEM employed to discretize the RBC membrane using shell-type elements. Gracka et al. 

(49) developed a numerical CFD model with a finite-volume parallel solver for multiphase blood flow simulation, where an updated Maxwell viscoelasticity model and a Discrete Phase Model are adopted. In the study, the adapted IBM, based on unstructured grids, simulates the flow behavior and shape change of the RBCs through fluid-structure coupling. It was found that the hybrid Euler–Lagrange (E–L) approach 

(50) for the development of the multiphase model offered better results in the simulated CFL region in the microchannels.To study the dynamics of individual behaviors of RBCs and the consequent non-Newtonian blood flow, cell-shape-resolved computational models are often adapted. The use of the boundary integral method has become prevalent in minimizing computational expenses, particularly in the exclusive determination of fluid velocity on the surfaces of RBCs, incorporating the option of employing IBM or particle-based techniques. The cell-shaped-resolved method has enabled an examination of cell to cell interactions within complex ambient or pulsatile flow conditions 

(51) surrounding RBC membranes. Recently, Rydquist et al. 

(52) have looked to integrate statistical information from macroscale simulations to obtain a comprehensive overview of RBC behavior within the immediate proximity of the flow through introduction of respective models characterizing membrane shape definition, tension, bending stresses of RBC membranes.At a macroscopic scale, continuum models have conventionally been adapted for assessing blood flow dynamics through the application of elasticity theory and fluid dynamics. However, particle-based methods are known for their simplicity and adaptability in modeling complex multiscale fluid structures. Meshless methods, such as the boundary element method (BEM), smoothed particle hydrodynamics (SPH), and dissipative particle dynamics (DPD), are often used in particle-based characterization of RBCs and the surrounding fluid. By representing the fluid as discrete particles, meshless methods provide insights into the status and movement of the multiphase fluid. These methods allow for the investigation of cellular structures and microscopic interactions that affect blood rheology. Non-confronting mesh methods like IBM can also be used to couple a fluid solver such as FEM, FVM, or the Lattice Boltzmann Method (LBM) through membrane representation of RBCs. In comparison to conventional CFD methods, LBM has been viewed as a favorable numerical approach for solving the N–S equations and the simulation of multiphase flows. LBM exhibits the notable advantage of being amenable to high-performance parallel computing environments due to its inherently local dynamics. In contrast to DPD and SPH where RBC membranes are modeled as physically interconnected particles, LBM employs the IBM to account for the deformation dynamics of RBCs 

(53,54) under shear flows in complex channel geometries. 

(54,55) However, it is essential to acknowledge that the utilization of LBM in simulating RBC flows often entails a significant computational overhead, being a primary challenge in this context. Krüger et al. 

(56) proposed utilizing LBM as a fluid solver, IBM to couple the fluid and FEM to compute the response of membranes to deformation under immersed fluids. This approach decouples the fluid and membranes but necessitates significant computational effort due to the requirements of both meshes and particles.Despite the accuracy of current blood flow models, simulating complex conditions remains challenging because of the high computational load and cost. Balachandran Nair et al. 

(57) suggested a reduced order model of RBC under the framework of DEM, where the RBC is represented by overlapping constituent rigid spheres. The Morse potential force is adapted to account for the RBC aggregation exhibited by cell to cell interactions among RBCs at different distances. Based upon the IBM, the reduced-order RBC model is adapted to simulate blood flow transport for validation under both single and multiple RBCs with a resolved CFD-DEM solver. 

(58) In the resolved CFD-DEM model, particle sizes are larger than the grid size for a more accurate computation of the surrounding flow field. A continuous forcing approach is taken to describe the momentum source of the governing equation prior to discretization, which is different from a Direct Forcing Method (DFM). 

(59) As no body-conforming moving mesh is required, the continuous forcing approach offers lower complexity and reduced cost when compared to the DFM. Piquet et al. 

(60) highlighted the high complexity of the DFM due to its reliance on calculating an additional immersed boundary flux for the velocity field to ensure its divergence-free condition.The fluid–structure interaction (FSI) method has been advocated to connect the dynamic interplay of RBC membranes and fluid plasma within blood flow such as the coupling of continuum–particle interactions. However, such methodology is generally adapted for anatomical configurations such as arteries 

(61,62) and capillaries, 

(63) where both the structural components and the fluid domain undergo substantial deformation due to the moving boundaries. Due to the scope of the Review being blood flow simulation within microchannels of LOC devices without deformable boundaries, the Review of the FSI method will not be further carried out.In general, three numerical methods are broadly used: mesh-based, particle-based, and hybrid mesh–particle techniques, based on the spatial scale and the fundamental numerical approach, mesh-based methods tend to neglect the effects of individual particles, assuming a continuum and being efficient in terms of time and cost. However, the particle-based approach highlights more of the microscopic and mesoscopic level, where the influence of individual RBCs is considered. A review from Freund et al. 

(64) addressed the three numerical methodologies and their respective modeling approaches of RBC dynamics. Given the complex mechanics and the diverse levels of study concerning numerical simulations of blood and cellular flow, a broad spectrum of numerical methods for blood has been subjected to extensive review. 

(64−70) Ye at al. 

(65) offered an extensive review of the application of the DPD, SPH, and LBM for numerical simulations of RBC, while Rathnayaka et al. 

(67) conducted a review of the particle-based numerical modeling for liquid marbles through drawing parallels to the transport of RBCs in microchannels. A comparative analysis between conventional CFD methods and particle-based approaches for cellular and blood flow dynamic simulation can be found under the review by Arabghahestani et al. 

(66) Literature by Li et al. 

(68) and Beris et al. 

(69) offer an overview of both continuum-based models at micro/macroscales and multiscale particle-based models encompassing various length and temporal dimensions. Furthermore, these reviews deliberate upon the potential of coupling continuum-particle methods for blood plasma and RBC modeling. Arciero et al. 

(70) investigated various modeling approaches encompassing cellular interactions, such as cell to cell or plasma interactions and the individual cellular phases. A concise overview of the reviews is provided in Table 2 for reference.

Table 2. List of Reviews for Numerical Approaches Employed in Blood Flow Simulation

ReferenceNumerical methods
Li et al. (2013) (68)Continuum-based modeling (BIM), particle-based modeling (LBM, LB-FE, SPH, DPD)
Freund (2014) (64)RBC dynamic modeling (continuum-based modeling, complementary discrete microstructure modeling), blood flow dynamic modeling (FDM, IBM, LBM, particle-mesh methods, coupled boundary integral and mesh-based methods, DPD)
Ye et al. (2016) (65)DPD, SPH, LBM, coupled IBM-Smoothed DPD
Arciero et al. (2017) (70)LBM, IBM, DPD, conventional CFD Methods (FDM, FVM, FEM)
Arabghahestani et al. (2019) (66)Particle-based methods (LBM, DPD, direct simulation Monte Carlo, molecular dynamics), SPH, conventional CFD methods (FDM, FVM, FEM)
Beris et al. (2021) (69)DPD, smoothed DPD, IBM, LBM, BIM
Rathnayaka (2022) (67)SPH, CG, LBM

3. Capillary Driven Blood Flow in LOC Systems

ARTICLE SECTIONS

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3.1. Capillary Driven Flow Phenomena

Capillary driven (CD) flow is a pivotal mechanism in passive microfluidic flow systems 

(9) such as the blood circulation system and LOC systems. 

(71) CD flow is essentially the movement of a liquid to flow against drag forces, where the capillary effect exerts a force on the liquid at the borders, causing a liquid–air meniscus to flow despite gravity or other drag forces. A capillary pressure drops across the liquid–air interface with surface tension in the capillary radius and contact angle. The capillary effect depends heavily on the interaction between the different properties of surface materials. Different values of contact angles can be manipulated and obtained under varying levels of surface wettability treatments to manipulate the surface properties, resulting in different CD blood delivery rates for medical diagnostic device microchannels. CD flow techniques are appealing for many LOC devices, because they require no external energy. However, due to the passive property of liquid propulsion by capillary forces and the long-term instability of surface treatments on channel walls, the adaptability of CD flow in geometrically complex LOC devices may be limited.

3.2. Theoretical and Numerical Modeling of Capillary Driven Blood Flow

3.2.1. Theoretical Basis and Assumptions of Microfluidic Flow

The study of transport phenomena regarding either blood flow driven by capillary forces or externally applied forces under microfluid systems all demands a comprehensive recognition of the significant differences in flow dynamics between microscale and macroscale. The fundamental assumptions and principles behind fluid transport at the microscale are discussed in this section. Such a comprehension will lay the groundwork for the following analysis of the theoretical basis of capillary forces and their role in blood transport in LOC systems.

At the macroscale, fluid dynamics are often strongly influenced by gravity due to considerable fluid mass. However, the high surface to volume ratio at the microscale shifts the balance toward surface forces (e.g., surface tension and viscous forces), much larger than the inertial force. This difference gives rise to transport phenomena unique to microscale fluid transport, such as the prevalence of laminar flow due to a very low Reynolds number (generally lower than 1). Moreover, the fluid in a microfluidic system is often assumed to be incompressible due to the small flow velocity, indicating constant fluid density in both space and time.Microfluidic flow behaviors are governed by the fundamental principles of mass and momentum conservation, which are encapsulated in the continuity equation and the Navier–Stokes (N–S) equation. The continuity equation describes the conservation of mass, while the N–S equation captures the spatial and temporal variations in velocity, pressure, and other physical parameters. Under the assumption of the negligible influence of gravity in microfluidic systems, the continuity equation and the Eulerian representation of the incompressible N–S equation can be expressed as follows:

∇·𝐮⇀=0∇·�⇀=0

(7)

−∇𝑝+𝜇∇2𝐮⇀+∇·𝝉⇀−𝐅⇀=0−∇�+�∇2�⇀+∇·�⇀−�⇀=0

(8)Here, p is the pressure, u is the fluid viscosity, 

𝝉⇀�⇀ represents the stress tensor, and F is the body force exerted by external forces if present.

3.2.2. Theoretical Basis and Modeling of Capillary Force in LOC Systems

The capillary force is often the major driving force to manipulate and transport blood without an externally applied force in LOC systems. Forces induced by the capillary effect impact the free surface of fluids and are represented not directly in the Navier–Stokes equations but through the pressure boundary conditions of the pressure term p. For hydrophilic surfaces, the liquid generally induces a contact angle between 0° and 30°, encouraging the spread and attraction of fluid under a positive cos θ condition. For this condition, the pressure drop becomes positive and generates a spontaneous flow forward. A hydrophobic solid surface repels the fluid, inducing minimal contact. Generally, hydrophobic solids exhibit a contact angle larger than 90°, inducing a negative value of cos θ. Such a value will result in a negative pressure drop and a flow in the opposite direction. The induced contact angle is often utilized to measure the wall exposure of various surface treatments on channel walls where different wettability gradients and surface tension effects for CD flows are established. Contact angles between different interfaces are obtainable through standard values or experimental methods for reference. 

(72)For the characterization of the induced force by the capillary effect, the Young–Laplace (Y–L) equation 

(73) is widely employed. In the equation, the capillary is considered a pressure boundary condition between the two interphases. Through the Y–L equation, the capillary pressure force can be determined, and subsequently, the continuity and momentum balance equations can be solved to obtain the blood filling rate. Kim et al. 

(74) studied the effects of concentration and exposure time of a nonionic surfactant, Silwet L-77, on the performance of a polydimethylsiloxane (PDMS) microchannel in terms of plasma and blood self-separation. The study characterized the capillary pressure force by incorporating the Y–L equation and further evaluated the effects of the changing contact angle due to different levels of applied channel wall surface treatments. The expression of the Y–L equation utilized by Kim et al. 

(74) is as follows:

𝑃=−𝜎(cos𝜃b+cos𝜃tℎ+cos𝜃l+cos𝜃r𝑤)�=−�(cos⁡�b+cos⁡�tℎ+cos⁡�l+cos⁡�r�)

(9)where σ is the surface tension of the liquid and θ

b, θ

t, θ

l, and θ

r are the contact angle values between the liquid and the bottom, top, left, and right walls, respectively. A numerical simulation through Coventor software is performed to evaluate the dynamic changes in the filling rate within the microchannel. The simulation results for the blood filling rate in the microchannel are expressed at a specific time stamp, shown in Figure 2. The results portray an increasing instantaneous filling rate of blood in the microchannel following the decrease in contact angle induced by a higher concentration of the nonionic surfactant treated to the microchannel wall.

Figure 2. Numerical simulation of filling rate of capillary driven blood flow under various contact angle conditions at a specific timestamp. (74) Reproduced with permission from ref (74). Copyright 2010 Elsevier.

When in contact with hydrophilic or hydrophobic surfaces, blood forms a meniscus with a contact angle due to surface tension. The Lucas–Washburn (L–W) equation 

(75) is one of the pioneering theoretical definitions for the position of the meniscus over time. In addition, the L–W equation provides the possibility for research to obtain the velocity of the blood formed meniscus through the derivation of the meniscus position. The L–W equation 

(75) can be shown below:

𝐿(𝑡)=𝑅𝜎cos(𝜃)𝑡2𝜇⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�(�)=��⁡cos(�)�2�

(10)Here L(t) represents the distance of the liquid driven by the capillary forces. However, the generalized L–W equation solely assumes the constant physical properties from a Newtonian fluid rather than considering the non-Newtonian fluid behavior of blood. Cito et al. 

(76) constructed an enhanced version of the L–W equation incorporating the power law to consider the RBC aggregation and the FL effect. The non-Newtonian fluid apparent viscosity under the Power Law model is defined as

𝜇=𝑘·(𝛾˙)𝑛−1�=�·(�˙)�−1

(11)where γ̇ is the strain rate tensor defined as 

𝛾˙=12𝛾˙𝑖𝑗𝛾˙𝑗𝑖⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√�˙=12�˙���˙��. The stress tensor term τ is computed as τ = μγ̇

ij. The updated L–W equation by Cito 

(76) is expressed as

𝐿(𝑡)=𝑅[(𝑛+13𝑛+1)(𝜎cos(𝜃)𝑅𝑘)1/𝑛𝑡]𝑛/𝑛+1�(�)=�[(�+13�+1)(�⁡cos(�)��)1/��]�/�+1

(12)where k is the flow consistency index and n is the power law index, respectively. The power law index, from the Power Law model, characterizes the extent of the non-Newtonian behavior of blood. Both the consistency and power law index rely on blood properties such as hematocrit, the appearance of the FL effect, the formation of RBC aggregates, etc. The updated L–W equation computes the location and velocity of blood flow caused by capillary forces at specified time points within the LOC devices, taking into account the effects of blood flow characteristics such as RBC aggregation and the FL effect on dynamic blood viscosity.Apart from the blood flow behaviors triggered by inherent blood properties, unique flow conditions driven by capillary forces that are portrayed under different microchannel geometries also hold crucial implications for CD blood delivery. Berthier et al. 

(77) studied the spontaneous Concus–Finn condition, the condition to initiate the spontaneous capillary flow within a V-groove microchannel, as shown in Figure 3(a) both experimentally and numerically. Through experimental studies, the spontaneous Concus–Finn filament development of capillary driven blood flow is observed, as shown in Figure 3(b), while the dynamic development of blood flow is numerically simulated through CFD simulation.

Figure 3. (a) Sketch of the cross-section of Berthier’s V-groove microchannel, (b) experimental view of blood in the V-groove microchannel, (78) (c) illustration of the dynamic change of the extension of filament from FLOW 3D under capillary flow at three increasing time intervals. (78) Reproduced with permission from ref (78). Copyright 2014 Elsevier.

Berthier et al. 

(77) characterized the contact angle needed for the initiation of the capillary driving force at a zero-inlet pressure, through the half-angle (α) of the V-groove geometry layout, and its relation to the Concus–Finn filament as shown below:

𝜃<𝜋2−𝛼sin𝛼1+2(ℎ2/𝑤)sin𝛼<cos𝜃{�<�2−�sin⁡�1+2(ℎ2/�)⁡sin⁡�<cos⁡�

(13)Three possible regimes were concluded based on the contact angle value for the initiation of flow and development of Concus–Finn filament:

𝜃>𝜃1𝜃1>𝜃>𝜃0𝜃0no SCFSCF without a Concus−Finn filamentSCF without a Concus−Finn filament{�>�1no SCF�1>�>�0SCF without a Concus−Finn filament�0SCF without a Concus−Finn filament

(14)Under Newton’s Law, the force balance with low Reynolds and Capillary numbers results in the neglect of inertial terms. The force balance between the capillary forces and the viscous force induced by the channel wall is proposed to derive the analytical fluid velocity. This relation between the two forces offers insights into the average flow velocity and the penetration distance function dependent on time. The apparent blood viscosity is defined by Berthier et al. 

(78) through Casson’s law, 

(23) given in eq 1. The research used the FLOW-3D program from Flow Science Inc. software, which solves transient, free-surface problems using the FDM in multiple dimensions. The Volume of Fluid (VOF) method 

(79) is utilized to locate and track the dynamic extension of filament throughout the advancing interface within the channel ahead of the main flow at three progressing time stamps, as depicted in Figure 3(c).

4. Electro-osmotic Flow (EOF) in LOC Systems

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The utilization of external forces, such as electric fields, has significantly broadened the possibility of manipulating microfluidic flow in LOC systems. 

(80) Externally applied electric field forces induce a fluid flow from the movement of ions in fluid terms as the “electro-osmotic flow” (EOF).Unique transport phenomena, such as enhanced flow velocity and flow instability, induced by non-Newtonian fluids, particularly viscoelastic fluids, under EOF, have sparked considerable interest in microfluidic devices with simple or complicated geometries within channels. 

(81) However, compared to the study of Newtonian fluids and even other electro-osmotic viscoelastic fluid flows, the literature focusing on the theoretical and numerical modeling of electro-osmotic blood flow is limited due to the complexity of blood properties. Consequently, to obtain a more comprehensive understanding of the complex blood flow behavior under EOF, theoretical and numerical studies of the transport phenomena in the EOF section will be based on the studies of different viscoelastic fluids under EOF rather than that of blood specifically. Despite this limitation, we believe these studies offer valuable insights that can help understand the complex behavior of blood flow under EOF.

4.1. EOF Phenomena

Electro-osmotic flow occurs at the interface between the microchannel wall and bulk phase solution. When in contact with the bulk phase, solution ions are absorbed or dissociated at the solid–liquid interface, resulting in the formation of a charge layer, as shown in Figure 4. This charged channel surface wall interacts with both negative and positive ions in the bulk sample, causing repulsion and attraction forces to create a thin layer of immobilized counterions, known as the Stern layer. The induced electric potential from the wall gradually decreases with an increase in the distance from the wall. The Stern layer potential, commonly termed the zeta potential, controls the intensity of the electrostatic interactions between mobile counterions and, consequently, the drag force from the applied electric field. Next to the Stern layer is the diffuse mobile layer, mainly composed of a mobile counterion. These two layers constitute the “electrical double layer” (EDL), the thickness of which is directly proportional to the ionic strength (concentration) of the bulk fluid. The relationship between the two parameters is characterized by a Debye length (λ

D), expressed as

𝜆𝐷=𝜖𝑘B𝑇2(𝑍𝑒)2𝑐0⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√��=��B�2(��)2�0

(15)where ϵ is the permittivity of the electrolyte solution, k

B is the Boltzmann constant, T is the electron temperature, Z is the integer valence number, e is the elementary charge, and c

0 is the ionic density.

Figure 4. Schematic diagram of an electro-osmotic flow in a microchannel with negative surface charge. (82) Reproduced with permission from ref (82). Copyright 2012 Woodhead Publishing.

When an electric field is applied perpendicular to the EDL, viscous drag is generated due to the movement of excess ions in the EDL. Electro-osmotic forces can be attributed to the externally applied electric potential (ϕ) and the zeta potential, the system wall induced potential by charged walls (ψ). As illustrated in Figure 4, the majority of ions in the bulk phase have a uniform velocity profile, except for a shear rate condition confined within an extremely thin Stern layer. Therefore, EOF displays a unique characteristic of a “near flat” or plug flow velocity profile, different from the parabolic flow typically induced by pressure-driven microfluidic flow (Hagen–Poiseuille flow). The plug-shaped velocity profile of the EOF possesses a high shear rate above the Stern layer.Overall, the EOF velocity magnitude is typically proportional to the Debye Length (λ

D), zeta potential, and magnitude of the externally applied electric field, while a more viscous liquid reduces the EOF velocity.

4.2. Modeling on Electro-osmotic Viscoelastic Fluid Flow

4.2.1. Theoretical Basis of EOF Mechanisms

The EOF of an incompressible viscoelastic fluid is commonly governed by the continuity and incompressible N–S equations, as shown in eqs 7 and 8, where the stress tensor and the electrostatic force term are coupled. The electro-osmotic body force term F, representing the body force exerted by the externally applied electric force, is defined as 

𝐹⇀=𝑝𝐸𝐸⇀�⇀=���⇀, where ρ

E and 

𝐸⇀�⇀ are the net electric charge density and the applied external electric field, respectively.Numerous models are established to theoretically study the externally applied electric potential and the system wall induced potential by charged walls. The following Laplace equation, expressed as eq 16, is generally adapted and solved to calculate the externally applied potential (ϕ).

∇2𝜙=0∇2�=0

(16)Ion diffusion under applied electric fields, together with mass transport resulting from convection and diffusion, transports ionic solutions in bulk flow under electrokinetic processes. The Nernst–Planck equation can describe these transport methods, including convection, diffusion, and electro-diffusion. Therefore, the Nernst–Planck equation is used to determine the distribution of the ions within the electrolyte. The electric potential induced by the charged channel walls follows the Poisson–Nernst–Plank (PNP) equation, which can be written as eq 17.

∇·[𝐷𝑖∇𝑛𝑖−𝑢⇀𝑛𝑖+𝑛𝑖𝐷𝑖𝑧𝑖𝑒𝑘𝑏𝑇∇(𝜙+𝜓)]=0∇·[��∇��−�⇀��+����������∇(�+�)]=0

(17)where D

i, n

i, and z

i are the diffusion coefficient, ionic concentration, and ionic valence of the ionic species I, respectively. However, due to the high nonlinearity and numerical stiffness introduced by different lengths and time scales from the PNP equations, the Poisson–Boltzmann (PB) model is often considered the major simplified method of the PNP equation to characterize the potential distribution of the EDL region in microchannels. In the PB model, it is assumed that the ionic species in the fluid follow the Boltzmann distribution. This model is typically valid for steady-state problems where charge transport can be considered negligible, the EDLs do not overlap with each other, and the intrinsic potentials are low. It provides a simplified representation of the potential distribution in the EDL region. The PB equation governing the EDL electric potential distribution is described as

∇2𝜓=(2𝑒𝑧𝑛0𝜀𝜀0)sinh(𝑧𝑒𝜓𝑘b𝑇)∇2�=(2���0��0)⁡sinh(����b�)

(18)where n

0 is the ion bulk concentration, z is the ionic valence, and ε

0 is the electric permittivity in the vacuum. Under low electric potential conditions, an even further simplified model to illustrate the EOF phenomena is the Debye–Hückel (DH) model. The DH model is derived by obtaining a charge density term by expanding the exponential term of the Boltzmann equation in a Taylor series.

4.2.2. EOF Modeling for Viscoelastic Fluids

Many studies through numerical modeling were performed to obtain a deeper understanding of the effect exhibited by externally applied electric fields on viscoelastic flow in microchannels under various geometrical designs. Bello et al. 

(83) found that methylcellulose solution, a non-Newtonian polymer solution, resulted in stronger electro-osmotic mobility in experiments when compared to the predictions by the Helmholtz–Smoluchowski equation, which is commonly used to define the velocity of EOF of a Newtonian fluid. Being one of the pioneers to identify the discrepancies between the EOF of Newtonian and non-Newtonian fluids, Bello et al. attributed such discrepancies to the presence of a very high shear rate in the EDL, resulting in a change in the orientation of the polymer molecules. Park and Lee 

(84) utilized the FVM to solve the PB equation for the characterization of the electric field induced force. In the study, the concept of fractional calculus for the Oldroyd-B model was adapted to illustrate the elastic and memory effects of viscoelastic fluids in a straight microchannel They observed that fluid elasticity and increased ratio of viscoelastic fluid contribution to overall fluid viscosity had a significant impact on the volumetric flow rate and sensitivity of velocity to electric field strength compared to Newtonian fluids. Afonso et al. 

(85) derived an analytical expression for EOF of viscoelastic fluid between parallel plates using the DH model to account for a zeta potential condition below 25 mV. The study established the understanding of the electro-osmotic viscoelastic fluid flow under low zeta potential conditions. Apart from the electrokinetic forces, pressure forces can also be coupled with EOF to generate a unique fluid flow behavior within the microchannel. Sousa et al. 

(86) analytically studied the flow of a standard viscoelastic solution by combining the pressure gradient force with an externally applied electric force. It was found that, at a near wall skimming layer and the outer layer away from the wall, macromolecules migrating away from surface walls in viscoelastic fluids are observed. In the study, the Phan-Thien Tanner (PTT) constitutive model is utilized to characterize the viscoelastic properties of the solution. The approach is found to be valid when the EDL is much thinner than the skimming layer under an enhanced flow rate. Zhao and Yang 

(87) solved the PB equation and Carreau model for the characterization of the EOF mechanism and non-Newtonian fluid respectively through the FEM. The numerical results depict that, different from the EOF of Newtonian fluids, non-Newtonian fluids led to an increase of electro-osmotic mobility for shear thinning fluids but the opposite for shear thickening fluids.Like other fluid transport driving forces, EOF within unique geometrical layouts also portrays unique transport phenomena. Pimenta and Alves 

(88) utilized the FVM to perform numerical simulations of the EOF of viscoelastic fluids considering the PB equation and the Oldroyd-B model, in a cross-slot and flow-focusing microdevices. It was found that electroelastic instabilities are formed due to the development of large stresses inside the EDL with streamlined curvature at geometry corners. Bezerra et al. 

(89) used the FDM to numerically analyze the vortex formation and flow instability from an electro-osmotic non-Newtonian fluid flow in a microchannel with a nozzle geometry and parallel wall geometry setting. The PNP equation is utilized to characterize the charge motion in the EOF and the PTT model for non-Newtonian flow characterization. A constriction geometry is commonly utilized in blood flow adapted in LOC systems due to the change in blood flow behavior under narrow dimensions in a microchannel. Ji et al. 

(90) recently studied the EOF of viscoelastic fluid in a constriction microchannel connected by two relatively big reservoirs on both ends (as seen in Figure 5) filled with the polyacrylamide polymer solution, a viscoelastic fluid, and an incompressible monovalent binary electrolyte solution KCl.

Figure 5. Schematic diagram of a negatively charged constriction microchannel connected to two reservoirs at both ends. An electro-osmotic flow is induced in the system by the induced potential difference between the anode and cathode. (90) Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

In studying the EOF of viscoelastic fluids, the Oldroyd-B model is often utilized to characterize the polymeric stress tensor and the deformation rate of the fluid. The Oldroyd-B model is expressed as follows:

𝜏=𝜂p𝜆(𝐜−𝐈)�=�p�(�−�)

(19)where η

p, λ, c, and I represent the polymer dynamic viscosity, polymer relaxation time, symmetric conformation tensor of the polymer molecules, and the identity matrix, respectively.A log-conformation tensor approach is taken to prevent convergence difficulty induced by the viscoelastic properties. The conformation tensor (c) in the polymeric stress tensor term is redefined by a new tensor (Θ) based on the natural logarithm of the c. The new tensor is defined as

Θ=ln(𝐜)=𝐑ln(𝚲)𝐑Θ=ln(�)=�⁡ln(�)�

(20)in which Λ is the diagonal matrix and R is the orthogonal matrix.Under the new conformation tensor, the induced EOF of a viscoelastic fluid is governed by the continuity and N–S equations adapting the Oldroyd-B model, which is expressed as

∂𝚯∂𝑡+𝐮·∇𝚯=𝛀Θ−ΘΩ+2𝐁+1𝜆(eΘ−𝐈)∂�∂�+�·∇�=�Θ−ΘΩ+2�+1�(eΘ−�)

(21)where Ω and B represent the anti-symmetric matrix and the symmetric traceless matrix of the decomposition of the velocity gradient tensor ∇u, respectively. The conformation tensor can be recovered by c = exp(Θ). The PB model and Laplace equation are utilized to characterize the charged channel wall induced potential and the externally applied potential.The governing equations are numerically solved through the FVM by RheoTool, 

(42) an open-source viscoelastic EOF solver on the OpenFOAM platform. A SIMPLEC (Semi-Implicit Method for Pressure Linked Equations-Consistent) algorithm was applied to solve the velocity-pressure coupling. The pressure field and velocity field were computed by the PCG (Preconditioned Conjugate Gradient) solver and the PBiCG (Preconditioned Biconjugate Gradient) solver, respectively.Ranging magnitudes of an applied electric field or fluid concentration induce both different streamlines and velocity magnitudes at various locations and times of the microchannel. In the study performed by Ji et al., 

(90) notable fluctuation of streamlines and vortex formation is formed at the upper stream entrance of the constriction as shown in Figure 6(a) and (b), respectively, due to the increase of electrokinetic effect, which is seen as a result of the increase in polymeric stress (τ

xx). 

(90) The contraction geometry enhances the EOF velocity within the constriction channel under high E

app condition (600 V/cm). Such phenomena can be attributed to the dependence of electro-osmotic viscoelastic fluid flow on the system wall surface and bulk fluid properties. 

(91)

Figure 6. Schematic diagram of vortex formation and streamlines of EOF depicting flow instability at (a) 1.71 s and (b) 1.75 s. Spatial distribution of the elastic normal stress at (c) high Eapp condition. Streamline of an electro-osmotic flow under Eapp of 600 V/cm (90) for (d) non-Newtonian and (e) Newtonian fluid through a constriction geometry. Reproduced with permission from ref (90). Copyright 2021 The Authors, under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

As elastic normal stress exceeds the local shear stress, flow instability and vortex formation occur. The induced elastic stress under EOF not only enhances the instability of the flow but often generates an irregular secondary flow leading to strong disturbance. 

(92) It is also vital to consider the effect of the constriction layout of microchannels on the alteration of the field strength within the system. The contraction geometry enhances a larger electric field strength compared with other locations of the channel outside the constriction region, resulting in a higher velocity gradient and stronger extension on the polymer within the viscoelastic solution. Following the high shear flow condition, a higher magnitude of stretch for polymer molecules in viscoelastic fluids exhibits larger elastic stresses and enhancement of vortex formation at the region. 

(93)As shown in Figure 6(c), significant elastic normal stress occurs at the inlet of the constriction microchannel. Such occurrence of a polymeric flow can be attributed to the dominating elongational flow, giving rise to high deformation of the polymers within the viscoelastic fluid flow, resulting in higher elastic stress from the polymers. Such phenomena at the entrance result in the difference in velocity streamline as circled in Figure 6(d) compared to that of the Newtonian fluid at the constriction entrance in Figure 6(e). 

(90) The difference between the Newtonian and polymer solution at the exit, as circled in Figure 6(d) and (e), can be attributed to the extrudate swell effect of polymers 

(94) within the viscoelastic fluid flow. The extrudate swell effect illustrates that, as polymers emerge from the constriction exit, they tend to contract in the flow direction and grow in the normal direction, resulting in an extrudate diameter greater than the channel size. The deformation of polymers within the polymeric flow at both the entrance and exit of the contraction channel facilitates the change in shear stress conditions of the flow, leading to the alteration in streamlines of flows for each region.

4.3. EOF Applications in LOC Systems

4.3.1. Mixing in LOC Systems

Rather than relying on the micromixing controlled by molecular diffusion under low Reynolds number conditions, active mixers actively leverage convective instability and vortex formation induced by electro-osmotic flows from alternating current (AC) or direct current (DC) electric fields. Such adaptation is recognized as significant breakthroughs for promotion of fluid mixing in chemical and biological applications such as drug delivery, medical diagnostics, chemical synthesis, and so on. 

(95)Many researchers proposed novel designs of electro-osmosis micromixers coupled with numerical simulations in conjunction with experimental findings to increase their understanding of the role of flow instability and vortex formation in the mixing process under electrokinetic phenomena. Matsubara and Narumi 

(96) numerically modeled the mixing process in a microchannel with four electrodes on each side of the microchannel wall, which generated a disruption through unstable electro-osmotic vortices. It was found that particle mixing was sensitive to both the convection effect induced by the main and secondary vortex within the micromixer and the change in oscillation frequency caused by the supplied AC voltage when the Reynolds number was varied. Qaderi et al. 

(97) adapted the PNP equation to numerically study the effect of the geometry and zeta potential configuration of the microchannel on the mixing process with a combined electro-osmotic pressure driven flow. It was reported that the application of heterogeneous zeta potential configuration enhances the mixing efficiency by around 23% while the height of the hurdles increases the mixing efficiency at most 48.1%. Cho et al. 

(98) utilized the PB model and Laplace equation to numerically simulate the electro-osmotic non-Newtonian fluid mixing process within a wavy and block layout of microchannel walls. The Power Law model is adapted to describe the fluid rheological characteristic. It was found that shear-thinning fluids possess a higher volumetric flow rate, which could result in poorer mixing efficiency compared to that of Newtonian fluids. Numerous studies have revealed that flow instability and vortex generation, in particular secondary vortices produced by barriers or greater magnitudes of heterogeneous zeta potential distribution, enhance mixing by increasing bulk flow velocity and reducing flow distance.To better understand the mechanism of disturbance formed in the system due to externally applied forces, known as electrokinetic instability, literature often utilize the Rayleigh (Ra) number, 

(1) as described below:

𝑅𝑎𝑣=𝑢ev𝑢eo=(𝛾−1𝛾+1)2𝑊𝛿2𝐸el2𝐻2𝜁𝛿Ra�=�ev�eo=(�−1�+1)2��2�el2�2��

(22)where γ is the conductivity ratio of the two streams and can be written as 

𝛾=𝜎el,H𝜎el,L�=�el,H�el,L. The Ra number characterizes the ratio between electroviscous and electro-osmotic flow. A high Ra

v value often results in good mixing. It is evident that fluid properties such as the conductivity (σ) of the two streams play a key role in the formation of disturbances to enhance mixing in microsystems. At the same time, electrokinetic parameters like the zeta potential (ζ) in the Ra number is critical in the characterization of electro-osmotic velocity and a slip boundary condition at the microchannel wall.To understand the mixing result along the channel, the concentration field can be defined and simulated under the assumption of steady state conditions and constant diffusion coefficient for each of the working fluid within the system through the convection–diffusion equation as below:

∂𝑐𝒊∂𝑡+∇⇀(𝑐𝑖𝑢⇀−𝐷𝑖∇⇀𝑐𝒊)=0∂��∂�+∇⇀(���⇀−��∇⇀��)=0

(23)where c

i is the species concentration of species i and D

i is the diffusion coefficient of the corresponding species.The standard deviation of concentration (σ

sd) can be adapted to evaluate the mixing quality of the system. 

(97) The standard deviation for concentration at a specific portion of the channel may be calculated using the equation below:

𝜎sd=∫10(𝐶∗(𝑦∗)−𝐶m)2d𝑦∗∫10d𝑦∗⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯�sd=∫01(�*(�*)−�m)2d�*∫01d�*

(24)where C*(y*) and C

m are the non-dimensional concentration profile and the mean concentration at the portion, respectively. C* is the non-dimensional concentration and can be calculated as 

𝐶∗=𝐶𝐶ref�*=��ref, where C

ref is the reference concentration defined as the bulk solution concentration. The mean concentration profile can be calculated as 

𝐶m=∫10(𝐶∗(𝑦∗)d𝑦∗∫10d𝑦∗�m=∫01(�*(�*)d�*∫01d�*. With the standard deviation of concentration, the mixing efficiency 

(97) can then be calculated as below:

𝜀𝑥=1−𝜎sd𝜎sd,0��=1−�sd�sd,0

(25)where σ

sd,0 is the standard derivation of the case of no mixing. The value of the mixing efficiency is typically utilized in conjunction with the simulated flow field and concentration field to explore the effect of geometrical and electrokinetic parameters on the optimization of the mixing results.

5. Summary

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5.1. Conclusion

Viscoelastic fluids such as blood flow in LOC systems are an essential topic to proceed with diagnostic analysis and research through microdevices in the biomedical and pharmaceutical industries. The complex blood flow behavior is tightly controlled by the viscoelastic characteristics of blood such as the dynamic viscosity and the elastic property of RBCs under various shear rate conditions. Furthermore, the flow behaviors under varied driving forces promote an array of microfluidic transport phenomena that are critical to the management of blood flow and other adapted viscoelastic fluids in LOC systems. This review addressed the blood flow phenomena, the complicated interplay between shear rate and blood flow behaviors, and their numerical modeling under LOC systems through the lens of the viscoelasticity characteristic. Furthermore, a theoretical understanding of capillary forces and externally applied electric forces leads to an in-depth investigation of the relationship between blood flow patterns and the key parameters of the two driving forces, the latter of which is introduced through the lens of viscoelastic fluids, coupling numerical modeling to improve the knowledge of blood flow manipulation in LOC systems. The flow disturbances triggered by the EOF of viscoelastic fluids and their impact on blood flow patterns have been deeply investigated due to their important role and applications in LOC devices. Continuous advancements of various numerical modeling methods with experimental findings through more efficient and less computationally heavy methods have served as an encouraging sign of establishing more accurate illustrations of the mechanisms for multiphase blood and other viscoelastic fluid flow transport phenomena driven by various forces. Such progress is fundamental for the manipulation of unique transport phenomena, such as the generated disturbances, to optimize functionalities offered by microdevices in LOC systems.

The following section will provide further insights into the employment of studied blood transport phenomena to improve the functionality of micro devices adapting LOC technology. A discussion of the novel roles that external driving forces play in microfluidic flow behaviors is also provided. Limitations in the computational modeling of blood flow and electrokinetic phenomena in LOC systems will also be emphasized, which may provide valuable insights for future research endeavors. These discussions aim to provide guidance and opportunities for new paths in the ongoing development of LOC devices that adapt blood flow.

5.2. Future Directions

5.2.1. Electro-osmosis Mixing in LOC Systems

Despite substantial research, mixing results through flow instability and vortex formation phenomena induced by electro-osmotic mixing still deviate from the effective mixing results offered by chaotic mixing results such as those seen in turbulent flows. However, recent discoveries of a mixing phenomenon that is generally observed under turbulent flows are found within electro-osmosis micromixers under low Reynolds number conditions. Zhao 

(99) experimentally discovered a rapid mixing process in an AC applied micromixer, where the power spectrum of concentration under an applied voltage of 20 V

p-p induces a −5/3 slope within a frequency range. This value of the slope is considered as the O–C spectrum in macroflows, which is often visible under relatively high Re conditions, such as the Taylor microscale Reynolds number Re > 500 in turbulent flows. 

(100) However, the Re value in the studied system is less than 1 at the specific location and applied voltage. A secondary flow is also suggested to occur close to microchannel walls, being attributed to the increase of convective instability within the system.Despite the experimental phenomenon proposed by Zhao et al., 

(99) the range of effects induced by vital parameters of an EOF mixing system on the enhanced mixing results and mechanisms of disturbance generated by the turbulent-like flow instability is not further characterized. Such a gap in knowledge may hinder the adaptability and commercialization of the discovery of micromixers. One of the parameters for further evaluation is the conductivity gradient of the fluid flow. A relatively strong conductivity gradient (5000:1) was adopted in the system due to the conductive properties of the two fluids. The high conductivity gradients may contribute to the relatively large Rayleigh number and differences in EDL layer thickness, resulting in an unusual disturbance in laminar flow conditions and enhanced mixing results. However, high conductivity gradients are not always achievable by the working fluids due to diverse fluid properties. The reliance on turbulent-like phenomena and rapid mixing results in a large conductivity gradient should be established to prevent the limited application of fluids for the mixing system. In addition, the proposed system utilizes distinct zeta potential distributions at the top and bottom walls due to their difference in material choices, which may be attributed to the flow instability phenomena. Further studies should be made on varying zeta potential magnitude and distribution to evaluate their effect on the slip boundary conditions of the flow and the large shear rate condition close to the channel wall of EOF. Such a study can potentially offer an optimized condition in zeta potential magnitude through material choices and geometrical layout of the zeta potential for better mixing results and manipulation of mixing fluid dynamics. The two vital parameters mentioned above can be varied with the aid of numerical simulation to understand the effect of parameters on the interaction between electro-osmotic forces and electroviscous forces. At the same time, the relationship of developed streamlines of the simulated velocity and concentration field, following their relationship with the mixing results, under the impact of these key parameters can foster more insight into the range of impact that the two parameters have on the proposed phenomena and the microfluidic dynamic principles of disturbances.

In addition, many of the current investigations of electrokinetic mixers commonly emphasize the fluid dynamics of mixing for Newtonian fluids, while the utilization of biofluids, primarily viscoelastic fluids such as blood, and their distinctive response under shear forces in these novel mixing processes of LOC systems are significantly less studied. To develop more compatible microdevice designs and efficient mixing outcomes for the biomedical industry, it is necessary to fill the knowledge gaps in the literature on electro-osmotic mixing for biofluids, where properties of elasticity, dynamic viscosity, and intricate relationship with shear flow from the fluid are further considered.

5.2.2. Electro-osmosis Separation in LOC Systems

Particle separation in LOC devices, particularly in biological research and diagnostics, is another area where disturbances may play a significant role in optimization. 

(101) Plasma analysis in LOC systems under precise control of blood flow phenomena and blood/plasma separation procedures can detect vital information about infectious diseases from particular antibodies and foreign nucleic acids for medical treatments, diagnostics, and research, 

(102) offering more efficient results and simple operating procedures compared to that of the traditional centrifugation method for blood and plasma separation. However, the adaptability of LOC devices for blood and plasma separation is often hindered by microchannel clogging, where flow velocity and plasma yield from LOC devices is reduced due to occasional RBC migration and aggregation at the filtration entrance of microdevices. 

(103)It is important to note that the EOF induces flow instability close to microchannel walls, which may provide further solutions to clogging for the separation process of the LOC systems. Mohammadi et al. 

(104) offered an anti-clogging effect of RBCs at the blood and plasma separating device filtration entry, adjacent to the surface wall, through RBC disaggregation under high shear rate conditions generated by a forward and reverse EOF direction.

Further theoretical and numerical research can be conducted to characterize the effect of high shear rate conditions near microchannel walls toward the detachment of binding blood cells on surfaces and the reversibility of aggregation. Through numerical modeling with varying electrokinetic parameters to induce different degrees of disturbances or shear conditions at channel walls, it may be possible to optimize and better understand the process of disrupting the forces that bind cells to surface walls and aggregated cells at filtration pores. RBCs that migrate close to microchannel walls are often attracted by the adhesion force between the RBC and the solid surface originating from the van der Waals forces. Following RBC migration and attachment by adhesive forces adjacent to the microchannel walls as shown in Figure 7, the increase in viscosity at the region causes a lower shear condition and encourages RBC aggregation (cell–cell interaction), which clogs filtering pores or microchannels and reduces flow velocity at filtration region. Both the impact that shear forces and disturbances may induce on cell binding forces with surface walls and other cells leading to aggregation may suggest further characterization. Kinetic parameters such as activation energy and the rate-determining step for cell binding composition attachment and detachment should be considered for modeling the dynamics of RBCs and blood flows under external forces in LOC separation devices.

Figure 7. Schematic representations of clogging at a microchannel pore following the sequence of RBC migration, cell attachment to channel walls, and aggregation. (105) Reproduced with permission from ref (105). Copyright 2018 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

5.2.3. Relationship between External Forces and Microfluidic Systems

In blood flow, a thicker CFL suggests a lower blood viscosity, suggesting a complex relationship between shear stress and shear rate, affecting the blood viscosity and blood flow. Despite some experimental and numerical studies on electro-osmotic non-Newtonian fluid flow, limited literature has performed an in-depth investigation of the role that applied electric forces and other external forces could play in the process of CFL formation. Additional studies on how shear rates from external forces affect CFL formation and microfluidic flow dynamics can shed light on the mechanism of the contribution induced by external driving forces to the development of a separate phase of layer, similar to CFL, close to the microchannel walls and distinct from the surrounding fluid within the system, then influencing microfluidic flow dynamics.One of the mechanisms of phenomena to be explored is the formation of the Exclusion Zone (EZ) region following a “Self-Induced Flow” (SIF) phenomenon discovered by Li and Pollack, 

(106) as shown in Figure 8(a) and (b), respectively. A spontaneous sustained axial flow is observed when hydrophilic materials are immersed in water, resulting in the buildup of a negative layer of charges, defined as the EZ, after water molecules absorb infrared radiation (IR) energy and break down into H and OH

+–.

Figure 8. Schematic representations of (a) the Exclusion Zone region and (b) the Self Induced Flow through visualization of microsphere movement within a microchannel. (106) Reproduced with permission from ref (106). Copyright 2020 The Authors under the terms of the Creative Commons (CC BY 4.0) License https://creativecommons.org/licenses/by/4.0/.

Despite the finding of such a phenomenon, the specific mechanism and role of IR energy have yet to be defined for the process of EZ development. To further develop an understanding of the role of IR energy in such phenomena, a feasible study may be seen through the lens of the relationships between external forces and microfluidic flow. In the phenomena, the increase of SIF velocity under a rise of IR radiation resonant characteristics is shown in the participation of the external electric field near the microchannel walls under electro-osmotic viscoelastic fluid flow systems. The buildup of negative charges at the hydrophilic surfaces in EZ is analogous to the mechanism of electrical double layer formation. Indeed, research has initiated the exploration of the core mechanisms for EZ formation through the lens of the electrokinetic phenomena. 

(107) Such a similarity of the role of IR energy and the transport phenomena of SIF with electrokinetic phenomena paves the way for the definition of the unknown SIF phenomena and EZ formation. Furthermore, Li and Pollack 

(106) suggest whether CFL formation might contribute to a SIF of blood using solely IR radiation, a commonly available source of energy in nature, as an external driving force. The proposition may be proven feasible with the presence of the CFL region next to the negatively charged hydrophilic endothelial glycocalyx layer, coating the luminal side of blood vessels. 

(108) Further research can dive into the resonating characteristics between the formation of the CFL region next to the hydrophilic endothelial glycocalyx layer and that of the EZ formation close to hydrophilic microchannel walls. Indeed, an increase in IR energy is known to rapidly accelerate EZ formation and SIF velocity, depicting similarity to the increase in the magnitude of electric field forces and greater shear rates at microchannel walls affecting CFL formation and EOF velocity. Such correlation depicts a future direction in whether SIF blood flow can be observed and characterized theoretically further through the lens of the relationship between blood flow and shear forces exhibited by external energy.

The intricate link between the CFL and external forces, more specifically the externally applied electric field, can receive further attention to provide a more complete framework for the mechanisms between IR radiation and EZ formation. Such characterization may also contribute to a greater comprehension of the role IR can play in CFL formation next to the endothelial glycocalyx layer as well as its role as a driving force to propel blood flow, similar to the SIF, but without the commonly assumed pressure force from heart contraction as a source of driving force.

5.3. Challenges

Although there have been significant improvements in blood flow modeling under LOC systems over the past decade, there are still notable constraints that may require special attention for numerical simulation applications to benefit the adaptability of the designs and functionalities of LOC devices. Several points that require special attention are mentioned below:

1.The majority of CFD models operate under the relationship between the viscoelasticity of blood and the shear rate conditions of flow. The relative effect exhibited by the presence of highly populated RBCs in whole blood and their forces amongst the cells themselves under complex flows often remains unclearly defined. Furthermore, the full range of cell populations in whole blood requires a much more computational load for numerical modeling. Therefore, a vital goal for future research is to evaluate a reduced modeling method where the impact of cell–cell interaction on the viscoelastic property of blood is considered.
2.Current computational methods on hemodynamics rely on continuum models based upon non-Newtonian rheology at the macroscale rather than at molecular and cellular levels. Careful considerations should be made for the development of a constructive framework for the physical and temporal scales of micro/nanoscale systems to evaluate the intricate relationship between fluid driving forces, dynamic viscosity, and elasticity.
3.Viscoelastic fluids under the impact of externally applied electric forces often deviate from the assumptions of no-slip boundary conditions due to the unique flow conditions induced by externally applied forces. Furthermore, the mechanism of vortex formation and viscoelastic flow instability at laminar flow conditions should be better defined through the lens of the microfluidic flow phenomenon to optimize the prediction of viscoelastic flow across different geometrical layouts. Mathematical models and numerical methods are needed to better predict such disturbance caused by external forces and the viscoelasticity of fluids at such a small scale.
4.Under practical situations, zeta potential distribution at channel walls frequently deviates from the common assumption of a constant distribution because of manufacturing faults or inherent surface charges prior to the introduction of electrokinetic influence. These discrepancies frequently lead to inconsistent surface potential distribution, such as excess positive ions at relatively more negatively charged walls. Accordingly, unpredicted vortex formation and flow instability may occur. Therefore, careful consideration should be given to these discrepancies and how they could trigger the transport process and unexpected results of a microdevice.

Author Information

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  • Corresponding Authors
    • Zhe Chen – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: zaccooky@sjtu.edu.cn
    • Bo Ouyang – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Email: bouy93@sjtu.edu.cn
    • Zheng-Hong Luo – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-9011-6020; Email: luozh@sjtu.edu.cn
  • Authors
    • Bin-Jie Lai – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0009-0002-8133-5381
    • Li-Tao Zhu – Department of Chemical Engineering, School of Chemistry and Chemical Engineering, State Key Laboratory of Metal Matrix Composites, Shanghai Jiao Tong University, Shanghai 200240, P. R. China;  Orcidhttps://orcid.org/0000-0001-6514-8864
  • NotesThe authors declare no competing financial interest.

Acknowledgments

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This work was supported by the National Natural Science Foundation of China (No. 22238005) and the Postdoctoral Research Foundation of China (No. GZC20231576).

Vocabulary

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Microfluidicsthe field of technological and scientific study that investigates fluid flow in channels with dimensions between 1 and 1000 μm
Lab-on-a-Chip Technologythe field of research and technological development aimed at integrating the micro/nanofluidic characteristics to conduct laboratory processes on handheld devices
Computational Fluid Dynamics (CFD)the method utilizing computational abilities to predict physical fluid flow behaviors mathematically through solving the governing equations of corresponding fluid flows
Shear Ratethe rate of change in velocity where one layer of fluid moves past the adjacent layer
Viscoelasticitythe property holding both elasticity and viscosity characteristics relying on the magnitude of applied shear stress and time-dependent strain
Electro-osmosisthe flow of fluid under an applied electric field when charged solid surface is in contact with the bulk fluid
Vortexthe rotating motion of a fluid revolving an axis line

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Fig. 9 From: An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

Abstract

웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 웨어)을 사용하여 웨어 모양, 웨어 간격, 웨어의 오리피스 존재, 흐름 영역에 대한 바닥 경사와 같은 기하학적 매개변수의 영향을 평가했습니다.

유량과 수심의 관계, 수심 평균 속도의 변화와 분포, 난류 특성, 어도에서의 에너지 소산. 흐름 조건에 미치는 영향을 조사하기 위해 FLOW-3D® 소프트웨어를 사용하여 전산 유체 역학 시뮬레이션을 수행했습니다.

수치 모델은 계산된 표면 프로파일과 속도를 문헌의 실험적으로 측정된 값과 비교하여 검증되었습니다. 수치 모델과 실험 데이터의 결과, 급락유동의 표면 프로파일과 표준화된 속도 프로파일에 대한 평균 제곱근 오차와 평균 절대 백분율 오차가 각각 0.014m와 3.11%로 나타나 수치 모델의 능력을 확인했습니다.

수영장과 둑의 흐름 특성을 예측합니다. 각 모델에 대해 L/B = 1.83(L: 웨어 거리, B: 수로 폭) 값에서 급락 흐름이 발생할 수 있고 L/B = 0.61에서 스트리밍 흐름이 발생할 수 있습니다. 직사각형 미로보 모델은 기존 모델보다 무차원 방류량(Q+)이 더 큽니다.

수중 흐름의 기존 보와 직사각형 미로 보의 경우 Q는 각각 1.56과 1.47h에 비례합니다(h: 보 위 수심). 기존 웨어의 풀 내 평균 깊이 속도는 직사각형 미로 웨어의 평균 깊이 속도보다 높습니다.

그러나 주어진 방류량, 바닥 경사 및 웨어 간격에 대해 난류 운동 에너지(TKE) 및 난류 강도(TI) 값은 기존 웨어에 비해 직사각형 미로 웨어에서 더 높습니다. 기존의 웨어는 직사각형 미로 웨어보다 에너지 소산이 더 낮습니다.

더 낮은 TKE 및 TI 값은 미로 웨어 상단, 웨어 하류 벽 모서리, 웨어 측벽과 채널 벽 사이에서 관찰되었습니다. 보와 바닥 경사면 사이의 거리가 증가함에 따라 평균 깊이 속도, 난류 운동 에너지의 평균값 및 난류 강도가 증가하고 수영장의 체적 에너지 소산이 감소했습니다.

둑에 개구부가 있으면 평균 깊이 속도와 TI 값이 증가하고 풀 내에서 가장 높은 TKE 범위가 감소하여 두 모델 모두에서 물고기를 위한 휴식 공간이 더 넓어지고(TKE가 낮아짐) 에너지 소산율이 감소했습니다.

원문보기

Two different arrangements of the weir (i.e., straight weir and rectangular labyrinth weir) were used to evaluate the effects of geometric parameters such as weir shape, weir spacing, presence of an orifice at the weir, and bed slope on the flow regime and the relationship between discharge and depth, variation and distribution of depth-averaged velocity, turbulence characteristics, and energy dissipation at the fishway. Computational fluid dynamics simulations were performed using FLOW-3D® software to examine the effects on flow conditions. The numerical model was validated by comparing the calculated surface profiles and velocities with experimentally measured values from the literature. The results of the numerical model and experimental data showed that the root-mean-square error and mean absolute percentage error for the surface profiles and normalized velocity profiles of plunging flows were 0.014 m and 3.11%, respectively, confirming the ability of the numerical model to predict the flow characteristics of the pool and weir. A plunging flow can occur at values of L/B = 1.83 (L: distance of the weir, B: width of the channel) and streaming flow at L/B = 0.61 for each model. The rectangular labyrinth weir model has larger dimensionless discharge values (Q+) than the conventional model. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q is proportional to 1.56 and 1.47h, respectively (h: the water depth above the weir). The average depth velocity in the pool of a conventional weir is higher than that of a rectangular labyrinth weir. However, for a given discharge, bed slope, and weir spacing, the turbulent kinetic energy (TKE) and turbulence intensity (TI) values are higher for a rectangular labyrinth weir compared to conventional weir. The conventional weir has lower energy dissipation than the rectangular labyrinth weir. Lower TKE and TI values were observed at the top of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall. As the distance between the weirs and the bottom slope increased, the average depth velocity, the average value of turbulent kinetic energy and the turbulence intensity increased, and the volumetric energy dissipation in the pool decreased. The presence of an opening in the weir increased the average depth velocity and TI values and decreased the range of highest TKE within the pool, resulted in larger resting areas for fish (lower TKE), and decreased the energy dissipation rates in both models.

1 Introduction

Artificial barriers such as detour dams, weirs, and culverts in lakes and rivers prevent fish from migrating and completing the upstream and downstream movement cycle. This chain is related to the life stage of the fish, its location, and the type of migration. Several riverine fish species instinctively migrate upstream for spawning and other needs. Conversely, downstream migration is a characteristic of early life stages [1]. A fish ladder is a waterway that allows one or more fish species to cross a specific obstacle. These structures are constructed near detour dams and other transverse structures that have prevented such migration by allowing fish to overcome obstacles [2]. The flow pattern in fish ladders influences safe and comfortable passage for ascending fish. The flow’s strong turbulence can reduce the fish’s speed, injure them, and delay or prevent them from exiting the fish ladder. In adult fish, spawning migrations are usually complex, and delays are critical to reproductive success [3].

Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [1, 2]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].

figure 1
Fig. 1

Extensive experimental studies have been conducted to investigate flow patterns for various physical geometries (i.e., bed slope, pool length, and weir height) [2]. Guiny et al. [7] modified the standard design by adding vertical slots, orifices, and weirs in fishways. The efficiency of the orifices and vertical slots was related to the velocities at their entrances. In the laboratory experiments of Yagci [8], the three-dimensional (3D) mean flow and turbulence structure of a pool weir fishway combined with an orifice and a slot is investigated. It is shown that the energy dissipation per unit volume and the discharge have a linear relationship.

Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [7, 9]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.

Considering that an alternative method to study the flow characteristics in a fishway with a pool weir is based on numerical methods and modeling from computational fluid dynamics (CFD), which can easily change the geometry of the fishway for different flow fields, this study uses the powerful package CFD and the software FLOW-3D to evaluate the proposed weir design and compare it with the conventional one to extend the application of the fishway. The main objective of this study was to evaluate the hydraulic performance of the rectangular labyrinth pool and the weir with submerged openings in different hydraulic configurations. The primary objective of creating a new weir configuration for suitable flow patterns is evaluated based on the swimming capabilities of different fish species. Specifically, the following questions will be answered: (a) How do the various hydraulic and geometric parameters relate to the effects of water velocity and turbulence, expressed as turbulent kinetic energy (TKE) and turbulence intensity (TI) within the fishway, i.e., are conventional weirs more affected by hydraulics than rectangular labyrinth weirs? (b) Which weir configurations have the greatest effect on fish performance in the fishway? (c) In the presence of an orifice plate, does the performance of each weir configuration differ with different weir spacing, bed gradients, and flow regimes from that without an orifice plate?

2 Materials and Methods

2.1 Physical Model Configuration

This paper focuses on Ead et al. [6]’s laboratory experiments as a reference, testing ten pool weirs (Fig. 2). The experimental flume was 6 m long, 0.56 m wide, and 0.6 m high, with a bottom slope of 10%. Field measurements were made at steady flow with a maximum flow rate of 0.165 m3/s. Discharge was measured with magnetic flow meters in the inlets and water level with point meters (see Ead et al. [6]. for more details). Table 1 summarizes the experimental conditions considered for model calibration in this study.

figure 2
Fig. 2

Table 1 Experimental conditions considered for calibration

Full size table

2.2 Numerical Models

Computational fluid dynamics (CFD) simulations were performed using FLOW-3D® v11.2 to validate a series of experimental liner pool weirs by Ead et al. [6] and to investigate the effects of the rectangular labyrinth pool weir with an orifice. The dimensions of the channel and data collection areas in the numerical models are the same as those of the laboratory model. Two types of pool weirs were considered: conventional and labyrinth. The proposed rectangular labyrinth pool weirs have a symmetrical cross section and are sized to fit within the experimental channel. The conventional pool weir model had a pool length of l = 0.685 and 0.342 m, a weir height of w = 0.141 m, a weir width of B = 0.56 m, and a channel slope of S0 = 5 and 10%. The rectangular labyrinth weirs have the same front width as the offset, i.e., a = b = c = 0.186 m. A square underwater opening with a width of 0.05 m and a depth of 0.05 m was created in the middle of the weir. The weir configuration considered in the present study is shown in Fig. 3.

figure 3
Fig. 3

2.3 Governing Equations

FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (x, y, z, t). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [4, 13]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (x, y, z) applicable to the model are as follows:

�f∂�∂�+∂(���x)∂�+∂(���y)∂�+∂(���z)∂�=�SOR

(1)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�x+�x

(2)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�y+�y

(3)

∂�∂�+1�f(��x∂�∂�+��y∂�∂�+��z∂�∂�)=−1�∂�∂�+�z+�z

(4)

where (u, v, w) are the velocity components, (Ax, Ay, Az) are the flow area components, (Gx, Gy, Gz) are the mass accelerations, and (fx, fy, fz) are the viscous accelerations in the directions (x, y, z), ρ is the fluid density, RSOR is the spring term, Vf is the volume fraction associated with the flow, and P is the pressure. The k–ε turbulence model (RNG) was used in this study to solve the turbulence of the flow field. This model is a modified version of the standard k–ε model that improves performance. The model is a two-equation model; the first equation (Eq. 5) expresses the turbulence’s energy, called turbulent kinetic energy (k) [14]. The second equation (Eq. 6) is the turbulent dissipation rate (ε), which determines the rate of dissipation of kinetic energy [15]. These equations are expressed as follows Dasineh et al. [4]:

∂(��)∂�+∂(����)∂��=∂∂��[������∂�∂��]+��−�ε

(5)

∂(�ε)∂�+∂(�ε��)∂��=∂∂��[�ε�eff∂ε∂��]+�1εε��k−�2ε�ε2�

(6)

In these equations, k is the turbulent kinetic energy, ε is the turbulent energy consumption rate, Gk is the generation of turbulent kinetic energy by the average velocity gradient, with empirical constants αε = αk = 1.39, C1ε = 1.42, and C2ε = 1.68, eff is the effective viscosity, μeff = μ + μt [15]. Here, μ is the hydrodynamic density coefficient, and μt is the turbulent density of the fluid.

2.4 Meshing and the Boundary Conditions in the Model Setup

The numerical area is divided into three mesh blocks in the X-direction. The meshes are divided into different sizes, a containing mesh block for the entire spatial domain and a nested block with refined cells for the domain of interest. Three different sizes were selected for each of the grid blocks. By comparing the accuracy of their results based on the experimental data, the reasonable mesh for the solution domain was finally selected. The convergence index method (GCI) evaluated the mesh sensitivity analysis. Based on this method, many researchers, such as Ahmadi et al. [16] and Ahmadi et al. [15], have studied the independence of numerical results from mesh size. Three different mesh sizes with a refinement ratio (r) of 1.33 were used to perform the convergence index method. The refinement ratio is the ratio between the larger and smaller mesh sizes (r = Gcoarse/Gfine). According to the recommendation of Celik et al. [17], the recommended number for the refinement ratio is 1.3, which gives acceptable results. Table 2 shows the characteristics of the three mesh sizes selected for mesh sensitivity analysis.Table 2 Characteristics of the meshes tested in the convergence analysis

Full size table

The results of u1 = umax (u1 = velocity component along the x1 axis and umax = maximum velocity of u1 in a section perpendicular to the invert of the fishway) at Q = 0.035 m3/s, × 1/l = 0.66, and Y1/b = 0 in the pool of conventional weir No. 4, obtained from the output results of the software, were used to evaluate the accuracy of the calculation range. As shown in Fig. 4, x1 = the distance from a given weir in the x-direction, Y1 = the water depth measured in the y-direction, Y0 = the vertical distance in the Cartesian coordinate system, h = the water column at the crest, b = the distance between the two points of maximum velocity umax and zero velocity, and l = the pool length.

figure 4
Fig. 4

The apparent index of convergence (p) in the GCI method is calculated as follows:

�=ln⁡(�3−�2)(�2−�1)/ln⁡(�)

(7)

f1, f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:

GCIfine=1.25|ε|��−1

(8)

Here, ε = (f2 − f1)/f1 is the relative error, and f2 and f3 are the values of hydraulic parameters considered for medium and small grids, respectively. GCI12 and GCI23 dimensionless indices can be calculated as:

GCI12=1.25|�2−�1�1|��−1

(9)

Then, the independence of the network is preserved. The convergence index of the network parameters obtained by Eqs. (7)–(9) for all three network variables is shown in Table 3. Since the GCI values for the smaller grid (GCI12) are lower compared to coarse grid (GCI23), it can be concluded that the independence of the grid is almost achieved. No further change in the grid size of the solution domain is required. The calculated values (GCI23/rpGCI12) are close to 1, which shows that the numerical results obtained are within the convergence range. As a result, the meshing of the solution domain consisting of a block mesh with a mesh size of 0.012 m and a block mesh within a larger block mesh with a mesh size of 0.009 m was selected as the optimal mesh (Fig. 5).Table 3 GCI calculation

Full size table

figure 5
Fig. 5

The boundary conditions applied to the area are shown in Fig. 6. The boundary condition of specific flow rate (volume flow rate-Q) was used for the inlet of the flow. For the downstream boundary, the flow output (outflow-O) condition did not affect the flow in the solution area. For the Zmax boundary, the specified pressure boundary condition was used along with the fluid fraction = 0 (P). This type of boundary condition considers free surface or atmospheric pressure conditions (Ghaderi et al. [19]). The wall boundary condition is defined for the bottom of the channel, which acts like a virtual wall without friction (W). The boundary between mesh blocks and walls were considered a symmetrical condition (S).

figure 6
Fig. 6

The convergence of the steady-state solutions was controlled during the simulations by monitoring the changes in discharge at the inlet boundary conditions. Figure 7 shows the time series plots of the discharge obtained from the Model A for the three main discharges from the numerical results. The 8 s to reach the flow equilibrium is suitable for the case of the fish ladder with pool and weir. Almost all discharge fluctuations in the models are insignificant in time, and the flow has reached relative stability. The computation time for the simulations was between 6 and 8 h using a personal computer with eight cores of a CPU (Intel Core i7-7700K @ 4.20 GHz and 16 GB RAM).

figure 7
Fig. 7

3 Results

3.1 Verification of Numerical Results

Quantitative outcomes, including free surface and normalized velocity profiles obtained using FLOW-3D software, were reviewed and compared with the results of Ead et al. [6]. The fourth pool was selected to present the results and compare the experiment and simulation. For each quantity, the percentage of mean absolute error (MAPE (%)) and root-mean-square error (RMSE) are calculated. Equations (10) and (11) show the method used to calculate the errors.

MAPE(%)100×1�∑1�|�exp−�num�exp|

(10)

RMSE(−)1�∑1�(�exp−�num)2

(11)

Here, Xexp is the value of the laboratory data, Xnum is the numerical data value, and n is the amount of data. As shown in Fig. 8, let x1 = distance from a given weir in the x-direction and Y1 = water depth in the y-direction from the bottom. The trend of the surface profiles for each of the numerical results is the same as that of the laboratory results. The surface profiles of the plunging flows drop after the flow enters and then rises to approach the next weir. The RMSE and MAPE error values for Model A are 0.014 m and 3.11%, respectively, indicating acceptable agreement between numerical and laboratory results. Figure 9 shows the velocity vectors and plunging flow from the numerical results, where x and y are horizontal and vertical to the flow direction, respectively. It can be seen that the jet in the fish ladder pool has a relatively high velocity. The two vortices, i.e., the enclosed vortex rotating clockwise behind the weir and the surface vortex rotating counterclockwise above the jet, are observed for the regime of incident flow. The point where the jet meets the fish passage bed is shown in the figure. The normalized velocity profiles upstream and downstream of the impact points are shown in Fig. 10. The figure shows that the numerical results agree well with the experimental data of Ead et al. [6].

figure 8
Fig. 8
figure 9
Fig. 9
figure 10
Fig. 10

3.2 Flow Regime and Discharge-Depth Relationship

Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [2, 20]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:

��∗=���0���

(12)

Q is the total discharge, B is the width of the channel, S0 is the slope of the bed, and g is the gravity acceleration. Figure 11 shows different ranges for each flow regime based on the slope of the bed and the distance between the pools in this study. The results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22] were used for this comparison. The distance between the pools affects the changes in the regime of the fish ladder. So, if you decrease the distance between weirs, the flow regime more likely becomes. This study determined all three flow regimes in a fish ladder. When the corresponding range of Qt* is less than 0.6, the flow regime can dip at values of L/B = 1.83. If the corresponding range of Qt* is greater than 0.5, transitional flow may occur at L/B = 1.22. On the other hand, when Qt* is greater than 1, streamwise flow can occur at values of L/B = 0.61. These observations agree well with the results of Baki et al. [21], Ead et al. [6] and Dizabadi et al. [22].

figure 11
Fig. 11

For plunging flows, another dimensionless discharge (Q+) versus h/w given by Ead et al. [6] was used for further evaluation:

�+=��ℎ�ℎ=23�d�

(13)

where h is the water depth above the weir, and Cd is the discharge coefficient. Figure 12a compares the numerical and experimental results of Ead et al. [6]. In this figure, Rehbock’s empirical equation is used to estimate the discharge coefficient of Ead et al. [6].

�d=0.57+0.075ℎ�

(14)

figure 12
Fig. 12

The numerical results for the conventional weir (Model A) and the rectangular labyrinth weir (Model B) of this study agree well with the laboratory results of Ead et al. [6]. When comparing models A and B, it is also found that a rectangular labyrinth weir has larger Q + values than the conventional weir as the length of the weir crest increases for a given channel width and fixed headwater elevation. In Fig. 12b, Models A and B’s flow depth plot shows the plunging flow regime. The power trend lines drawn through the data are the best-fit lines. The data shown in Fig. 12b are for different bed slopes and weir geometries. For the conventional weir and the rectangular labyrinth weir at submerged flow, Q can be assumed to be proportional to 1.56 and 1.47h, respectively. In the results of Ead et al. [6], Q is proportional to 1.5h. If we assume that the flow through the orifice is Qo and the total outflow is Q, the change in the ratio of Qo/Q to total outflow for models A and B can be shown in Fig. 13. For both models, the flow through the orifice decreases as the total flow increases. A logarithmic trend line was also found between the total outflow and the dimensionless ratio Qo/Q.

figure 13
Fig. 13

3.3 Depth-Averaged Velocity Distributions

To ensure that the target fish species can pass the fish ladder with maximum efficiency, the average velocity in the fish ladder should be low enough [4]. Therefore, the average velocity in depth should be as much as possible below the critical swimming velocities of the target fishes at a constant flow depth in the pool [20]. The contour plot of depth-averaged velocity was used instead of another direction, such as longitudinal velocity because fish are more sensitive to depth-averaged flow velocity than to its direction under different hydraulic conditions. Figure 14 shows the distribution of depth-averaged velocity in the pool for Models A and B in two cases with and without orifice plates. Model A’s velocity within the pool differs slightly in the spanwise direction. However, no significant variation in velocity was observed. The flow is gradually directed to the sides as it passes through the rectangular labyrinth weir. This increases the velocity at the sides of the channel. Therefore, the high-velocity zone is located at the sides. The low velocity is in the downstream apex of the weir. This area may be suitable for swimming target fish. The presence of an opening in the weir increases the flow velocity at the opening and in the pool’s center, especially in Model A. The flow velocity increase caused by the models’ opening varied from 7.7 to 12.48%. Figure 15 illustrates the effect of the inverted slope on the averaged depth velocity distribution in the pool at low and high discharge. At constant discharge, flow velocity increases with increasing bed slope. In general, high flow velocity was found in the weir toe sidewall and the weir and channel sidewalls.

figure 14
Fig. 14
figure 15
Fig. 15

On the other hand, for a constant bed slope, the high-velocity area of the pool increases due to the increase in runoff. For both bed slopes and different discharges, the most appropriate path for fish to travel from upstream to downstream is through the middle of the cross section and along the top of the rectangular labyrinth weirs. The maximum dominant velocities for Model B at S0 = 5% were 0.83 and 1.01 m/s; at S0 = 10%, they were 1.12 and 1.61 m/s at low and high flows, respectively. The low mean velocities for the same distance and S0 = 5 and 10% were 0.17 and 0.26 m/s, respectively.

Figure 16 shows the contour of the averaged depth velocity for various distances from the weir at low and high discharge. The contour plot shows a large variation in velocity within short distances from the weir. At L/B = 0.61, velocities are low upstream and downstream of the top of the weir. The high velocities occur in the side walls of the weir and the channel. At L/B = 1.22, the low-velocity zone displaces the higher velocity in most of the pool. Higher velocities were found only on the sides of the channel. As the discharge increases, the velocity zone in the pool becomes wider. At L/B = 1.83, there is an area of higher velocities only upstream of the crest and on the sides of the weir. At high discharge, the prevailing maximum velocities for L/B = 0.61, 1.22, and 1.83 were 1.46, 1.65, and 1.84 m/s, respectively. As the distance between weirs increases, the range of maximum velocity increases.

figure 16
Fig. 16

On the other hand, the low mean velocity for these distances was 0.27, 0.44, and 0.72 m/s, respectively. Thus, the low-velocity zone decreases with increasing distance between weirs. Figure 17 shows the pattern distribution of streamlines along with the velocity contour at various distances from the weir for Q = 0.05 m3/s. A stream-like flow is generally formed in the pool at a small distance between weirs (L/B = 0.61). The rotation cell under the jet forms clockwise between the two weirs. At the distances between the spillways (L/B = 1.22), the transition regime of the flow is formed. The transition regime occurs when or shortly after the weir is flooded. The rotation cell under the jet is clockwise smaller than the flow regime and larger than the submergence regime. At a distance L/B = 1.83, a plunging flow is formed so that the plunging jet dips into the pool and extends downstream to the center of the pool. The clockwise rotation of the cell is bounded by the dipping jet of the weir and is located between the bottom and the side walls of the weir and the channel.

figure 17
Fig. 17

Figure 18 shows the average depth velocity bar graph for each weir at different bed slopes and with and without orifice plates. As the distance between weirs increases, all models’ average depth velocity increases. As the slope of the bottom increases and an orifice plate is present, the average depth velocity in the pool increases. In addition, the average pool depth velocity increases as the discharge increases. Among the models, Model A’s average depth velocity is higher than Model B’s. The variation in velocity ranged from 8.11 to 12.24% for the models without an orifice plate and from 10.26 to 16.87% for the models with an orifice plate.

figure 18
Fig. 18

3.4 Turbulence Characteristics

The turbulent kinetic energy is one of the important parameters reflecting the turbulent properties of the flow field [23]. When the k value is high, more energy and a longer transit time are required to migrate the target species. The turbulent kinetic energy is defined as follows:

�=12(�x′2+�y′2+�z′2)

(15)

where ux, uy, and uz are fluctuating velocities in the x, y, and z directions, respectively. An illustration of the TKE and the effects of the geometric arrangement of the weir and the presence of an opening in the weir is shown in Fig. 19. For a given bed slope, in Model A, the highest TKE values are uniformly distributed in the weir’s upstream portion in the channel’s cross section. In contrast, for the rectangular labyrinth weir (Model B), the highest TKE values are concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value in Models A and B is 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%). In the downstream portion of the conventional weir and within the crest of the weir and the walls of the rectangular labyrinth, there was a much lower TKE value that provided the best conditions for fish to recover in the pool between the weirs. The average of the lowest TKE for bottom slopes of 5 and 10% in Model A is 0.041 and 0.056 J/kg, and for Model B, is 0.047 and 0.064 J/kg. The presence of an opening in the weirs reduces the area of the highest TKE within the pool. It also increases the resting areas for fish (lower TKE). The highest TKE at the highest bottom slope in Models A and B with an orifice is 0.208 and 0.191 J/kg, respectively.

figure 19
Fig. 19

Figure 20 shows the effect of slope on the longitudinal distribution of TKE in the pools. TKE values significantly increase for a given discharge with an increasing bottom slope. Thus, for a low bed slope (S0 = 5%), a large pool area has expanded with average values of 0.131 and 0.168 J/kg for low and high discharge, respectively. For a bed slope of S0 = 10%, the average TKE values are 0.176 and 0.234 J/kg. Furthermore, as the discharge increases, the area with high TKE values within the pool increases. Lower TKE values are observed at the apex of the labyrinth weir, at the corner of the wall downstream of the weir, and between the side walls of the weir and the channel wall for both bottom slopes. The effect of distance between weirs on TKE is shown in Fig. 21. Low TKE values were observed at low discharge and short distances between weirs. Low TKE values are located at the top of the rectangular labyrinth weir and the downstream corner of the weir wall. There is a maximum value of TKE at the large distances between weirs, L/B = 1.83, along the center line of the pool, where the dip jet meets the bottom of the bed. At high discharge, the maximum TKE value for the distance L/B = 0.61, 1.22, and 1.83 was 0.246, 0.322, and 0.417 J/kg, respectively. In addition, the maximum TKE range increases with the distance between weirs.

figure 20
Fig. 20
figure 21
Fig. 21

For TKE size, the average value (TKEave) is plotted against q in Fig. 22. For all models, the TKE values increase with increasing q. For example, in models A and B with L/B = 0.61 and a slope of 10%, the TKE value increases by 41.66 and 86.95%, respectively, as q increases from 0.1 to 0.27 m2/s. The TKE values in Model B are higher than Model A for a given discharge, bed slope, and weir distance. The TKEave in Model B is higher compared to Model A, ranging from 31.46 to 57.94%. The presence of an orifice in the weir reduces the TKE values in both weirs. The intensity of the reduction is greater in Model B. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, an orifice reduces TKEave values by 60.35 and 19.04%, respectively. For each model, increasing the bed slope increases the TKEave values in the pool. For example, for Model B with q = 0.18 m2/s, increasing the bed slope from 5 to 10% increases the TKEave value by 14.34%. Increasing the distance between weirs increases the TKEave values in the pool. For example, in Model B with S0 = 10% and q = 0.3 m2/s, the TKEave in the pool increases by 34.22% if you increase the distance between weirs from L/B = 0.61 to L/B = 0.183.

figure 22
Fig. 22

Cotel et al. [24] suggested that turbulence intensity (TI) is a suitable parameter for studying fish swimming performance. Figure 23 shows the plot of TI and the effects of the geometric arrangement of the weir and the presence of an orifice. In Model A, the highest TI values are found upstream of the weirs and are evenly distributed across the cross section of the channel. The TI values increase as you move upstream to downstream in the pool. For the rectangular labyrinth weir, the highest TI values were concentrated on the sides of the pool, between the top of the weir and the side wall of the channel, and along the top of the weir. Downstream of the conventional weir, within the apex of the weir, and at the corners of the walls of the rectangular labyrinth weir, the percentage of TI was low. At the highest discharge, the average range of TI in Models A and B was 24–45% and 15–62%, respectively. The diversity of TI is greater in the rectangular labyrinth weir than the conventional weir. Fish swimming performance is reduced due to higher turbulence intensity. However, fish species may prefer different disturbance intensities depending on their swimming abilities; for example, Salmo trutta prefers a disturbance intensity of 18–53% [25]. Kupferschmidt and Zhu [26] found a higher range of TI for fishways, such as natural rock weirs, of 40–60%. The presence of an orifice in the weir increases TI values within the pool, especially along the middle portion of the cross section of the fishway. With an orifice in the weir, the average range of TI in Models A and B was 28–59% and 22–73%, respectively.

figure 23
Fig. 23

The effect of bed slope on TI variation is shown in Fig. 24. TI increases in different pool areas as the bed slope increases for a given discharge. For a low bed slope (S0 = 5%), a large pool area has increased from 38 to 63% and from 56 to 71% for low and high discharge, respectively. For a bed slope of S0 = 10%, the average values of TI are 45–67% and 61–73% for low and high discharge, respectively. Therefore, as runoff increases, the area with high TI values within the pool increases. A lower TI is observed for both bottom slopes in the corner of the wall, downstream of the crest walls, and between the side walls in the weir and channel. Figure 25 compares weir spacing with the distribution of TI values within the pool. The TI values are low at low flows and short distances between weirs. A maximum value of TI occurs at long spacing and where the plunging stream impinges on the bed and the area around the bed. TI ranges from 36 to 57%, 58–72%, and 47–76% for the highest flow in a wide pool area for L/B = 0.61, 1.22, and 1.83, respectively.

figure 24
Fig. 24
figure 25
Fig. 25

The average value of turbulence intensity (TIave) is plotted against q in Fig. 26. The increase in TI values with the increase in q values is seen in all models. For example, the average values of TI for Models A and B at L/B = 0.61 and slope of 10% increased from 23.9 to 33.5% and from 42 to 51.8%, respectively, with the increase in q from 0.1 to 0.27 m2/s. For a given discharge, a given gradient, and a given spacing of weirs, the TIave is higher in Model B than Model A. The presence of an orifice in the weirs increases the TI values in both types. For example, in Models A and B with L/B = 0.61 and q = 0.1 m2/s, the presence of an orifice increases TIave from 23.9 to 37.1% and from 42 to 48.8%, respectively. For each model, TIave in the pool increases with increasing bed slope. For Model B with q = 0.18 m2/s, TIave increases from 37.5 to 45.8% when you increase the invert slope from 5 to 10%. Increasing the distance between weirs increases the TIave in the pool. In Model B with S0 = 10% and q = 0.3 m2/s, the TIave in the pool increases from 51.8 to 63.7% as the distance between weirs increases from L/B = 0.61 to L/B = 0.183.

figure 26
Fig. 26

3.5 Energy Dissipation

To facilitate the passage of various target species through the pool of fishways, it is necessary to pay attention to the energy dissipation of the flow and to keep the flow velocity in the pool slow. The average volumetric energy dissipation (k) in the pool is calculated using the following basic formula:

�=����0��

(16)

where ρ is the water density, and H is the average water depth of the pool. The change in k versus Q for all models at two bottom slopes, S0 = 5%, and S0 = 10%, is shown in Fig. 27. Like the results of Yagci [8] and Kupferschmidt and Zhu [26], at a constant bottom slope, the energy dissipation in the pool increases with increasing discharge. The trend of change in k as a function of Q from the present study at a bottom gradient of S0 = 5% is also consistent with the results of Kupferschmidt and Zhu [26] for the fishway with rock weir. The only difference between the results is the geometry of the fishway and the combination of boulders instead of a solid wall. Comparison of the models shows that the conventional model has lower energy dissipation than the rectangular labyrinth for a given discharge. Also, increasing the distance between weirs decreases the volumetric energy dissipation for each model with the same bed slope. Increasing the slope of the bottom leads to an increase in volumetric energy dissipation, and an opening in the weir leads to a decrease in volumetric energy dissipation for both models. Therefore, as a guideline for volumetric energy dissipation, if the value within the pool is too high, the increased distance of the weir, the decreased slope of the bed, or the creation of an opening in the weir would decrease the volumetric dissipation rate.

figure 27
Fig. 27

To evaluate the energy dissipation inside the pool, the general method of energy difference in two sections can use:

ε=�1−�2�1

(17)

where ε is the energy dissipation rate, and E1 and E2 are the specific energies in Sects. 1 and 2, respectively. The distance between Sects. 1 and 2 is the same. (L is the distance between two upstream and downstream weirs.) Figure 28 shows the changes in ε relative to q (flow per unit width). The rectangular labyrinth weir (Model B) has a higher energy dissipation rate than the conventional weir (Model A) at a constant bottom gradient. For example, at S0 = 5%, L/B = 0.61, and q = 0.08 m3/s.m, the energy dissipation rate in Model A (conventional weir) was 0.261. In Model B (rectangular labyrinth weir), however, it was 0.338 (22.75% increase). For each model, the energy dissipation rate within the pool increases as the slope of the bottom increases. For Model B with L/B = 1.83 and q = 0.178 m3/s.m, the energy dissipation rate at S0 = 5% and 10% is 0.305 and 0.358, respectively (14.8% increase). Figure 29 shows an orifice’s effect on the pools’ energy dissipation rate. With an orifice in the weir, both models’ energy dissipation rates decreased. Thus, the reduction in energy dissipation rate varied from 7.32 to 9.48% for Model A and from 8.46 to 10.57 for Model B.

figure 28
Fig. 28
figure 29
Fig. 29

4 Discussion

This study consisted of entirely of numerical analysis. Although this study was limited to two weirs, the hydraulic performance and flow characteristics in a pooled fishway are highlighted by the rectangular labyrinth weir and its comparison with the conventional straight weir. The study compared the numerical simulations with laboratory experiments in terms of surface profiles, velocity vectors, and flow characteristics in a fish ladder pool. The results indicate agreement between the numerical and laboratory data, supporting the reliability of the numerical model in capturing the observed phenomena.

When the configuration of the weir changes to a rectangular labyrinth weir, the flow characteristics, the maximum and minimum area, and even the location of each hydraulic parameter change compared to a conventional weir. In the rectangular labyrinth weir, the flow is gradually directed to the sides as it passes the weir. This increases the velocity at the sides of the channel [21]. Therefore, the high-velocity area is located on the sides. In the downstream apex of the weir, the flow velocity is low, and this area may be suitable for swimming target fish. However, no significant change in velocity was observed at the conventional weir within the fish ladder. This resulted in an average increase in TKE of 32% and an average increase in TI of about 17% compared to conventional weirs.

In addition, there is a slight difference in the flow regime for both weir configurations. In addition, the rectangular labyrinth weir has a higher energy dissipation rate for a given discharge and constant bottom slope than the conventional weir. By reducing the distance between the weirs, this becomes even more intense. Finally, the presence of an orifice in both configurations of the weir increased the flow velocity at the orifice and in the middle of the pool, reducing the highest TKE value and increasing the values of TI within the pool of the fish ladder. This resulted in a reduction in volumetric energy dissipation for both weir configurations.

The results of this study will help the reader understand the direct effects of the governing geometric parameters on the hydraulic characteristics of a fishway with a pool and weir. However, due to the limited configurations of the study, further investigation is needed to evaluate the position of the weir’s crest on the flow direction and the difference in flow characteristics when combining boulders instead of a solid wall for this type of labyrinth weir [26]. In addition, hydraulic engineers and biologists must work together to design an effective fishway with rectangular labyrinth configurations. The migration habits of the target species should be considered when designing the most appropriate design [27]. Parametric studies and field observations are recommended to determine the perfect design criteria.

The current study focused on comparing a rectangular labyrinth weir with a conventional straight weir. Further research can explore other weir configurations, such as variations in crest position, different shapes of labyrinth weirs, or the use of boulders instead of solid walls. This would help understand the influence of different geometric parameters on hydraulic characteristics.

5 Conclusions

A new layout of the weir was evaluated, namely a rectangular labyrinth weir compared to a straight weir in a pool and weir system. The differences between the weirs were highlighted, particularly how variations in the geometry of the structures, such as the shape of the weir, the spacing of the weir, the presence of an opening at the weir, and the slope of the bottom, affect the hydraulics within the structures. The main findings of this study are as follows:

  • The calculated dimensionless discharge (Qt*) confirmed three different flow regimes: when the corresponding range of Qt* is smaller than 0.6, the regime of plunging flow occurs for values of L/B = 1.83. (L: distance of the weir; B: channel width). When the corresponding range of Qt* is greater than 0.5, transitional flow occurs at L/B = 1.22. On the other hand, if Qt* is greater than 1, the streaming flow is at values of L/B = 0.61.
  • For the conventional weir and the rectangular labyrinth weir with the plunging flow, it can be assumed that the discharge (Q) is proportional to 1.56 and 1.47h, respectively (h: water depth above the weir). This information is useful for estimating the discharge based on water depth in practical applications.
  • In the rectangular labyrinth weir, the high-velocity zone is located on the side walls between the top of the weir and the channel wall. A high-velocity variation within short distances of the weir. Low velocity occurs within the downstream apex of the weir. This area may be suitable for swimming target fish.
  • As the distance between weirs increased, the zone of maximum velocity increased. However, the zone of low speed decreased. The prevailing maximum velocity for a rectangular labyrinth weir at L/B = 0.61, 1.22, and 1.83 was 1.46, 1.65, and 1.84 m/s, respectively. The low mean velocities for these distances were 0.27, 0.44, and 0.72 m/s, respectively. This finding highlights the importance of weir spacing in determining the flow characteristics within the fishway.
  • The presence of an orifice in the weir increased the flow velocity at the orifice and in the middle of the pool, especially in a conventional weir. The increase ranged from 7.7 to 12.48%.
  • For a given bottom slope, in a conventional weir, the highest values of turbulent kinetic energy (TKE) are uniformly distributed in the upstream part of the weir in the cross section of the channel. In contrast, for the rectangular labyrinth weir, the highest TKE values were concentrated on the sides of the pool between the crest of the weir and the channel wall. The highest TKE value for the conventional and the rectangular labyrinth weir was 0.224 and 0.278 J/kg, respectively, at the highest bottom slope (S0 = 10%).
  • For a given discharge, bottom slope, and weir spacing, the average values of TI are higher for the rectangular labyrinth weir than for the conventional weir. At the highest discharge, the average range of turbulence intensity (TI) for the conventional and rectangular labyrinth weirs was between 24 and 45% and 15% and 62%, respectively. This reveals that the rectangular labyrinth weir may generate more turbulent flow conditions within the fishway.
  • For a given discharge and constant bottom slope, the rectangular labyrinth weir has a higher energy dissipation rate than the conventional weir (22.75 and 34.86%).
  • Increasing the distance between weirs decreased volumetric energy dissipation. However, increasing the gradient increased volumetric energy dissipation. The presence of an opening in the weir resulted in a decrease in volumetric energy dissipation for both model types.

Availability of data and materials

Data is contained within the article.

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Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

Yupeng Ren abc, Huiguang Zhou cd, Houjie Wang ab, Xiao Wu ab, Guohui Xu cd, Qingsheng Meng cd

Abstract

해저 퇴적물 흐름은 퇴적물을 심해로 운반하는 주요 수단 중 하나이며, 종종 장거리를 이동하고 수십 또는 수백 킬로미터에 걸쳐 상당한 양의 퇴적물을 운반합니다. 그것의 강력한 파괴력은 종종 이동 과정에서 잠수함 유틸리티에 심각한 손상을 초래합니다.

퇴적물 흐름의 퇴적물 농도는 주변 해수와의 밀도차를 결정하며, 이 밀도 차이는 퇴적물 흐름의 흐름 능력을 결정하여 이송된 퇴적물의 최종 퇴적 위치에 영향을 미칩니다. 본 논문에서는 다양한 미사 및 점토 중량비(미사/점토 비율이라고 함)를 갖는 다양한 퇴적물 농도의 퇴적물 흐름을 수로 테스트를 통해 연구합니다.

우리의 테스트 결과는 특정 퇴적물 구성에 대해 퇴적물 흐름이 가장 빠르게 이동하는 임계 퇴적물 농도가 있음을 나타냅니다. 4가지 미사/점토 비율 각각에 대한 임계 퇴적물 농도와 이에 상응하는 최대 속도가 구해집니다. 결과는 점토 함량이 임계 퇴적물 농도와 선형적으로 음의 상관 관계가 있음을 나타냅니다.

퇴적물 농도가 증가함에 따라 퇴적물의 흐름 거동은 흐름 상태에서 붕괴된 상태로 변환되고 흐름 거동이 변화하는 두 탁한 현탁액의 유체 특성은 모두 Bingham 유체입니다.

또한 본 논문에서는 퇴적물 흐름 내 입자 배열을 분석하여 위에서 언급한 결과에 대한 미시적 설명도 제공합니다.

Submarine sediment flows is one of the main means for transporting sediment to the deep sea, often traveling long-distance and transporting significant volumes of sediment for tens or even hundreds of kilometers. Its strong destructive force often causes serious damage to submarine utilities on its course of movement. The sediment concentration of the sediment flow determines its density difference with the ambient seawater, and this density difference determines the flow ability of the sediment flow, and thus affects the final deposition locations of the transported sediment. In this paper, sediment flows of different sediment concentration with various silt and clay weight ratios (referred to as silt/clay ratio) are studied using flume tests. Our test results indicate that there is a critical sediment concentration at which sediment flows travel the fastest for a specific sediment composition. The critical sediment concentrations and their corresponding maximum velocities for each of the four silt/clay ratios are obtained. The results further indicate that the clay content is linearly negatively correlated with the critical sediment concentration. As the sediment concentration increases, the flow behaviors of sediment flows transform from the flow state to the collapsed state, and the fluid properties of the two turbid suspensions with changing flow behaviors are both Bingham fluids. Additionally, this paper also provides a microscopic explanation of the above-mentioned results by analyzing the arrangement of particles within the sediment flow.

Introduction

Submarine sediment flows are important carriers for sea floor sediment movement and may carry and transport significant volumes of sediment for tens or even hundreds of kilometers (Prior et al., 1987; Pirmez and Imran, 2003; Zhang et al., 2018). Earthquakes, storms, and floods may all trigger submarine sediment flow events (Hsu et al., 2008; Piper and Normark, 2009; Pope et al., 2017b; Gavey et al., 2017). Sediment flows have strong forces during the movement, which will cause great harm to submarine structures such as cables and pipelines (Pope et al., 2017a). It was first confirmed that the cable breaking event caused by the sediment flow occurred in 1929. The sediment flow triggered by the Grand Banks earthquake damaged 12 cables. According to the time sequence of the cable breaking, the maximum velocity of the sediment flow is as high as 28 m/s (Heezen and Ewing, 1952; Kuenen, 1952; Heezen et al., 1954). Subsequent research shows that the lowest turbidity velocity that can break the cable also needs to reach 19 m/s (Piper et al., 1988). Since then, there have been many damage events of submarine cables and oil and gas pipelines caused by sediment flows in the world (Hsu et al., 2008; Carter et al., 2012; Cattaneo et al., 2012; Carter et al., 2014). During its movement, the sediment flow will gradually deposit a large amount of sediment carried by it along the way, that is, the deposition process of the sediment flow. On the one hand, this process brings a large amount of terrestrial nutrients and other materials to the ocean, while on the other hand, it causes damage and burial to benthic organisms, thus forming the largest sedimentary accumulation on Earth – submarine fans, which are highly likely to become good reservoirs for oil and gas resources (Daly, 1936; Yuan et al., 2010; Wu et al., 2022). The study on sediment flows (such as, the study of flow velocity and the forces acting on seabed structures) can provide important references for the safe design of seabed structures, the protection of submarine ecosystems, and exploration of turbidity sediments related oil and gas deposits. Therefore, it is of great significance to study the movement of sediment flows.

The sediment flow, as a highly sediment-concentrated fluid flowing on the sea floor, has a dense bottom layer and a dilute turbulent cloud. Observations at the Monterey Canyon indicated that the sediment flow can maintain its movement over long distances if its bottom has a relatively high sediment concentration. This dense bottom layer can be very destructive along its movement path to any facilities on the sea floor (Paull et al., 2018; Heerema et al., 2020; Wang et al., 2020). The sediment flow mentioned in this research paper is the general term of sediment density flow.

The sediment flow, which occurs on the seafloor, has the potential to cause erosion along its path. In this process, the suspended sediment is replenished, allowing the sediment flow to maintain its continuous flow capacity (Zhao et al., 2018). The dynamic force of sediment flow movement stem from its own gravity and density difference with surrounding water. In cases that the gravity drive of the slope is absent (on a flat sea floor), the flow velocity and distance of sediment flows are essentially determined by the sediment composition and concentration of the sediment flows as previous studies have demonstrated. Ilstad et al. (2004) conducted underwater flow tests in a sloped tank and employed high speed video camera to perform particle tracking. The results indicated that the premixed sand-rich and clay-rich slurries demonstrated different flow velocity and flow behavior. Using mixed kaolinite(d50 = 6 μm) and silica flour(d50 = 9 μm) in three compositions with total volumetric concentration ranged 22% or 28%, Felix and Peakall (2006) carried out underwater flow tests in a 5° slope Perspex channel and found that the flow ability of sediment flows is different depending on sediment compositions and concentrations. Sumner et al. (2009) used annular flume experiments to investigate the depositional dynamics and deposits of waning sediment-laden flows, finding that decelerating fast flows with fixed sand content and variable mud content resulted in four different deposit types. Chowdhury and Testik (2011) used lock-exchange tank, and experimented the kaolin clay sediment flows in the concentration range of 25–350 g/L, and predicted the fluid mud sediment flows propagation characteristics, but this study focused on giving sediment flows propagate phase transition time parameters, and is limited to clay. Lv et al. (2017) found through experiments that the rheological properties and flow behavior of kaolin clay (d50 = 3.7 μm) sediment flows were correlated to clay concentrations. In the field monitoring conducted by Liu et al. (2023) at the Manila Trench in the South China Sea in 2021, significant differences in the velocity, movement distance, and flow morphology of turbidity currents were observed. These differences may be attributed to variations in the particle composition of the turbidity currents.

On low and gentle slopes, although sediment flow with sand as the main sediment composition moves faster, it is difficult to propagate over long distances because sand has greater settling velocity and subaqueous angle of repose. Whereas the sediment flows with silt and clay as main composition may maintain relatively stable currents. Although its movement speed is slow, it has the ability to propagate over long distances because of the low settling rate of the fine particles (Ilstad et al., 2004; Liu et al., 2023). In a field observation at the Gaoping submarine canyon, the sediments collected from the sediment flows exhibited grain size gradation and the sediment was mostly composed of silt and clay (Liu et al., 2012). At the largest deltas in the world, for instance, the Mississippi River Delta, the sediments are mainly composed of silt and clay, which generally distributed along the coast in a wide range and provided the sediment sources for further distribution. The sediment flows originated and transported sediment from the coast to the deep sea are therefore share the same sediment compositions as delta sediments. To study the sediment flows composed of silt and clay is of great importance.

The sediment concentration of the sediment flows determines the density difference between the sediment flows and the ambient water and plays a key role in its flow ability. For the sediment flow with sediment composed of silt and clay, low sediment concentration means low density and therefore leads to low flow ability; however, although high sediment concentration results in high density, since there is cohesion between fine particles, it changes fluid properties and leads to low flow ability as well. Therefore, there should be a critical sediment concentration with mixed composition of silt and clay, at which the sediment flow maintains its strongest flow capacity and have the highest movement speed. In other words, the two characteristics of particle diameter and concentration of the sediment flow determine its own motion ability, which, if occurs, may become the most destructive force to submarine structures.

The objectives of this work was to study how the sediment composition (measured in relative weight of silt and clay, and referred as silt/clay ratio) and sediment concentration affect flow ability and behavior of the sediment flows, and to quantify the critical sediment concentration at which the sediment flows reached the greatest flow velocity under the experiment setting. We used straight flume without slope and conducted a series of flume tests with varying sediment compositions (silt-rich or clay-rich) and concentrations (96 to 1212 g/L). Each sediment flow sample was tested and analyzed for rheological properties using a rheometer, in order to characterize the relationship between flow behavior and rheological properties. Combined with the particle diameter, density and viscosity characteristics of the sediment flows measured in the experiment, a numerical modeling study is conducted, which are mutually validated with the experimental results.

The sediment concentration determines the arrangements of the sediment particles in the turbid suspension, and the arrangement impacts the fluid properties of the turbid suspension. The microscopic mode of particle arrangement in the turbid suspension can be constructed to further analyze the relationship between the fluid properties of turbid suspension and the flow behaviors of the sediment flow, and then characterize the critical sediment concentration at which the sediment flow runs the fastest. A simplified microscopic model of particle arrangement in turbid suspension was constructed to analyze the microscopic arrangement characteristics of sediment particles in turbid suspension with the fastest velocity.

Section snippets

Equipment and materials

The sediment flows flow experiments were performed in a Perspex channel with smooth transparent walls. The layout and dimensions of the experimental set-up were shown in Fig. 1. The bottom of the channel was flat and straight, and a gate was arranged to separate the two tanks. In order to study the flow capacity of turbidity currents from the perspective of their own composition (particle size distribution and concentration), we used a straight channel instead of an inclined one, to avoid any

Relationship between sediment flow flow velocity and sediment concentration

After the sediment flow is generated, its movement in the first half (50 cm) of the channel is relatively stable, and there is obvious shock diffusion in the second half. The reason is that the excitation wave (similar to the surge) will be formed during the sediment flow movement, and its speed is much faster than the speed of the sediment flow head. When the excitation wave reaches the tail of the channel, it will be reflected, thus affecting the subsequent flow of the sediment flow.

Sediment flows motion simulation based on FLOW-3D

As a relatively mature 3D fluid simulation software, FLOW-3D can accurately predict the free surface flow, and has been used to simulate the movement process of sediment flows for many times (Heimsund, 2007). The model adopted in this paper is RNG turbulence model, which can better deal with the flow with high strain rate and is suitable for the simulation of sediment flows with variable shape during movement. The governing equations of the numerical model involved include continuity equation,

Conclusions

In this study, we conducted a series of sediment flow flume tests with mixed silt and clay sediment samples in four silt/clay ratios on a flat slope. Rheological measurements were carried out on turbid suspension samples and microstructure analysis of the sediment particle arrangements was conducted, we concluded that:

  • (1)The flow velocity of the sediment flow is controlled by the sediment concentration and its own particle diameter composition, the flow velocity increased with the increase of the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China [Grant no. 42206055]; the National Natural Science Foundation of China [Grant no. 41976049]; and the National Natural Science Foundation of China [Grant no. 42272327].

References (39)

There are more references available in the full text version of this article.

원본 보기
Figure 2-15: Système expérimental du plan incliné

새로운 콘크리트의 유체 흐름 모델링

Sous la direction de :
Marc Jolin, directeur de recherche
Benoit Bissonnette, codirecteur de recherche

Modélisation de l’écoulement du béton frais

Abstract

현재의 기후 비상 사태와 기후 변화에 관한 다양한 과학적 보고서를 고려할 때 인간이 만든 오염을 대폭 줄이는 것은 필수적이며 심지어 중요합니다. 최신 IPCC(기후변화에 관한 정부 간 패널) 보고서(2022)는 2030년까지 배출량을 절반으로 줄여야 함을 나타내며, 지구 보존을 위해 즉각적인 조치를 취해야 한다고 강력히 강조합니다.

이러한 의미에서 콘크리트 생산 산업은 전체 인간 이산화탄소 배출량의 4~8%를 담당하고 있으므로 환경에 미치는 영향을 줄이기 위한 진화가 시급히 필요합니다.

본 연구의 주요 목적은 이미 사용 가능한 기술적 품질 관리 도구를 사용하여 생산을 최적화하고 혼합 시간을 단축하며 콘크리트 폐기물을 줄이기 위한 신뢰할 수 있고 활용 가능한 수치 모델을 개발함으로써 이러한 산업 전환에 참여하는 것입니다.

실제로, 혼합 트럭 내부의 신선한 콘크리트의 거동과 흐름 프로파일을 더 잘 이해할 수 있는 수치 시뮬레이션을 개발하면 혼합 시간과 비용을 더욱 최적화할 수 있으므로 매우 유망합니다. 이러한 복잡한 수치 도구를 활용할 수 있으려면 수치 시뮬레이션을 검증, 특성화 및 보정하기 위해 기본 신 콘크리트 흐름 모델의 구현이 필수적입니다.

이 논문에서는 세 가지 단순 유동 모델의 개발이 논의되고 얻은 결과는 신선한 콘크리트 유동의 수치적 거동을 검증하는 데 사용됩니다. 이러한 각 모델은 강점과 약점을 갖고 있으며, 신선한 콘크리트의 유변학과 유동 거동을 훨씬 더 잘 이해할 수 있는 수치 작업 환경을 만드는 데 기여합니다.

따라서 이 연구 프로젝트는 새로운 콘크리트 생산의 완전한 모델링을 위한 진정한 관문입니다.

In view of the current climate emergency and the various scientific reports on climate change, it is essential and even vital to drastically reduce man-made pollution. The latest IPCC (Intergovernmental Panel on Climate Change) report (2022) indicates that emissions must be halved by 2030 and strongly emphasizes the need to act immediately to preserve the planet. In this sense, the concrete production industry is responsible for 4-8% of total human carbon dioxide emissions and therefore urgently needs to evolve to reduce its environmental impact. The main objective of this study is to participate in this industrial transition by developing a reliable and exploitable numerical model to optimize the production, reduce mixing time and also reduce concrete waste by using technological quality control tools already available. Indeed, developing a numerical simulation allowing to better understand the behavior and flow profiles of fresh concrete inside a mixing-truck is extremely promising as it allows for further optimization of mixing times and costs. In order to be able to exploit such a complex numerical tool, the implementation of elementary fresh concrete flow models is essential to validate, characterize and calibrate the numerical simulations. In this thesis, the development of three simple flow models is discussed and the results obtained are used to validate the numerical behavior of fresh concrete flow. Each of these models has strengths and weaknesses and contributes to the creation of a numerical working environment that provides a much better understanding of the rheology and flow behavior of fresh concrete. This research project is therefore a real gateway to a full modelling of fresh concrete production.


Key words

fresh concrete, rheology, numerical simulation, mixer-truck, rheological probe.

Figure 2-15: Système expérimental du plan incliné
Figure 2-15: Système expérimental du plan incliné
Figure 2-19: Essai d'affaissement au cône d'Abrams
Figure 2-19: Essai d’affaissement au cône d’Abrams

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Figure 1. Three-dimensional finite element model of local scouring of semi-exposed submarine cable.

반노출 해저케이블의 국부 정련과정 및 영향인자에 대한 수치적 연구

Numerical Study of the Local Scouring Process and Influencing Factors of Semi-Exposed Submarine Cables

by Qishun Li,Yanpeng Hao *,Peng Zhang,Haotian Tan,Wanxing Tian,Linhao Chen andLin Yang

School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China

*Author to whom correspondence should be addressed.J. Mar. Sci. Eng.2023, 11(7), 1349; https://doi.org/10.3390/jmse11071349

Received: 10 June 2023 / Revised: 19 June 2023 / Accepted: 27 June 2023 / Published: 1 July 2023(This article belongs to the Section Ocean Engineering)

일부 수식이 손상되어 표시될 수 있습니다. 이 경우 원문을 참조하시기 바랍니다.

Abstract

Local scouring might result in the spanning of submarine cables, endangering their mechanical and electrical properties. In this contribution, a three-dimensional computational fluid dynamics simulation model is developed using FLOW-3D, and the scouring process of semi-exposed submarine cables is investigated. The effects of the sediment critical Shields number, sediment density, and ocean current velocity on local scouring are discussed, and variation rules for the submarine cables’ spanning time are provided. The results indicate that three scouring holes are formed around the submarine cables. The location of the bottom of the holes corresponds to that of the maximum shear velocity. The continuous development of scouring holes at the wake position leads to the spanning of the submarine cables. The increase in the sediment’s critical Shields number and sediment density, as well as the decrease in the ocean current velocity, will extend the time for maintaining the stability of the upstream scouring hole and retard the development velocity of the wake position and downstream scouring holes. The spanning time has a cubic relationship with the sediment’s critical Shields number, a linear relationship with the sediment density, and an exponential relationship with the ocean current velocity. In this paper, the local scouring process of semi-exposed submarine cables is studied, which provides a theoretical basis for the operation and maintenance of submarine cables.

Keywords: 

submarine cable; local scouring; numerical simulation; computational fluid dynamics

1. Introduction

As a key piece of equipment in cross-sea power grids, submarine cables are widely used to connect autonomous power grids, supply power to islands or offshore platforms, and transmit electric power generated by marine renewable energy installations to onshore substations [1]. Once submarine cables break down due to natural disasters or human-made damage, the normal operation of other marine electric power equipment connected to them may be affected. These chain reactions will cause great economic losses and serious social impacts [2].

To protect submarine cables, they are usually buried 1 to 3 m below the seabed [3]. However, submarine cables are still confronted with potential threats from the complex subsea environment. Under the influence of fishing, anchor damage, ocean current scouring, and other factors, the sediment above submarine cables will always inevitably migrate. When a submarine cable is partially exposed, the scouring at this position will be exacerbated; eventually, it will cause the submarine cable to span. According to a field investigation of the 500 kV oil-filled submarine cable that is part of the Hainan networking system, the total length of the span is 49 m [4]. Under strong ocean currents, spanning submarine cables may experience vortex-induced vibrations. Fatigue stress caused by vortex-induced vibrations may lead to metal sheath rupture [5], which endangers the mechanical and electrical properties of submarine cables. Therefore, understanding the local scouring processes of partially exposed submarine cables is crucial for predicting scouring patterns. This is the basis for developing effective operation and maintenance strategies for submarine cables.

The mechanism and influencing factors of sediment erosion have been examined by researchers around the world. In 1988, Sumer [6] conducted experiments to show that the shedding vortex in the wake of a pipeline would increase the Shields parameter by 3–4 times, which would result in severe scouring. In 1991, Chiew [7] performed experiments to prove that the maximum scouring depth could be obtained when the pipeline was located on a flat bed and was scoured by a unidirectional water flow. Based on the test results, they provided a prediction formula for the maximum scouring depth. In 2003, Mastbergen [8] proposed a one-dimensional, steady-state numerical model of turbidity currents, which considered the negative pore pressures in the seabed. The calculated results of this model were basically consistent with the actual scouring of a submarine canyon. In 2007, Dey [9] presented a semitheoretical model for the computation of the maximum clear-water scour depth below underwater pipelines in uniform sediments under a steady flow, and the predicted scour depth in clear water satisfactorily agreed with the observed values. In 2008, Dey [10] conducted experiments on clear-water scour below underwater pipelines under a steady flow and obtained a variation pattern of the depth of the scouring hole. In 2008, Liang [11] used a two-dimensional numerical simulation to study the scouring process of a tube bundle under the action of currents and waves. They discovered that, compared with the scouring of a single tube, the scouring depth of the tube bundle was deeper, and the scouring time was longer. In 2012, Yang [12] found that placing rubber sheets under pipes can greatly accelerate their self-burial. The rubber sheets had the best performance when their length was about 1.5 times the size of the pipe. In 2020, Li [13] investigated the two-dimensional local scour beneath two submarine pipelines in tandem under wave-plus-current conditions via numerical simulation. They found that for conditions involving waves plus a low-strength current, the scour pattern beneath the two pipelines behaved like that in the pure-wave condition. Conversely, when the current had equal strength to the wave-induced flow, the scour pattern beneath the two pipelines resembled that in the pure-current condition. In 2020, Guan [14] studied and discussed the interactive coupling effects among a vibrating pipeline, flow field, and scour process through experiments, and the experimental data showed that the evolution of the scour hole had significant influences on the pipeline vibrations. In 2021, Liu [15] developed a two-dimensional finite element numerical model and researched the local scour around a vibrating pipeline. The numerical results showed that the maximum vibration amplitude of the pipeline could reach about 1.2 times diameter, and the maximum scour depth occurred on the wake side of the vibrating pipeline. In 2021, Huang [16] carried out two-dimensional numerical simulations to investigate the scour beneath a single pipeline and piggyback pipelines subjected to an oscillatory flow condition at a KC number of 11 and captured typical steady-streaming structures around the pipelines due to the oscillatory flow condition. In 2021, Cui [17] investigated the characteristics of the riverbed scour profile for a pipeline buried at different depths under the condition of riverbed sediments with different particle sizes. The results indicated that, in general, the equilibrium scour depth changed in a spoon shape with the gradual increase in the embedment ratio. In 2022, Li [18] used numerical simulation to study the influence of the burial depth of partially buried pipelines on the surrounding flow field, but they did not investigate the scour depth. In 2022, Zhu [19] performed experiments to prove that the scour hole propagation rate under a pipeline decreases with an increasing pipeline embedment ratio and rises with the KC number. In 2022, Najafzadeh [20] proposed equations for the prediction of the scouring propagation rate around pipelines due to currents based on a machine learning model, and the prediction results were consistent with the experimental data. In 2023, Ma [21] used the computational fluid dynamics coarse-grained discrete element method to simulate the scour process around a pipeline. The results showed that this method can effectively reduce the considerable need for computing resources and excessive computation time. In 2023, through numerical simulations, Hu [22] discovered that the water velocity and the pipeline diameter had a significant effect on the depth of scouring.

In the preceding works, the researchers investigated the mechanism of sediment scouring and the effect of various factors on the local scouring of submarine pipelines. However, submarine cables are buried beneath the seabed, while submarine pipelines are erected above the seabed. The difference in laying methods leads to a large discrepancy between their local scouring processes. Therefore, the conclusions of the above investigations are not applicable to the local scouring of submarine cables. Currently, there is no report on the research of the local scouring of partially exposed submarine cables.

In this paper, a three-dimensional computational fluid dynamics (CFD) finite element model, based on two-phase flow, is established using FLOW-3D. The local scouring process of semi-exposed submarine cables under steady-state ocean currents is studied, and the variation rules of the depth and the shape of the scouring holes, as well as the shear velocity with time, are obtained. By setting different critical Shields numbers of the sediment, different sediment densities, and different ocean current velocities, the change rule of the scouring holes’ development rate and the time required for the spanning of submarine cables are explored.

2. Sediment Scouring Model

In the sediment scouring model, the sediment is set as the dispersed particle, which is regarded as a kind of quasifluid. In this context, sediment scouring is considered as a two-phase flow process between the liquid phase and solid particle phase. The sediment in this process is further divided into two categories: one is suspended in the fluid, and the other is deposited on the bottom.When the local Shields number of sediment is greater than the critical Shields number, the deposited sediment will be transformed into the suspended sediment under the action of ocean currents. The calculation formulae of the local Shields numbers θ and the critical Shields numbers 

θcr of sediment is given as [23,24

]

𝜃=𝑈2𝑓(𝜌𝑠/𝜌𝑓−1)𝑔𝑑50,�=��2(��/��−1)��50,(1)

𝜃𝑐𝑟=0.31+1.2𝐷∗+0.055(1−𝑒−0.02𝐷∗),���=0.31+1.2�*+0.055(1−�−0.02�*),(2)

𝐷∗=𝑑50𝜌𝑓(𝜌𝑠−𝜌𝑓)𝑔/𝜇2−−−−−−−−−−−−−−√3,�*=�50��(��−��)�/�23,(3)where 

Uf is the shearing velocity of bed surface, 

ρs is the density of the sediment particle, 

ρf is the fluid density, g is the acceleration of gravity, d

50 is the median size of sediment, and μ is the dynamic viscosity of sediment.And each sediment particle suspended in the fluid obeys the equations for mass conservation and energy conservation

∂𝑐𝑠∂𝑡+∇⋅(𝑢𝑐𝑠)=0,∂��∂�+∇⋅(�¯��)=0,(4)

∂𝑢𝑠∂𝑡+𝑢⋅∇𝑢𝑠=−1𝜌𝑠∇𝑃+𝐹−𝐾𝑓𝑠𝜌𝑠𝑢𝑟,∂��∂�+�¯⋅∇��=−1��∇�+�−�������,(5)where 

cs is the concentration of the sediment particle, 

𝑢�¯ is the mean velocity vector of the fluid and the sediment particle, 

us is the velocity of the sediment particle, 

fs is the volume fraction of the sediment particle, P is the pressure, F is the volumetric and viscous force, K is the drag force, and 

ur is the relative velocity.

3. Numerical Setup and Modeling

In this paper, a three-dimensional submarine cable local scouring simulation model is established by FLOW-3D. Based on the numerical simulation, the process of the submarine cable, which gradually changes from semi-exposed to the spanning state under the steady-state ocean current, is studied. The geometric modeling, the mesh division, the physical field setup, and the grid independent test of CFD numerical model are as follows.

3.1. Geometric Modeling and Mesh Division

A three-dimensional (3D) numerical model of the local scouring of a semi-exposed submarine cable is established, which is shown in Figure 1. The dimensions of the model are marked in Figure 1. The inlet direction of the ocean current is defined as the upstream of the submarine cable (referred to as upstream), and the outlet direction of the ocean current is defined as the downstream of the submarine cable (referred to as downstream).

Jmse 11 01349 g001 550

Figure 1. Three-dimensional finite element model of local scouring of semi-exposed submarine cable.

The submarine cable with a diameter of 0.2 m is positioned on sediment that is initially in a semi-exposed state. When the length of the span is short, the submarine cable will not show obvious deformation due to gravity or scouring from the ocean current. Therefore, the submarine cable surface is set as the fixed boundary. The model’s left boundary is set as the inlet, the right boundary is set as the outlet, the front and rear boundaries are set as symmetry, and the bottom boundary is set as the non-slip wall. Since the water depth above the submarine cable is more than 0.6 m in practice, the top boundary of the model is also set as symmetry. The sediment near the inlet and the outlet will be carried by ocean currents, which leads to the abnormal scouring terrain. At each end of the sediment, a baffle (thickness of 3 cm) is installed to ensure that the simulation results can reflect the real situation.

Due to the fact that the flow field around the semi-exposed submarine cable is not a simple two-dimensional symmetrical distribution, it should be solved by three-dimensional numerical simulation. Considering the accuracy and efficiency of the calculation, the size of mesh is set to 0.02 m. The total number of meshes after the dissection is 133,254.

3.2. Physical Field Setup

The CFD finite element model contains four physical field modules: sediment scouring module, gravity and non-inertial reference frame module, density evaluation module, and viscosity and turbulence module. In this paper, the renormalization group (RNG) k–ε turbulence model is used, which has high computational accuracy for turbulent vortices. Therefore, this turbulence model is suitable for calculating the sediment scouring process around the semi-exposed submarine cable [25]. The key parameters of the numerical simulation are referring to the survey results of submarine sediments in the Korean Peninsula [26], as listed in Table 1.Table 1. Key parameters of numerical simulation.

Table

3.3. Mesh Independent Test

In order to eliminate errors caused by the quantity of grids in the calculation process, two sizes of mesh are set on the validation model, and the scour profiles under different mesh sizes are compared. The validation model is shown in Figure 2, and the scouring terrain under different mesh size is given in Figure 3.

Jmse 11 01349 g002 550

Figure 2. Validation model.

Jmse 11 01349 g003 550

Figure 3. Scouring terrain under different mesh sizes.

It can be seen from Figure 3 that with the increase in the number of meshes, the scouring terrain of the verification model changes slightly, and the scouring depth is basically unchanged. Considering the accuracy of the numerical simulation and the calculation’s time cost, it is reasonable to consider setting the mesh size to 0.02 m.

4. Results and Analysis

4.1. Analysis of Local Scouring Process

Based on the CFD finite element numerical simulation, the local scouring process of the submarine cable under the steady-state ocean current is analyzed. The end time of the simulation is 9 h, the initial time step is 0.01 s, and the fluid velocity is 0.40 m/s. Simulation results are saved every minute. Figure 4 illustrates the scouring terrain around the semi-exposed submarine cable, which has been scoured by the steady-state current for 5 h.

Jmse 11 01349 g004 550

Figure 4. Scouring terrain around semi-exposed submarine cable (scour for 5 h).

As can be seen from Figure 4, three scouring holes were separately formed in the upstream wake position and downstream of the semi-exposed submarine cable. The scouring holes are labeled according to their locations. The variation of the scouring terrain around the semi-exposed submarine cable over time is given in Figure 5. The red circle in the picture corresponds to the position of the submarine cable, and the red box in the legend marks the time when the submarine cable is spanning.

Jmse 11 01349 g005 550

Figure 5. Variation of scouring terrain around semi-exposed submarine cable adapted to time.

From Figure 5, in the first hour of scouring, the upstream (−0.5 m to −0.1 m) and downstream (0.43 m to 1.5 m) scouring holes appeared. The upstream scouring hole was relatively flat with depth of 0.04 m. The depth of the downstream scouring hole increased with the increase in distance, and the maximum depth was 0.13 m. The scouring hole that developed at the wake position was very shallow, and its depth was only 0.007 m.

In the second hour of scouring, the upstream scouring hole’s depth remained nearly constant. The depth of the downstream scouring hole only increased by 0.002 m. The scouring hole at the wake position developed steadily, and its depth increased from 0.007 m to 0.014 m.

The upstream and downstream scouring holes did not continue to develop during the third to the sixth hour. Compared to the first two hours, the development of scouring holes at the wake position accelerated significantly, with an average growth rate of 0.028 m/h. The growth rate in the fifth hour of the scouring hole at the wake position was slightly faster than the other times. After 6 h of scouring, the sediment on the right side of the submarine cable had been hollowed out.

In the seventh and the eighth hour of scouring, the upstream scouring hole’s depth increased slightly, the downstream scouring hole still remained stable, and the depth of the scouring hole at wake position increased by 0.019 m. The sediment under the submarine cable was gradually eroded as well. By the end of the eighth hour, the lower right part of the submarine cable had been exposed to water as well.

At 8 h 21 min of the scouring, the submarine cable was completely spanned, and the scouring holes were connected to each other. Within the next 10 min, the development of the scouring holes sped up significantly, and the maximum depth of scouring holes increased greatly to 0.27 m.

In reference [17], researchers have studied the local scouring process of semi-buried pipelines in sandy riverbeds through experiments. The test results show that the scouring process can be divided into a start-up stage, micropore formation stage, extension stage, and equilibrium stage. In this paper, the first three stages are simulated, and the results are in good agreement with the experiment, which proves the accuracy of the present numerical model.

In this research, the velocity of ocean currents at the sediment surface is defined as the shear velocity, which plays an important role in the process of local scouring. Figure 6 provides visual data on how the shear velocity varies over time.

Jmse 11 01349 g006 550

Figure 6. Shear velocity changes in the scouring process.

The semi-exposed submarine cable protrudes from the seabed, which makes the shear velocity of its surface much higher than other locations. After the submarine cable is spanned, the shear velocity of the scouring hole surface below it is taken. This is the reason for the sudden change of shear velocity at the submarine cable’s location in Figure 6.The shear velocity in the initial state of the upstream scouring hole is obviously greater than in subsequent times. After 1 h of scouring, the shear velocity in the upstream scouring hole rapidly decreased from 1.1 × 10

−2 m/s to 3.98 × 10

−3 m/s and remained stable until the end of the sixth hour. This phenomenon explains why the upstream scouring hole developed rapidly in the first hour but remained stable for the following 5 h.The shear velocity in the downstream scouring hole reduced at first and then increased; its initial value was 1.41 × 10

−2 m/s. It took approximately 5 h for the shear velocity to stabilize, and the stable shear velocity was 2.26 × 10

−3 m/s. Therefore, compared with the upstream scouring hole, the downstream scouring hole was deeper and required more time to reach stability.The initial shear velocity in the scouring hole at the wake position was only 7.1 × 10

−3 m/s, which almost does not change in the first hour. This leads to a very slow development of the scouring hole at the wake position in the early stages. The maximum shear velocity in this scouring hole gradually increased to 1.05 × 10

−2 m/s from the second to the fifth hour, and then decreased to 6.61 × 10

−3 m/s by the end of the eighth hour. This is why the scouring hole at the wake position grows fastest around the fifth hour. Consistent with the pattern of change in the scouring hole’s terrain, the location of the maximal shear velocity also shifted to the right with time.

The shear velocity of all three scouring holes rose dramatically in the last hour. Combined with the terrain in Figure 5, this can be attributed to the complete spanning of the submarine cable.

From Equations (3)–(5), one can see the movement of the sediment is related directly with the sediment’s critical Shields number, sediment density, and ocean current velocity. Based on the parameters in Table 1, the influence of the above parameters on the local scouring process of semi-exposed submarine cables will be discussed.

4.2. Influence Factors

4.2.1. Sediment’s Critical Shields Number

The sediment’s critical Shields number 

θcr is set as 0.02, 0.03, 0.04, 0.05, 0.06, and 0.07, and the variations of scouring terrain over time under each 

θcr are displayed in Figure 7.

Jmse 11 01349 g007 550

Figure 7. Influence of sediment’s critical Shields number 

θcr on local scouring around semi-exposed submarine cable: (a

) θcr = 0.02; (b

) θcr = 0.03; (c

) θcr = 0.04; (d

) θcr = 0.05; (e

) θcr = 0.06; and (f

) θcr = 0.07.From Figure 7, one can see that a change in 

θcr will affect the depth of the upstream scouring hole and the development speed of the scouring hole at the wake position, but it will have no significant impact on the expansion of the downstream scouring hole.Under conditions of different 

θcr, the upstream scouring hole will reach a temporary plateau within 1 h, at which time the stable depth will be about 0.04 m. When 

θcr ≤ 0.05, the upstream scouring hole will continue to expand after a few hours. The stable time is obviously affected by 

θcr, which will gradually increase from 1 h to 11 h with the increase in 

θcr. The terrain of the upstream scouring hole will gradually convert to deep on the left and to shallow on the right. Since the scouring hole at the wake position has not been stable, its state at the time of submarine cable spanning is studied emphatically. In the whole process of scouring, the scouring hole at the wake position continues to develop and does not reach a stable state. With the increase in 

θcr, the development velocity of the scouring hole at the wake position will decrease considerably. Its average evolution velocity decreases from 3.88 cm/h to 1.62 cm/h, and its depth decreases from 21.9 cm to 18.8 cm. Under the condition of each 

θcr, the downstream scouring hole will stabilize within 1 h, and the stable depth will be basically unchanged (all about 13.5 cm).As 

θcr increases, so does the sediment’s ability to withstand shearing forces, which will cause it to become increasingly difficult to be eroded or carried away by ocean currents. This effect has been directly reflected in the depth of scouring holes (upstream and wake position). Due to the blocking effect of semi-exposed submarine cables, the wake is elongated, which is why the downstream scouring hole develops before the scouring hole at the wake position and quickly reaches a stable state. However, due to the high wake intensity, this process is not significantly affected by the change of 

θcr.

4.2.2. Sediment Density

The density of sediment 

ρs is set as 1550 kg/m

3, 1600 kg/m

3, 1650 kg/m

3, 1700 kg/m

3, 1750 kg/m

3, and 1800 kg/m

3, and the variation of scouring terrain over time under each 

ρs are displayed in Figure 8.

Jmse 11 01349 g008 550

Figure 8. Influence of sediment density 

ρs on local scouring around semi-exposed submarine cable: (a

) ρs = 1550 kg/m

3; (b) ρs = 1600 kg/m

3; (c) ρs = 1650 kg/m

3; (d) ρs = 1700 kg/m

3; (e) ρs = 1750 kg/m

3; and (f

) ρs = 1800 kg/m

3.From Figure 8, one can see that a change in 

ρs will also affect the depth of the upstream scouring hole and the development speed of the scouring hole at the wake position. In addition, it can even have an impact on the downstream scouring hole depth.Under different 

ρs conditions, the upstream scouring hole will always reach a temporary stable state in 1 h, at which time the stable depth will be 0.04 m. When 

ρs ≤ 1750 kg/m

3, the upstream scouring hole will continue to expand after a few hours. The stabilization time of upstream scouring hole is more clearly affected by 

ρs, which will gradually increase from 3 h to 13 h with the increase in 

ρs. The terrain of the upstream scouring hole will gradually change to deep on the left and to shallow on the right. Since the scouring hole at the wake position has not been stable, its state at the time of the submarine cable spanning is studied emphatically, too. In the whole process of scouring, the scouring hole at the wake position continues to develop and does not reach a stable state. When 

ρs is large, the development rate of scouring hole obviously decreased with time. With the increase in 

ρs, the development velocity of the scouring hole at the wake position reduces from 3.38 cm/h to 1.14 cm/h, and the depth of this scouring hole declines from 20 cm to 15 cm. As 

ρs increases, the stabilization time of the downstream scouring hole increases from less than 1 h to about 2 h, but the stabilization depth of the downstream scouring hole remains essentially the same (all around 13.5 cm).As can be seen from Equation (1), the increase in 

ρs will reduce the Shields number, thus weakening the shear action of the sediment by the ocean current, which explains the extension of the stability time of the upstream scouring hole. At the same time, with the increase in the depth of scouring hole at the wake position, its shear velocity will decreases. Therefore, under a larger 

ρs value, the development speed of scouring hole at the wake position will decrease significantly with time. Possibly for the same reason, 

ρs can affect the development rate of downstream scouring hole.

4.2.3. Ocean Current Velocity

The ocean current velocity v is set as 0.35 m/s, 0.40 m/s, 0.45 m/s, 0.50 m/s, 0.55 m/s, and 0.60 m/s. Figure 9 presents the variation in scouring terrain with time for each v.

Jmse 11 01349 g009 550

Figure 9. Influence of ocean current velocity v on local scouring around semi-exposed submarine cable: (a) v = 0.35 m/s; (b) v = 0.40 m/s; (c) v = 0.45 m/s; (d) v = 0.50 m/s; (e) v = 0.55 m/s; and (f) v = 0.60 m/s.

Changes in v affect the depth of the upstream and downstream scouring holes, as well as the development velocity of the wake position and downstream scouring holes.

When v ≤ 0.45 m/s, the upstream scouring hole will reach a temporary stable state within 1 h, at which point the stable depth will be 0.04 m. The stabilization time of the upstream scouring hole is affected by v, which will gradually decrease from 15 h to 3 h with the increase in v. When v > 0.45 m/s, the upstream scouring hole is going to expand continuously. With the increase in v, its average development velocity increases from 6.68 cm/h to 8.66 cm/h, and its terrain changes to deep on the left and to shallow on the right. When the submarine cable is spanning, special attention should be paid to the depth of the scouring hole at the wake position. Throughout whole scouring process, the scouring hole at the wake position continues to develop and does not reach a stable state. With the increase in v, the depth of scouring hole at the wake position will increase from 14 cm to 20 cm, and the average development velocity will increase from 0.91 cm/h to 10.43 cm/h. As v increases, the time required to stabilize the downstream scouring hole is shortened from 1to 2 h to less than 1 h, but the stable depth is remains nearly constant at 13.5 cm.

An increase in v will increase the shear velocity. Therefore, when the depth of the scouring hole increases, the shear velocity in the hole will also increase, which can deepen both the upstream and downstream scouring hole. According to Equation (1), the Shields number is proportional to the square of the shear velocity. The increase in shear velocity significantly intensifies local scouring, which increases the development rate of scouring holes at the wake position and downstream.

4.3. Variation Rule of Spanning Time

In this paper, the spanning time is defined as the time taken for a semi-exposed submarine cable (initial state) to become a spanning submarine cable. Figure 10 illustrates the effect of the above parameters on the spanning time of the semi-exposed submarine cable.

Jmse 11 01349 g010 550

Figure 10. Influence of different parameters on spanning time of the semi-exposed submarine cable: (a) Sediment critical Shields number; (b) Sediment density; and (c) Ocean current velocity.From Figure 10a, the spanning time monotonically increases with the increase in the critical Shields number of sediment. However, the slope of the curve decreases first and then increases, and the inflection point is at 

θcr = 4.59 × 10

−2. The relationship between spanning time t and sediment’s critical Shields number 

θcr can be formulated by a cubic function as shown in Equation (6):

𝑡=−2.98+6.76𝜃𝑐𝑟−1.45𝜃2𝑐𝑟+0.11𝜃3𝑐𝑟.�=−2.98+6.76���−1.45���2+0.11���3.(6)It can be seen from Figure 10b that with the increase in the sediment density, the spanning time increases monotonically and linearly. The relationship between the spanning time t and the sediment’s density 

ρs can be formulated by the first order function as shown in Equation (7):

𝑡=−41.59+30.54𝜌𝑠.�=−41.59+30.54��.(7)Figure 10c shows that with the increase in the ocean current velocity, the spanning time decreases monotonically. The slope of the curve increases with the increase in the ocean current velocity, so it can be considered that there is saturation of the ocean current velocity effect. The relationship between the spanning time t and the ocean current velocity v can be formulated by the exponential function

𝑡=0.15𝑣−4.38.�=0.15�−4.38.(8)

5. Conclusions

In this paper, a three-dimensional CFD finite element numerical simulation model is established, which is used to research the local scouring process of the semi-exposed submarine cable under the steady-state ocean current. The relationship between shear velocity and scouring terrain is discussed, the influence of sediment critical Shields number, sediment density and ocean current velocity on the local scouring process is analyzed, and the variation rules of the spanning time of the semi-exposed submarine cable is given. The conclusions are as follows:

  • Under the steady-state ocean currents, scouring holes will be formed at the upstream, wake position and downstream of the semi-exposed submarine cable. The upstream and downstream scouring holes develop faster, which will reach a temporary stable state at about 1 h after the start of the scouring. The scouring hole at the wake position will continue to expand at a slower rate and eventually lead to the spanning of the submarine cable.
  • There is a close relationship between the distribution of shear velocity and the scouring terrain. As the local scouring process occurs, the location of the maximum shear velocity within the scouring hole shifts and causes the bottom of the hole to move as well.
  • When the sediment’s critical Shields number and density are significantly large and ocean current velocity is sufficiently low, the duration of the stable state of the upstream scouring hole will be prolonged, and the average development velocity of the scouring holes at the wake position and downstream will be reduced.
  • The relationship between the spanning time and the critical Shields number θcr can be formulated as a cubic function, in which the curve’s inflection point is θcr = 4.59 × 10−2. The relationship between spanning time and sediment density can be formulated as a linear function. The relationship between spanning time and ocean current velocity can be formulated by exponential function.

Based on the conclusions of this paper, even when it is too late to take measures or when the exposed position of the submarine cable cannot be located, the degree of burial depth development still can be predicted. This prediction is important for the operation and maintenance of the submarine cable. However, the study still leaves something to be desired. Only the local scouring process under the steady-state ocean current was studied, which is an extreme condition. In practice, exposed submarine cables are more likely to be scoured by reciprocating ocean currents. In the future, we will investigate the local scouring of submarine cables under the reciprocating ocean current.

Author Contributions

Conceptualization, Y.H. and Q.L.; methodology, Q.L., P.Z. and H.T.; software, Q.L.; validation, Q.L., L.C. and W.T.; writing—original draft preparation, Q.L.; writing—review and editing, Y.H. and Q.L.; supervision, Y.H. and L.Y. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the [Smart Grid Joint Fund Key Project between National Natural Science Foundation of China and State Grid Corporation] grant number [U1766220].

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data supporting the reported results cannot be shared at this time, as they have been used in producing more publications on this research.

Acknowledgments

This work is supported by the Smart Grid Joint Fund Key Project of the National Natural Science Foundation of China and State Grid Corporation (Grant No. U1766220).

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 11. Sketch of scour mechanism around USAF under random waves.

Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves

by Ruigeng Hu 1,Hongjun Liu 2,Hao Leng 1,Peng Yu 3 andXiuhai Wang 1,2,*

1College of Environmental Science and Engineering, Ocean University of China, Qingdao 266000, China

2Key Lab of Marine Environment and Ecology (Ocean University of China), Ministry of Education, Qingdao 266000, China

3Qingdao Geo-Engineering Survering Institute, Qingdao 266100, China

*Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 2021, 9(8), 886; https://doi.org/10.3390/jmse9080886

Received: 6 July 2021 / Revised: 8 August 2021 / Accepted: 13 August 2021 / Published: 17 August 2021

(This article belongs to the Section Ocean Engineering)

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Abstract

A series of numerical simulation were conducted to study the local scour around umbrella suction anchor foundation (USAF) under random waves. In this study, the validation was carried out firstly to verify the accuracy of the present model. Furthermore, the scour evolution and scour mechanism were analyzed respectively. In addition, two revised models were proposed to predict the equilibrium scour depth Seq around USAF. At last, a parametric study was carried out to study the effects of the Froude number Fr and Euler number Eu for the Seq. The results indicate that the present numerical model is accurate and reasonable for depicting the scour morphology under random waves. The revised Raaijmakers’s model shows good agreement with the simulating results of the present study when KCs,p < 8. The predicting results of the revised stochastic model are the most favorable for n = 10 when KCrms,a < 4. The higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Keywords: 

scour; numerical investigation; random waves; equilibrium scour depth; KC number

1. Introduction

The rapid expansion of cities tends to cause social and economic problems, such as environmental pollution and traffic jam. As a kind of clean energy, offshore wind power has developed rapidly in recent years. The foundation of offshore wind turbine (OWT) supports the upper tower, and suffers the cyclic loading induced by waves, tides and winds, which exerts a vital influence on the OWT system. The types of OWT foundation include the fixed and floating foundation, and the fixed foundation was used usually for nearshore wind turbine. After the construction of fixed foundation, the hydrodynamic field changes in the vicinity of the foundation, leading to the horseshoe vortex formation and streamline compression at the upside and sides of foundation respectively [1,2,3,4]. As a result, the neighboring soil would be carried away by the shear stress induced by vortex, and the scour hole would emerge in the vicinity of foundation. The scour holes increase the cantilever length, and weaken the lateral bearing capacity of foundation [5,6,7,8,9]. Moreover, the natural frequency of OWT system increases with the increase of cantilever length, causing the resonance occurs when the system natural frequency equals the wave or wind frequency [10,11,12]. Given that, an innovative foundation called umbrella suction anchor foundation (USAF) has been designed for nearshore wind power. The previous studies indicated the USAF was characterized by the favorable lateral bearing capacity with the low cost [6,13,14]. The close-up of USAF is shown in Figure 1, and it includes six parts: 1-interal buckets, 2-external skirt, 3-anchor ring, 4-anchor branch, 5-supporting rod, 6-telescopic hook. The detailed description and application method of USAF can be found in reference [13].

Jmse 09 00886 g001 550

Figure 1. The close-up of umbrella suction anchor foundation (USAF).

Numerical and experimental investigations of scour around OWT foundation under steady currents and waves have been extensively studied by many researchers [1,2,15,16,17,18,19,20,21,22,23,24]. The seabed scour can be classified as two types according to Shields parameter θ, i.e., clear bed scour (θ < θcr) or live bed scour (θ > θcr). Due to the set of foundation, the adverse hydraulic pressure gradient exists at upstream foundation edges, resulting in the streamline separation between boundary layer flow and seabed. The separating boundary layer ascended at upstream anchor edges and developed into the horseshoe vortex. Then, the horseshoe vortex moved downstream gradually along the periphery of the anchor, and the vortex shed off continually at the lee-side of the anchor, i.e., wake vortex. The core of wake vortex is a negative pressure center, liking a vacuum cleaner. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortexes. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow when the turbulence energy could not support the survival of wake vortex. According to Tavouktsoglou et al. [25], the scale of pile wall boundary layer is proportional to 1/ln(Rd) (Rd is pile Reynolds), which means the turbulence intensity induced by the flow-structure interaction would decrease with Rd increases, but the effects of Rd can be neglected only if the flow around the foundation is fully turbulent [26]. According to previous studies [1,15,27,28,29,30,31,32], the scour development around pile foundation under waves was significantly influenced by Shields parameter θ and KC number simultaneously (calculated by Equation (1)). Sand ripples widely existed around pile under waves in the case of live bed scour, and the scour morphology is related with θ and KC. Compared with θ, KC has a greater influence on the scour morphology [21,27,28]. The influence mechanism of KC on the scour around the pile is reflected in two aspects: the horseshoe vortex at upstream and wake vortex shedding at downstream.

KC=UwmTD��=�wm��(1)

where, Uwm is the maximum velocity of the undisturbed wave-induced oscillatory flow at the sea bottom above the wave boundary layer, T is wave period, and D is pile diameter.

There are two prerequisites to satisfy the formation of horseshoe vortex at upstream pile edges: (1) the incoming flow boundary layer with sufficient thickness and (2) the magnitude of upstream adverse pressure gradient making the boundary layer separating [1,15,16,18,20]. The smaller KC results the lower adverse pressure gradient, and the boundary layer cannot separate, herein, there is almost no horseshoe vortex emerging at upside of pile. Sumer et al. [1,15] carried out several sets of wave flume experiments under regular and irregular waves respectively, and the experiment results show that there is no horseshoe vortex when KC is less than 6. While the scale and lifespan of horseshoe vortex increase evidently with the increase of KC when KC is larger than 6. Moreover, the wake vortex contributes to the scour at lee-side of pile. Similar with the case of horseshoe vortex, there is no wake vortex when KC is less than 6. The wake vortex is mainly responsible for scour around pile when KC is greater than 6 and less than O(100), while horseshoe vortex controls scour nearly when KC is greater than O(100).

Sumer et al. [1] found that the equilibrium scour depth was nil around pile when KC was less than 6 under regular waves for live bed scour, while the equilibrium scour depth increased with the increase of KC. Based on that, Sumer proposed an equilibrium scour depth predicting equation (Equation (2)). Carreiras et al. [33] revised Sumer’s equation with m = 0.06 for nonlinear waves. Different with the findings of Sumer et al. [1] and Carreiras et al. [33], Corvaro et al. [21] found the scour still occurred for KC ≈ 4, and proposed the revised equilibrium scour depth predicting equation (Equation (3)) for KC > 4.

Rudolph and Bos [2] conducted a series of wave flume experiments to investigate the scour depth around monopile under waves only, waves and currents combined respectively, indicting KC was one of key parameters in influencing equilibrium scour depth, and proposed the equilibrium scour depth predicting equation (Equation (4)) for low KC (1 < KC < 10). Through analyzing the extensive data from published literatures, Raaijmakers and Rudolph [34] developed the equilibrium scour depth predicting equation (Equation (5)) for low KC, which was suitable for waves only, waves and currents combined. Khalfin [35] carried out several sets of wave flume experiments to study scour development around monopile, and proposed the equilibrium scour depth predicting equation (Equation (6)) for low KC (0.1 < KC < 3.5). Different with above equations, the Khalfin’s equation considers the Shields parameter θ and KC number simultaneously in predicting equilibrium scour depth. The flow reversal occurred under through in one wave period, so sand particles would be carried away from lee-side of pile to upside, resulting in sand particles backfilled into the upstream scour hole [20,29]. Considering the backfilling effects, Zanke et al. [36] proposed the equilibrium scour depth predicting equation (Equation (7)) around pile by theoretical analysis, and the equation is suitable for the whole range of KC number under regular waves and currents combined.

S/D=1.3(1−exp([−m(KC−6)])�/�=1.3(1−exp(−�(��−6))(2)

where, m = 0.03 for linear waves.

S/D=1.3(1−exp([−0.02(KC−4)])�/�=1.3(1−exp(−0.02(��−4))(3)

S/D=1.3γKwaveKhw�/�=1.3��wave�ℎw(4)

where, γ is safety factor, depending on design process, typically γ = 1.5, Kwave is correction factor considering wave action, Khw is correction factor considering water depth.

S/D=1.5[tanh(hwD)]KwaveKhw�/�=1.5tanh(ℎw�)�wave�ℎw(5)

where, hw is water depth.

S/D=0.0753(θθcr−−−√−0.5)0.69KC0.68�/�=0.0753(��cr−0.5)0.69��0.68(6)

where, θ is shields parameter, θcr is critical shields parameter.

S/D=2.5(1−0.5u/uc)xrelxrel=xeff/(1+xeff)xeff=0.03(1−0.35ucr/u)(KC−6)⎫⎭⎬⎪⎪�/�=2.5(1−0.5�/��)��������=����/(1+����)����=0.03(1−0.35�cr/�)(��−6)(7)

where, u is near-bed orbital velocity amplitude, uc is critical velocity corresponding the onset of sediment motion.

S/D=1.3{1−exp[−0.03(KC2lnn+36)1/2−6]}�/�=1.31−exp−0.03(��2ln�+36)1/2−6(8)

where, n is the 1/n’th highest wave for random waves

For predicting equilibrium scour depth under irregular waves, i.e., random waves, Sumer and Fredsøe [16] found it’s suitable to take Equation (2) to predict equilibrium scour depth around pile under random waves with the root-mean-square (RMS) value of near-bed orbital velocity amplitude Um and peak wave period TP to calculate KC. Khalfin [35] recommended the RMS wave height Hrms and peak wave period TP were used to calculate KC for Equation (6). References [37,38,39,40] developed a series of stochastic theoretical models to predict equilibrium scour depth around pile under random waves, nonlinear random waves plus currents respectively. The stochastic approach thought the 1/n’th highest wave were responsible for scour in vicinity of pile under random waves, and the KC was calculated in Equation (8) with Um and mean zero-crossing wave period Tz. The results calculated by Equation (8) agree well with experimental values of Sumer and Fredsøe [16] if the 1/10′th highest wave was used. To author’s knowledge, the stochastic approach proposed by Myrhaug and Rue [37] is the only theoretical model to predict equilibrium scour depth around pile under random waves for the whole range of KC number in published documents. Other methods of predicting scour depth under random waves are mainly originated from the equation for regular waves-only, waves and currents combined, which are limited to the large KC number, such as KC > 6 for Equation (2) and KC > 4 for Equation (3) respectively. However, situations with relatively low KC number (KC < 4) often occur in reality, for example, monopile or suction anchor for OWT foundations in ocean environment. Moreover, local scour around OWT foundations under random waves has not yet been investigated fully. Therefore, further study are still needed in the aspect of scour around OWT foundations with low KC number under random waves. Given that, this study presents the scour sediment model around umbrella suction anchor foundation (USAF) under random waves. In this study, a comparison of equilibrium scour depth around USAF between this present numerical models and the previous theoretical models and experimental results was presented firstly. Then, this study gave a comprehensive analysis for the scour mechanisms around USAF. After that, two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] respectively to predict the equilibrium scour depth. Finally, a parametric study was conducted to study the effects of the Froude number (Fr) and Euler number (Eu) to equilibrium scour depth respectively.

2. Numerical Method

2.1. Governing Equations of Flow

The following equations adopted in present model are already available in Flow 3D software. The authors used these theoretical equations to simulate scour in random waves without modification. The incompressible viscous fluid motion satisfies the Reynolds-averaged Navier-Stokes (RANS) equation, so the present numerical model solves RANS equations:

∂u∂t+1VF(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρf∂p∂x+Gx+fx∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(9)

∂v∂t+1VF(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρf∂p∂y+Gy+fy∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(10)

∂w∂t+1VF(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρf∂p∂z+Gz+fz∂�∂�+1��(���∂�∂�+���∂�∂�+���∂�∂�)=−1�f∂�∂�+��+��(11)

where, VF is the volume fraction; u, v, and w are the velocity components in x, y, z direction respectively with Cartesian coordinates; Ai is the area fraction; ρf is the fluid density, fi is the viscous fluid acceleration, Gi is the fluid body acceleration (i = x, y, z).

2.2. Turbulent Model

The turbulence closure is available by the turbulent model, such as one-equation, the one-equation k-ε model, the standard k-ε model, RNG k-ε turbulent model and large eddy simulation (LES) model. The LES model requires very fine mesh grid, so the computational time is large, which hinders the LES model application in engineering. The RNG k-ε model can reduce computational time greatly with high accuracy in the near-wall region. Furthermore, the RNG k-ε model computes the maximum turbulent mixing length dynamically in simulating sediment scour model. Therefore, the RNG k-ε model was adopted to study the scour around anchor under random waves [41,42].

∂kT∂T+1VF(uAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z)=PT+GT+DiffkT−εkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=��+��+������−���(12)

∂εT∂T+1VF(uAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z)=CDIS1εTkT(PT+CDIS3GT)+Diffε−CDIS2ε2TkT∂��∂�+1��(���∂��∂�+���∂��∂�+���∂��∂�)=����1����(��+����3��)+�����−����2��2��(13)

where, kT is specific kinetic energy involved with turbulent velocity, GT is the turbulent energy generated by buoyancy; εT is the turbulent energy dissipating rate, PT is the turbulent energy, Diffε and DiffkT are diffusion terms associated with VF, Ai; CDIS1, CDIS2 and CDIS3 are dimensionless parameters, and CDIS1, CDIS3 have default values of 1.42, 0.2 respectively. CDIS2 can be obtained from PT and kT.

2.3. Sediment Scour Model

The sand particles may suffer four processes under waves, i.e., entrainment, bed load transport, suspended load transport, and deposition, so the sediment scour model should depict the above processes efficiently. In present numerical simulation, the sediment scour model includes the following aspects:

2.3.1. Entrainment and Deposition

The combination of entrainment and deposition determines the net scour rate of seabed in present sediment scour model. The entrainment lift velocity of sand particles was calculated as [43]:

ulift,i=αinsd0.3∗(θ−θcr)1.5∥g∥di(ρi−ρf)ρf−−−−−−−−−−−−√�lift,i=�����*0.3(�−�cr)1.5���(��−�f)�f(14)

where, αi is the entrainment parameter, ns is the outward point perpendicular to the seabed, d* is the dimensionless diameter of sand particles, which was calculated by Equation (15), θcr is the critical Shields parameter, g is the gravity acceleration, di is the diameter of sand particles, ρi is the density of seabed species.

d∗=di(∥g∥ρf(ρi−ρf)μ2f)1/3�*=��(��f(��−�f)�f2)1/3(15)

where μf is the fluid dynamic viscosity.

In Equation (14), the entrainment parameter αi confirms the rate at which sediment erodes when the given shear stress is larger than the critical shear stress, and the recommended value 0.018 was adopted according to the experimental data of Mastbergen and Von den Berg [43]. ns is the outward pointing normal to the seabed interface, and ns = (0,0,1) according to the Cartesian coordinates used in present numerical model.

The shields parameter was obtained from the following equation:

θ=U2f,m(ρi/ρf−1)gd50�=�f,m2(��/�f−1)��50(16)

where, Uf,m is the maximum value of the near-bed friction velocity; d50 is the median diameter of sand particles. The detailed calculation procedure of θ was available in Soulsby [44].

The critical shields parameter θcr was obtained from the Equation (17) [44]

θcr=0.31+1.2d∗+0.055[1−exp(−0.02d∗)]�cr=0.31+1.2�*+0.0551−exp(−0.02�*)(17)

The sand particles begin to deposit on seabed when the turbulence energy weaken and cann’t support the particles suspending. The setting velocity of the particles was calculated from the following equation [44]:

usettling,i=νfdi[(10.362+1.049d3∗)0.5−10.36]�settling,�=�f��(10.362+1.049�*3)0.5−10.36(18)

where νf is the fluid kinematic viscosity.

2.3.2. Bed Load Transport

This is called bed load transport when the sand particles roll or bounce over the seabed and always have contact with seabed. The bed load transport velocity was computed by [45]:

ubedload,i=qb,iδicb,ifb�bedload,�=�b,����b,��b(19)

where, qb,i is the bed load transport rate, which was obtained from Equation (20), δi is the bed load thickness, which was calculated by Equation (21), cb,i is the volume fraction of sand i in the multiple species, fb is the critical packing fraction of the seabed.

qb,i=8[∥g∥(ρi−ρfρf)d3i]1/2�b,�=8�(��−�f�f)��31/2(20)

δi=0.3d0.7∗(θθcr−1)0.5di��=0.3�*0.7(��cr−1)0.5��(21)

2.3.3. Suspended Load Transport

Through the following transport equation, the suspended sediment concentration could be acquired.

∂Cs,i∂t+∇(us,iCs,i)=∇∇(DfCs,i)∂�s,�∂�+∇(�s,��s,�)=∇∇(�f�s,�)(22)

where, Cs,i is the suspended sand particles mass concentration of sand i in the multiple species, us,i is the sand particles velocity of sand i, Df is the diffusivity.

The velocity of sand i in the multiple species could be obtained from the following equation:

us,i=u¯¯+usettling,ics,i�s,�=�¯+�settling,��s,�(23)

where, u¯�¯ is the velocity of mixed fluid-particles, which can be calculated by the RANS equation with turbulence model, cs,i is the suspended sand particles volume concentration, which was computed from Equation (24).

cs,i=Cs,iρi�s,�=�s,���(24)

3. Model Setup

The seabed-USAF-wave three-dimensional scour numerical model was built using Flow-3D software. As shown in Figure 2, the model includes sandy seabed, USAF model, sea water, two baffles and porous media. The dimensions of USAF are shown in Table 1. The sandy bed (210 m in length, 30 m in width and 11 m in height) is made up of uniform fine sand with median diameter d50 = 0.041 cm. The USAF model includes upper steel tube with the length of 20 m, which was installed in the middle of seabed. The location of USAF is positioned at 140 m from the upstream inflow boundary and 70 m from the downstream outflow boundary. Two baffles were installed at two ends of seabed. In order to eliminate the wave reflection basically, the porous media was set at the outflow side on the seabed.

Jmse 09 00886 g002 550

Figure 2. (a) The sketch of seabed-USAF-wave three-dimensional model; (b) boundary condation:Wv-wave boundary, S-symmetric boundary, O-outflow boundary; (c) USAF model.

Table 1. Numerical simulating cases.

Table

3.1. Mesh Geometric Dimensions

In the simulation of the scour under the random waves, the model includes the umbrella suction anchor foundation, seabed and fluid. As shown in Figure 3, the model mesh includes global mesh grid and nested mesh grid, and the total number of grids is 1,812,000. The basic procedure for building mesh grid consists of two steps. Step 1: Divide the global mesh using regular hexahedron with size of 0.6 × 0.6. The global mesh area is cubic box, embracing the seabed and whole fluid volume, and the dimensions are 210 m in length, 30 m in width and 32 m in height. The details of determining the grid size can see the following mesh sensitivity section. Step 2: Set nested fine mesh grid in vicinity of the USAF with size of 0.3 × 0.3 so as to shorten the computation cost and improve the calculation accuracy. The encryption range is −15 m to 15 m in x direction, −15 m to 15 m in y direction and 0 m to 32 m in z direction, respectively. In order to accurately capture the free-surface dynamics, such as the fluid-air interface, the volume of fluid (VOF) method was adopted for tracking the free water surface. One specific algorithm called FAVORTM (Fractional Area/Volume Obstacle Representation) was used to define the fractional face areas and fractional volumes of the cells which are open to fluid flow.

Jmse 09 00886 g003 550

Figure 3. The sketch of mesh grid.

3.2. Boundary Conditions

As shown in Figure 2, the initial fluid length is 210 m as long as seabed. A wave boundary was specified at the upstream offshore end. The details of determining the random wave spectrum can see the following wave parameters section. The outflow boundary was set at the downstream onshore end. The symmetry boundary was used at the top and two sides of the model. The symmetric boundaries were the better strategy to improve the computation efficiency and save the calculation cost [46]. At the seabed bottom, the wall boundary was adopted, which means the u = v = w= 0. Besides, the upper steel tube of USAF was set as no-slip condition.

3.3. Wave Parameters

The random waves with JONSWAP wave spectrum were used for all simulations as realistic representation of offshore conditions. The unidirectional JONSWAP frequency spectrum was described as [47]:

S(ω)=αg2ω5exp[−54(ωpω)4]γexp[−(ω−ωp)22σ2ω2p]�(�)=��2�5exp−54(�p�)4�exp−(�−�p)22�2�p2(25)

where, α is wave energy scale parameter, which is calculated by Equation (26), ω is frequency, ωp is wave spectrum peak frequency, which can be obtained from Equation (27). γ is wave spectrum peak enhancement factor, in this study γ = 3.3. σ is spectral width factor, σ equals 0.07 for ω ≤ ωp and 0.09 for ω > ωp respectively.

α=0.0076(gXU2)−0.22�=0.0076(���2)−0.22(26)

ωp=22(gU)(gXU2)−0.33�p=22(��)(���2)−0.33(27)

where, X is fetch length, U is average wind velocity at 10 m height from mean sea level.

In present numerical model, the input key parameters include X and U for wave boundary with JONSWAP wave spectrum. The objective wave height and period are available by different combinations of X and U. In this study, we designed 9 cases with different wave heights, periods and water depths for simulating scour around USAF under random waves (see Table 2). For random waves, the wave steepness ε and Ursell number Ur were acquired form Equations (28) and (29) respectively

ε=2πgHsT2a�=2���s�a2(28)

Ur=Hsk2h3w�r=�s�2ℎw3(29)

where, Hs is significant wave height, Ta is average wave period, k is wave number, hw is water depth. The Shield parameter θ satisfies θ > θcr for all simulations in current study, indicating the live bed scour prevails.

Table 2. Numerical simulating cases.

Table

3.4. Mesh Sensitivity

In this section, a mesh sensitivity analysis was conducted to investigate the influence of mesh grid size to results and make sure the calculation is mesh size independent and converged. Three mesh grid size were chosen: Mesh 1—global mesh grid size of 0.75 × 0.75, nested fine mesh grid size of 0.4 × 0.4, and total number of grids 1,724,000, Mesh 2—global mesh grid size of 0.6 × 0.6, nested fine mesh grid size of 0.3 × 0.3, and total number of grids 1,812,000, Mesh 3—global mesh grid size of 0.4 × 0.4, nested fine mesh grid size of 0.2 × 0.2, and total number of grids 1,932,000. The near-bed shear velocity U* is an important factor for influencing scour process [1,15], so U* at the position of (4,0,11.12) was evaluated under three mesh sizes. As the Figure 4 shown, the maximum error of shear velocity ∆U*1,2 is about 39.8% between the mesh 1 and mesh 2, and 4.8% between the mesh 2 and mesh 3. According to the mesh sensitivity criterion adopted by Pang et al. [48], it’s reasonable to think the results are mesh size independent and converged with mesh 2. Additionally, the present model was built according to prototype size, and the mesh size used in present model is larger than the mesh size adopted by Higueira et al. [49] and Corvaro et al. [50]. If we choose the smallest cell size, it will take too much time. For example, the simulation with Mesh3 required about 260 h by using a computer with Intel Xeon Scalable Gold 4214 CPU @24 Cores, 2.2 GHz and 64.00 GB RAM. Therefore, in this case, considering calculation accuracy and computation efficiency, the mesh 2 was chosen for all the simulation in this study.

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Figure 4. Comparison of near-bed shear velocity U* with different mesh grid size.

The nested mesh block was adopted for seabed in vicinity of the USAF, which was overlapped with the global mesh block. When two mesh blocks overlap each other, the governing equations are by default solved on the mesh block with smaller average cell size (i.e., higher grid resolution). It is should be noted that the Flow 3D software used the moving mesh captures the scour evolution and automatically adjusts the time step size to be as large as possible without exceeding any of the stability limits, affecting accuracy, or unduly increasing the effort required to enforce the continuity condition [51].

3.5. Model Validation

In order to verify the reliability of the present model, the results of present study were compared with the experimental data of Khosronejad et al. [52]. The experiment was conducted in an open channel with a slender vertical pile under unidirectional currents. The comparison of scour development between the present results and the experimental results is shown in Figure 5. The Figure 5 reveals that the present results agree well with the experimental data of Khosronejad et al. [52]. In the first stage, the scour depth increases rapidly. After that, the scour depth achieves a maximum value gradually. The equilibrium scour depth calculated by the present model is basically corresponding with the experimental results of Khosronejad et al. [52], although scour depth in the present model is slightly larger than the experimental results at initial stage.

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Figure 5. Comparison of time evolution of scour between the present study and Khosronejad et al. [52], Petersen et al. [17].

Secondly, another comparison was further conducted between the results of present study and the experimental data of Petersen et al. [17]. The experiment was carried out in a flume with a circular vertical pile in combined waves and current. Figure 4 shows a comparison of time evolution of scour depth between the simulating and the experimental results. As Figure 5 indicates, the scour depth in this study has good overall agreement with the experimental results proposed in Petersen et al. [17]. The equilibrium scour depth calculated by the present model is 0.399 m, which equals to the experimental value basically. Overall, the above verifications prove the present model is accurate and capable in dealing with sediment scour under waves.

In addition, in order to calibrate and validate the present model for hydrodynamic parameters, the comparison of water surface elevation was carried out with laboratory experiments conducted by Stahlmann [53] for wave gauge No. 3. The Figure 6 depicts the surface wave profiles between experiments and numerical model results. The comparison indicates that there is a good agreement between the model results and experimental values, especially the locations of wave crest and trough. Comparison of the surface elevation instructs the present model has an acceptable relative error, and the model is a calibrated in terms of the hydrodynamic parameters.

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Figure 6. Comparison of surface elevation between the present study and Stahlmann [53].

Finally, another comparison was conducted for equilibrium scour depth or maximum scour depth under random waves with the experimental data of Sumer and Fredsøe [16] and Schendel et al. [22]. The Figure 7 shows the comparison between the numerical results and experimental data of Run01, Run05, Run21 and Run22 in Sumer and Fredsøe [16] and test A05 and A09 in Schendel et al. [22]. As shown in Figure 7, the equilibrium scour depth or maximum scour depth distributed within the ±30 error lines basically, meaning the reliability and accuracy of present model for predicting equilibrium scour depth around foundation in random waves. However, compared with the experimental values, the present model overestimated the equilibrium scour depth generally. Given that, a calibration for scour depth was carried out by multiplying the mean reduced coefficient 0.85 in following section.

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Figure 7. Comparison of equilibrium (or maximum) scour depth between the present study and Sumer and Fredsøe [16], Schendel et al. [22].

Through the various examination for hydrodynamic and morphology parameters, it can be concluded that the present model is a validated and calibrated model for scour under random waves. Thus, the present numerical model would be utilized for scour simulation around foundation under random waves.

4. Numerical Results and Discussions

4.1. Scour Evolution

Figure 8 displays the scour evolution for case 1–9. As shown in Figure 8a, the scour depth increased rapidly at the initial stage, and then slowed down at the transition stage, which attributes to the backfilling occurred in scour holes under live bed scour condition, resulting in the net scour decreasing. Finally, the scour reached the equilibrium state when the amount of sediment backfilling equaled to that of scouring in the scour holes, i.e., the net scour transport rate was nil. Sumer and Fredsøe [16] proposed the following formula for the scour development under waves

St=Seq(1−exp(−t/Tc))�t=�eq(1−exp(−�/�c))(30)

where Tc is time scale of scour process.

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Figure 8. Time evolution of scour for case 1–9: (a) Case 1–5; (b) Case 6–9.

The computing time is 3600 s and the scour development curves in Figure 8 kept fluctuating, meaning it’s still not in equilibrium scour stage in these cases. According to Sumer and Fredsøe [16], the equilibrium scour depth can be acquired by fitting the data with Equation (30). From Figure 8, it can be seen that the scour evolution obtained from Equation (30) is consistent with the present study basically at initial stage, but the scour depth predicted by Equation (30) developed slightly faster than the simulating results and the Equation (30) overestimated the scour depth to some extent. Overall, the whole tendency of the results calculated by Equation (30) agrees well with the simulating results of the present study, which means the Equation (30) is applicable to depict the scour evolution around USAF under random waves.

4.2. Scour Mechanism under Random Waves

The scour morphology and scour evolution around USAF are similar under random waves in case 1~9. Taking case 7 as an example, the scour morphology is shown in Figure 9.

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Figure 9. Scour morphology under different times for case 7.

From Figure 9, at the initial stage (t < 1200 s), the scour occurred at upstream foundation edges between neighboring anchor branches. The maximum scour depth appeared at the lee-side of the USAF. Correspondingly, the sediments deposited at the periphery of the USAF, and the location of the maximum accretion depth was positioned at an angle of about 45° symmetrically with respect to the wave propagating direction in the lee-side of the USAF. After that, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.

According to previous studies [1,15,16,19,30,31], the horseshoe vortex, streamline compression and wake vortex shedding were responsible for scour around foundation. The Figure 10 displays the distribution of flow velocity in vicinity of foundation, which reflects the evolving processes of horseshoe vertex.

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Figure 10. Velocity profile around USAF: (a) Flow runup and down stream at upstream anchor edges; (b) Horseshoe vortex at upstream anchor edges; (c) Flow reversal during wave through stage at lee side.

As shown in Figure 10, the inflow tripped to the upstream edges of the USAF and it was blocked by the upper tube of USAF. Then, the downflow formed the horizontal axis clockwise vortex and rolled on the seabed bypassing the tube, that is, the horseshoe vortex (Figure 11). The Figure 12 displays the turbulence intensity around the tube on the seabed. From Figure 12, it can be seen that the turbulence intensity was high-intensity with respect to the region of horseshoe vortex. This phenomenon occurred because of drastic water flow momentum exchanging in the horseshoe vortex. As a result, it created the prominent shear stress on the seabed, causing the local scour at the upstream edges of USAF. Besides, the horseshoe vortex moved downstream gradually along the periphery of the tube and the wake vortex shed off continually at the lee-side of the USAF, i.e., wake vortex.

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Figure 11. Sketch of scour mechanism around USAF under random waves.

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Figure 12. Turbulence intensity: (a) Turbulence intensity of horseshoe vortex; (b) Turbulence intensity of wake vortex; (c) Turbulence intensity of accretion area.

The core of wake vortex is a negative pressure center, liking a vacuum cleaner [11,42]. Hence, the soil particles were swirled into the negative pressure core and carried away by wake vortex. At the same time, the onset of scour at rear side occurred. Finally, the wake vortex became downflow at the downside of USAF. As is shown in Figure 12, the turbulence intensity was low where the downflow occurred at lee-side, which means the turbulence energy may not be able to support the survival of wake vortex, leading to accretion happening. As mentioned in previous section, the formation of horseshoe vortex was dependent with adverse pressure gradient at upside of foundation. As shown in Figure 13, the evaluated range of pressure distribution is −15 m to 15 m in x direction. The t = 450 s and t = 1800 s indicate that the wave crest and trough arrived at the upside and lee-side of the foundation respectively, and the t = 350 s was neither the wave crest nor trough. The adverse gradient pressure reached the maximum value at t = 450 s corresponding to the wave crest phase. In this case, it’s helpful for the wave boundary separating fully from seabed, which leads to the formation of horseshoe vortex with high turbulence intensity. Therefore, the horseshoe vortex is responsible for the local scour between neighboring anchor branches at upside of USAF. What’s more, due to the combination of the horseshoe vortex and streamline compression, the maximum scour depth occurred at the upside of the USAF with an angle of about 45° corresponding to the wave propagating direction. This is consistent with the findings of Pang et al. [48] and Sumer et al. [1,15] in case of regular waves. At the wave trough phase (t = 1800 s), the pressure gradient became positive at upstream USAF edges, which hindered the separating of wave boundary from seabed. In the meantime, the flow reversal occurred (Figure 10) and the adverse gradient pressure appeared at downstream USAF edges, but the magnitude of adverse gradient pressure at lee-side was lower than the upstream gradient pressure under wave crest. In this way, the intensity of horseshoe vortex behind the USAF under wave trough was low, which explains the difference of scour depth at upstream and downstream, i.e., the scour asymmetry. In other words, the scour asymmetry at upside and downside of USAF was attributed to wave asymmetry for random waves, and the phenomenon became more evident for nonlinear waves [21]. Briefly speaking, the vortex system at wave crest phase was mainly related to the scour process around USAF under random waves.

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Figure 13. Pressure distribution around USAF.

4.3. Equilibrium Scour Depth

The KC number is a key parameter for horseshoe vortex emerging and evolving under waves. According to Equation (1), when pile diameter D is fixed, the KC depends on the maximum near-bed velocity Uwm and wave period T. For random waves, the Uwm can be denoted by the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms or the significant value of near-bed velocity amplitude Uwm,s. The Uwm,rms and Uwm,s for all simulating cases of the present study are listed in Table 3 and Table 4. The T can be denoted by the mean up zero-crossing wave period Ta, peak wave period Tp, significant wave period Ts, the maximum wave period Tm, 1/10′th highest wave period Tn = 1/10 and 1/5′th highest wave period Tn = 1/5 for random waves, so the different combinations of Uwm and T will acquire different KC. The Table 3 and Table 4 list 12 types of KC, for example, the KCrms,s was calculated by Uwm,rms and Ts. Sumer and Fredsøe [16] conducted a series of wave flume experiments to investigate the scour depth around monopile under random waves, and found the equilibrium scour depth predicting equation (Equation (2)) for regular waves was applicable for random waves with KCrms,p. It should be noted that the Equation (2) is only suitable for KC > 6 under regular waves or KCrms,p > 6 under random waves.

Table 3. Uwm,rms and KC for case 1~9.

Table

Table 4. Uwm,s and KC for case 1~9.

Table

Raaijmakers and Rudolph [34] proposed the equilibrium scour depth predicting model (Equation (5)) around pile under waves, which is suitable for low KC. The format of Equation (5) is similar with the formula proposed by Breusers [54], which can predict the equilibrium scour depth around pile at different scour stages. In order to verify the applicability of Raaijmakers’s model for predicting the equilibrium scour depth around USAF under random waves, a validation of the equilibrium scour depth Seq between the present study and Raaijmakers’s equation was conducted. The position where the scour depth Seq was evaluated is the location of the maximum scour depth, and it was depicted in Figure 14. The Figure 15 displays the comparison of Seq with different KC between the present study and Raaijmakers’s model.

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Figure 14. Sketch of the position where the Seq was evaluated.

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Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (a) KCrms,s, KCrms,a; (b) KCrms,p, KCrms,m; (c) KCrms,n = 1/10, KCrms,n = 1/5; (d) KCs,s, KCs,a; (e) KCs,p, KCs,m; (f) KCs,n = 1/10, KCs,n = 1/5.

As shown in Figure 15, there is an error in predicting Seq between the present study and Raaijmakers’s model, and Raaijmakers’s model underestimates the results generally. Although the error exists, the varying trend of Seq with KC obtained from Raaijmakers’s model is consistent with the present study basically. What’s more, the error is minimum and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves by using KCs,p. Based on this, a further revision was made to eliminate the error as much as possible, i.e., add the deviation value ∆S/D in the Raaijmakers’s model. The revised equilibrium scour depth predicting equation based on Raaijmakers’s model can be written as

S′eq/D=1.95[tanh(hD)](1−exp(−0.012KCs,p))+ΔS/D�eq′/�=1.95tanh(ℎ�)(1−exp(−0.012��s,p))+∆�/�(31)

As the Figure 16 shown, through trial-calculation, when ∆S/D = 0.05, the results calculated by Equation (31) show good agreement with the simulating results of the present study. The maximum error is about 18.2% and the engineering requirements have been met basically. In order to further verify the accuracy of the revised model for large KC (KCs,p > 4) under random waves, a validation between the revised model and the previous experimental results [21]. The experiment was conducted in a flume (50 m in length, 1.0 m in width and 1.3 m in height) with a slender vertical pile (D = 0.1 m) under random waves. The seabed is composed of 0.13 m deep layer of sand with d50 = 0.6 mm and the water depth is 0.5 m for all tests. The significant wave height is 0.12~0.21 m and the KCs,p is 5.52~11.38. The comparison between the predicting results by Equation (31) and the experimental results of Corvaro et al. [21] is shown in Figure 17. From Figure 17, the experimental data evenly distributes around the predicted results and the prediction accuracy is favorable when KCs,p < 8. However, the gap between the predicting results and experimental data becomes large and the Equation (31) overestimates the equilibrium scour depth to some extent when KCs,p > 8.

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Figure 16. Comparison of Seq between the simulating results and the predicting values by Equation (31).

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Figure 17. Comparison of Seq/D between the Experimental results of Corvaro et al. [21] and the predicting values by Equation (31).

In ocean environment, the waves are composed of a train of sinusoidal waves with different frequencies and amplitudes. The energy of constituent waves with very large and very small frequencies is relatively low, and the energy of waves is mainly concentrated in a certain range of moderate frequencies. Myrhaug and Rue [37] thought the 1/n’th highest wave was responsible for scour and proposed the stochastic model to predict the equilibrium scour depth around pile under random waves for full range of KC. Noteworthy is that the KC was denoted by KCrms,a in the stochastic model. To verify the application of the stochastic model for predicting scour depth around USAF, a validation between the simulating results of present study and predicting results by the stochastic model with n = 2,3,5,10,20,500 was carried out respectively.

As shown in Figure 18, compared with the simulating results, the stochastic model underestimates the equilibrium scour depth around USAF generally. Although the error exists, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. What’s more, the gap between the predicting values by stochastic model and the simulating results decreases with the increase of n, but for large n, for example n = 500, the varying trend diverges between the predicting values and simulating results, meaning it’s not feasible only by increasing n in stochastic model to predict the equilibrium scour depth around USAF.

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Figure 18. Comparison of Seq between the simulating results and the predicting values by Equation (8).

The Figure 19 lists the deviation value ∆Seq/D′ between the predicting values and simulating results with different KCrms,a and n. Then, fitted the relationship between the ∆S′and n under different KCrms,a, and the fitting curve can be written by Equation (32). The revised stochastic model (Equation (33)) can be acquired by adding ∆Seq/D′ to Equation (8).

ΔSeq/D=0.052*exp(−n/6.566)+0.068∆�eq/�=0.052*exp(−�/6.566)+0.068(32)

S′eq¯/D=S′eq/D+0.052*exp(−n/6.566)+0.068�eq′¯/�=�eq′/�+0.052*exp(−�/6.566)+0.068(33)

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Figure 19. The fitting line between ∆S′and n.

The comparison between the predicting results by Equation (33) and the simulating results of present study is shown in Figure 20. According to the Figure 20, the varying trend of Seq with KCrms,a obtained from the stochastic model is consistent with the present study basically. Compared with predicting results by the stochastic model, the results calculated by Equation (33) is favorable. Moreover, comparison with simulating results indicates that the predicting results are the most favorable for n = 10, which is consistent with the findings of Myrhaug and Rue [37] for equilibrium scour depth predicting around slender pile in case of random waves.

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Figure 20. Comparison of Seq between the simulating results and the predicting values by Equation (33).

In order to further verify the accuracy of the Equation (33) for large KC (KCrms,a > 4) under random waves, a validation was conducted between the Equation (33) and the previous experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. The details of experiments conducted by Corvaro et al. [21] were described in above section. Sumer and Fredsøe [16] investigated the local scour around pile under random waves. The experiments were conducted in a wave basin with a slender vertical pile (D = 0.032, 0.055 m). The seabed is composed of 0.14 m deep layer of sand with d50 = 0.2 mm and the water depth was maintained at 0.5 m. The JONSWAP wave spectrum was used and the KCrms,a was 5.29~16.95. The comparison between the predicting results by Equation (33) and the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] are shown in Figure 21. From Figure 21, contrary to the case of low KCrms,a (KCrms,a < 4), the error between the predicting values and experimental results increases with decreasing of n for KCrms,a > 4. Therefore, the predicting results are the most favorable for n = 2 when KCrms,a > 4.

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Figure 21. Comparison of Seq between the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21] and the predicting values by Equation (33).

Noteworthy is that the present model was built according to prototype size, so the errors between the numerical results and experimental data of References [16,21] may be attribute to the scale effects. In laboratory experiments on scouring process, it is typically impossible to ensure a rigorous similarity of all physical parameters between the model and prototype structure, leading to the scale effects in the laboratory experiments. To avoid a cohesive behaviour, the bed material was not scaled geometrically according to model scale. As a consequence, the relatively large-scaled sediments sizes may result in the overestimation of bed load transport and underestimation of suspended load transport compared with field conditions. What’s more, the disproportional scaled sediment presumably lead to the difference of bed roughness between the model and prototype, and thus large influences for wave boundary layer on the seabed and scour process. Besides, according to Corvaro et al. [21] and Schendel et al. [55], the pile Reynolds numbers and Froude numbers both affect the scour depth for the condition of non fully developed turbulent flow in laboratory experiments.

4.4. Parametric Study

4.4.1. Influence of Froude Number

As described above, the set of foundation leads to the adverse pressure gradient appearing at upstream, leading to the wave boundary layer separating from seabed, then horseshoe vortex formatting and the horseshoe vortex are mainly responsible for scour around foundation (see Figure 22). The Froude number Fr is the key parameter to influence the scale and intensity of horseshoe vortex. The Fr under waves can be calculated by the following formula [42]

Fr=UwgD−−−√�r=�w��(34)

where Uw is the mean water particle velocity during 1/4 cycle of wave oscillation, obtained from the following formula. Noteworthy is that the root-mean-square (RMS) value of near-bed velocity amplitude Uwm,rms is used for calculating Uwm.

Uw=1T/4∫0T/4Uwmsin(t/T)dt=2πUwm�w=1�/4∫0�/4�wmsin(�/�)��=2��wm(35)

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Figure 22. Sketch of flow field at upstream USAF edges.

Tavouktsoglou et al. [25] proposed the following formula between Fr and the vertical location of the stagnation y

yh∝Fer�ℎ∝�r�(36)

where e is constant.

The Figure 23 displays the relationship between Seq/D and Fr of the present study. In order to compare with the simulating results, the experimental data of Corvaro et al. [21] was also depicted in Figure 23. As shown in Figure 23, the equilibrium scour depth appears a logarithmic increase as Fr increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increase of Fr, which is benefit for the wave boundary layer separating from seabed, resulting in the high-intensity horseshoe vortex, hence, causing intensive scour around USAF. Based on the previous study of Tavouktsoglou et al. [25] for scour around pile under currents, the high Fr leads to the stagnation point is closer to the mean sea level for shallow water, causing the stronger downflow kinetic energy. As mentioned in previous section, the energy of downflow at upstream makes up the energy of the subsequent horseshoe vortex, so the stronger downflow kinetic energy results in the more intensive horseshoe vortex. Therefore, the higher Fr leads to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably. Qi and Gao [19] carried out a series of flume tests to investigate the scour around pile under regular waves, and proposed the fitting formula between Seq/D and Fr as following

lg(Seq/D)=Aexp(B/Fr)+Clg(�eq/�)=�exp(�/�r)+�(37)

where A, B and C are constant.

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Figure 23. The fitting curve between Seq/D and Fr.

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Figure 24. Sketch of adverse pressure gradient at upstream USAF edges.

Took the Equation (37) to fit the simulating results with A = −0.002, B = 0.686 and C = −0.808, and the results are shown in Figure 23. From Figure 23, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Fr in present study is consistent with Equation (37) basically, meaning the Equation (37) is applicable to express the relationship of Seq/D with Fr around USAF under random waves.

4.4.2. Influence of Euler Number

The Euler number Eu is the influencing factor for the hydrodynamic field around foundation. The Eu under waves can be calculated by the following formula. The Eu can be represented by the Equation (38) for uniform cylinders [25]. The root-mean-square (RMS) value of near-bed velocity amplitude Um,rms is used for calculating Um.

Eu=U2mgD�u=�m2��(38)

where Um is depth-averaged flow velocity.

The Figure 25 displays the relationship between Seq/D and Eu of the present study. In order to compare with the simulating results, the experimental data of Sumer and Fredsøe [16] and Corvaro et al. [21] were also plotted in Figure 25. As shown in Figure 25, similar with the varying trend of Seq/D and Fr, the equilibrium scour depth appears a logarithmic increase as Eu increases and approaches the mathematical asymptotic value, which is also consistent with the experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21]. According to Figure 24, the adverse pressure gradient pressure at upstream USAF edges increases with the increasing of Eu, which is benefit for the wave boundary layer separating from seabed, inducing the high-intensity horseshoe vortex, hence, causing intensive scour around USAF.

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Figure 25. The fitting curve between Seq/D and Eu.

Therefore, the variation of Fr and Eu reflect the magnitude of adverse pressure gradient pressure at upstream. Given that, the Equation (37) also was used to fit the simulating results with A = 8.875, B = 0.078 and C = −9.601, and the results are shown in Figure 25. From Figure 25, the simulating results evenly distribute around the Equation (37) and the varying trend of Seq/D and Eu in present study is consistent with Equation (37) basically, meaning the Equation (37) is also applicable to express the relationship of Seq/D with Eu around USAF under random waves. Additionally, according to the above description of Fr, it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex by influencing the position of stagnation point y presumably.

5. Conclusions

A series of numerical models were established to investigate the local scour around umbrella suction anchor foundation (USAF) under random waves. The numerical model was validated for hydrodynamic and morphology parameters by comparing with the experimental data of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22]. Based on the simulating results, the scour evolution and scour mechanisms around USAF under random waves were analyzed respectively. Two revised models were proposed according to the model of Raaijmakers and Rudolph [34] and the stochastic model developed by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves. Finally, a parametric study was carried out with the present model to study the effects of the Froude number Fr and Euler number Eu to the equilibrium scour depth around USAF under random waves. The main conclusions can be described as follows.(1)

The packed sediment scour model and the RNG k−ε turbulence model were used to simulate the sand particles transport processes and the flow field around UASF respectively. The scour evolution obtained by the present model agrees well with the experimental results of Khosronejad et al. [52], Petersen et al. [17], Sumer and Fredsøe [16] and Schendel et al. [22], which indicates that the present model is accurate and reasonable for depicting the scour morphology around UASF under random waves.(2)

The vortex system at wave crest phase is mainly related to the scour process around USAF under random waves. The maximum scour depth appeared at the lee-side of the USAF at the initial stage (t < 1200 s). Subsequently, when t > 2400 s, the location of the maximum scour depth shifted to the upside of the USAF at an angle of about 45° with respect to the wave propagating direction.(3)

The error is negligible and the Raaijmakers’s model is of relatively high accuracy for predicting scour around USAF under random waves when KC is calculated by KCs,p. Given that, a further revision model (Equation (31)) was proposed according to Raaijmakers’s model to predict the equilibrium scour depth around USAF under random waves and it shows good agreement with the simulating results of the present study when KCs,p < 8.(4)

Another further revision model (Equation (33)) was proposed according to the stochastic model established by Myrhaug and Rue [37] to predict the equilibrium scour depth around USAF under random waves, and the predicting results are the most favorable for n = 10 when KCrms,a < 4. However, contrary to the case of low KCrms,a, the predicting results are the most favorable for n = 2 when KCrms,a > 4 by the comparison with experimental results of Sumer and Fredsøe [16] and Corvaro et al. [21].(5)

The same formula (Equation (37)) is applicable to express the relationship of Seq/D with Eu or Fr, and it can be inferred that the higher Fr and Eu both lead to the more intensive horseshoe vortex and larger Seq.

Author Contributions

Conceptualization, H.L. (Hongjun Liu); Data curation, R.H. and P.Y.; Formal analysis, X.W. and H.L. (Hao Leng); Funding acquisition, X.W.; Writing—original draft, R.H. and P.Y.; Writing—review & editing, X.W. and H.L. (Hao Leng); The final manuscript has been approved by all the authors. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Fundamental Research Funds for the Central Universities (grant number 202061027) and the National Natural Science Foundation of China (grant number 41572247).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Conflicts of Interest

The authors declare no conflict of interest.

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Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng. 2021, 9, 886. https://doi.org/10.3390/jmse9080886

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Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886

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Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

Optimized Vegetation Density to Dissipate Energy of Flood Flow in Open Canals

열린 운하에서 홍수 흐름의 에너지를 분산시키기 위해 최적화된 식생 밀도

Mahdi Feizbahr,1Navid Tonekaboni,2Guang-Jun Jiang,3,4and Hong-Xia Chen3,4
Academic Editor: Mohammad Yazdi

Abstract

강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.

Abstract

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [1–14]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [15–27]. Consequently, it is necessary to study the effects of the passive factors on the active domain [28–36]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [38–41].

One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [43–45]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [47, 48].

Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity  is another form of current resistance. The reason for using the  ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where n, f, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.

On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

By using equation (6), equation (5) is converted as follows:

Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the  ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [45, 55].

One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [47, 57, 58] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [45, 59–61]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [49, 63–66] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where  is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where  are mass accelerations in the directions x, y, z and  are viscosity accelerations in the directions x, y, z and are obtained from the following equations:

Shear stresses  in equation (11) are obtained from the following equations:

The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).

Table 1 

The studied models.

The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After  seconds, this model reached a convergence accuracy of .

Figure 1 

The simulated model and its boundary conditions.

Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

Any control and simulation system has some inputs that we should determine to test any technology [70–77]. Determination and true implementation of such parameters is one of the key steps of any simulation [23, 78–81] and computing procedure [82–86]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [87, 88]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

Figure 2 

Modeling the plant with cylindrical tubes at the bottom of the canal.

Figure 3 

Velocity profiles in positions 2 and 5.

The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

2. Modeling Results

After analyzing the models, the results were shown in graphs (Figures 4–14 ). The total number of experiments in this study was 48 due to the limitations of modeling.


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Figure 4 

Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5 

Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6 

Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7 

Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8 

Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.


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Figure 9 

Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10 

Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11 

Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12 

Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13 

Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.


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Figure 14 

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5–10, which can be justified by increasing the speed and, of course, increasing the Froude number.

With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 5–8 and 10, 11), which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

Figure 15 

Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 16 

Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 17 

Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 18 

Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.


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Figure 19 

Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.


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Figure 20 

Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [2, 7, 8, 15, 18, 89–94]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [95–99].


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Figure 21 

Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

Nomenclature

n:Manning’s roughness coefficient
C:Chézy roughness coefficient
f:Darcy–Weisbach coefficient
V:Flow velocity
R:Hydraulic radius
g:Gravitational acceleration
y:Flow depth
Ks:Bed roughness
A:Constant coefficient
:Reynolds number
∂y/∂x:Depth of water change
S0:Slope of the canal floor
Sf:Slope of energy line
Fr:Froude number
D:Characteristic length of the canal
G:Mass acceleration
:Shear stresses.

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

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Figure 2: 3D (left) and 2D (right) views of wave elevation using case C

CFD 접근법을 사용하여 파도에서 하이드로포일의 SEAKEEPING 성능

SYAFIQ ZIKRYAND FITRIADHY*
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, 21030 Kuala
Terengganu, Terengganu, Malaysia
*
Corresponding author: naoe.afit@gmail.com http://doi.org/10.46754/umtjur.2021.07.017

Abstract

수중익선은 일반적으로 열악한 환경 조건으로 인해 승객의 편안함에 영향을 미칠 수 있는 높은 저항과 과도한 수직 운동(히브 및 피치)을 경험합니다. 따라서 복잡한 유체역학적 현상이 존재하기 때문에 파랑에서 수중익선의 내항성능을 규명할 필요가 있다.

이를 위해 수중익선 운동에 대한 CFD(Computational Fluid Dynamic) 해석을 제안한다. Froude Number 및 포일 받음각과 같은 여러 매개변수가 고려되었습니다.

그 결과 Froude Number의 후속 증가는 히브 및 피치 운동에 반비례한다는 것이 밝혀졌습니다. 본질적으로 이것은 높은 응답 진폭 연산자(RAO)의 형태로 제공되는 수중익선 항해 성능의 업그레이드로 이어졌습니다.

또한 포일 선수의 증가하는 각도는 히브 운동에 비례하는 반면, 포일 선미는 7.5o에서 낮은 히브 운동을 보였고, 그 다음으로 5o, 10o 순으로 나타났다. 피치모션의 경우 포일 보우의 증가는 5o에서 더 낮았고, 그 다음이 10o, 7.5o 순이었다. 포일 선미의 증가는 수중익선에 의한 피치 모션 경험에 비례했습니다.

일반적으로 이 CFD 시뮬레이션은 앞서 언급한 설계 매개변수와 관련하여 공해 상태에서 수중익선 설계의 운영 효율성을 보장하는 데 매우 유용합니다.

Keywords

CFD, hydrofoil, foil angle of attack, heave, pitch.

Figure 1: Overall mesh block being used in simulation
Figure 1: Overall mesh block being used in simulation
Figure 2: 3D (left) and 2D (right) views of wave elevation using case C
Figure 2: 3D (left) and 2D (right) views of wave elevation using case C

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Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0

Reorientation of Cryogenic Fluids Upon Step Reduction of Gravity

단계적 중력 감소 시 극저온 유체의 방향 전환

Malte Stief∗, Jens Gerstmann∗∗, and Michael E. Dreyer∗∗∗
ZARM, Center of Applied Space Technology and Microgravity, University of Bremen, Am Fallturm, D-28359 Bremen
Experiments to observe the surface oscillation of cryogenic liquids have been performed with liquid nitrogen inside a 50 mm
diameter right circular cylinder. The surface oscillation is driven by the capillary force that becomes dominant after a sudden
reduction of the gravity acceleration acting on the liquid. The experiments show differences from the speculated behavior and
enables one to observe new features.

Introduction and motivation

최근 몇 년 동안 Bremen의 낙하탑에서 중력의 단계적 감소 시 방향 재지향 거동과 표면 진동을 조사하기 위해 수많은 실험이 수행되었습니다[1]. 이 실험의 원리는 그림 1에 나와 있습니다.

그림 1의 왼쪽에 표시된 것처럼 오른쪽 원형 원통형 용기에 테스트 액체를 레벨 h0까지 채웁니다. 처음에 액체는 정지 상태이며 중앙에서 평평한 인터페이스를 형성합니다.

초기 중력 가속도 kzi ≈ 9.81 [m/s2]와 결과적으로 높은 BOND 수(Bo = ρkziR2/σ)로 인해 실린더의 대칭축에서. 낙하탑에서 실험 캡슐의 방출에 의해 확립된 μ-중력 환경 kz ≈ 0 [m/s2]로의 갑작스러운 전환과 함께 자유 표면은 진동 운동으로 새로운 평형 구성을 찾기 시작합니다(그림의 오른쪽) 1). 이러한 움직임은 그림 1의 중앙에 스케치되어 있습니다.

표면 진동의 구동력은 접착력과 결합된 표면 장력이며, 댐핑은 액체의 점도에 의해 제어됩니다. 위치가 zw인 벽에서 접촉선의 이동은 접촉각 γ에 의해 제어됩니다. 접촉각이 작은 액체용 γ ≈ 0◦

In recent years numerous experiments have been carried out to investigate the reorientation behavior and surface oscillations upon step reduction of gravity at the drop tower in Bremen [1]. The principals of these experiments are shown in figure 1. A right circular cylindrical container is filled up to the level h0 with the test liquid, as shown on the left of figure 1. Initially the liquid is quiescent and forms a flat interface at the center, in the symmetry axis of the cylinder, due to the initial gravity acceleration kzi ≈ 9.81 [m/s2] and the resulting high BOND number (Bo = ρkziR2/σ). With the sudden transition to the µ-gravity environment kz ≈ 0 [m/s2], which is established by the release of the experiment capsular in the drop tower, the free surface is initiated to search its new equilibrium configuration (right side of figure 1) with an oscillatory motion. These movements are sketched in the center of figure 1. The driving force for the surface oscillation is the surface tension in combination with the adhesion force where the damping is controlled by the viscosity of the liquid. The movement of the contact line at the wall, with its position zw, is governed by the contact angle γ. For liquids with small contact angle γ ≈ 0◦

Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0
Fig. 1 Oscillation of a free surface due to the step reduction of gravity acceleration from kzi ≈ 9.81 to kz ≈ 0
Fig. 2 Experiment picture-series showing the oscillation of the free surface at different times for a 50 mm diameter cylinder.
Fig. 2 Experiment picture-series showing the oscillation of the free surface at different times for a 50 mm diameter cylinder.

References

[1] M. Michaelis, Kapillarinduzierte Schwingungen freier Fl¨ussigkeitsoberfl¨achen, Dissertation Universit¨at Bremen, Fortschritt-Berichte
Nr. 454 (VDI Verlag, D¨usseldorf, 2003).

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Figure 5. Schematic view of flap and support structure [32]

Design Optimization of Ocean Renewable Energy Converter Using a Combined Bi-level Metaheuristic Approach

결합된 Bi-level 메타휴리스틱 접근법을 사용한 해양 재생 에너지 변환기의 설계 최적화

Erfan Amini a1, Mahdieh Nasiri b1, Navid Salami Pargoo a, Zahra Mozhgani c, Danial Golbaz d, Mehrdad Baniesmaeil e, Meysam Majidi Nezhad f, Mehdi Neshat gj, Davide Astiaso Garcia h, Georgios Sylaios i

Abstract

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

1. Introduction

The increase in energy demand, the limitations of fossil fuels, as well as environmental crises, such as air pollution and global warming, are the leading causes of calling more attention to harvesting renewable energy recently [1], [2], [3]. While still in its infancy, ocean wave energy has neither reached commercial maturity nor technological convergence. In recent decades, remarkable progress has been made in the marine energy domain, which is still in the early stage of development, to improve the technology performance level (TPL) [4], [5]and technology readiness level (TRL) of wave energy converters (WECs). This has been achieved using novel modeling techniques [6], [7], [8], [9], [10], [11], [12], [13], [14] to gain the following advantages [15]: (i) As a source of sustainable energy, it contributes to the mix of energy resources that leads to greater diversity and attractiveness for coastal cities and suppliers. [16] (ii) Since wave energy can be exploited offshore and does not require any land, in-land site selection would be less expensive and undesirable visual effects would be reduced. [17] (iii) When the best layout and location of offshore site are taken into account, permanent generation of energy will be feasible (as opposed to using solar energy, for example, which is time-dependent) [18].

In general, the energy conversion process can be divided into three stages in a WEC device, including primary, secondary, and tertiary stages [19], [20]. In the first stage of energy conversion, which is the subject of this study, the wave power is converted to mechanical power by wave-structure interaction (WSI) between ocean waves and structures. Moreover, the mechanical power is transferred into electricity in the second stage, in which mechanical structures are coupled with power take-off systems (PTO). At this stage, optimal control strategies are useful to tune the system dynamics to maximize power output [10], [13], [12]. Furthermore, the tertiary energy conversion stage revolves around transferring the non-standard AC power into direct current (DC) power for energy storage or standard AC power for grid integration [21], [22]. We discuss only the first stage regardless of the secondary and tertiary stages. While Page 1 of 16 WECs include several categories and technologies such as terminators, point absorbers, and attenuators [15], [23], we focus on oscillating surge wave energy converters (OSWECs) in this paper due to its high capacity for industrialization [24].

Over the past two decades, a number of studies have been conducted to understand how OSWECs’ structures and interactions between ocean waves and flaps affect converters performance. Henry et al.’s experiment on oscillating surge wave energy converters is considered as one of the most influential pieces of research [25], which demonstrated how the performance of oscillating surge wave energy converters (OSWECs) is affected by seven different factors, including wave period, wave power, flap’s relative density, water depth, free-board of the flap, the gap between the tubes, gap underneath the flap, and flap width. These parameters were assessed in their two models in order to estimate the absorbed energy from incoming waves [26], [27]. In addition, Folly et al. investigated the impact of water depth on the OSWECs performance analytically, numerically, and experimentally. According to this and further similar studies, the average annual incident wave power is significantly reduced by water depth. Based on the experimental results, both the surge wave force and the power capture of OSWECs increase in shallow water [28], [29]. Following this, Sarkar et al. found that under such circumstances, the device that is located near the coast performs much better than those in the open ocean [30]. On the other hand, other studies are showing that the size of the converter, including height and width, is relatively independent of the location (within similar depth) [31]. Subsequently, Schmitt et al. studied OSWECs numerically and experimentally. In fact, for the simulation of OSWEC, OpenFOAM was used to test the applicability of Reynolds-averaged Navier-Stokes (RANS) solvers. Then, the experimental model reproduced the numerical results with satisfying accuracy [32]. In another influential study, Wang et al. numerically assessed the effect of OSWEC’s width on their performance. According to their findings, as converter width increases, its efficiency decreases in short wave periods while increases in long wave periods [33]. One of the main challenges in the analysis of the OSWEC is the coupled effect of hydrodynamic and geometric variables. As a result, numerous cutting-edge geometry studies have been performed in recent years in order to find the optimal structure that maximizes power output and minimizes costs. Garcia et al. reviewed hull geometry optimization studies in the literature in [19]. In addition, Guo and Ringwood surveyed geometric optimization methods to improve the hydrodynamic performance of OSWECs at the primary stage [14]. Besides, they classified the hull geometry of OSWECs based on Figure 1. Subsequently, Whittaker et al. proposed a different design of OSWEC called Oyster2. There have been three examples of different geometries of oysters with different water depths. Based on its water depth, they determined the width and height of the converter. They also found that in the constant wave period the less the converter’s width, the less power captures the converter has [34]. Afterward, O’Boyle et al. investigated a type of OSWEC called Oyster 800. They compared the experimental and numerical models with the prototype model. In order to precisely reproduce the shape, mass distribution, and buoyancy properties of the prototype, a 40th-scale experimental model has been designed. Overall, all the models were fairly accurate according to the results [35].

Inclusive analysis of recent research avenues in the area of flap geometry has revealed that the interaction-based designs of such converters are emerging as a novel approach. An initiative workflow is designed in the current study to maximizing the wave energy extrication by such systems. To begin with, a sensitivity analysis plays its role of determining the best hydrodynamic values for installing the converter’s flap. Then, all flap dimensions and characteristics come into play to finalize the primary model. Following, interactive designs is proposed to increase the influence of incident waves on the body by adding ribs on both sides of the flap as a novel design. Finally, a new bi-level metaheuristic method is proposed to consider the effects of simultaneous changes in ribs properties and other design parameters. We hope this novel approach will be utilized to make big-scale projects less costly and justifiable. The efficiency of the method is also compared with four well known metaheuristic algorithms and out weight them for this application.

This paper is organized as follows. First, the research methodology is introduced by providing details about the numerical model implementation. To that end, we first introduced the primary model’s geometry and software details. That primary model is later verified with a benchmark study with regard to the flap angle of rotation and water surface elevation. Then, governing equations and performance criteria are presented. In the third part of the paper, we discuss the model’s sensitivity to lower and upper parts width (we proposed a two cross-sectional design for the flap), bottom elevation, and freeboard. Finally, the novel optimization approach is introduced in the final part and compared with four recent metaheuristic algorithms.

2. Numerical Methods

In this section, after a brief introduction of the numerical software, Flow3D, boundary conditions are defined. Afterwards, the numerical model implementation, along with primary model properties are described. Finally, governing equations, as part of numerical process, are discussed.

2.1. Model Setup

FLOW-3D is a powerful and comprehensive CFD simulation platform for studying fluid dynamics. This software has several modules to solve many complex engineering problems. In addition, modeling complex flows is simple and effective using FLOW-3D’s robust meshing capabilities [36]. Interaction between fluid and moving objects might alter the computational range. Dynamic meshes are used in our modeling to take these changes into account. At each time step, the computational node positions change in order to adapt the meshing area to the moving object. In addition, to choose mesh dimensions, some factors are taken into account such as computational accuracy, computational time, and stability. The final grid size is selected based on the detailed procedure provided in [37]. To that end, we performed grid-independence testing on a CFD model using three different mesh grid sizes of 0.01, 0.015, and 0.02 meters. The problem geometry and boundary conditions were defined the same, and simulations were run on all three grids under the same conditions. The predicted values of the relevant variable, such as velocity, was compared between the grids. The convergence behavior of the numerical solution was analyzed by calculating the relative L2 norm error between two consecutive grids. Based on the results obtained, it was found that the grid size of 0.02 meters showed the least error, indicating that it provided the most accurate and reliable solution among the three grids. Therefore, the grid size of 0.02 meters was selected as the optimal spatial resolution for the mesh grid.

In this work, the flume dimensions are 10 meters long, 0.1 meters wide, and 2.2 meters high, which are shown in figure2. In addition, input waves with linear characteristics have a height of 0.1 meters and a period of 1.4 seconds. Among the linear wave methods included in this software, RNGk-ε and k- ε are appropriate for turbulence model. The research of Lopez et al. shows that RNGk- ε provides the most accurate simulation of turbulence in OSWECs [21]. We use CATIA software to create the flap primary model and other innovative designs for this project. The flap measures 0.1 m x 0.65 m x 0.360 m in x, y and z directions, respectively. In Figure 3, the primary model of flap and its dimensions are shown. In this simulation, five boundaries have been defined, including 1. Inlet, 2. Outlet, 3. Converter flap, 4. Bed flume, and 5. Water surface, which are shown in figure 2. Besides, to avoid wave reflection in inlet and outlet zones, Flow3D is capable of defining some areas as damping zones, the length of which has to be one to one and a half times the wavelength. Therefore, in the model, this length is considered equal to 2 meters. Furthermore, there is no slip in all the boundaries. In other words, at every single time step, the fluid velocity is zero on the bed flume, while it is equal to the flap velocity on the converter flap. According to the wave theory defined in the software, at the inlet boundary, the water velocity is called from the wave speed to be fed into the model.

2.2. Verification

In the current study, we utilize the Schmitt experimental model as a benchmark for verification, which was developed at the Queen’s University of Belfast. The experiments were conducted on the flap of the converter, its rotation, and its interaction with the water surface. Thus, the details of the experiments are presented below based up on the experimental setup’s description [38]. In the experiment, the laboratory flume has a length of 20m and a width of 4.58m. Besides, in order to avoid incident wave reflection, a wave absorption source is devised at the end of the left flume. The flume bed, also, includes two parts with different slops. The flap position and dimensions of the flume can be seen in Figure4. In addition, a wave-maker with 6 paddles is installed at one end. At the opposite end, there is a beach with wire meshes. Additionally, there are 6 indicators to extract the water level elevation. In the flap model, there are three components: the fixed support structure, the hinge, and the flap. The flap measures 0.1m x 0.65m x 0.341m in x, y and z directions, respectively. In Figure5, the details are given [32]. The support structure consists of a 15 mm thick stainless steel base plate measuring 1m by 1.4m, which is screwed onto the bottom of the tank. The hinge is supported by three bearing blocks. There is a foam centerpiece on the front and back of the flap which is sandwiched between two PVC plates. Enabling changes of the flap, three metal fittings link the flap to the hinge. Moreover, in this experiment, the selected wave is generated based on sea wave data at scale 1:40. The wave height and the wave period are equal to 0.038 (m) and 2.0625 (s), respectively, which are tantamount to a wave with a period of 13 (s) and a height of 1.5 (m).

Two distinct graphs illustrate the numerical and experi-mental study results. Figure6 and Figure7 are denoting the angle of rotation of flap and surface elevation in computational and experimental models, respectively. The two figures roughly represent that the numerical and experimental models are a good match. However, for the purpose of verifying the match, we calculated the correlation coefficient (C) and root mean square error (RMSE). According to Figure6, correlation coefficient and RMSE are 0.998 and 0.003, respectively, and in Figure7 correlation coefficient and RMSE are respectively 0.999 and 0.001. Accordingly, there is a good match between the numerical and empirical models. It is worth mentioning that the small differences between the numerical and experimental outputs may be due to the error of the measuring devices and the calibration of the data collection devices.

Including continuity equation and momentum conserva- tion for incompressible fluid are given as [32], [39]:(1)

where P represents the pressure, g denotes gravitational acceleration, u represents fluid velocity, and Di is damping coefficient. Likewise, the model uses the same equation. to calculate the fluid velocity in other directions as well. Considering the turbulence, we use the two-equation model of RNGK- ε. These equations are:

(3)��t(��)+����(����)=����[�eff�������]+��-��and(4)���(��)+����(����)=����[�eff�������]+�1�∗����-��2��2�Where �2� and �1� are constants. In addition, �� and �� represent the turbulent Prandtl number of � and k, respectively.

�� also denote the production of turbulent kinetic energy of k under the effect of velocity gradient, which is calculated as follows:(5)��=�eff[�����+�����]�����(6)�eff=�+��(7)�eff=�+��where � is molecular viscosity,�� represents turbulence viscosity, k denotes kinetic energy, and ∊∊ is energy dissipation rate. The values of constant coefficients in the two-equation RNGK ∊-∊ model is as shown in the Table 1 [40].Table 2.

Table 1. Constant coefficients in RNGK-∊ model

Factors��0�1�2������
Quantity0.0124.381.421.681.391.390.084

Table 2. Flap properties

Joint height (m)0.476
Height of the center of mass (m)0.53
Weight (Kg)10.77

It is worth mentioning that the volume of fluid method is used to separate water and air phases in this software [41]. Below is the equation of this method [40].(8)����+����(���)=0where α and 1 − α are portion of water phase and air phase, respectively. As a weighting factor, each fluid phase portion is used to determine the mixture properties. Finally, using the following equations, we calculate the efficiency of converters [42], [34], [43]:(9)�=14|�|2�+�2+(�+�a)2(�n2-�2)2where �� represents natural frequency, I denotes the inertia of OSWEC, Ia is the added inertia, F is the complex wave force, and B denotes the hydrodynamic damping coefficient. Afterward, the capture factor of the converter is calculated by [44]:(10)��=�1/2��2����gw where �� represents the capture factor, which is the total efficiency of device per unit length of the wave crest at each time step [15], �� represent the dimensional amplitude of the incident wave, w is the flap’s width, and Cg is the group velocity of the incident wave, as below:(11)��=��0·121+2�0ℎsinh2�0ℎwhere �0 denotes the wave number, h is water depth, and H is the height of incident waves.

According to previous sections ∊,����-∊ modeling is used for all models simulated in this section. For this purpose, the empty boundary condition is used for flume walls. In order to preventing wave reflection at the inlet and outlet of the flume, the length of wave absorption is set to be at least one incident wavelength. In addition, the structured mesh is chosen, and the mesh dimensions are selected in two distinct directions. In each model, all grids have a length of 2 (cm) and a height of 1 (cm). Afterwards, as an input of the software for all of the models, we define the time step as 0.001 (s). Moreover, the run time of every simulation is 30 (s). As mentioned before, our primary model is Schmitt model, and the flap properties is given in table2. For all simulations, the flume measures 15 meters in length and 0.65 meters in width, and water depth is equal to 0.335 (m). The flap is also located 7 meters from the flume’s inlet.

Finally, in order to compare the results, the capture factor is calculated for each simulation and compared to the primary model. It is worth mentioning that capture factor refers to the ratio of absorbed wave energy to the input wave energy.

According to primary model simulation and due to the decreasing horizontal velocity with depth, the wave crest has the highest velocity. Considering the fact that the wave’s orbital velocity causes the flap to move, the contact between the upper edge of the flap and the incident wave can enhance its performance. Additionally, the numerical model shows that the dynamic pressure decreases as depth increases, and the hydrostatic pressure increases as depth increases.

To determine the OSWEC design, it is imperative to understand the correlation between the capture factor, wave period, and wave height. Therefore, as it is shown in Figure8, we plot the change in capture factor over the variations in wave period and wave height in 3D and 2D. In this diagram, the first axis features changes in wave period, the second axis displays changes in wave height, and the third axis depicts changes in capture factor. According to our wave properties in the numerical model, the wave period and wave height range from 2 to 14 seconds and 2 to 8 meters, respectively. This is due to the fact that the flap does not oscillate if the wave height is less than 2 (m), and it does not reverse if the wave height is more than 8 (m). In addition, with wave periods more than 14 (s), the wavelength would be so long that it would violate the deep-water conditions, and with wave periods less than 2 (s), the flap would not oscillate properly due to the shortness of wavelength. The results of simulation are shown in Figure 8. As it can be perceived from Figure 8, in a constant wave period, the capture factor is in direct proportion to the wave height. It is because of the fact that waves with more height have more energy to rotate the flap. Besides, in a constant wave height, the capture factor increases when the wave period increases, until a given wave period value. However, the capture factor falls after this point. These results are expected since the flap’s angular displacement is not high in lower wave periods, while the oscillating motion of that is not fast enough to activate the power take-off system in very high wave periods.

As is shown in Figure 9, we plot the change in capture factor over the variations in wave period (s) and water depth (m) in 3D. As it can be seen in this diagram, the first axis features changes in water depth (m), the second axis depicts the wave period (s), and the third axis displays OSWEC’s capture factor. The wave period ranges from 0 to 10 seconds based on our wave properties, which have been adopted from Schmitt’s model, while water depth ranges from 0 to 0.5 meters according to the flume and flap dimensions and laboratory limitations. According to Figure9, for any specific water depth, the capture factor increases in a varying rate when the wave period increases, until a given wave period value. However, the capture factor falls steadily after this point. In fact, the maximum capture factor occurs when the wave period is around 6 seconds. This trend is expected since, in a specific water depth, the flap cannot oscillate properly when the wavelength is too short. As the wave period increases, the flap can oscillate more easily, and consequently its capture factor increases. However, the capture factor drops in higher wave periods because the wavelength is too large to move the flap. Furthermore, in a constant wave period, by changing the water depth, the capture factor does not alter. In other words, the capture factor does not depend on the water depth when it is around its maximum value.

3. Sensitivity Analysis

Based on previous studies, in addition to the flap design, the location of the flap relative to the water surface (freeboard) and its elevation relative to the flume bed (flap bottom elevation) play a significant role in extracting energy from the wave energy converter. This study measures the sensitivity of the model to various parameters related to the flap design including upper part width of the flap, lower part width of the flap, the freeboard, and the flap bottom elevation. Moreover, as a novel idea, we propose that the flap widths differ in the lower and upper parts. In Figure10, as an example, a flap with an upper thickness of 100 (mm) and a lower thickness of 50 (mm) and a flap with an upper thickness of 50 (mm) and a lower thickness of 100 (mm) are shown. The influence of such discrepancy between the widths of the upper and lower parts on the interaction between the wave and the flap, or in other words on the capture factor, is evaluated. To do so, other parameters are remained constant, such as the freeboard, the distance between the flap and the flume bed, and the wave properties.

In Figure11, models are simulated with distinct upper and lower widths. As it is clear in this figure, the first axis depicts the lower part width of the flap, the second axis indicates the upper part width of the flap, and the colors represent the capture factor values. Additionally, in order to consider a sufficient range of change, the flap thickness varies from half to double the value of the primary model for each part.

According to this study, the greater the discrepancy in these two parts, the lower the capture factor. It is on account of the fact that when the lower part of the flap is thicker than the upper part, and this thickness difference in these two parts is extremely conspicuous, the inertia against the motion is significant at zero degrees of rotation. Consequently, it is difficult to move the flap, which results in a low capture factor. Similarly, when the upper part of the flap is thicker than the lower part, and this thickness difference in these two parts is exceedingly noticeable, the inertia is so great that the flap can not reverse at the maximum degree of rotation. As the results indicate, the discrepancy can enhance the performance of the converter if the difference between these two parts is around 20%. As it is depicted in the Figure11, the capture factor reaches its own maximum amount, when the lower part thickness is from 5 to 6 (cm), and the upper part thickness is between 6 and 7 (cm). Consequently, as a result of this discrepancy, less material will be used, and therefore there will be less cost.

As illustrated in Figure12, this study examines the effects of freeboard (level difference between the flap top and water surface) and the flap bottom elevation (the distance between the flume bed and flap bottom) on the converter performance. In this diagram, the first axis demonstrates the freeboard and the second axis on the left side displays the flap bottom elevation, while the colors indicate the capture factor. In addition, the feasible range of freeboard is between -15 to 15 (cm) due to the limitation of the numerical model, so that we can take the wave slamming and the overtopping into consideration. Additionally, based on the Schmitt model and its scaled model of 1:40 of the base height, the flap bottom should be at least 9 (cm) high. Since the effect of surface waves is distributed over the depth of the flume, it is imperative to maintain a reasonable flap height exposed to incoming waves. Thus, the maximum flap bottom elevation is limited to 19 (cm). As the Figure12 pictures, at constant negative values of the freeboard, the capture factor is in inverse proportion with the flap bottom elevation, although slightly.

Furthermore, at constant positive values of the freeboard, the capture factor fluctuates as the flap bottom elevation decreases while it maintains an overall increasing trend. This is on account of the fact that increasing the flap bottom elevation creates turbulence flow behind the flap, which encumbers its rotation, as well as the fact that the flap surface has less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, the capture factor increases by raising the freeboard. This is due to the fact that there is overtopping with adverse impacts on the converter performance when the freeboard is negative and the flap is under the water surface. Besides, increasing the freeboard makes the wave slam more vigorously, which improves the converter performance.

Adding ribs to the flap surface, as shown in Figure13, is a novel idea that is investigated in the next section. To achieve an optimized design for the proposed geometry of the flap, we determine the optimal number and dimensions of ribs based on the flap properties as our decision variables in the optimization process. As an example, Figure13 illustrates a flap with 3 ribs on each side with specific dimensions.

Figure14 shows the flow velocity field around the flap jointed to the flume bed. During the oscillation of the flap, the pressure on the upper and lower surfaces of the flap changes dynamically due to the changing angle of attack and the resulting change in the direction of fluid flow. As the flap moves upwards, the pressure on the upper surface decreases, and the pressure on the lower surface increases. Conversely, as the flap moves downwards, the pressure on the upper surface increases, and the pressure on the lower surface decreases. This results in a cyclic pressure variation around the flap. Under certain conditions, the pressure field around the flap can exhibit significant variations in magnitude and direction, forming vortices and other flow structures. These flow structures can affect the performance of the OSWEC by altering the lift and drag forces acting on the flap.

4. Design Optimization

We consider optimizing the design parameters of the flap of converter using a nature-based swarm optimization method, that fall in the category of metaheuristic algorithms [45]. Accordingly, we choose four state-of-the-art algorithms to perform an optimization study. Then, based on their performances to achieve the highest capture factor, one of them will be chosen to be combined with the Hill Climb algorithm to carry out a local search. Therefore, in the remainder of this section, we discuss the search process of each algorithm and visualize their performance and convergence curve as they try to find the best values for decision variables.

4.1. Metaheuristic Approaches

As the first considered algorithm, the Gray Wolf Optimizer (GWO) algorithm simulates the natural leadership and hunting performance of gray wolves which tend to live in colonies. Hunters must obey the alpha wolf, the leader, who is responsible for hunting. Then, the beta wolf is at the second level of the gray wolf hierarchy. A subordinate of alpha wolf, beta stands under the command of the alpha. At the next level in this hierarchy, there are the delta wolves. They are subordinate to the alpha and beta wolves. This category of wolves includes scouts, sentinels, elders, hunters, and caretakers. In this ranking, omega wolves are at the bottom, having the lowest level and obeying all other wolves. They are also allowed to eat the prey just after others have eaten. Despite the fact that they seem less important than others, they are really central to the pack survival. Since, it has been shown that without omega wolves, the entire pack would experience some problems like fighting, violence, and frustration. In this simulation, there are three primary steps of hunting including searching, surrounding, and finally attacking the prey. Mathematically model of gray wolves’ hunting technique and their social hierarchy are applied in determined by optimization. this study. As mentioned before, gray wolves can locate their prey and surround them. The alpha wolf also leads the hunt. Assuming that the alpha, beta, and delta have more knowledge about prey locations, we can mathematically simulate gray wolf hunting behavior. Hence, in addition to saving the top three best solutions obtained so far, we compel the rest of the search agents (also the omegas) to adjust their positions based on the best search agent. Encircling behavior can be mathematically modeled by the following equations: [46].(12)�→=|�→·��→(�)-�→(�)|(13)�→(�+1)=��→(�)-�→·�→(14)�→=2.�2→(15)�→=2�→·�1→-�→Where �→indicates the position vector of gray wolf, ��→ defines the vector of prey, t indicates the current iteration, and �→and �→are coefficient vectors. To force the search agent to diverge from the prey, we use �→ with random values greater than 1 or less than -1. In addition, C→ contains random values in the range [0,2], and �→ 1 and �2→ are random vectors in [0,1]. The second considered technique is the Moth Flame Optimizer (MFO) algorithm. This method revolves around the moths’ navigation mechanism, which is realized by positioning themselves and maintaining a fixed angle relative to the moon while flying. This effective mechanism helps moths to fly in a straight path. However, when the source of light is artificial, maintaining an angle with the light leads to a spiral flying path towards the source that causes the moth’s death [47]. In MFO algorithm, moths and flames are both solutions. The moths are actual search agents that fly in hyper-dimensional space by changing their position vectors, and the flames are considered pins that moths drop when searching the search space [48]. The problem’s variables are the position of moths in the space. Each moth searches around a flame and updates it in case of finding a better solution. The fitness value is the return value of each moth’s fitness (objective) function. The position vector of each moth is passed to the fitness function, and the output of the fitness function is assigned to the corresponding moth. With this mechanism, a moth never loses its best solution [49]. Some attributes of this algorithm are as follows:

  • •It takes different values to converge moth in any point around the flame.
  • •Distance to the flame is lowered to be eventually minimized.
  • •When the position gets closer to the flame, the updated positions around the flame become more frequent.

As another method, the Multi-Verse Optimizer is based on a multiverse theory which proposes there are other universes besides the one in which we all live. According to this theory, there are more than one big bang in the universe, and each big bang leads to the birth of a new universe [50]. Multi-Verse Optimizer (MVO) is mainly inspired by three phenomena in cosmology: white holes, black holes, and wormholes. A white hole has never been observed in our universe, but physicists believe the big bang could be considered a white hole [51]. Black holes, which behave completely in contrast to white holes, attract everything including light beams with their extremely high gravitational force [52]. In the multiverse theory, wormholes are time and space tunnels that allow objects to move instantly between any two corners of a universe (or even simultaneously from one universe to another) [53]. Based on these three concepts, mathematical models are designed to perform exploration, exploitation, and local search, respectively. The concept of white and black holes is implied as an exploration phase, while the concept of wormholes is considered as an exploitation phase by MVO. Additionally, each solution is analogous to a universe, and each variable in the solution represents an object in that universe. Furthermore, each solution is assigned an inflation rate, and the time is used instead of iterations. Following are the universe rules in MVO:

  • •The possibility of having white hole increases with the inflation rate.
  • •The possibility of having black hole decreases with the inflation rate.
  • •Objects tend to pass through black holes more frequently in universes with lower inflation rates.
  • •Regardless of inflation rate, wormholes may cause objects in universes to move randomly towards the best universe. [54]

Modeling the white/black hole tunnels and exchanging objects of universes mathematically was accomplished by using the roulette wheel mechanism. With every iteration, the universes are sorted according to their inflation rates, then, based on the roulette wheel, the one with the white hole is selected as the local extremum solution. This is accomplished through the following steps:

Assume that

(16)���=����1<��(��)����1≥��(��)

Where ��� represents the jth parameter of the ith universe, Ui indicates the ith universe, NI(Ui) is normalized inflation rate of the ith universe, r1 is a random number in [0,1], and j xk shows the jth parameter of the kth universe selected by a roulette wheel selection mechanism [54]. It is assumed that wormhole tunnels always exist between a universe and the best universe formed so far. This mechanism is as follows:(17)���=if�2<���:��+���×((���-���)×�4+���)�3<0.5��-���×((���-���)×�4+���)�3≥0.5����:���where Xj indicates the jth parameter of the best universe formed so far, TDR and WEP are coefficients, where Xj indicates the jth parameter of the best universelbjshows the lower bound of the jth variable, ubj is the upper bound of the jth variable, and r2, r3, and r4 are random numbers in [1], [54].

Finally, one of the newest optimization algorithms is WOA. The WOA algorithm simulates the movement of prey and the whale’s discipline when looking for their prey. Among several species, Humpback whales have a specific method of hunting [55]. Humpback whales can recognize the location of prey and encircle it before hunting. The optimal design position in the search space is not known a priori, and the WOA algorithm assumes that the best candidate solution is either the target prey or close to the optimum. This foraging behavior is called the bubble-net feeding method. Two maneuvers are associated with bubbles: upward spirals and double loops. A unique behavior exhibited only by humpback whales is bubble-net feeding. In fact, The WOA algorithm starts with a set of random solutions. At each iteration, search agents update their positions for either a randomly chosen search agent or the best solution obtained so far [56], [55]. When the best search agent is determined, the other search agents will attempt to update their positions toward that agent. It is important to note that humpback whales swim around their prey simultaneously in a circular, shrinking circle and along a spiral-shaped path. By using a mathematical model, the spiral bubble-net feeding maneuver is optimized. The following equation represents this behavior:(18)�→(�+1)=�′→·�bl·cos(2��)+�∗→(�)

Where:(19)�′→=|�∗→(�)-�→(�)|

X→(t+ 1) indicates the distance of the it h whale to the prey (best solution obtained so far),� is a constant for defining the shape of the logarithmic spiral, l is a random number in [−1, 1], and dot (.) is an element-by-element multiplication [55].

Comparing the four above-mentioned methods, simulations are run with 10 search agents for 400 iterations. In Figure 15, there are 20 plots the optimal values of different parameters in optimization algorithms. The five parameters of this study are freeboard, bottom elevations, number of ribs on the converter, rib thickness, and rib Height. The optimal value for each was found by optimization algorithms, naming WOA, MVO, MFO, and GWO. By looking through the first row, the freeboard parameter converges to its maximum possible value in the optimization process of GWO after 300 iterations. Similarly, MFO finds the same result as GWO. In contrast, the freeboard converges to its minimum possible value in MVO optimizing process, which indicates positioning the converter under the water. Furthermore, WOA found the optimal value of freeboard as around 0.02 after almost 200 iterations. In the second row, the bottom elevation is found at almost 0.11 (m) in all algorithms; however, the curves follow different trends in each algorithm. The third row shows the number of ribs, where results immediately reveal that it should be over 4. All algorithms coincide at 5 ribs as the optimal number in this process. The fourth row displays the trends of algorithms to find optimal rib thickness. MFO finds the optimal value early and sets it to around 0.022, while others find the same value in higher iterations. Finally, regarding the rib height, MVO, MFO, and GWO state that the optimal value is 0.06 meters, but WOA did not find a higher value than 0.039.

4.2. HCMVO Bi-level Approach

Despite several strong search characteristics of MVO and its high performance in various optimization problems, it suffers from a few deficiencies in local and global search mechanisms. For instance, it is trapped in the local optimum when wormholes stochastically generate many solutions near the best universe achieved throughout iterations, especially in solving complex multimodal problems with high dimensions [57]. Furthermore, MVO needs to be modified by an escaping strategy from the local optima to enhance the global search abilities. To address these shortages, we propose a fast and effective meta-algorithm (HCMVO) to combine MVO with a Random-restart hill-climbing local search. This meta-algorithm uses MVO on the upper level to develop global tracking and provide a range of feasible and proper solutions. The hill-climbing algorithm is designed to develop a comprehensive neighborhood search around the best-found solution proposed by the upper-level (MVO) when MVO is faced with a stagnation issue or falling into a local optimum. The performance threshold is formulated as follows.(20)Δ����THD=∑�=1�����TH��-����TH��-1�where BestTHDis the best-found solution per generation, andM is related to the domain of iterations to compute the average performance of MVO. If the proposed best solution by the local search is better than the initial one, the global best of MVO will be updated. HCMVO iteratively runs hill climbing when the performance of MVO goes down, each time with an initial condition to prepare for escaping such undesirable situations. In order to get a better balance between exploration and exploitation, the search step size linearly decreases as follows:(21)��=��-����Ma�iter��+1where iter and Maxiter are the current iteration and maximum number of evaluation, respectively. �� stands for the step size of the neighborhood search. Meanwhile, this strategy can improve the convergence rate of MVO compared with other algorithms.

Algorithm 1 shows the technical details of the proposed optimization method (HCMVO). The initial solution includes freeboard (�), bottom elevation (�), number of ribs (Nr), rib thickness (�), and rib height(�).

5. Conclusion

The high trend of diminishing worldwide energy resources has entailed a great crisis upon vulnerable societies. To withstand this effect, developing renewable energy technologies can open doors to a more reliable means, among which the wave energy converters will help the coastal residents and infrastructure. This paper set out to determine the optimized design for such devices that leads to the highest possible power output. The main goal of this research was to demonstrate the best design for an oscillating surge wave energy converter using a novel metaheuristic optimization algorithm. In this regard, the methodology was devised such that it argued the effects of influential parameters, including wave characteristics, WEC design, and interaction criteria.

To begin with, a numerical model was developed in Flow 3D software to simulate the response of the flap of a wave energy converter to incoming waves, followed by a validation study based upon a well-reputed experimental study to verify the accuracy of the model. Secondly, the hydrodynamics of the flap was investigated by incorporating the turbulence. The effect of depth, wave height, and wave period are also investigated in this part. The influence of two novel ideas on increasing the wave-converter interaction was then assessed: i) designing a flap with different widths in the upper and lower part, and ii) adding ribs on the surface of the flap. Finally, four trending single-objective metaheuristic optimization methods

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:�=30,�=5▹���������������������������������
03:�=〈F1,B1,N,R,H1〉,…〈FN,B2,N,R,HN〉⇒lb1N⩽�⩽ubN
04:Initialize parameters�ER,�DR,�EP,Best�,���ite��▹Wormhole existence probability (WEP)
05:��=����(��)
06:��=Normalize the inflation rate��
07:for iter in[1,⋯,���iter]do
08:for�in[1,⋯,�]do
09:Update�EP,�DR,Black����Index=�
10:for���[1,⋯,�]��
11:�1=����()
12:if�1≤��(��)then
13:White HoleIndex=Roulette�heelSelection(-��)
14:�(Black HoleIndex,�)=��(White HoleIndex,�)
15:end if
16:�2=����([0,�])
17:if�2≤�EPthen
18:�3=����(),�4=����()
19:if�3<0.5then
20:�1=((��(�)-��(�))�4+��(�))
21:�(�,�)=Best�(�)+�DR�
22:else
23:�(�,�)=Best�(�)-�DR�
24:end if
25:end if
26:end for
27:end for
28:�HD=����([�1,�2,⋯,�Np])
29:Bes�TH�itr=����HD
30:ΔBestTHD=∑�=1�BestTII��-BestTII��-1�
31:ifΔBestTHD<��then▹Perform hill climbing local search
32:BestTHD=����-�lim��������THD
33:end if
34:end for
35:return�,BestTHD▹Final configuration
36:end procedure

The implementation details of the hill-climbing algorithm applied in HCMPA can be seen in Algorithm 2. One of the critical parameters isg, which denotes the resolution of the neighborhood search around the proposed global best by MVO. If we set a small step size for hill-climbing, the convergence speed will be decreased. On the other hand, a large step size reinforces the exploration ability. Still, it may reduce the exploitation ability and in return increase the act of jumping from a global optimum or surfaces with high-potential solutions. Per each decision variable, the neighborhood search evaluates two different direct searches, incremental or decremental. After assessing the generated solutions, the best candidate will be selected to iterate the search algorithm. It is noted that the hill-climbing algorithm should not be applied in the initial iteration of the optimization process due to the immense tendency for converging to local optima. Meanwhile, for optimizing largescale problems, hill-climbing is not an appropriate selection. In order to improve understanding of the proposed hybrid optimization algorithm’s steps, the flowchart of HCMVO is designed and can be seen in Figure 16.

Figure 17 shows the observed capture factor (which is the absorbed energy with respect to the available energy) by each optimization algorithm from iterations 1 to 400. The algorithms use ten search agents in their modified codes to find the optimal solutions. While GWO and MFO remain roughly constant after iterations 54 and 40, the other three algorithms keep improving the capture factor. In this case, HCMVO and MVO worked very well in the optimizing process with a capture factor obtained by the former as 0.594 and by the latter as 0.593. MFO almost found its highest value before the iteration 50, which means the exploration part of the algorithm works out well. Similarly, HCMVO does the same. However, it keeps finding the better solution during the optimization process until the last iteration, indicating the strong exploitation part of the algorithm. GWO reveals a weakness in exploration and exploitation because not only does it evoke the least capture factor value, but also the curve remains almost unchanged throughout 350 iterations.

Figure 18 illustrates complex interactions between the five optimization parameters and the capture factor for HCMVO (a), MPA (b), and MFO (c) algorithms. The first interesting observation is that there is a high level of nonlinear relationships among the setting parameters that can make a multi-modal search space. The dark blue lines represent the best-found configuration throughout the optimisation process. Based on both HCMVO (a) and MVO (b), we can infer that the dark blue lines concentrate in a specific range, showing the high convergence ability of both HCMVO and MVO. However, MFO (c) could not find the exact optimal range of the decision variables, and the best-found solutions per generation distribute mostly all around the search space.

Empty CellAlgorithm 1: Hill Climb Multiverse Optimization
01:procedure HCMVO
02:Initialization
03:Initialize the constraints��1�,��1�
04:�1�=Mi�1�+���1�/�▹Compute the step size,�is search resolution
05:So�1=〈�,�,�,�,�〉▹���������������
06:�������1=����So�1▹���������ℎ���������
07:Main loop
08:for iter≤���ita=do
09:���=���±��
10:while�≤���(Sol1)do
11:���=���+�,▹����ℎ���ℎ��������ℎ
12:fitness��iter=�������
13:t = t+1
14:end while
15:〈�����,������max〉=����������
16:���itev=���Inde�max▹�������ℎ�������������������������������ℎ�������
17:��=��-����Max��+1▹�����������������
18:end for
19:return���iter,����
20:end procedure

were utilized to illuminate the optimum values of the design parameters, and the best method was chosen to develop a new algorithm that performs both local and global search methods.

The correlation between hydrodynamic parameters and the capture factor of the converter was supported by the results. For any given water depth, the capture factor increases as the wave period increases, until a certain wave period value (6 seconds) is reached, after which the capture factor gradually decreases. It is expected since the flap cannot oscillate effectively when the wavelength is too short for a certain water depth. Conversely, when the wavelength is too long, the capture factor decreases. Furthermore, under a constant wave period, increasing the water depth does not affect the capture factor. Regarding the sensitivity analysis, the study found that increasing the flap bottom elevation causes turbulence flow behind the flap and limitation of rotation, which leads to less interaction with the incoming waves. Furthermore, while keeping the flap bottom elevation constant, increasing the freeboard improves the capture factor. Overtopping happens when the freeboard is negative and the flap is below the water surface, which has a detrimental influence on converter performance. Furthermore, raising the freeboard causes the wave impact to become more violent, which increases converter performance.

In the last part, we discussed the search process of each algorithm and visualized their performance and convergence curves as they try to find the best values for decision variables. Among the four selected metaheuristic algorithms, the Multi-verse Optimizer proved to be the most effective in achieving the best answer in terms of the WEC capture factor. However, the MVO needed modifications regarding its escape approach from the local optima in order to improve its global search capabilities. To overcome these constraints, we presented a fast and efficient meta-algorithm (HCMVO) that combines MVO with a Random-restart hill-climbing local search. On a higher level, this meta-algorithm employed MVO to generate global tracking and present a range of possible and appropriate solutions. Taken together, the results demonstrated that there is a significant degree of nonlinearity among the setup parameters that might result in a multimodal search space. Since MVO was faced with a stagnation issue or fell into a local optimum, we constructed a complete neighborhood search around the best-found solution offered by the upper level. In sum, the newly-developed algorithm proved to be highly effective for the problem compared to other similar optimization methods. The strength of the current findings may encourage future investigation on design optimization of wave energy converters using developed geometry as well as the novel approach.

CRediT authorship contribution statement

Erfan Amini: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Mahdieh Nasiri: Conceptualization, Methodology, Validation, Data curation, Writing – original draft, Writing – review & editing, Visualization. Navid Salami Pargoo: Writing – original draft, Writing – review & editing. Zahra Mozhgani: Conceptualization, Methodology. Danial Golbaz: Writing – original draft. Mehrdad Baniesmaeil: Writing – original draft. Meysam Majidi Nezhad: . Mehdi Neshat: Supervision, Conceptualization, Writing – original draft, Writing – review & editing, Visualization. Davide Astiaso Garcia: Supervision. Georgios Sylaios: Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research has been carried out within ILIAD (Inte-grated Digital Framework for Comprehensive Maritime Data and Information Services) project that received funding from the European Union’s H2020 programme.

Data availability

Data will be made available on request.

References

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Figure 5 A schematic of the water model of reactor URO 200.

Physical and Numerical Modeling of the Impeller Construction Impact on the Aluminum Degassing Process

알루미늄 탈기 공정에 미치는 임펠러 구성의 물리적 및 수치적 모델링

Kamil Kuglin,1 Michał Szucki,2 Jacek Pieprzyca,3 Simon Genthe,2 Tomasz Merder,3 and Dorota Kalisz1,*

Mikael Ersson, Academic Editor

Author information Article notes Copyright and License information Disclaimer

Associated Data

Data Availability Statement

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Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

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1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

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2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1, Figure 2, Figure 3 and Figure 4, were printed on a 3D printer using the PLA (polylactide) material. The impeller design models differ in their shape and the number of holes through which the inert gas flows. Figure 1, Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

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Figure 1

A 3D model—impeller with four holes—variant B4.

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Figure 2

A 3D model—impeller with eight holes—variant B8.

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Figure 3

A 3D model—impeller with twelve holes—variant B12.

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Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g005.jpg

Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000–
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip–
Size of computational cell0.0034m

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In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g006.jpg

Figure 6

The velocity of the water depending on the size of the computational grid.

The quality of the generated computational meshes was checked using the criterion skewness angle QEAS [18]. This criterion is described by the following relationship:

QEAS=max{βmax−βeq180−βeq,βeq−βminβeq},

(1)

where βmax, βmin are the maximal and minimal angles (in degrees) between the edges of the cell, and βeq is the angle corresponding to an ideal cell, which for cubic cells is 90°.

Normalized in the interval [0;1], the value of QEAS should not exceed 0.75, which identifies the permissible skewness angle of the generated mesh. For the computed meshes, this value was equal to 0.55–0.65.

Moreover, when generating the computational grids in the studied facility, they were compacted in the areas of the highest gradients of the calculated values, where higher turbulence is to be expected (near the impeller). The obtained results of water velocity in the studied object at constant gas flow rate are shown in Figure 6.

The analysis of the obtained water velocity distributions (see Figure 6) along the line inside the object revealed that, with the density of the grid of nodal points, the velocity changed and its changes for the test cases of 7,889,512, 11,569,230, and 14,115,049 were insignificant. Therefore, it was assumed that a grid containing not less than 7,900,000 (7,889,512) cells would not affect the result of CFD calculations.

A single-block mesh of regular cells with a size of 0.0034 m was used in the numerical calculations. The total number of cells was approximately 7,900,000 (7,889,512). This grid resolution (see Figure 7) allowed the geometry of the system to be properly represented, maintaining acceptable computation time (about 3 days on a workstation with 2× CPU and 12 computing cores).

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g007.jpg

Figure 7

Structured equidistant mesh used in numerical calculations: (a) mesh with smoothed, surface cells (the so-called FAVOR method) used in Flow-3D; (b) visualization of the applied mesh resolution.

The calculations were conducted with an explicit scheme. The timestep was selected by the program automatically and controlled by stability and convergence. From the moment of the initial velocity field generation (start of particle generation), it was 0.0001 s.

When modeling the degassing process, three fluids are present in the system: water, gas supplied through the rotor head (impeller), and the surrounding air. Modeling such a multiphase flow is a numerically very complex issue. The necessity to overcome the liquid backpressure by the gas flowing out from the impeller leads to the formation of numerical instabilities in the volume of fluid (VOF)-based approach used by Flow-3D software. Therefore, a mixed description of the analyzed flow was used here. In this case, water was treated as a continuous medium, while, in the case of gas bubbles, the discrete phase model (DPM) model was applied. The way in which the air surrounding the system was taken into account is later described in detail.

The following additional assumptions were made in the modeling:

  • —The liquid phase was considered as an incompressible Newtonian fluid.
  • —The effect of chemical reactions during the refining process was neglected.
  • —The composition of each phase (gas and liquid) was considered homogeneous; therefore, the viscosity and surface tension were set as constants.
  • —Only full turbulence existed in the liquid, and the effect of molecular viscosity was neglected.
  • —The gas bubbles were shaped as perfect spheres.
  • —The mutual interaction between gas bubbles (particles) was neglected.

2.3.1. Modeling of Liquid Flow 

The motion of the real fluid (continuous medium) is described by the Navier–Stokes Equation [20].

dudt=−1ρ∇p+ν∇2u+13ν∇(∇⋅ u)+F,

(2)

where du/dt is the time derivative, u is the velocity vector, t is the time, and F is the term accounting for external forces including gravity (unit components denoted by X, Y, Z).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm		Bubbles Diameter
m		Corresponding Gas Flow Rate
dm3·min−1		NoRotor Speed (Rotational Speed)
rpm		Bubbles Diameter
m		Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

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The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

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3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

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Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

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The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

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Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g008.jpg

Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

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Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters k, A, and uB can be calculated using the below equations [33].

k=2D⋅uBdB⋅π−−−−−−√,

(16)

A=6Q⋅hdB⋅uB,

(17)

uB=1.02g⋅dB,−−−−−√

(18)

where D is the diffusion coefficient, and dB is the bubble diameter.

After substituting appropriate values, we get

dB=3.03×104(πD)−2/5g−1/5h4/5Q0.344N−1.48.

(19)

According to the last equation, the size of the gas bubble decreases with the increasing rotational speed (see Figure 10).

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g010.jpg

Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)		Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax		0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax		0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax		0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

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3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11, Figure 12, Figure 13 and Figure 14.

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Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

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Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11, Figure 12, Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

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Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g016.jpg

Figure 16

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 5.4 s.: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

CFD results are presented for all analyzed variants (impeller RT3) at two selected calculation timesteps of 1 and 5.40 s. They show the velocity field of the medium (water) and the dispersion of gas bubbles.

Figure 15 shows the initial refining phase after 1 s of the process. In this case, the gas bubble formation and flow were observed in an area close to contact with the rotor. Figure 16 shows the phase when the dispersion and flow of gas bubbles were advanced in the reactor area of the URO-200 model.

The quantitative evaluation of the obtained results of physical and numerical model tests was based on the comparison of the degree of gas dispersion in the model liquid. The degree of gas bubble dispersion in the volume of the model liquid and the areas of strong turbulent zones formation were evaluated during the analysis of the results of visualization and numerical simulations. These two effects sufficiently characterize the required course of the process from the physical point of view. The known scheme of the below description was adopted as a basic criterion for the evaluation of the degree of dispersion of gas bubbles in the model liquid.

  • Minimal dispersion—single bubbles ascending in the region of their formation along the ladle axis; lack of mixing in the whole bath volume.
  • Accurate dispersion—single and well-mixed bubbles ascending toward the bath mirror in the region of the ladle axis; no dispersion near the walls and in the lower part of the ladle.
  • Uniform dispersion—most desirable; very good mixing of fine bubbles with model liquid.
  • Excessive dispersion—bubbles join together to form chains; large turbulence zones; uneven flow of gas.

The numerical simulation results give a good agreement with the experiments performed with the physical model. For all studied variants (used process parameters), the single bubbles were observed in the area of water surface in the vessel. For variants presented in Figure 13 (200 rpm, gas flow 20 and dm3·min−1) and relevant examples in numerical simulation Figure 16, the worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further use. The areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model (physical model). This means that the presented impeller model had the best performance in terms of dispersion of gas bubbles in the model liquid. The worst bubble dispersion results were obtained because the dead zones were identified in the area near the bottom and side walls of the vessel, which disqualifies these work parameters for further use.

Figure 17 presents exemplary results of model tests (CFD and physical model) with marked gas bubble dispersion zones. All variants of tests were analogously compared, and this comparison allowed validating the numerical model.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g017.jpg

Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

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Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

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4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

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Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

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Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

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Institutional Review Board Statement

Not applicable.

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Informed Consent Statement

Not applicable.

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Data Availability Statement

Data are contained within the article.

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Conflicts of Interest

The authors declare no conflict of interest.

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Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Figure 1: Mold drawings

3D Flow and Temperature Analysis of Filling a Plutonium Mold

플루토늄 주형 충전의 3D 유동 및 온도 분석

Authors: Orenstein, Nicholas P. [1]

Publication Date:2013-07-24
Research Org.: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.: DOE/LANL
OSTI Identifier: 1088904
Report Number(s): LA-UR-13-25537
DOE Contract Number: AC52-06NA25396
Resource Type: Technical Report
Country of Publication: United States
Language: English
Subject: Engineering(42); Materials Science(36); Radiation Chemistry, Radiochemistry, & Nuclear Chemistry(38)

Introduction

The plutonium foundry at Los Alamos National Laboratory casts products for various special nuclear applications. However, plutonium’s radioactivity, material properties, and security constraints complicate the ability to perform experimental analysis of mold behavior. The Manufacturing Engineering and Technologies (MET-2) group previously developed a graphite mold to vacuum cast small plutonium disks to be used by the Department of Homeland Security as point sources for radiation sensor testing.

A two-stage pouring basin consisting of a funnel and an angled cavity directs the liquid into a vertical runner. A stack of ten disk castings connect to the runner by horizontal gates. Volumetric flow rates were implemented to limit overflow into the funnel and minimize foundry returns. Models using Flow-3D computational fluid dynamics software are employed here to determine liquid Pu flow paths, optimal pour regimes, temperature changes, and pressure variations.

Setup

Hardcopy drawings provided necessary information to create 3D .stl models for import into Flow-3D (Figs. 1 and 2). The mesh was refined over several iterations to isolate the disk cavities, runner, angled cavity, funnel, and input pour. The final flow and mold-filling simulation utilizes a fine mesh with ~5.5 million total cells. For the temperature study, the mesh contained 1/8 as many cells to reduce computational time and set temperatures to 850 °C for the molten plutonium and 500 °C for the solid graphite mold components (Fig. 3).

Flow-3D solves mass continuity and Navier-Stokes momentum equations over the structured rectangular grid model using finite difference and finite volume numerical algorithms. The solver includes terms in the momentum equation for body and viscous accelerations and uses convective heat transfer.

Simulation settings enabled Flow-3D physics calculations for gravity at 980.665 cm/s 2 in the negative Z direction (top of mold to bottom); viscous, turbulent, incompressible flow using dynamically-computed Renormalized Group Model turbulence calculations and no-slip/partial slip wall shear, and; first order, full energy equation heat transfer.

Mesh boundaries were all set to symmetric boundary conditions except for the Zmin boundary set to outflow and the Zmax boundary set to a volume flow. Vacuum casting conditions and the high reactivity of remaining air molecules with Pu validate the assumption of an initially fluidless void.

Results

The flow follows a unique three-dimensional path. The mold fills upwards with two to three disks receiving fluid in a staggered sequence. Figures 5-9 show how the fluid fills the cavity, and Figure 7 includes the color scale for pressure levels in these four figures. The narrow gate causes a high pressure region which forces the fluid to flow down the cavity centerline.

It proceeds to splash against the far wall and then wrap around the circumference back to the gate (Figs. 5 and 6). Flow in the angled region of the pouring basin cascades over the bottom ledge and attaches to the far wall of the runner, as seen in Figure 7.

This channeling becomes less pronounced as fluid volume levels increase. Finally, two similar but non-uniform depressed regions form about the centerline. These regions fill from their perimeter and bottom until completion (Fig. 8). Such a pattern is counter, for example, to a steady scenario in which a circle of molten Pu encompassing the entire bottom surface rises as a growing cylinder.

Cavity pressure becomes uniform when the cavity is full. Pressure levels build in the rising well section of the runner, where impurities were found to settle in actual casting. Early test simulations optimized the flow as three pours so that the fluid would never overflow to the funnel, the cavities would all fill completely, and small amounts of fluid would remain as foundry returns in the angled cavity.

These rates and durations were translated to the single 2.7s pour at 100 cm 3 per second used here. Figure 9 shows anomalous pressure fluctuations which occurred as the cavities became completely filled. Multiple simulations exhibited a rapid change in pressure from positive to negative and back within the newly-full disk and surrounding, already-full disks.

The time required to completely fill each cavity is plotted in Figure 10. Results show negligible temperature change within the molten Pu during mold filling and, as seen in Figure 11, at fill completion.

Figure 1: Mold drawings
Figure 1: Mold drawings
Figure 2: Mold Assembly
Figure 2: Mold Assembly
Figure 4: Actual mold and cast Pu
Figure 4: Actual mold and cast Pu
Figure 5: Bottom cavity filling from runner
Figure 5: Bottom cavity filling from runner
Figure 6: Pouring and filling
Figure 6: Pouring and filling
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 8: Edge detection of cavity fill geometry. Two similar depressed areas form about the centerline. Top cavity shown; same pressure scale as other figures
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant
Figure 10: Cavity fill times,from first fluid contact with pouring basin, Figure 11:Fluid temperature remains essentially constant

Conclusions

Non-uniform cavity filling could cause crystal microstructure irregularities during solidification. However, the small temperature changes seen – due to large differences in specific heat between Pu and graphite – over a relatively short time make such problems unlikely in this case.

In the actual casting, cooling required approximately ten minutes. This large difference in time scales further reduces the chance for temperature effects in such a superheated scenario. Pouring basin emptying decreases pressure at the gate which extends fill time of the top two cavities.

The bottom cavity takes longer to fill because fluid must first enter the runner and fill the well. Fill times continue linearly until the top two cavities. The anomalous pressure fluctuations may be due to physical attempts by the system to reach equilibrium, but they are more likely due to numerical errors in the Flow3D solver.

Unsuccessful tests were performed to remove them by halving fluid viscosity. The fine mesh reduced, but did not eliminate, the extent of the fluctuations. Future work is planned to study induction and heat transfer in the full Pu furnace system, including quantifying temporal lag of the cavity void temperature to the mold wall temperature during pre-heat and comparing heat flux levels between furnace components during cool-down.

Thanks to Doug Kautz for the opportunity to work with MET-2 and for assigning an interesting unclassified project. Additional thanks to Mike Bange for CFD guidance, insight of the project’s history, and draft review.

원본 보기
Fig. 6 LH2 isotherms at 1020 s.

액체-수소 탱크를 위한 결합된 열역학-유체-역학 솔루션

Coupled thermodynamic-fluid-dynamic solution for a liquid-hydrogen tank

G. D. Grayson

Published Online:23 May 2012 https://doi.org/10.2514/3.26706

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Introduction

ROPELLANT 열 성층화 및 외부 교란에 대한 유체 역학적 반응은 발사체와 우주선 모두에서 중요합니다. 과거에는 결합된 솔루션을 제공할 수 있는 충분한 계산 기술이 부족하여 이러한 문제를 개별적으로 해결했습니다.1

이로 인해 모델링 기술의 불확실성을 허용하기 위해 큰 안전 계수를 가진 시스템이 과도하게 설계되었습니다. 고중력 환경과 저중력 환경 모두에서 작동하도록 설계된 미래 시스템은 기술적으로나 재정적으로 실현 가능하도록 과잉 설계 및 안전 요소가 덜 필요합니다.

이러한 유체 시스템은 열역학 및 유체 역학이 모두 중요한 환경에서 모델의 기능을 광범위하게 검증한 후에만 고충실도 수치 모델을 기반으로 할 수 있습니다. 상용 컴퓨터 코드 FLOW-3D2는 유체 역학 및 열 모델링 모두에서 가능성을 보여주었으며,1 따라서 열역학-유체-역학 엔지니어링 문제에서 결합된 질량, 운동량 및 에너지 방정식을 푸는 데 적합함을 시사합니다.

발사체의 복잡한 액체 가스 시스템에 대한 포괄적인 솔루션을 달성하기 위한 첫 번째 단계로 액체 유체 역학과 열역학을 통합하는 제안된 상단 단계 액체-수소(Lit) 탱크의 간단한 모델이 여기에 제시됩니다. FLOW-3D FLOW-3D 프로그램은 Los Alamos Scientific Laboratory에서 시작되었으며 마커 및 셀 방법에서 파생된 것입니다.3 현재 상태로 가져오기 위해 수년에 걸쳐 광범위한 코드 수정이 이루어졌습니다.2

프로그램은 다음과 같습니다. 일반 Navier-Stokes 방정식을 풀기 위해 수치 근사의 중앙 유한 차분 방법을 사용하는 3차원 유체 역학 솔버입니다. 모멘텀 및 에너지 방정식의 섹션은 특정 응용 프로그램에 따라 활성화 또는 비활성화할 수 있습니다.

코드는 1994년 9월 13일 접수를 인용하기 위해 무액체 표면, 복잡한 용기 기하학, 여러 점성 모델, 표면 장력, 다공성 매체를 통한 흐름 및 응고와 함께 압축성 또는 비압축성 유동 가정을 제공합니다. 1995년 1월 15일에 받은 개정; 1995년 2월 17일 출판 승인.

ROPELLANT thermal stratification and fluid-dynamic response to external disturbances are of concern in both launch vehicles and spacecraft. In the past these problems have been addressed separately for want of sufficient computational technology to provide for coupled solutions.1 This has resulted in overdesigned systems with large safety factors to allow for the uncertainty in modeling techniques. Future systems designed to perform in both highand low-gravity environments will require less overdesign and safety factors to be technically and financially feasible. Such fluid systems can be based on high-fidelity numerical models only after extensive validation of the models’ capabilities in environments where both the thermodynamics and the fluid dynamics are important. The commercial computer code FLOW-3D2 has shown promise in both fluid-dynamic and thermal modeling,1 thus suggesting suitability for solving the coupled mass, momentum, and energy equations in thermodynamic-fluid-dynamic engineering problems. As a first step to achieving a comprehensive solution for complex liquidgas systems in a launch vehicle, a simple model of a proposed upper-stage liquid-hydrogen (Lit) tank incorporating the liquid fluid dynamics and thermodynamics is presented here. FLOW-3D The FLOW-3D program originated at the Los Alamos Scientific Laboratory and is a derivative of the marker-and-cell method.3 Extensive code modifications have been made over the years to bring it to its present state.2 The program is a three-dimensional fluiddynamic solver that uses a central finite-difference method of numerical approximation to solve the general Navier-Stokes equations. Sections of the momentum and energy equations can be enabled or disabled depending on the particular application. The code provides compressible or incompressible flow assumptions with liquid free surfaces, complex container geometries, several viscosity models, surface tension, flow though porous media, and solidification, to cite Received Sept. 13, 1994; revision received Jan. 15, 1995; accepted for publication Feb. 17, 1995. Copyright © 1995 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. *Engineer/Scientist, Propulsion Analysis and Hydraulics, Space Transportation Division, MS 13-3, 5301 Bolsa Avenue. Member AIAA. a few of the possibilities. Further information on FLOW-3D’s capabilities and details of the numerical algorithms can be found in Ref. 2

Fig. 1 Axial-acceleration history.
Fig. 1 Axial-acceleration history.
Fig. 2 Heat flux histories.
Fig. 2 Heat flux histories.
Fig. 3 LHi isotherms at 50 s.
Fig. 3 LHi isotherms at 50 s.
Fig. 4 LH2 isotherms at 300 s
Fig. 4 LH2 isotherms at 300 s
Fig. 5 LH2 isotherms at 880 s.
Fig. 5 LH2 isotherms at 880 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 6 LH2 isotherms at 1020 s.
Fig. 7 Tank-outlet temperature history.
Fig. 7 Tank-outlet temperature history.
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Sketch of approach channel and spillway of the Kamal-Saleh dam

CFD modeling of flow pattern in spillway’s approach channel

Sustainable Water Resources Management volume 1, pages245–251 (2015)Cite this article

Abstract

Analysis of behavior and hydraulic characteristics of flow over the dam spillway is a complicated task that takes lots of money and time in water engineering projects planning. To model those hydraulic characteristics, several methods such as physical and numerical methods can be used. Nowadays, by utilizing new methods in computational fluid dynamics (CFD) and by the development of fast computers, the numerical methods have become accessible for use in the analysis of such sophisticated flows. The CFD softwares have the capability to analyze two- and three-dimensional flow fields. In this paper, the flow pattern at the guide wall of the Kamal-Saleh dam was modeled by Flow 3D. The results show that the current geometry of the left wall causes instability in the flow pattern and making secondary and vortex flow at beginning approach channel. This shape of guide wall reduced the performance of weir to remove the peak flood discharge.

댐 여수로 흐름의 거동 및 수리학적 특성 분석은 물 공학 프로젝트 계획에 많은 비용과 시간이 소요되는 복잡한 작업입니다. 이러한 수력학적 특성을 모델링하기 위해 물리적, 수치적 방법과 같은 여러 가지 방법을 사용할 수 있습니다. 요즘에는 전산유체역학(CFD)의 새로운 방법을 활용하고 빠른 컴퓨터의 개발로 이러한 정교한 흐름의 해석에 수치 방법을 사용할 수 있게 되었습니다. CFD 소프트웨어에는 2차원 및 3차원 유동장을 분석하는 기능이 있습니다. 본 논문에서는 Kamal-Saleh 댐 유도벽의 흐름 패턴을 Flow 3D로 모델링하였다. 결과는 왼쪽 벽의 현재 형상이 흐름 패턴의 불안정성을 유발하고 시작 접근 채널에서 2차 및 와류 흐름을 만드는 것을 보여줍니다. 이러한 형태의 안내벽은 첨두방류량을 제거하기 위해 둑의 성능을 저하시켰다.

Introduction

Spillways are one of the main structures used in the dam projects. Design of the spillway in all types of dams, specifically earthen dams is important because the inability of the spillway to remove probable maximum flood (PMF) discharge may cause overflow of water which ultimately leads to destruction of the dam (Das and Saikia et al. 2009; E 2013 and Novak et al. 2007). So study on the hydraulic characteristics of this structure is important. Hydraulic properties of spillway including flow pattern at the entrance of the guide walls and along the chute. Moreover, estimating the values of velocity and pressure parameters of flow along the chute is very important (Chanson 2004; Chatila and Tabbara 2004). The purpose of the study on the flow pattern is the effect of wall geometry on the creation transverse waves, flow instability, rotating and reciprocating flow through the inlet of spillway and its chute (Parsaie and Haghiabi 2015a, b; Parsaie et al. 2015; Wang and Jiang 2010). The purpose of study on the values of velocity and pressure is to calculate the potential of the structure to occurrence of phenomena such as cavitation (Fattor and Bacchiega 2009; Ma et al. 2010). Sometimes, it can be seen that the spillway design parameters of pressure and velocity are very suitable, but geometry is considered not suitable for conducting walls causing unstable flow pattern over the spillway, rotating flows at the beginning of the spillway and its design reduced the flood discharge capacity (Fattor and Bacchiega 2009). Study on spillway is usually conducted using physical models (Su et al. 2009; Suprapto 2013; Wang and Chen 2009; Wang and Jiang 2010). But recently, with advances in the field of computational fluid dynamics (CFD), study on hydraulic characterist–ics of this structure has been done with these techniques (Chatila and Tabbara 2004; Zhenwei et al. 2012). Using the CFD as a powerful technique for modeling the hydraulic structures can reduce the time and cost of experiments (Tabbara et al. 2005). In CFD field, the Navier–Stokes equation is solved by powerful numerical methods such as finite element method and finite volumes (Kim and Park 2005; Zhenwei et al. 2012). In order to obtain closed-form Navier–Stokes equations turbulence models, such k − ε and Re-Normalisation Group (RNG) models have been presented. To use the technique of computational fluid dynamics, software packages such as Fluent and Flow 3D, etc., are provided. Recently, these two software packages have been widely used in hydraulic engineering because the performance and their accuracy are very suitable (Gessler 2005; Kim 2007; Kim et al. 2012; Milési and Causse 2014; Montagna et al. 2011). In this paper, to assess the flow pattern at Kamal-Saleh guide wall, numerical method has been used. All the stages of numerical modeling were conducted in the Flow 3D software.

Materials and methods

Firstly, a three-dimensional model was constructed according to two-dimensional map that was prepared for designing the spillway. Then a small model was prepared with scale of 1:80 and entered into the Flow 3D software; all stages of the model construction was conducted in AutoCAD 3D. Flow 3D software numerically solved the Navier–Stokes equation by finite volume method. Below is a brief reference on the equations that used in the software. Figure 1 shows the 3D sketch of Kamal-Saleh spillway and Fig. 2 shows the uploading file of the Kamal-Saleh spillway in Flow 3D software.

figure 1
Fig. 1
figure 2
Fig. 2

Review of the governing equations in software Flow 3D

Continuity equation at three-dimensional Cartesian coordinates is given as Eq (1).

vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,vf∂ρ∂t+∂∂x(uAx)+∂∂x(vAy)+∂∂x(wAz)=PSORρ,

(1)

where u, v, z are velocity component in the x, y, z direction; A x, A y, A z cross-sectional area of the flow; ρ fluid density; PSOR the source term; v f is the volume fraction of the fluid and three-dimensional momentum equations given in Eq (2).

∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,∂u∂t+1vf(uAx∂u∂x+vAy∂u∂y+wAz∂u∂z)=−1ρ∂P∂x+Gx+fx∂v∂t+1vf(uAx∂v∂x+vAy∂v∂y+wAz∂v∂z)=−1ρ∂P∂y+Gy+fy∂w∂t+1vf(uAx∂w∂x+vAy∂w∂y+wAz∂w∂z)=−1ρ∂P∂y+Gz+fz,

(2)

where P is the fluid pressure; G x, G y, G z the acceleration created by body fluids; f x, f y, f z viscosity acceleration in three dimensions and v f is related to the volume of fluid, defined by Eq. (3). For modeling of free surface profile the VOF technique based on the volume fraction of the computational cells has been used. Since the volume fraction F represents the amount of fluid in each cell, it takes value between 0 and 1.

∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0∂F∂t+1vf[∂∂x(FAxu)+∂∂y(FAyv)+∂∂y(FAzw)]=0

(3)

Turbulence models

Flow 3D offers five types of turbulence models: Prantl mixing length, k − ε equation, RNG models, Large eddy simulation model. Turbulence models that have been proposed recently are based on Reynolds-averaged Navier–Stokes equations. This approach involves statistical methods to extract an averaged equation related to the turbulence quantities.

Steps of solving a problem in Flow 3D software

(1) Preparing the 3D model of spillway by AutoCAD software. (2) Uploading the file of 3D model in Flow 3D software and defining the problem in the software and checking the final mesh. (3) Choosing the basic equations that should be solved. (4) Defining the characteristics of fluid. (5) Defining the boundary conditions; it is notable that this software has a wide range of boundary conditions. (6) Initializing the flow field. (7) Adjusting the output. (8) Adjusting the control parameters, choice of the calculation method and solution formula. (9) Start of calculation. Figure 1 shows the 3D model of the Kamal-Saleh spillway; in this figure, geometry of the left and right guide wall is shown.

Figure 2 shows the uploading of the 3D spillway dam in Flow 3D software. Moreover, in this figure the considered boundary condition in software is shown. At the entrance and end of spillway, the flow rate or fluid elevation and outflow was considered as BC. The bottom of spillway was considered as wall and left and right as symmetry.

Model calibration

Calibration of the Flow 3D for modeling the effect of geometry of guide wall on the flow pattern is included for comparing the results of Flow 3D with measured water surface profile. Calibration the Flow 3D software could be conducted in two ways: first, changing the value of upstream boundary conditions is continued until the results of water surface profile of the Flow 3D along the spillway successfully covered the measurement water surface profile; second is the assessment the mesh sensitivity. Analyzing the size of mesh is a trial-and-error process where the size of mesh is evaluated form the largest to the smallest. With fining the size of mesh the accuracy of model is increased; whereas, the cost of computation is increased. In this research, the value of upstream boundary condition was adjusted with measured data during the experimental studies on the scaled model and the mesh size was equal to 1 × 1 × 1 cm3.

Results and discussion

The behavior of water in spillway is strongly affected by the flow pattern at the entrance of the spillway, the flow pattern formation at the entrance is affected by the guide wall, and choice of an optimized form for the guide wall has a great effect on rising the ability of spillway for easy passing the PMF, so any nonuniformity in flow in the approach channel can cause reduction of spillway capacity, reduction in discharge coefficient of spillway, and even probability of cavitation. Optimizing the flow guiding walls (in terms of length, angle and radius) can cause the loss of turbulence and flow disturbances on spillway. For this purpose, initially geometry proposed for model for the discharge of spillway dam, Kamal-Saleh, 80, 100, and 120 (L/s) were surveyed. These discharges of flow were considered with regard to the flood return period, 5, 100 and 1000 years. Geometric properties of the conducting guidance wall are given in Table 1.Table 1 Characteristics and dimensions of the guidance walls tested

Full size table

Results of the CFD simulation for passing the flow rate 80 (L/s) are shown in Fig. 3. Figure 3 shows the secondary flow and vortex at the left guide wall.

figure 3
Fig. 3

For giving more information about flow pattern at the left and right guide wall, Fig. 4 shows the flow pattern at the right side guide wall and Fig. 5 shows the flow pattern at the left side guide wall.

figure 4
Fig. 4
figure 5
Fig. 5

With regard to Figs. 4 and 5 and observing the streamlines, at discharge equal to 80 (L/s), the right wall has suitable performance but the left wall has no suitable performance and the left wall of the geometric design creates a secondary and circular flow, and vortex motion in the beginning of the entrance of spillway that creates cross waves at the beginning of spillway. By increasing the flow rate (Q = 100 L/s), at the inlet spillway secondary flows and vortex were removed, but the streamline is severely distorted. Results of the guide wall performances at the Q = 100 (L/s) are shown in Fig. 6.

figure 6
Fig. 6

Also more information about the performance of each guide wall can be derived from Figs. 7 and 8. These figures uphold that the secondary and vortex flows were removed, but the streamlines were fully diverted specifically near the left side guide wall.

figure 7
Fig. 7
figure 8
Fig. 8

As mentioned in the past, these secondary and vortex flows and diversion in streamline cause nonuniformity and create cross wave through the spillway. Figure 9 shows the cross waves at the crest of the spillway.

figure 9
Fig. 9

The performance of guide walls at the Q = 120 (L/s) also was assessed. The result of simulation is shown in Fig. 10. Figures 11 and 12 show a more clear view of the streamlines near to right and left side guide wall, respectively. As seen in Fig. 12, the left side wall still causes vortex flow and creation of and diversion in streamline.

figure 10
Fig. 10
figure 11
Fig. 11
figure 12
Fig. 12

The results of the affected left side guide wall shape on the cross wave creation are shown in Fig. 13. As seen from Fig. 3, the left side guide wall also causes cross wave at the spillway crest.

figure 13
Fig. 13

As can be seen clearly in Figs. 9 and 13, by moving from the left side to the right side of the spillway, the cross waves and the nonuniformity in flow is removed. By reviewing Figs. 9 and 13, it is found that the right side guide wall removes the cross waves and nonuniformity. With this point as aim, a geometry similar to the right side guide wall was considered instead of the left side guide wall. The result of simulation for Q = 120 (L/s) is shown in Fig. 14. As seen from this figure, the proposed geometry for the left side wall has suitable performance smoothly passing the flow through the approach channel and spillway.

figure 14
Fig. 14

More information about the proposed shape for the left guide wall is shown in Fig. 15. As seen from this figure, this shape has suitable performance for removing the cross waves and vortex flows.

figure 15
Fig. 15

Figure 16 shows the cross section of flow at the crest of spillway. As seen in this figure, the proposed shape for the left side guide wall is suitable for removing the cross waves and secondary flows.

figure 16
Fig. 16

Conclusion

Analysis of behavior and hydraulic properties of flow over the spillway dam is a complicated task which is cost and time intensive. Several techniques suitable to the purposes of study have been undertaken in this research. Physical modeling, usage of expert experience, usage of mathematical models on simulation flow in one-dimensional, two-dimensional and three-dimensional techniques, are some of the techniques utilized to study this phenomenon. The results of the modeling show that the CFD technique is a suitable tool for simulating the flow pattern in the guide wall. Using this tools helps the designer for developing the optimal shape for hydraulic structure which the flow pattern through them are important.

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  1. Department of Water Engineering, Lorestan University, Khorram Abad, IranAbbas Parsaie, Amir Hamzeh Haghiabi & Amir Moradinejad

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Correspondence to Abbas Parsaie.

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Parsaie, A., Haghiabi, A.H. & Moradinejad, A. CFD modeling of flow pattern in spillway’s approach channel. Sustain. Water Resour. Manag. 1, 245–251 (2015). https://doi.org/10.1007/s40899-015-0020-9

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  • Received28 April 2015
  • Accepted28 August 2015
  • Published15 September 2015
  • Issue DateSeptember 2015
  • DOIhttps://doi.org/10.1007/s40899-015-0020-9

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Keywords

  • Approach channel
  • Kamal-Saleh dam
  • Guide wall
  • Flow pattern
  • Numerical modeling
  • Flow 3D software
    원문 보기
    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    영국 Dawlish의 방파제에 대한 온대 저기압 피해: 목격자 설명, 해수면 분석 및 수치 모델링

    Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling

    Natural Hazards (2022)Cite this article

    Abstract

    2014년 2월 영국 해협(영국)과 특히 Dawlish에 영향을 미친 온대 저기압 폭풍 사슬은 남서부 지역과 영국의 나머지 지역을 연결하는 주요 철도에 심각한 피해를 입혔습니다.

    이 사건으로 라인이 두 달 동안 폐쇄되어 5천만 파운드의 피해와 12억 파운드의 경제적 손실이 발생했습니다. 이 연구에서는 폭풍의 파괴력을 해독하기 위해 목격자 계정을 수집하고 해수면 데이터를 분석하며 수치 모델링을 수행합니다.

    우리의 분석에 따르면 이벤트의 재난 관리는 성공적이고 효율적이었으며 폭풍 전과 도중에 인명과 재산을 구하기 위해 즉각적인 조치를 취했습니다. 파도 부이 분석에 따르면 주기가 4–8, 8–12 및 20–25초인 복잡한 삼중 봉우리 바다 상태가 존재하는 반면, 조위계 기록에 따르면 최대 0.8m의 상당한 파도와 최대 1.5m의 파도 성분이 나타났습니다.

    이벤트에서 가능한 기여 요인으로 결합된 진폭. 최대 286 KN의 상당한 임펄스 파동이 손상의 시작 원인일 가능성이 가장 높았습니다. 수직 벽의 반사는 파동 진폭의 보강 간섭을 일으켜 파고가 증가하고 최대 16.1m3/s/m(벽의 미터 너비당)의 상당한 오버탑핑을 초래했습니다.

    이 정보와 우리의 공학적 판단을 통해 우리는 이 사고 동안 다중 위험 계단식 실패의 가장 가능성 있는 순서는 다음과 같다고 결론을 내립니다. 조적 파괴로 이어지는 파도 충격력, 충전물 손실 및 연속적인 조수에 따른 구조물 파괴.

    The February 2014 extratropical cyclonic storm chain, which impacted the English Channel (UK) and Dawlish in particular, caused significant damage to the main railway connecting the south-west region to the rest of the UK. The incident caused the line to be closed for two months, £50 million of damage and an estimated £1.2bn of economic loss. In this study, we collate eyewitness accounts, analyse sea level data and conduct numerical modelling in order to decipher the destructive forces of the storm. Our analysis reveals that the disaster management of the event was successful and efficient with immediate actions taken to save lives and property before and during the storm. Wave buoy analysis showed that a complex triple peak sea state with periods at 4–8, 8–12 and 20–25 s was present, while tide gauge records indicated that significant surge of up to 0.8 m and wave components of up to 1.5 m amplitude combined as likely contributing factors in the event. Significant impulsive wave force of up to 286 KN was the most likely initiating cause of the damage. Reflections off the vertical wall caused constructive interference of the wave amplitudes that led to increased wave height and significant overtopping of up to 16.1 m3/s/m (per metre width of wall). With this information and our engineering judgement, we conclude that the most probable sequence of multi-hazard cascading failure during this incident was: wave impact force leading to masonry failure, loss of infill and failure of the structure following successive tides.

    Introduction

    The progress of climate change and increasing sea levels has started to have wide ranging effects on critical engineering infrastructure (Shakou et al. 2019). The meteorological effects of increased atmospheric instability linked to warming seas mean we may be experiencing more frequent extreme storm events and more frequent series or chains of events, as well as an increase in the force of these events, a phenomenon called storminess (Mölter et al. 2016; Feser et al. 2014). Features of more extreme weather events in extratropical latitudes (30°–60°, north and south of the equator) include increased gusting winds, more frequent storm squalls, increased prolonged precipitation and rapid changes in atmospheric pressure and more frequent and significant storm surges (Dacre and Pinto 2020). A recent example of these events impacting the UK with simultaneous significant damage to coastal infrastructure was the extratropical cyclonic storm chain of winter 2013/2014 (Masselink et al. 2016; Adams and Heidarzadeh 2021). The cluster of storms had a profound effect on both coastal and inland infrastructure, bringing widespread flooding events and large insurance claims (RMS 2014).

    The extreme storms of February 2014, which had a catastrophic effect on the seawall of the south Devon stretch of the UK’s south-west mainline, caused a two-month closure of the line and significant disruption to the local and regional economy (Fig. 1b) (Network Rail 2014; Dawson et al. 2016; Adams and Heidarzadeh 2021). Restoration costs were £35 m, and economic effects to the south-west region of England were estimated up to £1.2bn (Peninsula Rail Taskforce 2016). Adams and Heidarzadeh (2021) investigated the disparate cascading failure mechanisms which played a part in the failure of the railway through Dawlish and attempted to put these in the context of the historical records of infrastructure damage on the line. Subsequent severe storms in 2016 in the region have continued to cause damage and disruption to the line in the years since 2014 (Met Office 2016). Following the events of 2014, Network Rail Footnote1 who owns the network has undertaken a resilience study. As a result, it has proposed a £400 m refurbishment of the civil engineering assets that support the railway (Fig. 1) (Network Rail 2014). The new seawall structure (Fig. 1a,c), which is constructed of pre-cast concrete sections, encases the existing Brunel seawall (named after the project lead engineer, Isambard Kingdom Brunel) and has been improved with piled reinforced concrete foundations. It is now over 2 m taller to increase the available crest freeboard and incorporates wave return features to minimise wave overtopping. The project aims to increase both the resilience of the assets to extreme weather events as well as maintain or improve amenity value of the coastline for residents and visitors.

    figure 1
    Fig. 1

    In this work, we return to the Brunel seawall and the damage it sustained during the 2014 storms which affected the assets on the evening of the 4th and daytime of the 5th of February and eventually resulted in a prolonged closure of the line. The motivation for this research is to analyse and model the damage made to the seawall and explain the damage mechanisms in order to improve the resilience of many similar coastal structures in the UK and worldwide. The innovation of this work is the multidisciplinary approach that we take comprising a combination of analysis of eyewitness accounts (social science), sea level and wave data analysis (physical science) as well as numerical modelling and engineering judgement (engineering sciences). We investigate the contemporary wave climate and sea levels by interrogating the real-time tide gauge and wave buoys installed along the south-west coast of the English Channel. We then model a typical masonry seawall (Fig. 2), applying the computational fluid dynamics package FLOW3D-Hydro,Footnote2 to quantify the magnitude of impact forces that the seawall would have experienced leading to its failure. We triangulate this information to determine the probable sequence of failures that led to the disaster in 2014.

    figure 2
    Fig. 2

    Data and methods

    Our data comprise eyewitness accounts, sea level records from coastal tide gauges and offshore wave buoys as well as structural details of the seawall. As for methodology, we analyse eyewitness data, process and investigate sea level records through Fourier transform and conduct numerical simulations using the Flow3D-Hydro package (Flow Science 2022). Details of the data and methodology are provided in the following.

    Eyewitness data

    The scale of damage to the seawall and its effects led the local community to document the first-hand accounts of those most closely affected by the storms including residents, local businesses, emergency responders, politicians and engineering contractors involved in the post-storm restoration work. These records now form a permanent exhibition in the local museum in DawlishFootnote3, and some of these accounts have been transcribed into a DVD account of the disaster (Dawlish Museum 2015). We have gathered data from the Dawlish Museum, national and international news reports, social media tweets and videos. Table 1 provides a summary of the eyewitness accounts. Overall, 26 entries have been collected around the time of the incident. Our analysis of the eyewitness data is provided in the third column of Table 1 and is expanded in Sect. 3.Table 1 Eyewitness accounts of damage to the Dawlish railway due to the February 2014 storm and our interpretations

    Full size table

    Sea level data and wave environment

    Our sea level data are a collection of three tide gauge stations (Newlyn, Devonport and Swanage Pier—Fig. 5a) owned and operated by the UK National Tide and Sea Level FacilityFootnote4 for the Environment Agency and four offshore wave buoys (Dawlish, West Bay, Torbay and Chesil Beach—Fig. 6a). The tide gauge sites are all fitted with POL-EKO (www.pol-eko.com.pl) data loggers. Newlyn has a Munro float gauge with one full tide and one mid-tide pneumatic bubbler system. Devonport has a three-channel data pneumatic bubbler system, and Swanage Pier consists of a pneumatic gauge. Each has a sampling interval of 15 min, except for Swanage Pier which has a sampling interval of 10 min. The tide gauges are located within the port areas, whereas the offshore wave buoys are situated approximately 2—3.3 km from the coast at water depths of 10–15 m. The wave buoys are all Datawell Wavemaker Mk III unitsFootnote5 and come with sampling interval of 0.78 s. The buoys have a maximum saturation amplitude of 20.5 m for recording the incident waves which implies that every wave larger than this threshold will be recorded at 20.5 m. The data are provided by the British Oceanographic Data CentreFootnote6 for tide gauges and the Channel Coastal ObservatoryFootnote7 for wave buoys.

    Sea level analysis

    The sea level data underwent quality control to remove outliers and spikes as well as gaps in data (e.g. Heidarzadeh et al. 2022; Heidarzadeh and Satake 2015). We processed the time series of the sea level data using the Matlab signal processing tool (MathWorks 2018). For calculations of the tidal signals, we applied the tidal package TIDALFIT (Grinsted 2008), which is based on fitting tidal harmonics to the observed sea level data. To calculate the surge signals, we applied a 30-min moving average filter to the de-tided data in order to remove all wind, swell and infra-gravity waves from the time series. Based on the surge analysis and the variations of the surge component before the time period of the incident, an error margin of approximately ± 10 cm is identified for our surge analysis. Spectral analysis of the wave buoy data is performed using the fast Fourier transform (FFT) of Matlab package (Mathworks 2018).

    Numerical modelling

    Numerical modelling of wave-structure interaction is conducted using the computational fluid dynamics package Flow3D-Hydro version 1.1 (Flow Science 2022). Flow3D-Hydro solves the transient Navier–Stokes equations of conservation of mass and momentum using a finite difference method and on Eulerian and Lagrangian frameworks (Flow Science 2022). The aforementioned governing equations are:

    ∇.u=0∇.u=0

    (1)

    ∂u∂t+u.∇u=−∇Pρ+υ∇2u+g∂u∂t+u.∇u=−∇Pρ+υ∇2u+g

    (2)

    where uu is the velocity vector, PP is the pressure, ρρ is the water density, υυ is the kinematic viscosity and gg is the gravitational acceleration. A Fractional Area/Volume Obstacle Representation (FAVOR) is adapted in Flow3D-Hydro, which applies solid boundaries within the Eulerian grid and calculates the fraction of areas and volume in partially blocked volume in order to compute flows on corresponding boundaries (Hirt and Nichols 1981). We validated the numerical modelling through comparing the results with Sainflou’s analytical equation for the design of vertical seawalls (Sainflou 1928; Ackhurst 2020), which is as follows:

    pd=ρgHcoshk(d+z)coshkdcosσtpd=ρgHcoshk(d+z)coshkdcosσt

    (3)

    where pdpd is the hydrodynamic pressure, ρρ is the water density, gg is the gravitational acceleration, HH is the wave height, dd is the water depth, kk is the wavenumber, zz is the difference in still water level and mean water level, σσ is the angular frequency and tt is the time. The Sainflou’s equation (Eq. 3) is used to calculate the dynamic pressure from wave action, which is combined with static pressure on the seawall.

    Using Flow3D-Hydro, a model of the Dawlish seawall was made with a computational domain which is 250.0 m in length, 15.0 m in height and 0.375 m in width (Fig. 3a). The computational domain was discretised using a single uniform grid with a mesh size of 0.125 m. The model has a wave boundary at the left side of the domain (x-min), an outflow boundary on the right side (x-max), a symmetry boundary at the bottom (z-min) and a wall boundary at the top (z-max). A wall boundary implies that water or waves are unable to pass through the boundary, whereas a symmetry boundary means that the two edges of the boundary are identical and therefore there is no flow through it. The water is considered incompressible in our model. For volume of fluid advection for the wave boundary (i.e. the left-side boundary) in our simulations, we utilised the “Split Lagrangian Method”, which guarantees the best accuracy (Flow Science, 2022).

    figure 3
    Fig. 3

    The stability of the numerical scheme is controlled and maintained through checking the Courant number (CC) as given in the following:

    C=VΔtΔxC=VΔtΔx

    (4)

    where VV is the velocity of the flow, ΔtΔt is the time step and ΔxΔx is the spatial step (i.e. grid size). For stability and convergence of the numerical simulations, the Courant number must be sufficiently below one (Courant et al. 1928). This is maintained by a careful adjustment of the ΔxΔx and ΔtΔt selections. Flow3D-Hydro applies a dynamic Courant number, meaning the program adjusts the value of time step (ΔtΔt) during the simulations to achieve a balance between accuracy of results and speed of simulation. In our simulation, the time step was in the range ΔtΔt = 0.0051—0.051 s.

    In order to achieve the most efficient mesh resolution, we varied cell size for five values of ΔxΔx = 0.1 m, 0.125 m, 0.15 m, 0.175 m and 0.20 m. Simulations were performed for all mesh sizes, and the results were compared in terms of convergence, stability and speed of simulation (Fig. 3). A linear wave with an amplitude of 1.5 m and a period of 6 s was used for these optimisation simulations. We considered wave time histories at two gauges A and B and recorded the waves from simulations using different mesh sizes (Fig. 3). Although the results are close (Fig. 3), some limited deviations are observed for larger mesh sizes of 0.20 m and 0.175 m. We therefore selected mesh size of 0.125 m as the optimum, giving an extra safety margin as a conservative solution.

    The pressure from the incident waves on the vertical wall is validated in our model by comparing them with the analytical equation of Sainflou (1928), Eq. (3), which is one of the most common set of equations for design of coastal structures (Fig. 4). The model was tested by running a linear wave of period 6 s and wave amplitude of 1.5 m against the wall, with a still water level of 4.5 m. It can be seen that the model results are very close to those from analytical equations of Sainflou (1928), indicating that our numerical model is accurately modelling the wave-structure interaction (Fig. 4).

    figure 4
    Fig. 4

    Eyewitness account analysis

    Contemporary reporting of the 4th and 5th February 2014 storms by the main national news outlets in the UK highlights the extreme nature of the events and the significant damage and disruption they were likely to have on the communities of the south-west of England. In interviews, this was reinforced by Network Rail engineers who, even at this early stage, were forecasting remedial engineering works to last for at least 6 weeks. One week later, following subsequent storms the cascading nature of the events was obvious. Multiple breaches of the seawall had taken place with up to 35 separate landslide events and significant damage to parapet walls along the coastal route also were reported. Residents of the area reported extreme effects of the storm, one likening it to an earthquake and reporting water ingress through doors windows and even through vertical chimneys (Table 1). This suggests extreme wave overtopping volumes and large wave impact forces. One resident described the structural effects as: “the house was jumping up and down on its footings”.

    Disaster management plans were quickly and effectively put into action by the local council, police service and National Rail. A major incident was declared, and decisions regarding evacuation of the residents under threat were taken around 2100 h on the night of 4th February when reports of initial damage to the seawall were received (Table 1). Local hotels were asked to provide short-term refuge to residents while local leisure facilities were prepared to accept residents later that evening. Initial repair work to the railway line was hampered by successive high spring tides and storms in the following days although significant progress was still made when weather conditions permitted (Table 1).

    Sea level observations and spectral analysis

    The results of surge and wave analyses are presented in Figs. 5 and 6. A surge height of up to 0.8 m was recorded in the examined tide gauge stations (Fig. 5b-d). Two main episodes of high surge heights are identified: the first surge started on 3rd February 2014 at 03:00 (UTC) and lasted until 4th of February 2014 at 00:00; the second event occurred in the period 4th February 2014 15:00 to 5th February 2014 at 17:00 (Fig. 5b-d). These data imply surge durations of 21 h and 26 h for the first and the second events, respectively. Based on the surge data in Fig. 5, we note that the storm event of early February 2014 and the associated surges was a relatively powerful one, which impacted at least 230 km of the south coast of England, from Land’s End to Weymouth, with large surge heights.

    figure 5
    Fig. 5
    figure 6
    Fig. 6

    Based on wave buoy records, the maximum recorded amplitudes are at least 20.5 m in Dawlish and West Bay, 1.9 m in Tor Bay and 4.9 m in Chesil (Fig. 6a-b). The buoys at Tor Bay and Chesil recorded dual peak period bands of 4–8 and 8–12 s, whereas at Dawlish and West Bay registered triple peak period bands at 4–8, 8–12 and 20–25 s (Fig. 6c, d). It is important to note that the long-period waves at 20–25 s occur with short durations (approximately 2 min) while the waves at the other two bands of 4–8 and 8–12 s appear to be present at all times during the storm event.

    The wave component at the period band of 4–8 s can be most likely attributed to normal coastal waves while the one at 8–12 s, which is longer, is most likely the swell component of the storm. Regarding the third component of the waves with long period of 20 -25 s, which occurs with short durations of 2 min, there are two hypotheses; it is either the result of a local (port and harbour) and regional (the Lyme Bay) oscillations (eg. Rabinovich 1997; Heidarzadeh and Satake 2014; Wang et al. 1992), or due to an abnormally long swell. To test the first hypothesis, we consider various water bodies such as Lyme Bay (approximate dimensions of 70 km × 20 km with an average water depth of 30 m; Fig. 6), several local bays (approximate dimensions of 3.6 km × 0.6 km with an average water depth of 6 m) and harbours (approximate dimensions of 0.5 km × 0.5 km with an average water depth of 4 m). Their water depths are based on the online Marine navigation website.Footnote8 According to Rabinovich (2010), the oscillation modes of a semi-enclosed rectangle basin are given by the following equation:

    Tmn=2gd−−√[(m2L)2+(nW)2]−1/2Tmn=2gd[(m2L)2+(nW)2]−1/2

    (5)

    where TmnTmn is the oscillation period, gg is the gravitational acceleration, dd is the water depth, LL is the length of the basin, WW is the width of the basin, m=1,2,3,…m=1,2,3,… and n=0,1,2,3,…n=0,1,2,3,…; mm and nn are the counters of the different modes. Applying Eq. (5) to the aforementioned water bodies results in oscillation modes of at least 5 min, which is far longer than the observed period of 20–25 s. Therefore, we rule out the first hypothesis and infer that the long period of 20–25 s is most likely a long swell wave coming from distant sources. As discussed by Rabinovich (1997) and Wang et al. (2022), comparison between sea level spectra before and after the incident is a useful method to distinguish the spectrum of the weather event. A visual inspection of Fig. 6 reveals that the forcing at the period band of 20–25 s is non-existent before the incident.

    Numerical simulations of wave loading and overtopping

    Based on the results of sea level data analyses in the previous section (Fig. 6), we use a dual peak wave spectrum with peak periods of 10.0 s and 25.0 s for numerical simulations because such a wave would be comprised of the most energetic signals of the storm. For variations of water depth (2.0–4.0 m), coastal wave amplitude (0.5–1.5 m) (Fig. 7) and storm surge height (0.5–0.8 m) (Fig. 5), we developed 20 scenarios (Scn) which we used in numerical simulations (Table 2). Data during the incident indicated that water depth was up to the crest level of the seawall (approximately 4 m water depth); therefore, we varied water depth from 2 to 4 m in our simulation scenarios. Regarding wave amplitudes, we referred to the variations at a nearby tide gauge station (West Bay) which showed wave amplitude up to 1.2 m (Fig. 7). Therefore, wave amplitude was varied from 0.5 m to 1.5 m by considering a factor a safety of 25% for the maximum wave amplitude. As for the storm surge component, time series of storm surges calculated at three coastal stations adjacent to Dawlish showed that it was in the range of 0.5 m to 0.8 m (Fig. 5). These 20 scenarios would help to study uncertainties associated with wave amplitudes and pressures. Figure 8 shows snapshots of wave propagation and impacts on the seawall at different times.

    figure 7
    Fig. 7

    Table 2 The 20 scenarios considered for numerical simulations in this study

    Full size table

    figure 8
    Fig. 8

    Results of wave amplitude simulations

    Large wave amplitudes can induce significant wave forcing on the structure and cause overtopping of the seawall, which could eventually cascade to other hazards such as erosion of the backfill and scour (Adams and Heidarzadeh, 2021). The first 10 scenarios of our modelling efforts are for the same incident wave amplitudes of 0.5 m, which occur at different water depths (2.0–4.0 m) and storm surge heights (0.5–0.8 m) (Table 2 and Fig. 9). This is because we aim at studying the impacts of effective water depth (deff—the sum of mean sea level and surge height) on the time histories of wave amplitudes as the storm evolves. As seen in Fig. 9a, by decreasing effective water depth, wave amplitude increases. For example, for Scn-1 with effective depth of 4.5 m, the maximum amplitude of the first wave is 1.6 m, whereas it is 2.9 m for Scn-2 with effective depth of 3.5 m. However, due to intensive reflections and interferences of the waves in front of the vertical seawall, such a relationship is barely seen for the second and the third wave peaks. It is important to note that the later peaks (second or third) produce the largest waves rather than the first wave. Extraordinary wave amplifications are seen for the Scn-2 (deff = 3.5 m) and Scn-7 (deff = 3.3 m), where the corresponding wave amplitudes are 4.5 m and 3.7 m, respectively. This may indicate that the effective water depth of deff = 3.3–3.5 m is possibly a critical water depth for this structure resulting in maximum wave amplitudes under similar storms. In the second wave impact, the combined wave height (i.e. the wave amplitude plus the effective water depth), which is ultimately an indicator of wave overtopping, shows that the largest wave heights are generated by Scn-2, 7 and 8 (Fig. 9a) with effective water depths of 3.5 m, 3.3 m and 3.8 m and combined heights of 8.0 m, 7.0 m and 6.9 m (Fig. 9b). Since the height of seawall is 5.4 m, the combined wave heights for Scn-2, 7 and 8 are greater than the crest height of the seawall by 2.6 m, 1.6 m and 1.5 m, respectively, which indicates wave overtopping.

    figure 9
    Fig. 9

    For scenarios 11–20 (Fig. 10), with incident wave amplitudes of 1.5 m (Table 2), the largest wave amplitudes are produced by Scn-17 (deff = 3.3 m), Scn-13 (deff = 2.5 m) and Scn-12 (deff = 3.5 m), which are 5.6 m, 5.1 m and 4.5 m. The maximum combined wave heights belong to Scn-11 (deff = 4.5 m) and Scn-17 (deff = 3.3 m), with combined wave heights of 9.0 m and 8.9 m (Fig. 10b), which are greater than the crest height of the seawall by 4.6 m and 3.5 m, respectively.

    figure 10
    Fig. 10

    Our simulations for all 20 scenarios reveal that the first wave is not always the largest and wave interactions, reflections and interferences play major roles in amplifying the waves in front of the seawall. This is primarily because the wall is fully vertical and therefore has a reflection coefficient of close to one (i.e. full reflection). Simulations show that the combined wave height is up to 4.6 m higher than the crest height of the wall, implying that severe overtopping would be expected.

    Results of wave loading calculations

    The pressure calculations for scenarios 1–10 are given in Fig. 11 and those of scenarios 11–20 in Fig. 12. The total pressure distribution in Figs. 11, 12 mostly follows a triangular shape with maximum pressure at the seafloor as expected from the Sainflou (1928) design equations. These pressure plots comprise both static (due to mean sea level in front of the wall) and dynamic (combined effects of surge and wave) pressures. For incident wave amplitudes of 0.5 m (Fig. 11), the maximum wave pressure varies in the range of 35–63 kPa. At the sea surface, it is in the range of 4–20 kPa (Fig. 11). For some scenarios (Scn-2 and 7), the pressure distribution deviates from a triangular shape and shows larger pressures at the top, which is attributed to the wave impacts and partial breaking at the sea surface. This adds an additional triangle-shaped pressure distribution at the sea surface elevation consistent with the design procedure developed by Goda (2000) for braking waves. The maximum force on the seawall due to scenarios 1–10, which is calculated by integrating the maximum pressure distribution over the wave-facing surface of the seawall, is in the range of 92–190 KN (Table 2).

    figure 11
    Fig. 11
    figure 12
    Fig. 12

    For scenarios 11–20, with incident wave amplitude of 1.5 m, wave pressures of 45–78 kPa and 7–120 kPa, for  the bottom and top of the wall, respectively, were observed (Fig. 12). Most of the plots show a triangular pressure distribution, except for Scn-11 and 15. A significant increase in wave impact pressure is seen for Scn-15 at the top of the structure, where a maximum pressure of approximately 120 kPa is produced while other scenarios give a pressure of 7–32 kPa for the sea surface. In other words, the pressure from Scn-15 is approximately four times larger than the other scenarios. Such a significant increase of the pressure at the top is most likely attributed to the breaking wave impact loads as detailed by Goda (2000) and Cuomo et al. (2010). The wave simulation snapshots in Fig. 8 show that the wave breaks before reaching the wall. The maximum force due to scenarios 11–20 is 120–286 KN.

    The breaking wave impacts peaking at 286 KN in our simulations suggest destabilisation of the upper masonry blocks, probably by grout malfunction. This significant impact force initiated the failure of the seawall which in turn caused extensive ballast erosion. Wave impact damage was proposed by Adams and Heidarzadeh (2021) as one of the primary mechanisms in the 2014 Dawlish disaster. In the multi-hazard risk model proposed by these authors, damage mechanism III (failure pathway 5 in Adams and Heidarzadeh, 2021) was characterised by wave impact force causing damage to the masonry elements, leading to failure of the upper sections of the seawall and loss of infill material. As blocks were removed, access to the track bed was increased for inbound waves allowing infill material from behind the seawall to be fluidised and subsequently removed by backwash. The loss of infill material critically compromised the stability of the seawall and directly led to structural failure. In parallel, significant wave overtopping (discussed in the next section) led to ballast washout and cascaded, in combination with masonry damage, to catastrophic failure of the wall and suspension of the rails in mid-air (Fig. 1b), leaving the railway inoperable for two months.

    Wave Overtopping

    The two most important factors contributing to the 2014 Dawlish railway catastrophe were wave impact forces and overtopping. Figure 13 gives the instantaneous overtopping rates for different scenarios, which experienced overtopping. It can be seen that the overtopping rates range from 0.5 m3/s/m to 16.1 m3/s/m (Fig. 13). Time histories of the wave overtopping rates show that the phenomenon occurs intermittently, and each time lasts 1.0–7.0 s. It is clear that the longer the overtopping time, the larger the volume of the water poured on the structure. The largest wave overtopping rates of 16.1 m3/s/m and 14.4 m3/s/m belong to Scn-20 and 11, respectively. These are the two scenarios that also give the largest combined wave heights (Fig. 10b).

    figure 13
    Fig. 13

    The cumulative overtopping curves (Figs. 14, 15) show the total water volume overtopped the structure during the entire simulation time. This is an important hazard factor as it determines the level of soil saturation, water pore pressure in the soil and soil erosion (Van der Meer et al. 2018). The maximum volume belongs to Scn-20, which is 65.0 m3/m (m-cubed of water per metre length of the wall). The overtopping volumes are 42.7 m3/m for Scn-11 and 28.8 m3/m for Scn-19. The overtopping volume is in the range of 0.7–65.0 m3/m for all scenarios.

    figure 14
    Fig. 14
    figure 15
    Fig. 15

    For comparison, we compare our modelling results with those estimated using empirical equations. For the case of the Dawlish seawall, we apply the equation proposed by Van Der Meer et al. (2018) to estimate wave overtopping rates, based on a set of decision criteria which are the influence of foreshore, vertical wall, possible breaking waves and low freeboard:

    qgH3m−−−−√=0.0155(Hmhs)12e(−2.2RcHm)qgHm3=0.0155(Hmhs)12e(−2.2RcHm)

    (6)

    where qq is the mean overtopping rate per metre length of the seawall (m3/s/m), gg is the acceleration due to gravity, HmHm is the incident wave height at the toe of the structure, RcRc is the wall crest height above mean sea level, hshs is the deep-water significant wave height and e(x)e(x) is the exponential function. It is noted that Eq. (6) is valid for 0.1<RcHm<1.350.1<RcHm<1.35. For the case of the Dawlish seawall and considering the scenarios with larger incident wave amplitude of 1.5 m (hshs= 1.5 m), the incident wave height at the toe of the structure is HmHm = 2.2—5.6 m, and the wall crest height above mean sea level is RcRc = 0.6–2.9 m. As a result, Eq. (6) gives mean overtopping rates up to approximately 2.9 m3/s/m. A visual inspection of simulated overtopping rates in Fig. 13 for Scn 11–20 shows that the mean value of the simulated overtopping rates (Fig. 13) is close to estimates using Eq. (6).

    Discussion and conclusions

    We applied a combination of eyewitness account analysis, sea level data analysis and numerical modelling in combination with our engineering judgement to explain the damage to the Dawlish railway seawall in February 2014. Main findings are:

    • Eyewitness data analysis showed that the extreme nature of the event was well forecasted in the hours prior to the storm impact; however, the magnitude of the risks to the structures was not well understood. Multiple hazards were activated simultaneously, and the effects cascaded to amplify the damage. Disaster management was effective, exemplified by the establishment of an emergency rendezvous point and temporary evacuation centre during the storm, indicating a high level of hazard awareness and preparedness.
    • Based on sea level data analysis, we identified triple peak period bands at 4–8, 8–12 and 20–25 s in the sea level data. Storm surge heights and wave oscillations were up to 0.8 m and 1.5 m, respectively.
    • Based on the numerical simulations of 20 scenarios with different water depths, incident wave amplitudes, surge heights and peak periods, we found that the wave oscillations at the foot of the seawall result in multiple wave interactions and interferences. Consequently, large wave amplitudes, up to 4.6 m higher than the height of the seawall, were generated and overtopped the wall. Extreme impulsive wave impact forces of up to 286 KN were generated by the waves interacting with the seawall.
    • We measured maximum wave overtopping rates of 0.5–16.1 m3/s/m for our scenarios. The cumulative overtopping water volumes per metre length of the wall were 0.7–65.0 m3/m.
    • Analysis of all the evidence combined with our engineering judgement suggests that the most likely initiating cause of the failure was impulsive wave impact forces destabilising one or more grouted joints between adjacent masonry blocks in the wall. Maximum observed pressures of 286 KN in our simulations are four times greater in magnitude than background pressures leading to block removal and initiating failure. Therefore, the sequence of cascading events was :1) impulsive wave impact force causing damage to masonry, 2) failure of the upper sections of the seawall, 3) loss of infill resulting in a reduction of structural strength in the landward direction, 4) ballast washout as wave overtopping and inbound wave activity increased and 5) progressive structural failure following successive tides.

    From a risk mitigation point of view, the stability of the seawall in the face of future energetic cyclonic storm events and sea level rise will become a critical factor in protecting the rail network. Mitigation efforts will involve significant infrastructure investment to strengthen the civil engineering assets combined with improved hazard warning systems consisting of meteorological forecasting and real-time wave observations and instrumentation. These efforts must take into account the amenity value of coastal railway infrastructure to local communities and the significant number of tourists who visit every year. In this regard, public awareness and active engagement in the planning and execution of the project will be crucial in order to secure local stakeholder support for the significant infrastructure project that will be required for future resilience.

    Notes

    1. https://www.networkrail.co.uk/..
    2. https://www.flow3d.com/products/flow-3d-hydro/.
    3. https://www.devonmuseums.net/Dawlish-Museum/Devon-Museums/.
    4. https://ntslf.org/.
    5. https://www.datawell.nl/Products/Buoys/DirectionalWaveriderMkIII.aspx.
    6. https://www.bodc.ac.uk/.
    7. https://coastalmonitoring.org/cco/.
    8. https://webapp.navionics.com/#boating@8&key=iactHlwfP.

    References

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    Acknowledgements

    We are grateful to Brunel University London for administering the scholarship awarded to KA. The Flow3D-Hydro used in this research for numerical modelling is licenced to Brunel University London through an academic programme contract. We sincerely thank Prof Harsh Gupta (Editor-in-Chief) and two anonymous reviewers for their constructive review comments.

    Funding

    This project was funded by the UK Engineering and Physical Sciences Research Council (EPSRC) through a PhD scholarship to Keith Adams.

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    Authors and Affiliations

    1. Department of Civil and Environmental Engineering, Brunel University London, Uxbridge, UB8 3PH, UKKeith Adams
    2. Department of Architecture and Civil Engineering, University of Bath, Bath, BA2 7AY, UKMohammad Heidarzadeh

    Corresponding author

    Correspondence to Keith Adams.

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    Adams, K., Heidarzadeh, M. Extratropical cyclone damage to the seawall in Dawlish, UK: eyewitness accounts, sea level analysis and numerical modelling. Nat Hazards (2022). https://doi.org/10.1007/s11069-022-05692-2

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    • Received17 May 2022
    • Accepted17 October 2022
    • Published14 November 2022
    • DOIhttps://doi.org/10.1007/s11069-022-05692-2

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    Keywords

    • Storm surge
    • Cyclone
    • Railway
    • Climate change
    • Infrastructure
    • Resilience
    원문보기
    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

    플라즈마 회전 전극 공정 중 분말 형성에 대한 공정 매개변수 및 냉각 가스의 영향

    Effects of process parameters and cooling gas on powder formation during the plasma rotating electrode process

    Yujie Cuia Yufan Zhaoa1 Haruko Numatab Kenta Yamanakaa Huakang Biana Kenta Aoyagia AkihikoChibaa
    aInstitute for Materials Research, Tohoku University, Sendai 980-8577, JapanbDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, Sendai 980-8577, Japan

    Highlights

    •The limitation of increasing the rotational speed in decreasing powder size was clarified.

    •Cooling and disturbance effects varied with the gas flowing rate.

    •Inclined angle of the residual electrode end face affected powder formation.

    •Additional cooling gas flowing could be applied to control powder size.

    Abstract

    The plasma rotating electrode process (PREP) is rapidly becoming an important powder fabrication method in additive manufacturing. However, the low production rate of fine PREP powder limits the development of PREP. Herein, we investigated different factors affecting powder formation during PREP by combining experimental methods and numerical simulations. The limitation of increasing the rotation electrode speed in decreasing powder size is attributed to the increased probability of adjacent droplets recombining and the decreased tendency of granulation. The effects of additional Ar/He gas flowing on the rotational electrode on powder formation is determined through the cooling effect, the disturbance effect, and the inclined effect of the residual electrode end face simultaneously. A smaller-sized powder was obtained in the He atmosphere owing to the larger inclined angle of the residual electrode end face compared to the Ar atmosphere. Our research highlights the route for the fabrication of smaller-sized powders using PREP.

    플라즈마 회전 전극 공정(PREP)은 적층 제조 에서 중요한 분말 제조 방법으로 빠르게 자리잡고 있습니다. 그러나 미세한 PREP 분말의 낮은 생산율은 PREP의 개발을 제한합니다. 여기에서 우리는 실험 방법과 수치 시뮬레이션을 결합하여 PREP 동안 분말 형성에 영향을 미치는 다양한 요인을 조사했습니다. 분말 크기 감소에서 회전 전극 속도 증가의 한계는 인접한 액적 재결합 확률 증가 및 과립화 경향 감소에 기인합니다.. 회전 전극에 흐르는 추가 Ar/He 가스가 분말 형성에 미치는 영향은 냉각 효과, 외란 효과 및 잔류 전극 단면의 경사 효과를 통해 동시에 결정됩니다. He 분위기에서는 Ar 분위기에 비해 잔류 전극 단면의 경사각이 크기 때문에 더 작은 크기의 분말이 얻어졌다. 우리의 연구는 PREP를 사용하여 더 작은 크기의 분말을 제조하는 경로를 강조합니다.

    Keywords

    Plasma rotating electrode process

    Ti-6Al-4 V alloy, Rotating speed, Numerical simulation, Gas flowing, Powder size

    Introduction

    With the development of additive manufacturing, there has been a significant increase in high-quality powder production demand [1,2]. The initial powder characteristics are closely related to the uniform powder spreading [3,4], packing density [5], and layer thickness observed during additive manufacturing [6], thus determining the mechanical properties of the additive manufactured parts [7,8]. Gas atomization (GA) [9–11], centrifugal atomization (CA) [12–15], and the plasma rotating electrode process (PREP) are three important powder fabrication methods.

    Currently, GA is the dominant powder fabrication method used in additive manufacturing [16] for the fabrication of a wide range of alloys [11]. GA produces powders by impinging a liquid metal stream to droplets through a high-speed gas flow of nitrogen, argon, or helium. With relatively low energy consumption and a high fraction of fine powders, GA has become the most popular powder manufacturing technology for AM.

    The entrapped gas pores are generally formed in the powder after solidification during GA, in which the molten metal is impacted by a high-speed atomization gas jet. In addition, satellites are formed in GA powder when fine particles adhere to partially molten particles.

    The gas pores of GA powder result in porosity generation in the additive manufactured parts, which in turn deteriorates its mechanical properties because pores can become crack initiation sites [17]. In CA, a molten metal stream is poured directly onto an atomizer disc spinning at a high rotational speed. A thin film is formed on the surface of the disc, which breaks into small droplets due to the centrifugal force. Metal powder is obtained when these droplets solidify.

    Compared with GA powder, CA powder exhibits higher sphericity, lower impurity content, fewer satellites, and narrower particle size distribution [12]. However, very high speed is required to obtain fine powder by CA. In PREP, the molten metal, melted using the plasma arc, is ejected from the rotating rod through centrifugal force. Compared with GA powder, PREP-produced powders also have higher sphericity and fewer pores and satellites [18].

    For instance, PREP-fabricated Ti6Al-4 V alloy powder with a powder size below 150 μm exhibits lower porosity than gas-atomized powder [19], which decreases the porosity of additive manufactured parts. Furthermore, the process window during electron beam melting was broadened using PREP powder compared to GA powder in Inconel 718 alloy [20] owing to the higher sphericity of the PREP powder.

    In summary, PREP powder exhibits many advantages and is highly recommended for powder-based additive manufacturing and direct energy deposition-type additive manufacturing. However, the low production rate of fine PREP powder limits the widespread application of PREP powder in additive manufacturing.

    Although increasing the rotating speed is an effective method to decrease the powder size [21,22], the reduction in powder size becomes smaller with the increased rotating speed [23]. The occurrence of limiting effects has not been fully clarified yet.

    Moreover, the powder size can be decreased by increasing the rotating electrode diameter [24]. However, these methods are quite demanding for the PREP equipment. For instance, it is costly to revise the PREP equipment to meet the demand of further increasing the rotating speed or electrode diameter.

    Accordingly, more feasible methods should be developed to further decrease the PREP powder size. Another factor that influences powder formation is the melting rate [25]. It has been reported that increasing the melting rate decreases the powder size of Inconel 718 alloy [26].

    In contrast, the powder size of SUS316 alloy was decreased by decreasing the plasma current within certain ranges. This was ascribed to the formation of larger-sized droplets from fluid strips with increased thickness and spatial density at higher plasma currents [27]. The powder size of NiTi alloy also decreases at lower melting rates [28]. Consequently, altering the melting rate, varied with the plasma current, is expected to regulate the PREP powder size.

    Furthermore, gas flowing has a significant influence on powder formation [27,29–31]. On one hand, the disturbance effect of gas flowing promotes fluid granulation, which in turn contributes to the formation of smaller-sized powder [27]. On the other hand, the cooling effect of gas flowing facilitates the formation of large-sized powder due to increased viscosity and surface tension. However, there is a lack of systematic research on the effect of different gas flowing on powder formation during PREP.

    Herein, the authors systematically studied the effects of rotating speed, electrode diameter, plasma current, and gas flowing on the formation of Ti-6Al-4 V alloy powder during PREP as additive manufactured Ti-6Al-4 V alloy exhibits great application potential [32]. Numerical simulations were conducted to explain why increasing the rotating speed is not effective in decreasing powder size when the rotation speed reaches a certain level. In addition, the different factors incited by the Ar/He gas flowing on powder formation were clarified.

    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.
    Fig. 1. Schematic figure showing the PREP with additional gas flowing on the end face of electrode.

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    원문보기
    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

    재료 압출 적층 제조에서 증착된 층의 안정성 및 변형

    Md Tusher Mollah Raphaël 사령관 Marcin P. Serdeczny David B. Pedersen Jon Spangenberg덴마크 공과 대학 기계 공학과, Kgs. 덴마크 링비

    2020년 12월 22일 접수, 2021년 5월 1일 수정, 2021년 7월 15일 수락, 2021년 7월 21일 온라인 사용 가능, 기록 버전 2021년 8월 17일 .

    Abstract

    이 문서는 재료 압출 적층 제조 에서 여러 레이어를 인쇄하는 동안 증착 흐름의 전산 유체 역학 시뮬레이션 을 제공합니다 . 개발된 모델은 증착된 레이어의 형태를 예측하고 점소성 재료 를 인쇄하는 동안 레이어 변형을 캡처합니다 . 물리학은 일반화된 뉴턴 유체 로 공식화된 Bingham 구성 모델의 연속성 및 운동량 방정식에 의해 제어됩니다. . 증착된 층의 단면 모양이 예측되고 재료의 다양한 구성 매개변수에 대해 층의 변형이 연구됩니다. 층의 변형은 인쇄물의 정수압과 압출시 압출압력으로 인한 것임을 알 수 있다. 시뮬레이션에 따르면 항복 응력이 높을수록 변형이 적은 인쇄물이 생성되는 반면 플라스틱 점도 가 높을수록 증착된 레이어에서변형이 커 집니다 . 또한, 인쇄 속도, 압출 속도 의 영향, 층 높이 및 인쇄된 층의 변형에 대한 노즐 직경을 조사합니다. 마지막으로, 이 모델은 후속 인쇄된 레이어의 정수압 및 압출 압력을 지원하기 위해 증착 후 점소성 재료가 요구하는 항복 응력의 필요한 증가에 대한 보수적인 추정치를 제공합니다.

    This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.

    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.
    Fig. 1. Model geometry with the computational domain, extrusion nozzle, toolpath, and boundary conditions. The model is presented while printing the fifth layer.

    키워드

    점성 플라스틱 재료, 재료 압출 적층 제조(MEX-AM), 다층 증착, 전산유체역학(CFD), 변형 제어
    Viscoplastic Materials, Material Extrusion Additive Manufacturing (MEX-AM), Multiple-Layers Deposition, Computational Fluid Dynamics (CFD), Deformation Control

    Introduction

    Three-dimensional printing of viscoplastic materials has grown in popularity over the recent years, due to the success of Material Extrusion Additive Manufacturing (MEX-AM) [1]. Viscoplastic materials, such as ceramic pastes [2,3], hydrogels [4], thermosets [5], and concrete [6], behave like solids when the applied load is below their yield stress, and like a fluid when the applied load exceeds their yield stress [7]. Viscoplastic materials are typically used in MEX-AM techniques such as Robocasting [8], and 3D concrete printing [9,10]. The differences between these technologies lie in the processing of the material before the extrusion and in the printing scale (from microscale to big area additive manufacturing). In these extrusion-based technologies, the structure is fabricated in a layer-by-layer approach onto a solid surface/support [11, 12]. During the process, the material is typically deposited on top of the previously printed layers that may be already solidified (wet-on-dry printing) or still deformable (wet-on-wet printing) [1]. In wet-on-wet printing, control over the deformation of layers is important for the stability and geometrical accuracy of the prints. If the material is too liquid after the deposition, it cannot support the pressure of the subsequently deposited layers. On the other hand, the material flowability is a necessity during extrusion through the nozzle. Several experimental studies have been performed to analyze the physics of the extrusion and deposition of viscoplastic materials, as reviewed in Refs. [13–16]. The experimental measurements can be supplemented with Computational Fluid Dynamics (CFD) simulations to gain a more complete picture of MEX-AM. A review of the CFD studies within the material processing and deposition in 3D concrete printing was presented by Roussel et al. [17]. Wolfs et al. [18] predicted numerically the failure-deformation of a cylindrical structure due to the self-weight by calculating the stiffness and strength of the individual layers. It was found that the deformations can take place in all layers, however the most critical deformation occurs in the bottom layer. Comminal et al. [19,20] presented three-dimensional simulations of the material deposition in MEX-AM, where the fluid was approximated as Newtonian. Subsequently, the model was experimentally validated in Ref. [21] for polymer-based MEX-AM, and extended to simulate the deposition of multiple layers in Ref. [22], where the previously printed material was assumed solid. Xia et al. [23] simulated the influence of the viscoelastic effects on the shape of deposited layers in MEX-AM. A numerical model for simulating the deposition of a viscoplastic material was recently presented and experimentally validated in Refs. [24] and [25]. These studies focused on predicting the cross-sectional shape of a single printed layer for different processing conditions (relative printing speed, and layer height). Despite these research efforts, a limited number of studies have focused on investigating the material deformations in wet-on-wet printing when multiple layers are deposited on top of each other. This paper presents CFD simulations of the extrusion-deposition flow of a viscoplastic material for several subsequent layers (viz. three- and five-layers). The material is continuously printed one layer over another on a fixed solid surface. The rheology of the viscoplastic material is approximated by the Bingham constitutive equation that is formulated using the Generalized Newtonian Fluid (GNF) model. The CFD model is used to predict the cross-sectional shapes of the layers and their deformations while printing the next layers on top. Moreover, the simulations are used to quantify the extrusion pressure applied by the deposited material on the substrate, and the previously printed layers. Numerically, it is investigated how the process parameters (i.e., the extrusion speed, printing speed, nozzle diameter, and layer height) and the material rheology affect the deformations of the deposited layers. Section 2 describes the methodology of the study. Section 3 presents and discusses the results. The study is summarized and concluded in Section 4.

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    원문 보기
    Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)

    고정 베드의 불침투성 토양에서 흐름 패턴의 수치 시뮬레이션

    NUMERICAL SIMULATION OF FLOW PATTERN IN SERIES OF IMPERMEABLE GROYNES IN FIXED BED

    Kafle, Mukesh Raj1
    1Asst. Professor, Department of Civil Engineering, Institute of Engineering, Pulchowk Campus, Nepal
    Email: mkafle@pcampus.edu.np

    Abstract

    This paper presents a numerical simulation of recirculating flow patterns in groyne fields. Moreover, it entails the concept determination of proper spacing of vertical unsubmerged and impermeable groynesin seriesto control the bank erosion. Flow pattern between the groynes varies along their space. The flow in groyne field may significantly affect the flow change, bed change, bank erosion and condition of habitat. In this regard, an assessment of flow along the space of groynes will yield important data needed to diversify the object of groyne installation. So, knowledge about determination of the proper spacing of groynes in groyne field is important. Space of vertical groynes was set from 1.5 to 10 times the length of groynes. The velocity field between groynes was simulated by using Computational Fluid Dynamics (CFD) model Nays 2D. Simulated velocity field was compared with existing experimentaldata for the same parameter, which agreed satisfactorily. Based on simulated results,the optimal spacing of vertical groynes to control the bank erosion was recommended.

    이 논문은 groyne 필드에서 재순환 흐름 패턴의 수치 시뮬레이션을 제공합니다. 더욱이, 그것은 제방 침식을 제어하기 위해 수직 비침수 및 불침투성 그로이네신 시리즈의 적절한 간격의 개념 결정을 수반합니다. groynes 사이의 흐름 패턴은 공간에 따라 다릅니다. groyne field의 흐름은 흐름 변화, 하상 변화, 제방 침식 및 서식지 상태에 중대한 영향을 미칠 수 있습니다. 이와 관련하여, groyne 공간을 따른 흐름의 평가는 groyne 설치 대상을 다양화하는 데 필요한 중요한 데이터를 산출할 것입니다. 따라서, groyne field에서 groyne의 적절한 간격 결정에 대한 지식이 중요합니다. 수직 여백의 간격은 여아 길이의 1.5배에서 10배 사이로 설정하였다. groyne 사이의 속도장은 CFD(Computational Fluid Dynamics) 모델 Nays 2D를 사용하여 시뮬레이션되었습니다. 시뮬레이션된 속도장은 동일한 매개변수에 대해 기존 실험 데이터와 비교되었으며 만족스럽게 일치했습니다. 모의 결과를 바탕으로 제방 침식을 억제하기 위한 최적의 수직 제방 간격을 제안하였다.

    1. Introduction
      Spur dikes or groynes are used to protect river banks from erosion and also keep the channel
      navigable.Depending upon the flow characteristics, spur-dikes may be classified as submerged and unsubmerged. Also, based on the permeability, spur dikes are further classified as permeable and
      impermeable. Herein, un-submerged !impermeable spur dikes are dealt. These structures are built from the river bank into the stream flow and usually built in group. Construction of groyne against the flow causes significant changes in flow pattern in channel. Those changes may result in scour phenomenon around groynes which may lead structure instability and changes in river morphology. Moreover, in series of groynes, spacing of groynes leads different types of recirculating flow patterns.Therefore, investigating the characteristics of flow pattern around groynes have been a great interest in river engineering. Numerous researchers like Sukhodolov et al. (2002), Hao Zhang et al.(2009), Beheshti (2010), Duan (2009), Naji(2010), Karami(2011) made a variety of experiments in order to determine the flow pattern around groynes. Most of these researchers studied effect of single groyne, while using series of groynes is more effective in protection of rivers. Besides experimental studies, variety of CFD models have been developed for computing flow pattern around hydraulic structures; like Fluent, Flow 3D, Nays 2D, Nays CUBE and SSIIM. In this study, Nays 2D numerical modelling has been used to investigate flow and recirculating pattern around a series of groynes and streamlines including components of velocities.
    1. Flow pattern in groyne fields
      Under conditions where the groynes are not submerged, the groyne fields are not really part of the wetted cross section of a river. Because of that, the flow pattern in the groyne-field is not directly the result of the discharge in the main channel. Reducing the main stream velocity has no effect on the flow pattern itself, whereas lowering the water level does (Uijttewaal et al.2001). Moreover, the flow pattern inside a groyne field may change with the change of its geometry, location along the river (inner curve, outer curve, or straight part), and/ or the groynes orientation( Przedwojski et al.1995). However, there is an indirect effect of the discharge on the flow pattern in the groyne field. Because of the flow that is diverted from the main channel into the groyne fields, water flows into the groyne field with low velocity through the downstream half of the interfacial section between the groyne field and the main channel. This water flows back to the main channel through a small width of, just downstream the upstream groyne of the groyne field ( Termes et al.1991). Flow separates on a groyne head and forms a secondary flow represented by a large scale vortex with a vertical axis of rotation called primary gyre. Deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre. Location, mutual interactions, and energy exchange between gyres are the factors that create a specific recirculation pattern, and, consequently assuming correspondence with sedimentation processes, they define deposition patterns.
    2. Model Formulation
      The CFD model selected for this study is the publically available software NAYS 2D (iRIC 2.0), which is an analytical solver for calculation of unsteady two-dimensional plane flow and riverbed deformation using boundary-fitted coordinates within general curvilinear coordinates. A numerical channel of length 8.0m and width 0.9m was created with grid size of 0.01m im stream wise and 0.03m in cross stream directions. Groynes or spur dikes of length 0.15 and width 0.01m were chosen in series. Groyne field with various aspect ratio (b/x) 0.7, 0.25, 0.17, 0.125 and 0.10, where b=length of spur dike, x=spacing of two dikes. Discharge of 0.0175 m3 /s was applied. For boundary conditions, water surface at downstream and velocity at upstream were considered as uniform flow. Relaxation coefficient for water surface calculation was considered as 0.8. For the finite-difference method, the CIP method was applied to the advection terms in equations of motion. For the turbulent field calculation, Constant eddy viscosity, Zero-equation model and k-G models were applied and compared. The model!s accuracy in predicting the velocity magnitudes is evaluated using statistical parameters- mean absolute error (MAE), mean square error(MSE), and root mean square error (RMSE). The comparison of results shows the importance of selecting an appropriate turbulence model in simulating flow field around a spur dike. From the comparison, k-I model is found superior over zero energy model and eddy viscosity model. So, k-I model is chosen as appropriate turbulence closure model.
    3. Model!s Validation
      The capability of CFD model Nays 2D to simulate the velocity field and recirculation pattern in groyne field was compared with experimental data of laboratory experiments by Sukhodolov et al. (2002). The numerical simulation was validated for aspect ratio (R=b/x=0.7) and R=0.25. For aspect ratio R=0.7, one gyre system occupies the whole area of the groyne field. The areas with lower-than-average velocity values are clearly seen in the central part of the gyre and near its corners. Velocities increase towards the margins of the gyre. For aspect ratio R=0.25, two gyre velocity fields were observed in the groyne field. In the downstream part of the groyne field a large gyre, covering two-thirds of the area is clearly visible. The left part(upstream) contains second gyre rotating much more slowly and in the direction opposed to the primary gyre. The simulated and observed velocity field pattern and gyre found satisfactorily agreed. Now, after validation, the model was used for further analysis of velocity field for various aspect ratios.
    Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
    Fig 2(b) Observed velocity field for aspect ratio 0.25(Sukhodolov 2002)
    1. Results and Discussions
      The calibrated model was applied to five different cases of un-submerged and impermeable groyne fields with aspect ratios R=0.70,0.25,0.17,0.125 & 0.10 and flow pattern was numerically simulated. For aspect ratio R=0.7 i.e x/b=1.5, Fig 1(a) only one lateral primary gyre was formed inside the groyne field. The circulation pattern in this case is distinguished by the main flow that is deflected outside the groyne field. The developed primary gyre prevents the main flow from penetrating the groyne field. Therefore, this pattern is desirable for navigation purposes as a continuous deep channel is maintained along the face of the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 1(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R= 0.25 i. e x/b=4 Fig 2(a) and flow pattern inside the groyne field was simulated. In this case, in the downstream part of the groyne field, a primary gyre occupying almost two-third area was formed. In addition, deflection of the flow inside the groyne field by banks and upstream groynes leads to the development of a secondary gyre with an opposite direction of rotation to the primary gyre covering almost one-third part of the groyne field. Likewise in the first case, the main current is maintained deflected outside the groyne field. Simulated velocity pattern satisfactorily agrees with the observed velocity field Fig 2(b) for the same aspect ratio by Sukhodolov (2002). The spacing of the groyne was further increased maintaining aspect ratio R=0.17 i.e x/b=6. In this case the flow pattern was similar to the aspect ratio R=0.25. The spacing of the groynes was further increased maintaining aspect ratio R=0.125 i. e x/b=8. In this case, similar to the previous scenarios two longitudinal gyres but with different positions are formed. The main current is directed in to the groyne field (Fig 3) creating a much more stronger eddy near the upstream groyne and greater turbulence along the upstream face and at the groyne lower head. As the spacing between groynes increased maintaining aspect ratio R=0.10 i. e x/b=10 (Fig 4), still primary and secondary gyres are generated. The formed gyres deflect the main flow thus preventing to enter in to the groyne field in upstream part. However, in the downstream of the primary gyre and just upstream of the second groyne, the flow attacks the bank directly. The resultant velocity profiles at the deflected region y/b=3 were plotted and how the spacing of second groyne affect the result was analyzed. Spacing of groynes makes little change in upstream resultant velocity. However, in the deflected region, its effect is significant. Higher value of spacing of groyne leads higher average deviation in resultant velocity. For aspect ratio R=0.7, the average deviation estimated as 0.02%. In the case of aspect ratio R=0.25, this value was reached to 1.57%. Further increment of spacing i. e decreasing the aspect ratio R=0.17, average deviation was found 3.82%. For the aspect ratio R=0.125, that value was estimated as 4.16%.
    3. Conclusions
      Geometry of the groyne fields; width and length of the groyne field mainly cause the specific flow patterns including number and shape of eddies or gyres. Eddies developed inside the groyne field deflects the main flow preventing it entering into the dead zone. An aspect ratio close to unity gives rise to a single eddy. A smaller aspect ratio (higher spacing between groynes) gives room to two stationary eddies, a large one called primary eddy, in the downstream part of the groyne field, and a smaller secondary eddy emerges near the upstream groyne. The extreme long groyne field -case of length to width ratio of larger thaneight shows penetration of main flow into the groyne field. The two eddies remain in a relatively stable position, while the main flow zone starts to penetrate into groyne field further downstream. In all cases, there is an eddy detaches from the upstream groyne tip that travels along the main channel groyne field interface and eventually merges with the primary eddy. The simulated results indicate that the spacing of groynes or spur dikes from the controlling of bank erosion point of view should be limited within six times the length of groyne.
    Fig 3 Computed velocity field for aspect ratio 0.125
    Fig 3 Computed velocity field for aspect ratio 0.125
    Fig 4 Computed velocity field for aspect ratio 0.10
    Fig 4 Computed velocity field for aspect ratio 0.10
    Fig 5 Resultant velocity profiles at y/b=3
    Fig 5 Resultant velocity profiles at y/b=3
    Fig 5 Resultant velocity profiles at y/b=3
    Fig 5 Resultant velocity profiles at y/b=3

    References

    1. Holtz, K.P  Numerical simulation of recirculating flow at groynes.Å Computer Methods in Water Resources, Vol 2, No 2 (1991).
    2. Hossein, Bassar; Abdollah, Ardeshir; Hojat, Karami.  Numerical simulation of flow pattern around spur dikes series in rigid bed.Å 9th international congress on civil engineering, May 8- 10,2012, Isfahan University of Technology (IUT) , Isfahan, Iran (2012).
    3. Kang, J.G; Yeo, H.K; Kim,S.J An experimental study on a characteristics of flow around groyne area by install conditions.Å www.SciRP.org/journal/eng(2012).
    4. Shimizu,Y; Nelson,JIntroduction of Nays solver in iRIC.Åwww.i-ric.org(2012).
    5. Sukhodolov, A. Uijttewaal, W. S. J., and Engelhardt, C. On the correspondence between morphological and hydro dynamical patterns of groyne fields.Å Earth Surf. Processes Landforms, 27(3) (2002).
    6. Uijttewall, W.S.J; Lehman,D; VanMazijk,A.  Exchange process between a river and its groyne fields-model experiments.Å Journal of Hydraulic Engineering, ASCE, 127(11) (2001).
    7. Uijttewall, W.S.J Groyne field velocity patterns determined with particle tracking
      velocimetryÅ.28th IAHR congress, Graz, Austria (1999).
    8. Yossef, Mohamed  Flow details near groynes: Experimental investigations.Å Journal of Hydraulic Engineering, ASCE, 137 (2011).
    Fig. 5. The predicted shapes of initial breach (a) Rectangular (b) V-notch. Fig. 6. Dam breaching stages.

    Investigating the peak outflow through a spatial embankment dam breach

    공간적 제방댐 붕괴를 통한 최대 유출량 조사

    Mahmoud T.GhonimMagdy H.MowafyMohamed N.SalemAshrafJatwaryFaculty of Engineering, Zagazig University, Zagazig 44519, Egypt

    Abstract

    Investigating the breach outflow hydrograph is an essential task to conduct mitigation plans and flood warnings. In the present study, the spatial dam breach is simulated by using a three-dimensional computational fluid dynamics model, FLOW-3D. The model parameters were adjusted by making a comparison with a previous experimental model. The different parameters (initial breach shape, dimensions, location, and dam slopes) are studied to investigate their effects on dam breaching. The results indicate that these parameters have a significant impact. The maximum erosion rate and peak outflow for the rectangular shape are higher than those for the V-notch by 8.85% and 5%, respectively. Increasing breach width or decreasing depth by 5% leads to increasing maximum erosion rate by 11% and 15%, respectively. Increasing the downstream slope angle by 4° leads to an increase in both peak outflow and maximum erosion rate by 2.0% and 6.0%, respectively.

    유출 유출 수문곡선을 조사하는 것은 완화 계획 및 홍수 경보를 수행하는 데 필수적인 작업입니다. 본 연구에서는 3차원 전산유체역학 모델인 FLOW-3D를 사용하여 공간 댐 붕괴를 시뮬레이션합니다. 이전 실험 모델과 비교하여 모델 매개변수를 조정했습니다.

    다양한 매개변수(초기 붕괴 형태, 치수, 위치 및 댐 경사)가 댐 붕괴에 미치는 영향을 조사하기 위해 연구됩니다. 결과는 이러한 매개변수가 상당한 영향을 미친다는 것을 나타냅니다. 직사각형 형태의 최대 침식율과 최대 유출량은 V-notch보다 각각 8.85%, 5% 높게 나타났습니다.

    위반 폭을 늘리거나 깊이를 5% 줄이면 최대 침식률이 각각 11% 및 15% 증가합니다. 하류 경사각을 4° 증가시키면 최대 유출량과 최대 침식률이 각각 2.0% 및 6.0% 증가합니다.

    Keywords

    Spatial dam breach; FLOW-3D; Overtopping erosion; Computational fluid dynamics (CFD)

    1. Introduction

    There are many purposes for dam construction, such as protection from flood disasters, water storage, and power generation. Embankment failures may have a catastrophic impact on lives and infrastructure in the downstream regions. One of the most common causes of embankment dam failure is overtopping. Once the overtopping of the dam begins, the breach formation will start in the dam body then end with the dam failure. This failure occurs within a very short time, which threatens to be very dangerous. Therefore, understanding and modeling the embankment breaching processes is essential for conducting mitigation plans, flood warnings, and forecasting flood damage.

    The analysis of the dam breaching process is implemented by different techniques: comparative methods, empirical models with dimensional and dimensionless solutions, physical-based models, and parametric models. These models were described in detail [1]. Parametric modeling is commonly used to simulate breach growth as a time-dependent linear process and calculate outflow discharge from the breach using hydraulics principles [2]. Alhasan et al. [3] presented a simple one-dimensional mathematical model and a computer code to simulate the dam breaching process. These models were validated by small dams breaching during the floods in 2002 in the Czech Republic. Fread [4] developed an erosion model (BREACH) based on hydraulics principles, sediment transport, and soil mechanics to estimate breach size, time of formation, and outflow discharge. Říha et al. [5] investigated the dam break process for a cascade of small dams using a simple parametric model for piping and overtopping erosion, as well as a 2D shallow-water flow model for the flood in downstream areas. Goodarzi et al. [6] implemented mathematical and statistical methods to assess the effect of inflows and wind speeds on the dam’s overtopping failure.

    Dam breaching studies can be divided into two main modes of erosion. The first mode is called “planar dam breach” where the flow overtops the whole dam width. While the second mode is called “spatial dam breach” where the flow overtops through the initial pilot channel (i.e., a channel created in the dam body). Therefore, the erosion will be in both vertical and horizontal directions [7].

    The erosion process through the embankment dams occurs due to the shear stress applied by water flows. The dam breaching evolution can be divided into three stages [8], [9], but Y. Yang et al. [10] divided the breach development into five stages: Stage I, the seepage erosion; Stage II, the initial breach formation; Stage III, the head erosion; Stage IV, the breach expansion; and Stage V, the re-equilibrium of the river channel through the breach. Many experimental tests have been carried out on non-cohesive embankment dams with an initial breach to examine the effect of upstream inflow discharges on the longitudinal profile evolution and the time to inflection point [11].

    Zhang et al. [12] studied the effect of changing downstream slope angle, sediment grain size, and dam crest length on erosion rates. They noticed that increasing dam crest length and decreasing downstream slope angle lead to decreasing sediment transport rate. While the increase in sediment grain size leads to an increased sediment transport rate at the initial stages. Höeg et al. [13] presented a series of field tests to investigate the stability of embankment dams made of various materials. Overtopping and piping were among the failure tests carried out for the dams composed of homogeneous rock-fill, clay, or gravel with a height of up to 6.0 m. Hakimzadeh et al. [14] constructed 40 homogeneous cohesive and non-cohesive embankment dams to study the effect of changing sediment diameter and dam height on the breaching process. They also used genetic programming (GP) to estimate the breach outflow. Refaiy et al. [15] studied different scenarios for the downstream drain geometry, such as length, height, and angle, to minimize the effect of piping phenomena and therefore increase dam safety.

    Zhu et al. [16] examined the effect of headcut erosion on dam breach growth, especially in the case of cohesive dams. They found that the breach growth in non-cohesive embankments is slower than cohesive embankments due to the little effect of headcut. Schmocker and Hager [7] proposed a relationship for estimating peak outflow from the dam breach process.(1)QpQin-1=1.7exp-20hc23d5013H0

    where: Qp = peak outflow discharge.

    Qin = inflow discharge.

    hc = critical flow depth.

    d50 = mean sediment diameter.

    Ho = initial dam height.

    Yu et al. [17] carried out an experimental study for homogeneous non-cohesive embankment dams in a 180° bending rectangular flume to determine the effect of overtopping flows on breaching formation. They found that the main factors influencing breach formation are water level, river discharge, and embankment material diameter.

    Wu et al. [18] carried out a series of experiments to investigate the effect of breaching geometry on both non-cohesive and cohesive embankment dams in a U-bend flume due to overtopping flows. In the case of non-cohesive embankments, the non-symmetrical lateral expansion was noticed during the breach formation. This expansion was described by a coefficient ranging from 2.7 to 3.3.

    The numerical models of the dam breach can be categorized according to different parameters, such as flow dimensions (1D, 2D, or 3D), flow governing equations, and solution methods. The 1D models are mainly used to predict the outflow hydrograph from the dam breach. Saberi et al. [19] applied the 1D Saint-Venant equation, which is solved by the finite difference method to investigate the outflow hydrograph during dam overtopping failure. Because of the ability to study dam profile evolution and breach formation, 2D models are more applicable than 1D models. Guan et al. [20] and Wu et al. [21] employed both 2D shallow water equations (SWEs) and sediment erosion equations, which are solved by the finite volume method to study the effect of the dam’s geometry parameters on outflow hydrograph and dam profile evolution. Wang et al. [22] also proposed a second-order hybrid-type of total variation diminishing (TVD) finite-difference to estimate the breach outflow by solving the 2D (SWEs). The accuracy of (SWEs) for both vertical flow contraction and surface roughness has been assessed [23]. They noted that the accuracy of (SWEs) is acceptable for milder slopes, but in the case of steeper slopes, modelers should be more careful. Generally, the accuracy of 2D models is still low, especially with velocity distribution over the flow depth, lateral momentum exchange, density-driven flows, and bottom friction [24]. Therefore, 3D models are preferred. Larocque et al. [25] and Yang et al. [26] started to use three-dimensional (3D) models that depend on the Reynolds-averaged Navier-Stokes (RANS) equations.

    Previous experimental studies concluded that there is no clear relationship between the peak outflow from the dam breach and the initial breach characteristics. Some of these studies depend on the sharp-crested weir fixed at the end of the flume to determine the peak outflow from the breach, which leads to a decrease in the accuracy of outflow calculations at the microscale. The main goals of this study are to carry out a numerical simulation for a spatial dam breach due to overtopping flows by using (FLOW-3D) software to find an empirical equation for the peak outflow discharge from the breach and determine the worst-case that leads to accelerating the dam breaching process.

    2. Numerical simulation

    The current study for spatial dam breach is simulated by using (FLOW-3D) software [27], which is a powerful computational fluid dynamics (CFD) program.

    2.1. Geometric presentations

    A stereolithographic (STL) file is prepared for each change in the initial breach geometry and dimensions. The CAD program is useful for creating solid objects and converting them to STL format, as shown in Fig. 1.

    2.2. Governing equations

    The governing equations for water flow are three-dimensional Reynolds Averaged Navier-Stokes equations (RANS).

    The continuity equation:(2)∂ui∂xi=0

    The momentum equation:(3)∂ui∂t+1VFuj∂ui∂xj=1ρ∂∂xj-pδij+ν∂ui∂xj+∂uj∂xi-ρu`iu`j¯

    where u is time-averaged velocity,ν is kinematic viscosity, VF is fractional volume open to flow, p is averaged pressure and -u`iu`j¯ are components of Reynold’s stress. The Volume of Fluid (VOF) technique is used to simulate the free surface profile. Hirt et al. [28] presented the VOF algorithm, which employs the function (F) to express the occupancy of each grid cell with fluid. The value of (F) varies from zero to unity. Zero value refers to no fluid in the grid cell, while the unity value refers to the grid cell being fully occupied with fluid. The free surface is formed in the grid cells having (F) values between zero and unity.(4)∂F∂t+1VF∂∂xFAxu+∂∂yFAyv+∂∂zFAzw=0

    where (u, v, w) are the velocity components in (x, y, z) coordinates, respectively, and (Ax, Ay, Az) are the area fractions.

    2.3. Boundary and initial conditions

    To improve the accuracy of the results, the boundary conditions should be carefully determined. In this study, two mesh blocks are used to minimize the time consumed in the simulation. The boundary conditions for mesh block 1 are as follows: The inlet and sides boundaries are defined as a wall boundary condition (wall boundary condition is usually used for bound fluid by solid regions. In the case of viscous flows, no-slip means that the tangential velocity is equal to the wall velocity and the normal velocity is zero), the outlet is defined as a symmetry boundary condition (symmetry boundary condition is usually used to reduce computational effort during CFD simulation. This condition allows the flow to be transferred from one mesh block to another. No inputs are required for this boundary condition except that its location should be defined accurately), the bottom boundary is defined as a uniform flow rate boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure. The boundary conditions for mesh block 2 are as follows: The inlet is defined as a symmetry boundary condition, the outlet is defined as a free flow boundary condition, the bottom and sides boundaries are defined as a wall boundary condition, and the top boundary is defined as a specific pressure boundary condition with assigned atmospheric pressure as shown in Fig. 2. The initial conditions required to be set for the fluid (i.e., water) inside of the domain include configuration, temperature, velocities, and pressure distribution. The configuration of water depends on the dimensions and shape of the dam reservoir. While the other conditions have been assigned as follows: temperature is normal water temperature (25 °c) and pressure distribution is hydrostatic with no initial velocity.

    2.4. Numerical method

    FLOW-3D uses the finite volume method (FVM) to solve the governing equation (Reynolds-averaged Navier-Stokes) over the computational domain. A finite-volume method is an Eulerian approach for representing and evaluating partial differential equations in algebraic equations form [29]. At discrete points on the mesh geometry, values are determined. Finite volume expresses a small volume surrounding each node point on a mesh. In this method, the divergence theorem is used to convert volume integrals with a divergence term to surface integrals. After that, these terms are evaluated as fluxes at each finite volume’s surfaces.

    2.5. Turbulent models

    Turbulence is the chaotic, unstable motion of fluids that occurs when there are insufficient stabilizing viscous forces. In FLOW-3D, there are six turbulence models available: the Prandtl mixing length model, the one-equation turbulent energy model, the two-equation (k – ε) model, the Renormalization-Group (RNG) model, the two-equation (k – ω) models, and a large eddy simulation (LES) model. For simulating flow motion, the RNG model is adopted to simulate the motion behavior better than the k – ε and k – ω.

    models [30]. The RNG model consists of two main equations for the turbulent kinetic energy KT and its dissipation.εT(5)∂kT∂t+1VFuAx∂kT∂x+vAy∂kT∂y+wAz∂kT∂z=PT+GT+DiffKT-εT(6)∂εT∂t+1VFuAx∂εT∂x+vAy∂εT∂y+wAz∂εT∂z=C1.εTKTPT+c3.GT+Diffε-c2εT2kT

    where KT is the turbulent kinetic energy, PT is the turbulent kinetic energy production, GT is the buoyancy turbulence energy, εT is the turbulent energy dissipation rate, DiffKT and Diffε are terms of diffusion, c1, c2 and c3 are dimensionless parameters, in which c1 and c3 have a constant value of 1.42 and 0.2, respectively, c2 is computed from the turbulent kinetic energy (KT) and turbulent production (PT) terms.

    2.6. Sediment scour model

    The sediment scour model available in FLOW-3D can calculate all the sediment transport processes including Entrainment transport, Bedload transport, Suspended transport, and Deposition. The erosion process starts once the water flows remove the grains from the packed bed and carry them into suspension. It happens when the applied shear stress by water flows exceeds critical shear stress. This process is represented by entrainment transport in the numerical model. After entrained, the grains carried by water flow are represented by suspended load transport. After that, some suspended grains resort to settling because of the combined effect of gravity, buoyancy, and friction. This process is described through a deposition. Finally, the grains sliding motions are represented by bedload transport in the model. For the entrainment process, the shear stress applied by the fluid motion on the packed bed surface is calculated using the standard wall function as shown in Eq.7.(7)ks,i=Cs,i∗d50

    where ks,i is the Nikuradse roughness and Cs,i is a user-defined coefficient. The critical bed shear stress is defined by a dimensionless parameter called the critical shields number as expressed in Eq.8.(8)θcr,i=τcr,i‖g‖diρi-ρf

    where θcr,i is the critical shields number, τcr,i is the critical bed shear stress, g is the absolute value of gravity acceleration, di is the diameter of the sediment grain, ρi is the density of the sediment species (i) and ρf is the density of the fluid. The value of the critical shields number is determined according to the Soulsby-Whitehouse equation.(9)θcr,i=0.31+1.2d∗,i+0.0551-exp-0.02d∗,i

    where d∗,i is the dimensionless diameter of the sediment, given by Eq.10.(10)d∗,i=diρfρi-ρf‖g‖μf213

    where μf is the fluid dynamic viscosity. For the sloping bed interface, the value of the critical shields number is modified according to Eq.11.(11)θ`cr,i=θcr,icosψsinβ+cos2βtan2φi-sin2ψsin2βtanφi

    where θ`cr,i is the modified critical shields number, φi is the angle of repose for the sediment, β is the angle of bed slope and ψ is the angle between the flow and the upslope direction. The effects of the rolling, hopping, and sliding motions of grains along the packed bed surface are taken by the bedload transport process. The volumetric bedload transport rate (qb,i) per width of the bed is expressed in Eq.12.(12)qb,i=Φi‖g‖ρi-ρfρfdi312

    where Φi is the dimensionless bedload transport rate is calculated by using Meyer Peter and Müller equation.(13)Φi=βMPM,iθi-θ`cr,i1.5cb,i

    where βMPM,i is the Meyer Peter and Müller user-defined coefficient and cb,i is the volume fraction of species i in the bed material. The suspended load transport is calculated as shown in Eq.14.(14)∂Cs,i∂t+∇∙Cs,ius,i=∇∙∇DCs,i

    where Cs,i is the suspended sediment mass concentration, D is the diffusivity, and us,i is the grain velocity of species i. Entrainment and deposition are two opposing processes that take place at the same time. The lifting and settling velocities for both entrainment and deposition processes are calculated according to Eq.15 and Eq.16, respectively.(15)ulifting,i=αid∗,i0.3θi-θ`cr,igdiρiρf-1(16)usettling,i=υfdi10.362+1.049d∗,i3-10.36

    where αi is the entrainment coefficient of species i and υf is the kinematic viscosity of the fluid.

    2.7. Grid type

    Using simple rectangular orthogonal elements in planes and hexahedral in volumes in the (FLOW-3D) program makes the mesh generation process easier, decreases the required memory, and improves numerical accuracy. Two mesh blocks were used in a joined form with a size ratio of 2:1. The first mesh block is coarser, which contains the reservoir water, and the second mesh block is finer, which contains the dam. For achieving accuracy and efficiency in results, the mesh size is determined by using a grid convergence test. The optimum uniform cell size for the first mesh block is 0.012 m and for the second mesh block is 0.006 m.

    2.8. Time step

    The maximum time step size is determined by using a Courant number, which controls the distance that the flow will travel during the simulation time step. In this study, the Courant number was taken equal to 0.25 to prevent the flow from traveling through more than one cell in the time step. Based on the Courant number, a maximum time step value of 0.00075 s was determined.

    2.9. Numerical model validation

    The numerical model accuracy was achieved by comparing the numerical model results with previous experimental results. The experimental study of Schmocker and Hager [7] was based on 31 tests with changes in six parameters (d50, Ho, Bo, Lk, XD, and Qin). All experimental tests were conducted in a straight open glass-sided flume. The horizontal flume has a rectangular cross-section with a width of 0.4 m and a height of 0.7 m. The flume was provided with a flow straightener and an intake with a length of 0.66 m. All tested dams were inserted at various distances (XD) from the intake. Test No.1 from this experimental program was chosen to validate the numerical model. The different parameters used in test No.1 are as follows:

    (1) uniform sediment with a mean diameter (d50 = 0.31 mm), (2) Ho = 0.2 m, (3) Bo = 0.2 m, (4) Lk = 0.1 m,

    (5) XD = 1.0 m, (6) Qin = 6.0 lit/s, (7) Su and Sd = 2:1, (8) mass density (ρs = 2650 kg/m3) (9) Homogenous and non-cohesive embankment dam. As shown in Fig. 2, the simulation is contained within a rectangular grid with dimensions: 3.56 m in the x-direction (where 0.66 m is used as inlet, 0.9 m as dam base width, and 1.0 m as outlet), in y-direction 0.2 m (dam length), and in the z-direction 0.3 m, which represents the dam height (0.2 m) with a free distance (0.1 m) above the dam. There are two main reasons that this experimental program is preferred for the validation process. The first reason is that this program deals with homogenous, non-cohesive soil, which is available in FLOW-3D. The second reason is that this program deals with small-scale models which saves time for numerical simulation. Finally, some important assumptions were considered during the validation process. The flow is assumed to be incompressible, viscous, turbulent, and three-dimensional.

    By comparing dam profiles at different time instants for the experimental test with the current numerical model, it appears that the numerical model gives good agreement as shown in Fig. 3 and Fig. 4, with an average error percentage of 9% between the experimental results and the numerical model.

    3. Analysis and discussions

    The current model is used to study the effects of different parameters such as (initial breach shapes, dimensions, locations, upstream and downstream dam slopes) on the peak outflow discharge, QP, time of peak outflow, tP, and rate of erosion, E.

    This study consists of a group of scenarios. The first scenario is changing the shapes of the initial breach according to Singh [1], the most predicted shapes are rectangular and V-notch as shown in Fig. 5. The second scenario is changing the initial breach dimensions (i.e., width and depth). While the third scenario is changing the location of the initial breach. Eventually, the last scenario is changing the upstream and downstream dam slopes.

    All scenarios of this study were carried out under the same conditions such as inflow discharge value (Qin=1.0lit/s), dimensions of the tested dam, where dam height (Ho=0.20m), crest width.

    (Lk=0.1m), dam length (Bo=0.20m), and homogenous & non-cohesive soil with a mean diameter (d50=0.31mm).

    3.1. Dam breaching process evolution

    The dam breaching process is a very complex process due to the quick changes in hydrodynamic conditions during dam failure. The dam breaching process starts once water flows reach the downstream face of the dam. During the initial stage of dam breaching, the erosion process is relatively quiet due to low velocities of flow. As water flows continuously, erosion rates increase, especially in two main zones: the crest and the downstream face. As soon as the dam crest is totally eroded, the water levels in the dam reservoir decrease rapidly, accompanied by excessive erosion in the dam body. The erosion process continues until the water levels in the dam reservoir equal the remaining height of the dam.

    According to Zhou et al. [11], the breaching process consists of three main stages. The first stage starts with beginning overtopping flow, then ends when the erosion point directed upstream and reached the inflection point at the inflection time (ti). The second stage starts from the end of the stage1 until the occurrence of peak outflow discharge at the peak outflow time (tP). The third stage starts from the end of the stage2 until the value of outflow discharge becomes the same as the value of inflow discharge at the final time (tf). The outflow discharge from the dam breach increases rapidly during stage1 and stage2 because of the large dam storage capacity (i.e., the dam reservoir is totally full of water) and excessive erosion. While at stage3, the outflow values start to decrease slowly because most of the dam’s storage capacity was run out. The end of stage3 indicates that the dam storage capacity was totally run out, so the outflow equalized with the inflow discharge as shown in Fig. 6 and Fig. 7.

    3.2. The effect of initial breach shape

    To identify the effect of the initial breach shape on the evolution of the dam breaching process. Three tests were carried out with different cross-section areas for each shape. The initial breach is created at the center of the dam crest. Each test had an ID to make the process of arranging data easier. The rectangular shape had an ID (Rec5h & 5b), which means that its depth and width are equal to 5% of the dam height, and the V-notch shape had an ID (V-noch5h & 1:1) which means that its depth is equal to 5% of the dam height and its side slope is equal to 1:1. The comparison between rectangular and V-notch shapes is done by calculating the ratio between maximum dam height at different times (ZMax) to the initial dam height (Ho), rate of erosion, and hydrograph of outflow discharge for each test. The rectangular shape achieves maximum erosion rate and minimum inflection time, in addition to a rapid decrease in the dam reservoir levels. Therefore, the dam breaching is faster in the case of a rectangular shape than in a V-notch shape, which has the same cross-section area as shown in Fig. 8.

    Also, by comparing the hydrograph for each test, the peak outflow discharge value in the case of a rectangular shape is higher than the V-notch shape by 5% and the time of peak outflow for the rectangular shape is shorter than the V-notch shape by 9% as shown in Fig. 9.

    3.3. The effect of initial breach dimensions

    The results of the comparison between the different initial breach shapes indicate that the worst initial breach shape is rectangular, so the second scenario from this study concentrated on studying the effect of a change in the initial rectangular breach dimensions. Groups of tests were carried out with different depths and widths for the rectangular initial breach. The first group had a depth of 5% from the dam height and with three different widths of 5,10, and 15% from the dam height, the second group had a depth of 10% with three different widths of 5,10, and 15%, the third group had a depth of 15% with three different widths of 5,10, and 15% and the final group had a width of 15% with three different heights of 5, 10, and 15% for a rectangular breach shape. The comparison was made as in the previous section to determine the worst case that leads to the quick dam failure as shown in Fig. 10.

    The results show that the (Rec 5 h&15b) test achieves a maximum erosion rate for a shorter period of time and a minimum ratio for (Zmax / Ho) as shown in Fig. 10, which leads to accelerating the dam failure process. The dam breaching process is faster with the minimum initial breach depth and maximum initial breach width. In the case of a minimum initial breach depth, the retained head of water in the dam reservoir is high and the crest width at the bottom of the initial breach (L`K) is small, so the erosion point reaches the inflection point rapidly. While in the case of the maximum initial breach width, the erosion perimeter is large.

    3.4. The effect of initial breach location

    The results of the comparison between the different initial rectangular breach dimensions indicate that the worst initial breach dimension is (Rec 5 h&15b), so the third scenario from this study concentrated on studying the effect of a change in the initial breach location. Three locations were checked to determine the worst case for the dam failure process. The first location is at the center of the dam crest, which was named “Center”, the second location is at mid-distance between the dam center and dam edge, which was named “Mid”, and the third location is at the dam edge, which was named “Edge” as shown in Fig. 11. According to this scenario, the results indicate that the time of peak outflow discharge (tP) is the same in the three cases, but the maximum value of the peak outflow discharge occurs at the center location. The difference in the peak outflow values between the three cases is relatively small as shown in Fig. 12.

    The rates of erosion were also studied for the three cases. The results show that the maximum erosion rate occurs at the center location as shown in Fig. 13. By making a comparison between the three cases for the dam storage volume. The results show that the center location had the minimum values for the dam storage volume, which means that a large amount of water has passed to the downstream area as shown in Fig. 14. According to these results, the center location leads to increased erosion rate and accelerated dam failure process compared with the two other cases. Because the erosion occurs on both sides, but in the case of edge location, the erosion occurs on one side.

    3.5. The effect of upstream and downstream dam slopes

    The results of the comparison between the different initial rectangular breach locations indicate that the worst initial breach location is the center location, so the fourth scenario from this study concentrated on studying the effect of a change in the upstream (Su) and downstream (Sd) dam slopes. Three slopes were checked individually for both upstream and downstream slopes to determine the worst case for the dam failure process. The first slope value is (2H:1V), the second slope value is (2.5H:1V), and the third slope value is (3H:1V). According to this scenario, the results show that the decreasing downstream slope angle leads to increasing time of peak outflow discharge (tP) and decreasing value of peak outflow discharge. The difference in the peak outflow values between the three cases for the downstream slope is 2%, as shown in Fig. 15, but changing the upstream slope has a negligible impact on the peak outflow discharge and its time as shown in Fig. 16.

    The rates of erosion were also studied in the three cases for both upstream and downstream slopes. The results show that the maximum erosion rate increases by 6.0% with an increasing downstream slope angle by 4°, as shown in Fig. 17. The results also indicate that the erosion rates aren’t affected by increasing or decreasing the upstream slope angle, as shown in Fig. 18. According to these results, increasing the downstream slope angle leads to increased erosion rate and accelerated dam failure process compared with the upstream slope angle. Because of increasing shear stress applied by water flows in case of increasing downstream slope.

    According to all previous scenarios, the dimensionless peak outflow discharge QPQin is presented for a fixed dam height (Ho) and inflow discharge (Qin). Fig. 19 illustrates the relationship between QP∗=QPQin and.

    Lr=ho2/3∗bo2/3Ho. The deduced relationship achieves R2=0.96.(17)QP∗=2.2807exp-2.804∗Lr

    4. Conclusions

    A spatial dam breaching process was simulated by using FLOW-3D Software. The validation process was performed by making a comparison between the simulated results of dam profiles and the dam profiles obtained by Schmocker and Hager [7] in their experimental study. And also, the peak outflow value recorded an error percentage of 12% between the numerical model and the experimental study. This model was used to study the effect of initial breach shape, dimensions, location, and dam slopes on peak outflow discharge, time of peak outflow, and the erosion process. By using the parameters obtained from the validation process, the results of this study can be summarized in eight points as follows.1.

    The rectangular initial breach shape leads to an accelerating dam failure process compared with the V-notch.2.

    The value of peak outflow discharge in the case of a rectangular initial breach is higher than the V-notch shape by 5%.3.

    The time of peak outflow discharge for a rectangular initial breach is shorter than the V-notch shape by 9%.4.

    The minimum depth and maximum width for the initial breach achieve maximum erosion rates (increasing breach width, b0, or decreasing breach depth, h0, by 5% from the dam height leads to an increase in the maximum rate of erosion by 11% and 15%, respectively), so the dam failure is rapid.5.

    The center location of the initial breach leads to an accelerating dam failure compared with the edge location.6.

    The initial breach location has a negligible effect on the peak outflow discharge value and its time.7.

    Increasing the downstream slope angle by 4° leads to an increase in both peak outflow discharge and maximum rate of erosion by 2.0% and 6.0%, respectively.8.

    The upstream slope has a negligible effect on the dam breaching process.

    References

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Prediction of embankment dam breach parameters: a literature review and needs assessment. 1998.Google Scholar[3]Z. Alhasan, J. Jandora, J. ŘíhaStudy of dam-break due to overtopping of four small dams in the Czech RepublicActa Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 63 (3) (2015), pp. 717-729 View PDFCrossRefView Record in ScopusGoogle Scholar[4]D. FreadBREACH, an erosion model for earthen dam failures: Hydrologic Research LaboratoryNOAA, National Weather Service (1988)Google Scholar[5]J. Říha, S. Kotaška, L. PetrulaDam Break Modeling in a Cascade of Small Earthen Dams: Case Study of the Čižina River in the Czech RepublicWater, 12 (8) (2020), p. 2309, 10.3390/w12082309 View PDFView Record in ScopusGoogle Scholar[6]E. Goodarzi, L. Teang Shui, M. ZiaeiDam overtopping risk using probabilistic concepts–Case study: The Meijaran DamIran Ain Shams Eng J, 4 (2) (2013), pp. 185-197ArticleDownload PDFView Record in ScopusGoogle Scholar[7]L. Schmocker, W.H. HagerPlane dike-breach due to overtopping: effects of sediment, dike height and dischargeJ Hydraul Res, 50 (6) (2012), pp. 576-586 View PDFCrossRefView Record in ScopusGoogle Scholar[8]J.S. Walder, R.M. Iverson, J.W. Godt, M. Logan, S.A. SolovitzControls on the breach geometry and flood hydrograph during overtopping of noncohesive earthen damsWater Resour Res, 51 (8) (2015), pp. 6701-6724View Record in ScopusGoogle Scholar[9]H. Wei, M. Yu, D. Wang, Y. LiOvertopping breaching of river levees constructed with cohesive sedimentsNat Hazards Earth Syst Sci, 16 (7) (2016), pp. 1541-1551 View PDFCrossRefView Record in ScopusGoogle Scholar[10]Y. Yang, S.-Y. Cao, K.-J. Yang, W.-P. LiYang K-j, Li W-p. 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    Effect of roughness on separation zone dimensions.

    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

    조도 계수 및 역전 수준 변화가 개선된 90도 측면 분출구에서의 유동에 대한 실험적 및 수치적 연구

    Maryam Bagheri; Seyed M. Ali Zomorodian; Masih Zolghadr; H. Md. Azamathulla; C. Venkata Siva Rama Prasad

    Abstract

    측면 분기기(흡입구)의 상류 측에서 흐름 분리는 분기기 입구에서 와류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 출력 용량 및 효율성을 감소시킵니다. 따라서 분리지대의 크기를 파악하고 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다. 본 연구에서는 분리 구역의 치수를 줄이기 위한 방법으로 7가지 유형의 거칠기 요소를 분기구 입구에 설치하고 4가지 다른 배출(총 84번의 실험을 수행)과 함께 3개의 서로 다른 베드 반전 레벨을 조사했습니다. 또한 3D CFD(Computational Fluid Dynamics) 모델을 사용하여 분리 영역의 흐름 패턴과 치수를 평가했습니다. 결과는 거칠기 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면, 드롭 구현 효과는 사용된 거칠기 계수를 기반으로 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 가지 방법을 결합하면 분리 영역 치수를 최대 63%까지 줄일 수 있습니다.

    Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions. Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone. Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

    HIGHLIGHTS

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    • Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance.
    • Installation of 7 types of roughening elements at the turnout entrance and 3 different bed level inverts were investigated.
    • Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow.
    • Combining both methods can reduce the separation zone dimensions by up to 63%.
    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
    Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

    Keywords

    discharge ratio, flow separation zone, intake, three dimensional simulation

    INTRODUCTION

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    Turnouts or intakes are amongst the oldest and most widely used hydraulic structures in irrigation networks. Turnouts are also used in water distribution, transmission networks, power generation facilities, and waste water treatment plants etc. The flows that enter a turnout have a strong momentum in the direction of the main waterway and that is why flow separation occurs inside the turnout. The horizontal vortex formed in the separation area is a suitable place for accumulation and deposition of sediments. The separation zone is a vulnerable area for sedimentation and for reduction of effective flow due to a contracted flow region in the lateral channel. Sedimentaion in the entrance of the intake can gradually be transfered into the lateral channel and decrease the capacity of the higher order channels over time (Jalili et al. 2011). On the other hand, the existence of coarse-grained materials causes erosion and destruction of the waterway side walls and bottom. In addition, sedimentation creates conditions for vegetation to take root and damage the waterway cover, which causes water to leak from its perimeter. Therefore, it is important to investigate the pattern of the flow separation area in turnouts and provide solutions to reduce the dimensions of this area.

    The three-dimensional flow structure at turnouts is quite complex. In an experimental study by Neary & Odgaard (1993) in a 90-degree water turnout it was found that the secondary currents and separation zone varies from the bed to the water surface. They also found that at a 90-degree water turnout, the bed roughness and discharge ratio play a critical role in flow structure. They asserted that an explanation of sediment behavior at a diversion entrance requires a comprehensive understanding of 3D flow patterns around the lateral-channel entrance. In addition, they suggested that there is a strong similarity between flow in a channel bend and a diversion channel, and that this similarity can rationalize the use of bend flow models for estimation of 3D flow structures in diversion channels.

    Some of the distinctive characteristics of dividing flow in a turnout include a zone of separation immediately near the entrance of the lateral turnout (separation zone), a contracted flow region in the branch channel (contracted flow), and a stagnation point near the downstream corner of the junction (stagnation zone). In the region downstream of the junction, along the continuous far wall, separation due to flow expansion may occur (Ramamurthy et al. 2007), that is, a separation zone. This can both reduce the turnout efficiency and the effective width of flow while increasing the sediment deposition in the turnout entrance (Jalili et al. 2011). Installation of submerged vanes in the turnout entrance is a method which is already applied to reduce the size of flow separation zones. The separation zone draws sediments and floating materials into themselves. This reduces effective cross-section area and reduces transmission capacity. These results have also been obtained in past studies, including by Ramamurthy et al. (2007) and in Jalili et al. (2011). Submerged vanes (Iowa vanes) are designed in order to modify the near-bed flow pattern and bed-sediment motion in the transverse direction of the river. The vanes are installed vertically on the channel bed, at an angle of attack which is usually oriented at 10–25 degrees to the local primary flow direction. Vane height is typically 0.2–0.5 times the local water depth during design flow conditions and vane length is 2–3 times its height (Odgaard & Wang 1991). They are vortex-generating devices that generate secondary circulation, thereby redistributing sediment within the channel cross section. Several factors affect the flow separation zone such as the ratio of lateral turnout discharge to main channel discharge, angle of lateral channel with respect to the main channel flow direction and size of applied submerged vanes. Nakato et al. (1990) found that sediment management using submerged vanes in the turnout entrance to Station 3 of the Council Bluffs plant, located on the Missouri River, is applicable and efficient. The results show submerged vanes are an appropriate solution for reduction of sediment deposition in a turnout entrance. The flow was treated as 3D and tests results were obtained for the flow characteristics of dividing flows in a 90-degree sharp-edged, junction. The main and lateral channel were rectangular with the same dimensions (Ramamurthy et al., 2007).

    Keshavarzi & Habibi (2005) carried out experiments on intake with angles of 45, 67, 79 and 90 degrees in different discharge ratios and reported the optimum angle for inlet flow with the lowest flow separation area to be about 55 degrees. The predicted flow characteristics were validated using experimental data. The results indicated that the width and length of the separation zone increases with the increase in the discharge ratio Qr (ratio of outflow per unit width in the turnout to inflow per unit width in the main channel).

    Abbasi et al. (2004) performed experiments to investigate the dimensions of the flow separation zone at a lateral turnout entrance. They demonstrated that the length and width of the separation zone decreases with the increasing ratio of lateral turn-out discharge. They also found that with a reducing angle of lateral turnout, the length of the separation zone scales up and width of separation zone reduces. Then they compared their observations with results of Kasthuri & Pundarikanthan (1987) who conducted some experiments in an open-channel junction formed by channels of equal width and an angle of lateral 90 degree turnout, which showed the dimensions of the separation zone in their experiments to be smaller than in previous studies. Kasthuri & Pundarikanthan (1987) studied vortex and flow separation dimensions at the entrance of a 90 degree channel. Results showed that increasing the diversion discharge ratio can reduce the length and width of the vortex area. They also showed that the length and width of the vortex area remain constant at diversion ratios greater than 0.7. Karami Moghaddam & Keshavarzi (2007) analyzed the flow characteristics in turnouts with angles of 55 and 90 degrees. They reported that the dimensions of the separation zone decrease by increasing the discharge ratio and reducing the turnout angle with respect to the main channel. Studies about flow separation zone can be found in Jalili et al. (2011), Nikbin & Borghei (2011), Seyedian et al. (2008).

    Jamshidi et al. (2016) measured the dimensions of a flow separation zone in the presence of submerged vanes with five arrangements (parallel, stagger, compound, piney and butterflies). Results showed that the ratio of the width to the length of the separation zone (shape index) was between 0.2 and 0.28 for all arrangements.

    Karami et al. (2017) developed a 3D computational fluid dynamic (CFD) code which was calibrated by measured data. They used the model to evaluate flow pattern, diversion ratio of discharge, strength of the secondary flow, and dimensions of the vortex inside the channel in various dikes and submerged vane installation scenarios. Results showed that the diversion ratio of discharge in the diversion channel is dependent on the width of the flow separation area in the main channel. A dike, perpendicular to the flow, doubles the ratio of diverted discharge and reduces the suspended sediment load compared with the base-line situation by creating outer arch conditions. In addition, increasing the longitudinal distance between vanes increases the velocity gradient between the vanes and leads to a more severe erosion of the bed near the vanes.Figure 1VIEW LARGEDOWNLOAD SLIDE

    Laboratory channel dimensions.

    Al-Zubaidy & Hilo (2021) used the Navier–Stokes equation to study the flow of incompressible fluids. Using the CFD software ANSYS Fluent 19.2, 3D flow patterns were simulated at a diversion channel. Their results showed good agreement using the comparison between the experimental and numerical results when the k-omega turbulence viscous model was employed. Simulation of the flow pattern was then done at the lateral channel junction using a variety of geometry designs. These improvements included changing the intake’s inclination angle and chamfering and rounding the inner corner of the intake mouth instead of the sharp edge. Flow parameters at the diversion including velocity streamlines, bed shear stress, and separation zone dimensions were computed in their study. The findings demonstrated that changing the 90° lateral intake geometry can improve the flow pattern and bed shear stress at the intake junction. Consequently, sedimentation and erosion problems are reduced. According to the conclusions of their study, a branching angle of 30° to 45° is the best configuration for increasing branching channel discharge, lowering branching channel sediment concentration.

    The review of the literature shows that most of the studies deal with turnout angle, discharge ratio and implementation of vanes as techniques to reduce the area of the separation zone. This study examines the effect of roughness coefficient and drop implementation at the entrance of a 90-degree lateral turnout on the dimensions of the separation zone. As far as the authors are aware, these two variables have never been studied as a remedy to decrease the separation zone dimensions whilst enhancing turnout efficiency. Additionally, a three-dimensional numerical model is applied to simulate the flow pattern around the turnout. The numerical results are verified against experimental data.

    METHOD

    Experimental setup

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    The experiments were conducted in a 90 degree dividing flow laboratory channel. The main channel is 15 m long, 0.5 m wide and 0.4 m high and the branch channel is 3 m long, 0.35 m wide and 0.4 m high, as shown in Figure 1. The tests were carried out at 9.65 m from the beginning of the flume and were far enough from the inlet, so we were sure that the flow was fully developed. According to Kirkgöz & Ardiçlioğlu (1997) the length of the developing region would be approximantly 65 and 72 times the flow depth. In this study, the depth is 9 cm, which makes this condition.

    Both the main and lateral channel had a slope of 0.0003 with side walls of concrete. A 100 hp pump discharged the water into a stilling basin at the entrance of the main flume. The discharge was measured using an ultrasonic discharge meter around the discharge pipe. Eighty-four experiments in total were carried out at range of 0.1<Fr<0.4 (Froude numbers in main channel and upstream of turnout). The depth of water in the main channel in the experiments was 9 cm, in which case the effect of surface tension can be considered; according to research by Zolghadr & Shafai Bejestan (2020) and Zolghadr et al. (2021), when the water depth is more than 6 cm, the effect of surface tension is reduced and can be ignored given that the separation phenomenon occurs in the boundary layer, the height of the roughness creates disturbances in growth and development of the boundary layer and, as a result, separation growth is also faced with disruption and its dimensions grow less compared to smooth surfaces. Similar conditions occur in case of drop implementation. A disturbance occurs in the growth of the boundary layer and as a result the separation zone dimensions decrease. In order to investigate the effect of roughness coefficient and drop implementation on the separation zone dimensions, four different discharges (16, 18, 21, 23 l/s) in subcritical conditions, seven Manning (Strickler) roughness coefficients (0.009, 0.011, 0.017, 0.023, 0.028, 0.030, 0.032) as shown in Figure 2 and three invert elevation differences between the main channel and lateral turnout invert (0, 5 and 10 cm) at the entrance of the turnout were considered. The Manning roughness coefficient values were selected based on available and feasible values for real conditions, so that 0.009 is equivalent to galvanized sheet roughness and selected for the baseline tests. 0.011 is for concrete with neat surface, 0.017 and 0.023 are for unfinished and gunite concrete respectively. 0.030 and 0.032 values are for concrete on irregular excavated rock (Chow 1959). The roughness coefficients were created by gluing sediment particles on a thin galvanized sheet which was installed at the upstream side of the lateral turnout. The values of roughness coefficients were calculated based on the Manning-Strickler formula. For this purpose, some uniformly graded sediment samples were prepared and the Manning roughness coefficient of each sample was determined with respect to the median size (D50) value pasted into the Manning-Strickler formula. Some KMnO4 was sifted in the main channel upstream to visualize and measure the dimensions of the separation zone. Consequently, when KMnO4 approached the lateral turnout a photo of the separation zone was taken from a top view. All the experiments were recorded and several photos were taken during the experiment after stablishment of steady flow conditions. The photos were then imported to AutoCAD to measure the separation zone dimensions. Because all the shooting was done with a high-definition camera and it was possible to zoom in, the results are very accurate.Figure 2VIEW LARGEDOWNLOAD SLIDE

    Roughness plates.

    The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in transverse direction (perpendicular to the flow direction).

    The water level was also measured by depth gauges with a accuracy of 0.1 mm, and velocity in one direction with a single-dimensional KENEK LP 1100 with an accuracy of ±0.02 m/s (0–1 m/s), ± 0.04 m/s (1–2 m/s), ± 0.08 m/s (2–4 m/s), ±0.10 m/s (4–5 m/s).

    Numerical simulation

    ListenA FLOW-3D numerical model was utilized as a solver of the Navier-Stokes equation to simulate the three-dimensional flow field at the entrance of the turnout. The governing equations included continuity momentum equations. The continuity equation, regardless of the density of the fluid in the form of Cartesian coordinates x, y, and z, is as follows:

    formula

    (1)where u, v, and w represent the velocity components in the x, y, and z directions, respectively; Ax, Ay, and Az are the surface flow fractions in the x, y, and z directions, respectively; VF denotes flow volume fraction; r is the density of the fluid; t is time; and Rsor refers to the source of the mass. Equations (2)–(4) show momentum equations in x, y and z dimensions respectively :

    formula

    (2)

    formula

    (3)

    formula

    (4)where Gx, Gy, and Gz are the accelerations caused by gravity in the x, y, and z directions, respectively; and fx, fy, and fz are the accelerations caused by viscosity in the x, y, and z directions, respectively.

    The turbulence models used in this study were the renormalized group (RNG) models. Evaluation of the concordance of the mentioned models with experimental studies showed that the RNG model provides more accurate results.

    Two blocks of mesh were used to simulate the main channels and lateral turnout. The meshes were denser in the vicinity of the entrance of the turnout in order to increase the accuracy of computations. Boundary conditions for the main mesh block included inflow for the channel entrance (volumetric flow rate), outflow for the channel exit, ‘wall’ for the bed and the right boundary and ‘symmetry’ for the top (free surface) and left boundaries (turnout). The side wall roughness coefficient was given to the software as the Manning number in surface roughness of any component. Considering the restrictions in the available processor, a main mesh block with appropriate mesh size was defined to simulate the main flow field in the channel, while the nested mesh-block technique was utilized to create a very dense solution field near the roughness plate in order to provide accurate results around the plates and near the entrance of the lateral turnout. This technique reduced the number of required mesh elements by up to 60% in comparison with the method in which the mesh size of the main solution field was decreased to the required extent.

    The numerical outputs are verified against experimental data. The hydraulic characteristics of the experiment are shown in Table 1.Table 1

    Hydraulic conditions of the flow

    Q(L/s)FrY1 (m)Q2/Q1
    16 0.449 0.09 0.22 
    18 0.335 0.09 0.61 
    21 0.242 0.09 0.71 
    23 0.180 0.09 1.04 

    RESULTS AND DISCUSSION

    Experimental results

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    During the experiments, the dimensions of the separation zone were recorded with an HD camera. Some photos were imported to AutoCad software. Then, the separation zones dimensions were measured and compared in different scenarios.

    At the beginning, the flow pattern in the separation zone for four different hydraulic conditions was studied for seven different Manning roughness coefficients from 0.009 to 0.032. To compare the obtained results, roughness of 0.009 was considered as the base line. The percentage of reduction in separation zone area in different roughness coefficients is shown in Figure 3. According to this figure, by increasing the roughness of the turnout side wall, the separation zone area ratio reduces (ratio of separation zone area to turnout area). In other words, in any desired Froud number, the highest dimensions of the separation zone area are related to the lowest roughness coefficients. In Figure 3, ‘A’ is the area of the separation zone and ‘Ai’ represents the total area of the turnout.Figure 3VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions.Figure 4VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions.

    It should be mentioned that the separation zone dimensions change with depth, so that the area is larger at the surface than near the bed. This study measured the dimensions of this area at the surface. Figure 4 show exactly where the roughness elements were located.Figure 5VIEW LARGEDOWNLOAD SLIDE

    Comparison of separation zone for n=0.023 and n=0.032.

    Figure 5 shows images of the separation zone at n=0.023 and n=0.032 as examples, and show that the separation area at n=0.032 is smaller than that of n=0.023.

    The difference between the effect of the two 0.032 and 0.030 roughnesses is minor. In other words, the dimensions of the separation zone decreased by increasing roughness up to 0.030 and then remained with negligable changes.

    In the next step, the effect of intake invert relative to the main stream (drop) on the dimensions of the separation zone was investigated. To do this, three different invert levels were considered: (1) without drop; (2) a 5 cm drop between the main canal and intake canal; and (3) a 10 cm drop between the main canal and intake canal. The without drop mode was considered as the control state. Figure 6 shows the effect of drop implementation on separation zone dimensions. Tables 2 and 3 show the reduced percentage of separation zone areas in 5 and 10 cm drop compared to no drop conditions as the base line. It was found that the best results were obtained when a 10 cm drop was implemented.Table 2

    Decrease percentage of separation zone area in 5 cm drop

    Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    0.08 10.56 11.06 25.27 33.03 35.57 36.5 
    0.121 7.66 11.14 11.88 15.93 34.59 36.25 
    0.353 1.38 2.63 8.17 14.39 31.20 31.29 
    0.362 3 11.54 19.56 25.73 37.89 38.31 

    Table 3

    Decrease percentage of separation zone area in 10 cm drop

    Frn=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    0.047 4.30 8.75 23.47 31.22 34.96 35.13 
    0.119 11.01 13.16 15.02 21.48 39.45 40.68 
    0.348 3.89 5.71 9.82 16.09 29 30.96 
    0.354 2.84 10.44 18.42 25.45 35.68 35.76 

    Figure 6VIEW LARGEDOWNLOAD SLIDE

    Effect of drop implementation on separation zone dimensions.

    The combined effect of drop and roughness is shown in Figure 7. According to this figure, by installing a drop structure at the entrance of the intake, the dimensions of the separation zone scales down in any desired roughness coefficient. Results indicated that by increasing the roughness coefficient or drop implementation individually, the separation zone area decreases up to 38 and 25% respectively. However, employing both techniques simultaneously can reduce the separation zone area up to 63% (Table 4). The reason for the reduction of the dimensions of the separation zone area by drop implementation can be attributed to the increase of discharge ratio. This reduces the dimensions of the separation zone area.Table 4

    Reduction in percentage of combined effect of roughness and 10 cm drop

    Qin=0.011n=0.017n=0.023n=0.028n=0.030n=0.032
    16 32.3 35.07 37.2 45.7 58.01 59.1 
    18 44.5 34.15 36.18 48.13 54.2 56.18 
    21 43.18 32.33 42.30 37.79 57.16 63.2 
    23 40.56 34.5 34.09 46.25 50.12 57.2 

    Figure 7VIEW LARGEDOWNLOAD SLIDE

    Combined effect of roughness and drop on separation zone dimensions.

    This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Some other researchers reported that increasing the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, these researchers employed other methods to enhance the discharge ratio. Drop implementation is simple and applicable in practice, since there is normally an elevation difference between the main and lateral canal in irrigation networks to ensure gravity flow occurance.

    Table 4 depicts the decrease in percentage of the separation zone compared to base line conditions in different arrangements of the combined tests.Figure 8VIEW LARGEDOWNLOAD SLIDE

    Velocity profiles for various roughness coefficients along turnout width.

    A comparison between the proposed methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. Figure 8 shows the comparison of the results. The comparison shows that the new techniques can be highly influential and still practical. In this research, with no change in structural geometry (enhancement of roughness coefficient) or minor changes with respect to drop implementation, the dimensions of the separation zone are decreased noticeably. The velocity values were also recorded by a one-dimensional velocity meter at 15 cm distance from the turnout entrance and in a transverse direction (perpendicular to the flow direction). The results are shown in Figure 9.Figure 9VIEW LARGEDOWNLOAD SLIDE

    Effect of roughness on separation zone dimensions in numerical study.

    Numerical results

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    This study examined the flow patterns around the entrance of a diversion channel due to various wall roughnesses in the diversion channel. Results indicated that increasing the discharge ratio in the main channel and diversion channel reduces the area of the separation zone in the diversion channel.Figure 10VIEW LARGEDOWNLOAD SLIDE

    Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).A laboratory and numerical error rate of 0.2605 was calculated from the following formula,

    formula

    where Uexp is the experimental result, Unum is the numerical result, and N is the number of data.

    Figure 9 shows the effect of roughness on separation zone dimensions in numerical study. Figure 10 compares the vortex area (software output) for three roughnesses, 0.009, 0.023 and 0.032 and Figure 11 shows the flow lines (tecplot output) that indicate the effect of roughness on flow in the separation zone. Numerical analysis shows that by increasing the roughness coefficient, the dimensions of the separation zone area decrease, as shown in Figure 10 where the separation zone area at n=0.032 is less than the separation zone area at n=0.009.Figure 11VIEW LARGEDOWNLOAD SLIDE

    Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.Figure 12VIEW LARGEDOWNLOAD SLIDE

    Velocity vector for flow condition Q1/422 l/s, near surface.

    The velocities intensified moving midway toward the turnout showing that the effective area is scaled down. The velocity values were almost equal to zero near the side walls as expected. As shown in Figure 12 the approach vortex area velocity decreases. Experimental and numerical measured velocity at x=0.15 m of the diversion channel compared in Figure 13 shows that away from the separation zone area, the velocity increases. All longitudinal velocity contours near the vortex area are distinctly different between different roughnesses. The separation zone is larger at less roughness both in length and width.Figure 13VIEW LARGEDOWNLOAD SLIDE

    Exprimental and numerical measured velocity.

    CONCLUSION

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    This study introduces practical and feasible methods for enhancing turnout efficiency by reducing the separation zone dimensions. Increasing the roughness coefficient and implementation of inlet drop were considered as remedies for reduction of separation zone dimensions. A data set has been compiled that fully describes the complex, 3D flow conditions present in a 90 degree turnout channel for selected flow conditions. The aim of this numerical model was to compare the results of a laboratory model in the area of the separation zone and velocity. Results showed that enhancing roughness coefficient reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%. Further research is proposed to investigate the effect of roughness and drop implementation on sedimentation pattern at lateral turnouts. The dimensions of the separation zone decreases with the increase of the non-dimensional parameter, due to the reduction ratio of turnout discharge increasing in all the experiments.

    This method increases the discharge ratio (ratio of turnout to main channel discharge). The results are compatible with the literature. Other researchers have reported that intensifying the discharge ratio can scale down the separation zone dimensions (Karami Moghaddam & Keshavarzi 2007; Ramamurthy et al. 2007). However, they employed other methods to enhance the discharge ratio. Employing both techniques simultaneously can decrease the separation zone dimensions up to 63%. A comparison between the new methods introduced in this paper and traditional methods such as installation of submerged vanes, and changing the inlet geometry (angle, radius) was performed. The comparison shows that the new techniques can be highly influential and still practical. The numerical and laboratory models are in good agreement and show that the method used in this study has been effective in reducing the separation area. This method is simple, economical and can prevent sediment deposition in the intake canal. Results show that CFD prediction of the fluid through the separation zone at the canal intake can be predicted reasonably well and the RNG model offers the best results in terms of predictability.

    DATA AVAILABILITY STATEMENT

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    All relevant data are included in the paper or its Supplementary Information.

    REFERENCES

    Abbasi A., Ghodsian M., Habibi M. & Salehi Neishabouri S. A. 2004 Experimental investigation on dimensions of flow separation zone at lateral intakeentrance. Research & Construction; Pajouhesh va Sazandegi 62, 38–44. (In Persian).Google Scholar Al-Zubaidy R. & Hilo A. 2021 Numerical investigation of flow behavior at the lateral intake using Computational Fluid Dynamics (CFD). Materials Today: Proceedings. https://doi.org/10.1016/j.matpr.2021.11.172.Google Scholar Chow V. T. 1959 Open Channel Hydraulics. McGraw-Hill, New York.Jalili H., Hosseinzadeh Dalir A. & Farsadizadeh D. 2011 Effect of intake geometry on the sediment transport and lateral flow pattern. Iranian Water Research Journal 5 (9), 1–10. (In Persian).Google Scholar Jamshidi A., Farsadizadeh D. & Hosseinzadeh Dalir A. 2016 Variations of flow separation zone at lateral intake entrance using submerged vanes. Journal of Civil Engineering Urban 6 (3), 54–63. Journal homepage. Available from: www.ojceu.ir/main.Google Scholar Karami Moghaddam K. & Keshavarzi A. 2007 Investigation of flow structure in lateral intakes of 55° and 90° with rounded entrance edge. In: 03 National Congress on Civil Engineering University of Tabriz. Available from: https://civilica.com/doc/16317. (In Persian).Google Scholar Karami H., Farzin S., Sadrabadi M. T. & Moazeni H. 2017 Simulation of flow pattern at rectangular lateral intake with different dike and submerged vane scenarios. Journal of Water Science and Engineering 10 (3), 246–255. https://doi.org/10.1016/j.wse.2017.10.001.Google ScholarCrossref  Kasthuri B. & Pundarikanthan N. V. 1987 Discussion on separation zone at open- channel junction. Journal of Hydraulic Engineering 113 (4), 543–548.Google ScholarCrossref  Keshavarzi A. & Habibi L. 2005 Optimizing water intake angle by flow separation analysis. Journal of Irrigation and Drain 54, 543–552. https://doi.org/10.1002/ird.207.Google ScholarCrossref  Kirkgöz M. S. & Ardiçlioğlu M. 1997 Velocity profiles of developing and developed open channel flow. Journal of Hydraulic Engineering 1099–1105. 10.1061/(ASCE)0733-9429(1997)123:12(1099).Google Scholar Nakato T., Kennedy J. F. & Bauerly D. 1990 Pumpstation intake-shoaling control with submerge vanes. Journal of Hydraulic Engineering. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:1(119).Google Scholar Neary V. S. & Odgaard J. A. 1993 Three-dimensional flow structure at open channel diversions. Journal of Hydraulic Engineering. ASCE 119 (11), 1224–1230. https://doi.org/10.1061/(ASCE)0733-9429(1993)119:11(1223).Google ScholarCrossref  Nikbin S. & Borghei S. M. 2011 Experimental investigation of submerged vanes effect on dimensions of flow separation zone at a 90° openchannel junction. In: 06rd National Congress on Civil Engineering University of Semnan. (In Persian). Available from: https://civilica.com/doc/120494.Google Scholar Odgaard J. A. & Wang Y. 1991 Sediment management with submerged vanes, I: theory. Journal of Hydraulic Engineering 117 (3), 267–283.Google ScholarCrossref  Ramamurthy A. S., Junying Q. & Diep V. 2007 Numerical and experimental study of dividing open-channel flows. Journal of Hydraulic Engineering. See: https://doi.org/10.1061/(ASCE)0733-9429(2007)133:10(1135).Google Scholar Seyedian S., Karami Moghaddam K. & Shafai Begestan M. 2008 Determining the optimal radius in lateral intakes of 55° and 90° using variation of flow velocity. In: 07th Iranian Hydraulic Conference. Power & Water University of Technology (PWUT). (In Persian). Available from: https://civilica.com/doc/56251.Google Scholar Zolghadr M. & Shafai Bejestan M. 2020 Six legged concrete (SLC) elements as scour countermeasures at wing wall bridge abutments. International Journal of River Basin Management. doi: 10.1080/15715124.2020.1726357.Google Scholar Zolghadr M., Zomorodian S. M. A., Shabani R. & Azamatulla H.Md. 2021 Migration of sand mining pit in rivers: an experimental, numerical and case study. Measurement. https://doi.org/10.1016/j.measurement.2020.108944.Google Scholar © 2022 The AuthorsThis is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY-NC-ND 4.0), which permits copying and redistribution for non-commercial purposes with no derivatives, provided the original work is properly cited (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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    Figure 6. Circular section of the viscosity and shear-rate clouds.

    Simulation and Visual Tester Verification of Solid Propellant Slurry Vacuum Plate Casting

    Wu Yue,Li Zhuo,Lu RongFirst published: 26 February 2020 https://doi.org/10.1002/prep.201900411Citations: 3

    Abstract

    Using an improved Carreau constitutive model, a numerical simulation of the casting process of a type of solid propellant slurry vacuum plate casting was carried out using the Flow3D software. Through the flow process in the orifice flow channel and the combustion chamber, the flow velocity of the slurry passing through the plate flow channel was quantitatively analyzed, and the viscosity, shear rate, and leveling characteristics of the slurry in the combustion chamber were qualitatively analyzed and predicted. The pouring time, pouring quality, and flow state predicted by the numerical simulation were verified using a visual tester consisting of a vacuum plate casting system in which a pouring experiment was carried out. Studies have shown that HTPB three-component propellant slurry is a typical yielding pseudoplastic fluid. When the slurry flows through the flower plate and the airfoil, the fluid shear rate reaches its maximum value and the viscosity of the slurry decreases. The visual pouring platform was built and the experiment was controlled according to the numerically-calculated parameters, ensuring the same casting speed. The comparison between the predicted casting quality and the one obtained in the verification test resulted in an error less than 10 %. Moreover, the error between the simulated casting completion time and the process verification test result was also no more than 10 %. Last, the flow state of the slurry during the simulation was consistent with the one during the experimental test. The overall leveling of the slurry in the combustion chamber was adequate and no relatively large holes and flaws developed during the pouring process.

    개선된 Carreau 구성 모델을 사용하여 FLOW-3D 소프트웨어를 사용하여 고체 추진제 슬러리 진공판 유형의 Casting Process에 대한 수치 시뮬레이션을 수행했습니다. 오리피스 유로와 연소실에서의 유동과정을 통해 판 유로를 통과하는 슬러리의 유속을 정량적으로 분석하고, 연소실에서 슬러리의 점도, 전단율, 레벨링 특성을 정성적으로 분석하하고, 예측하였습니다.

    타설시간, 타설품질, 수치해석으로 예측된 ​​유동상태는 타설실험을 수행한 진공판주조시스템으로 구성된 비주얼 테스터를 이용하여 검증하였습니다.

    연구에 따르면 HTPB 3성분 추진제 슬러리는 전형적인 생성 가소성 유체입니다. 슬러리가 플라워 플레이트와 에어포일을 통과할 때 유체 전단율이 최대값에 도달하고 슬러리의 점도가 감소합니다.

    시각적 주입 플랫폼이 구축되었고 동일한 주조 속도를 보장하기 위해 수치적으로 계산된 매개변수에 따라 실험이 제어되었습니다. 예측된 casting 품질과 검증 테스트에서 얻은 품질을 비교한 결과 10 % 미만의 오류가 발생했습니다.

    또한 모의 casting 완료시간과 공정검증시험 결과의 오차도 10 % 이하로 나타났습니다.

    마지막으로 시뮬레이션 중 슬러리의 흐름 상태는 실험 테스트 시와 일치하였다. 연소실에서 슬러리의 전체 레벨링은 적절했으며 주입 과정에서 상대적으로 큰 구멍과 결함이 발생하지 않았습니다.

    Figure 1. The equipment used in the vacuum flower-plate pouring process.
    Figure 1. The equipment used in the vacuum flower-plate pouring process.
    Figure 2. Calculation model.
    Figure 2. Calculation model.
    Figure 3. Grid block division unit.
    Figure 3. Grid block division unit.
    Figure 4. Circular section of the speed cloud.
    Figure 4. Circular section of the speed cloud.
    Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
    Figure 5. Viscosity and shear rate distribution cloud pattern flowing through the plate holes.
    Figure 6. Circular section of the viscosity and shear-rate clouds.
    Figure 6. Circular section of the viscosity and shear-rate clouds.
    Figure 7. Volume fraction cloud chart at different time.
    Figure 7. Volume fraction cloud chart at different time.
    Figure 8. Experimental program.
    Figure 8. Experimental program.
    Figure 9. Emulation experimental device.
    Figure 9. Emulation experimental device.
    Figure 10. Visualization of the flow state of the pulp inside the tester.
    Figure 10. Visualization of the flow state of the pulp inside the tester.

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    Full Test View
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].

    Application of Numerical and Experimental Modeling to Improve the Efficiency of Parshall Flumes: A Review of the State-of-the-Art

    Parshall Flumes의 효율성 향상을 위한 수치 및 실험 모델링의 적용: 최신 기술 검토

    Mehdi Heyrani 1,* , Abdolmajid Mohammadian 1, Ioan Nistor 1 and Omerul Faruk Dursun 2

    Abstract

    열린 채널에서 흐름을 관리하는 기본 단계 중 하나는 속성을 결정하는 것입니다. 개방 수로의 흐름에 관한 추가 정보를 제공하기 위해 경험적 방정식이 개발되었습니다. 이러한 실험 방정식을 얻는 것은 비용과 시간이 많이 소요됩니다. 따라서 대체 솔루션이 모색되었습니다.

    지난 세기 동안 움직이는 부분이 없는 정적 측정 장치인 Parshall 수로가 개방 수로의 흐름을 측정하는 데 중요한 역할을 했습니다. 많은 연구자들이 관개 및 폐수 관리와 같은 다양한 분야에서 Parshall 수로의 적용을 연구하는 데 관심을 집중해 왔습니다.

    여러 학자들이 실험 결과를 사용하여 Parshall 수로의 등급 방정식을 향상시켰지만 다른 학자들은 수치 시뮬레이션을 사용하여 높이-방전 관계 방정식을 재보정하기 위해 대체 데이터 소스를 사용했습니다. 컴퓨팅 하드웨어가 지난 수십 년 동안 크게 발전하여 과거에 경험했던 제한된 해상도를 뛰어넘는 것이 가능해짐에 따라 CFD(Computational Fluid Dynamic) 소프트웨어가 오늘날 대중화되고 있습니다.

    여러 CFD 모델은 가용성에 따라 오픈 소스 또는 상업적으로 허가되어 수위 결과를 생성하기 위해 다양한 구성의 수로, 특히 Parshall 수로에 대한 수치 시뮬레이션을 수행하는 데 사용되었습니다.

    FLOW-3D, Ansys Fluent, OpenFOAM 등 지금까지 사용되어 온 다양한 CFD 도구에 대해 실험 데이터로 정밀 교정한 결과, 출력이 안정적이고 실제 시나리오에 구현할 수 있음이 확인되었습니다.

    결과를 생성하기 위해 이 기술을 사용하는 이점은 필요한 경우 유속 또는 구조적 형상과 같은 초기 조건을 조정하는 CFD 접근 방식의 능력입니다. 수로 크기와 수로가 위치한 부지의 조건과 관련하여 상황에 적합한 특정 Parshall 수로로 선택이 좁혀집니다.

    표준 Parshall 수로를 선택하는 것이 항상 가능한 것은 아닙니다. 따라서 엔지니어는 가장 가까운 수로 크기에 약간의 수정을 제공하고 정확한 유량을 생성하기 위해 새로운 등급 곡선을 제공합니다.

    이 검토는 기존 등급 방정식을 향상시키거나 구조의 기하학에 대한 추가 수정을 제안하기 위해 Parshall 수로에서 수치 시뮬레이션 및 물리적 실험 데이터의 적용을 목표로 하는 여러 학자의 작업에 대해 수행되었습니다.

    One of the primary steps in managing the flow in an open channel is determining its properties. Empirical equations are developed to provide further information regarding the flow in open channels. Obtaining such experimental equations is expensive and time consuming; therefore, alternative solutions have been sought. Over the last century, the Parshall flume, a static measuring device with no moving parts, has played a significant role in measuring the flow in open channels. Many researchers have focused their interest on studying the application of Parshall flumes in various fields like irrigation and wastewater management. Although various scholars used experimental results to enhance the rating equation of the Parshall flume, others used an alternative source of data to recalibrate the height–discharge relation equation using numerical simulation. Computational Fluid Dynamic (CFD) software is becoming popular nowadays as computing hardware has advanced significantly within the last few decades, making it possible to go beyond the limited resolution that was experienced in the past. Multiple CFD models, depending on their availability, either open-source or commercially licensed, have been used to perform numerical simulations on different configurations of flumes, especially Parshall flumes, to produce water level results. Regarding various CFD tools that have been used, i.e., FLOW-3D, Ansys Fluent, or OpenFOAM, after precise calibration with experimental data, it has been determined that the output is reliable and can be implemented to the actual scenarios. The benefit of using this technique to produce results is the ability of the CFD approach to adjust the initial conditions, like flow velocity or structural geometry, where necessary. With respect to channel size and the condition of the site where the flume is located, the choices are narrowed to the specific Parshall flume suitable to the situation. It is not always possible to select the standard Parshall flume; therefore, engineers provide some modification to the closest flume size and provide a new rating curve to produce accurate flowrates. This review has been performed on the works of a number of scholars who targeted the application of numerical simulation and physical experimental data in Parshall flumes to either enhance the existing rating equation or propose further modification to the structure’s geometry.

    Keywords

    Parshall flume; CFD; OpenFOAM; FLOW-3D; numerical simulation; turbulence model

    Figure 1. Parshall flume measuring structure, installed [2].
    Figure 1. Parshall flume measuring structure, installed [2].
    Figure 2. Parshall flume measuring structure, uninstalled [3]
    Figure 2. Parshall flume measuring structure, uninstalled [3]
    Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells; (b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].
    Figure 4. Mesh sensitivity analysis: top view and side view of the Parshall flume: (a) contains 27,000 cells; (b) 52,000 cells; (c) 75,000 cells; (d) 270,000 cells. The C setup was used in their simulation [7].
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].
    Figure 7. The simulated velocity (a) and simulated pressure pattern (b) across the Parshall flume. The patterns match the physical behavior of actual Parshall flumes [7].
    Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b) demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from Ref. [11]. 2020 ELSEVIER). ).
    Figure 8. Computational grid system in the Side A flume. (a) contains a triangular grid system (b) demonstrates the rectangular grid system. (c) and (d) are three-dimensional schematics showing the superimposed grid system. (e) magnifies the dashed section in (b). (Reprinted with permission from Ref. [11]. 2020 ELSEVIER). ).
    Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]
    Figure 10. The results of flow patterns in different flumes; (a) Cutthroat flume, (b) airfoil-shaped flume, (c) airfoil pillar-shaped flume, (d) optimized airfoil-shaped flume [23]
    Figure 11. Experimental setup: contraction ratio used on each flume [23].
    Figure 11. Experimental setup: contraction ratio used on each flume [23].
    Figure 12. Entire flume geometry [25]
    Figure 12. Entire flume geometry [25]

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    PDF Download
    Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

    다공성 미디어 및 나노유체에 의해 강화된 수집기로 태양광 CCHP 시스템의 최적화

    Optimization of Solar CCHP Systems with Collector Enhanced by Porous Media and Nanofluid

    Navid Tonekaboni,1Mahdi Feizbahr,2 Nima Tonekaboni,1Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4

    Abstract

    태양열 집열기의 낮은 효율은 CCHP(Solar Combined Cooling, Heating, and Power) 사이클의 문제점 중 하나로 언급될 수 있습니다. 태양계를 개선하기 위해 나노유체와 다공성 매체가 태양열 집열기에 사용됩니다.

    다공성 매질과 나노입자를 사용하는 장점 중 하나는 동일한 조건에서 더 많은 에너지를 흡수할 수 있다는 것입니다. 이 연구에서는 평균 일사량이 1b인 따뜻하고 건조한 지역의 600 m2 건물의 전기, 냉방 및 난방을 생성하기 위해 다공성 매질과 나노유체를 사용하여 태양열 냉난방 복합 발전(SCCHP) 시스템을 최적화했습니다.

    본 논문에서는 침전물이 형성되지 않는 lb = 820 w/m2(이란) 정도까지 다공성 물질에서 나노유체의 최적량을 계산하였다. 이 연구에서 태양열 집열기는 구리 다공성 매체(95% 다공성)와 CuO 및 Al2O3 나노 유체로 향상되었습니다.

    나노유체의 0.1%-0.6%가 작동 유체로 물에 추가되었습니다. 나노유체의 0.5%가 태양열 집열기 및 SCCHP 시스템에서 가장 높은 에너지 및 엑서지 효율 향상으로 이어지는 것으로 밝혀졌습니다.

    본 연구에서 포물선형 집열기(PTC)의 최대 에너지 및 엑서지 효율은 각각 74.19% 및 32.6%입니다. 그림 1은 태양 CCHP의 주기를 정확하게 설명하기 위한 그래픽 초록으로 언급될 수 있습니다.

    The low efficiency of solar collectors can be mentioned as one of the problems in solar combined cooling, heating, and power (CCHP) cycles. For improving solar systems, nanofluid and porous media are used in solar collectors. One of the advantages of using porous media and nanoparticles is to absorb more energy under the same conditions. In this research, a solar combined cooling, heating, and power (SCCHP) system has been optimized by porous media and nanofluid for generating electricity, cooling, and heating of a 600 m2 building in a warm and dry region with average solar radiation of Ib = 820 w/m2 in Iran. In this paper, the optimal amount of nanofluid in porous materials has been calculated to the extent that no sediment is formed. In this study, solar collectors were enhanced with copper porous media (95% porosity) and CuO and Al2O3 nanofluids. 0.1%–0.6% of the nanofluids were added to water as working fluids; it is found that 0.5% of the nanofluids lead to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Maximum energy and exergy efficiency of parabolic thermal collector (PTC) riches in this study are 74.19% and 32.6%, respectively. Figure 1 can be mentioned as a graphical abstract for accurately describing the cycle of solar CCHP.

    1. Introduction

    Due to the increase in energy consumption, the use of clean energy is one of the important goals of human societies. In the last four decades, the use of cogeneration cycles has increased significantly due to high efficiency. Among clean energy, the use of solar energy has become more popular due to its greater availability [1]. Low efficiency of energy production, transmission, and distribution system makes a new system to generate simultaneously electricity, heating, and cooling as an essential solution to be widely used. The low efficiency of the electricity generation, transmission, and distribution system makes the CCHP system a basic solution to eliminate waste of energy. CCHP system consists of a prime mover (PM), a power generator, a heat recovery system (produce extra heating/cooling/power), and thermal energy storage (TES) [2]. Solar combined cooling, heating, and power (SCCHP) has been started three decades ago. SCCHP is a system that receives its propulsive force from solar energy; in this cycle, solar collectors play the role of propulsive for generating power in this system [3].

    Increasing the rate of energy consumption in the whole world because of the low efficiency of energy production, transmission, and distribution system causes a new cogeneration system to generate electricity, heating, and cooling energy as an essential solution to be widely used. Building energy utilization fundamentally includes power required for lighting, home electrical appliances, warming and cooling of building inside, and boiling water. Domestic usage contributes to an average of 35% of the world’s total energy consumption [4].

    Due to the availability of solar energy in all areas, solar collectors can be used to obtain the propulsive power required for the CCHP cycle. Solar energy is the main source of energy in renewable applications. For selecting a suitable area to use solar collectors, annual sunshine hours, the number of sunny days, minus temperature and frosty days, and the windy status of the region are essentially considered [5]. Iran, with an average of more than 300 sunny days, is one of the suitable countries to use solar energy. Due to the fact that most of the solar radiation is in the southern regions of Iran, also the concentration of cities is low in these areas, and transmission lines are far apart, one of the best options is to use CCHP cycles based on solar collectors [6]. One of the major problems of solar collectors is their low efficiency [7]. Low efficiency increases the area of collectors, which increases the initial cost of solar systems and of course increases the initial payback period. To increase the efficiency of solar collectors and improve their performance, porous materials and nanofluids are used to increase their workability.

    There are two ways to increase the efficiency of solar collectors and mechanical and fluid improvement. In the first method, using porous materials or helical filaments inside the collector pipes causes turbulence of the flow and increases heat transfer. In the second method, using nanofluids or salt and other materials increases the heat transfer of water. The use of porous materials has grown up immensely over the past twenty years. Porous materials, especially copper porous foam, are widely used in solar collectors. Due to the high contact surface area, porous media are appropriate candidates for solar collectors [8]. A number of researchers investigated Solar System performance in accordance with energy and exergy analyses. Zhai et al. [9] reviewed the performance of a small solar-powered system in which the energy efficiency was 44.7% and the electrical efficiency was 16.9%.

    Abbasi et al. [10] proposed an innovative multiobjective optimization to optimize the design of a cogeneration system. Results showed the CCHP system based on an internal diesel combustion engine was the applicable alternative at all regions with different climates. The diesel engine can supply the electrical requirement of 31.0% and heating demand of 3.8% for building.

    Jiang et al. [11] combined the experiment and simulation together to analyze the performance of a cogeneration system. Moreover, some research focused on CCHP systems using solar energy. It integrated sustainable and renewable technologies in the CCHP, like PV, Stirling engine, and parabolic trough collector (PTC) [2, 12–15].

    Wang et al. [16] optimized a cogeneration solar cooling system with a Rankine cycle and ejector to reach the maximum total system efficiency of 55.9%. Jing et al. analyzed a big-scale building with the SCCHP system and auxiliary heaters to produced electrical, cooling, and heating power. The maximum energy efficiency reported in their work is 46.6% [17]. Various optimization methods have been used to improve the cogeneration system, minimum system size, and performance, such as genetic algorithm [18, 19].

    Hirasawa et al. [20] investigated the effect of using porous media to reduce thermal waste in solar systems. They used the high-porosity metal foam on top of the flat plate solar collector and observed that thermal waste decreased by 7% due to natural heat transfer. Many researchers study the efficiency improvement of the solar collector by changing the collector’s shapes or working fluids. However, the most effective method is the use of nanofluids in the solar collector as working fluid [21]. In the experimental study done by Jouybari et al. [22], the efficiency enhancement up to 8.1% was achieved by adding nanofluid in a flat plate collector. In this research, by adding porous materials to the solar collector, collector efficiency increased up to 92% in a low flow regime. Subramani et al. [23] analyzed the thermal performance of the parabolic solar collector with Al2O3 nanofluid. They conducted their experiments with Reynolds number range 2401 to 7202 and mass flow rate 0.0083 to 0.05 kg/s. The maximum efficiency improvement in this experiment was 56% at 0.05 kg/s mass flow rate.

    Shojaeizadeh et al. [24] investigated the analysis of the second law of thermodynamic on the flat plate solar collector using Al2O3/water nanofluid. Their research showed that energy efficiency rose up to 1.9% and the exergy efficiency increased by a maximum of 0.72% compared to pure water. Tiwari et al. [25] researched on the thermal performance of solar flat plate collectors for working fluid water with different nanofluids. The result showed that using 1.5% (optimum) particle volume fraction of Al2O3 nanofluid as an absorbing medium causes the thermal efficiency to enhance up to 31.64%.

    The effect of porous media and nanofluids on solar collectors has already been investigated in the literature but the SCCHP system with a collector embedded by both porous media and nanofluid for enhancing the ratio of nanoparticle in nanofluid for preventing sedimentation was not discussed. In this research, the amount of energy and exergy of the solar CCHP cycles with parabolic solar collectors in both base and improved modes with a porous material (copper foam with 95% porosity) and nanofluid with different ratios of nanoparticles was calculated. In the first step, it is planned to design a CCHP system based on the required load, and, in the next step, it will analyze the energy and exergy of the system in a basic and optimize mode. In the optimize mode, enhanced solar collectors with porous material and nanofluid in different ratios (0.1%–0.7%) were used to optimize the ratio of nanofluids to prevent sedimentation.

    2. Cycle Description

    CCHP is one of the methods to enhance energy efficiency and reduce energy loss and costs. The SCCHP system used a solar collector as a prime mover of the cogeneration system and assisted the boiler to generate vapor for the turbine. Hot water flows from the expander to the absorption chiller in summer or to the radiator or fan coil in winter. Finally, before the hot water wants to flow back to the storage tank, it flows inside a heat exchanger for generating domestic hot water [26].

    For designing of solar cogeneration system and its analysis, it is necessary to calculate the electrical, heating (heating load is the load required for the production of warm water and space heating), and cooling load required for the case study considered in a residential building with an area of 600 m2 in the warm region of Iran (Zahedan). In Table 1, the average of the required loads is shown for the different months of a year (average of electrical, heating, and cooling load calculated with CARRIER software).Table 1 The average amount of electric charges, heating load, and cooling load used in the different months of the year in the city of Zahedan for a residential building with 600 m2.

    According to Table 1, the maximum magnitude of heating, cooling, and electrical loads is used to calculate the cogeneration system. The maximum electric load is 96 kW, the maximum amount of heating load is 62 kW, and the maximum cooling load is 118 kW. Since the calculated loads are average, all loads increased up to 10% for the confidence coefficient. With the obtained values, the solar collector area and other cogeneration system components are calculated. The cogeneration cycle is capable of producing 105 kW electric power, 140 kW cooling capacity, and 100 kW heating power.

    2.1. System Analysis Equations

    An analysis is done by considering the following assumptions:(1)The system operates under steady-state conditions(2)The system is designed for the warm region of Iran (Zahedan) with average solar radiation Ib = 820 w/m2(3)The pressure drops in heat exchangers, separators, storage tanks, and pipes are ignored(4)The pressure drop is negligible in all processes and no expectable chemical reactions occurred in the processes(5)Potential, kinetic, and chemical exergy are not considered due to their insignificance(6)Pumps have been discontinued due to insignificance throughout the process(7)All components are assumed adiabatic

    Schematic shape of the cogeneration cycle is shown in Figure 1 and all data are given in Table 2.

    Figure 1 Schematic shape of the cogeneration cycle.Table 2 Temperature and humidity of different points of system.

    Based on the first law of thermodynamic, energy analysis is based on the following steps.

    First of all, the estimated solar radiation energy on collector has been calculated:where α is the heat transfer enhancement coefficient based on porous materials added to the collector’s pipes. The coefficient α is increased by the porosity percentage, the type of porous material (in this case, copper with a porosity percentage of 95), and the flow of fluid to the collector equation.

    Collector efficiency is going to be calculated by the following equation [9]:

    Total energy received by the collector is given by [9]

    Also, the auxiliary boiler heat load is [2]

    Energy consumed from vapor to expander is calculated by [2]

    The power output form by the screw expander [9]:

    The efficiency of the expander is 80% in this case [11].

    In this step, cooling and heating loads were calculated and then, the required heating load to reach sanitary hot water will be calculated as follows:

    First step: calculating the cooling load with the following equation [9]:

    Second step: calculating heating loads [9]:

    Then, calculating the required loud for sanitary hot water will be [9]

    According to the above-mentioned equations, efficiency is [9]

    In the third step, calculated exergy analysis as follows.

    First, the received exergy collector from the sun is calculated [9]:

    In the previous equation, f is the constant of air dilution.

    The received exergy from the collector is [9]

    In the case of using natural gas in an auxiliary heater, the gas exergy is calculated from the following equation [12]:

    Delivering exergy from vapor to expander is calculated with the following equation [9]:

    In the fourth step, the exergy in cooling and heating is calculated by the following equation:

    Cooling exergy in summer is calculated [9]:

    Heating exergy in winter is calculated [9]:

    In the last step based on thermodynamic second law, exergy efficiency has been calculated from the following equation and the above-mentioned calculated loads [9]:

    3. Porous Media

    The porous medium that filled the test section is copper foam with a porosity of 95%. The foams are determined in Figure 2 and also detailed thermophysical parameters and dimensions are shown in Table 3.

    Figure 2 Copper foam with a porosity of 95%.Table 3 Thermophysical parameters and dimensions of copper foam.

    In solar collectors, copper porous materials are suitable for use at low temperatures and have an easier and faster manufacturing process than ceramic porous materials. Due to the high coefficient conductivity of copper, the use of copper metallic foam to increase heat transfer is certainly more efficient in solar collectors.

    Porous media and nanofluid in solar collector’s pipes were simulated in FLOW-3D software using the finite-difference method [27]. Nanoparticles Al2O3 and CUO are mostly used in solar collector enhancement. In this research, different concentrations of nanofluid are added to the parabolic solar collectors with porous materials (copper foam with porosity of 95%) to achieve maximum heat transfer in the porous materials before sedimentation. After analyzing PTC pipes with the nanofluid flow in FLOW-3D software, for energy and exergy efficiency analysis, Carrier software results were used as EES software input. Simulation PTC with porous media inside collector pipe and nanofluids sedimentation is shown in Figure 3.

    Figure 3 Simulation PTC pipes enhanced with copper foam and nanoparticles in FLOW-3D software.

    3.1. Nano Fluid

    In this research, copper and silver nanofluids (Al2O3, CuO) have been added with percentages of 0.1%–0.7% as the working fluids. The nanoparticle properties are given in Table 4. Also, system constant parameters are presented in Table 4, which are available as default input in the EES software.Table 4 Properties of the nanoparticles [9].

    System constant parameters for input in the software are shown in Table 5.Table 5 System constant parameters.

    The thermal properties of the nanofluid can be obtained from equations (18)–(21). The basic fluid properties are indicated by the index (bf) and the properties of the nanoparticle silver with the index (np).

    The density of the mixture is shown in the following equation [28]:where ρ is density and ϕ is the nanoparticles volume fraction.

    The specific heat capacity is calculated from the following equation [29]:

    The thermal conductivity of the nanofluid is calculated from the following equation [29]:

    The parameter β is the ratio of the nanolayer thickness to the original particle radius and, usually, this parameter is taken equal to 0.1 for the calculated thermal conductivity of the nanofluids.

    The mixture viscosity is calculated as follows [30]:

    In all equations, instead of water properties, working fluids with nanofluid are used. All of the above equations and parameters are entered in the EES software for calculating the energy and exergy of solar collectors and the SCCHP cycle. All calculation repeats for both nanofluids with different concentrations of nanofluid in the solar collector’s pipe.

    4. Results and Discussion

    In the present study, relations were written according to Wang et al. [16] and the system analysis was performed to ensure the correctness of the code. The energy and exergy charts are plotted based on the main values of the paper and are shown in Figures 4 and 5. The error rate in this simulation is 1.07%.

    Figure 4 Verification charts of energy analysis results.

    Figure 5 Verification charts of exergy analysis results.

    We may also investigate the application of machine learning paradigms [31–41] and various hybrid, advanced optimization approaches that are enhanced in terms of exploration and intensification [42–55], and intelligent model studies [56–61] as well, for example, methods such as particle swarm optimizer (PSO) [60, 62], differential search (DS) [63], ant colony optimizer (ACO) [61, 64, 65], Harris hawks optimizer (HHO) [66], grey wolf optimizer (GWO) [53, 67], differential evolution (DE) [68, 69], and other fusion and boosted systems [41, 46, 48, 50, 54, 55, 70, 71].

    At the first step, the collector is modified with porous copper foam material. 14 cases have been considered for the analysis of the SCCHP system (Table 6). It should be noted that the adding of porous media causes an additional pressure drop inside the collector [9, 22–26, 30, 72]. All fourteen cases use copper foam with a porosity of 95 percent. To simulate the effect of porous materials and nanofluids, the first solar PTC pipes have been simulated in the FLOW-3D software and then porous media (copper foam with porosity of 95%) and fluid flow with nanoparticles (AL2O3 and CUO) are generated in the software. After analyzing PTC pipes in FLOW-3D software, for analyzing energy and exergy efficiency, software outputs were used as EES software input for optimization ratio of sedimentation and calculating energy and exergy analyses.Table 6 Collectors with different percentages of nanofluids and porous media.

    In this research, an enhanced solar collector with both porous media and Nanofluid is investigated. In the present study, 0.1–0.5% CuO and Al2O3 concentration were added to the collector fully filled by porous media to achieve maximum energy and exergy efficiencies of solar CCHP systems. All steps of the investigation are shown in Table 6.

    Energy and exergy analyses of parabolic solar collectors and SCCHP systems are shown in Figures 6 and 7.

    Figure 6 Energy and exergy efficiencies of the PTC with porous media and nanofluid.

    Figure 7 Energy and exergy efficiency of the SCCHP.

    Results show that the highest energy and exergy efficiencies are 74.19% and 32.6%, respectively, that is achieved in Step 12 (parabolic collectors with filled porous media and 0.5% Al2O3). In the second step, the maximum energy efficiency of SCCHP systems with fourteen steps of simulation are shown in Figure 7.

    In the second step, where 0.1, −0.6% of the nanofluids were added, it is found that 0.5% leads to the highest energy and exergy efficiency enhancement in solar collectors and SCCHP systems. Using concentrations more than 0.5% leads to sediment in the solar collector’s pipe and a decrease of porosity in the pipe [73]. According to Figure 7, maximum energy and exergy efficiencies of SCCHP are achieved in Step 12. In this step energy efficiency is 54.49% and exergy efficiency is 18.29%. In steps 13 and 14, with increasing concentration of CUO and Al2O3 nanofluid solution in porous materials, decreasing of energy and exergy efficiency of PTC and SCCHP system at the same time happened. This decrease in efficiency is due to the formation of sediment in the porous material. Calculations and simulations have shown that porous materials more than 0.5% nanofluids inside the collector pipe cause sediment and disturb the porosity of porous materials and pressure drop and reduce the coefficient of performance of the cogeneration system. Most experience showed that CUO and AL2O3 nanofluids with less than 0.6% percent solution are used in the investigation on the solar collectors at low temperatures and discharges [74]. One of the important points of this research is that the best ratio of nanofluids in the solar collector with a low temperature is 0.5% (AL2O3 and CUO); with this replacement, the cost of solar collectors and SCCHP cycle is reduced.

    5. Conclusion and Future Directions

    In the present study, ways for increasing the efficiency of solar collectors in order to enhance the efficiency of the SCCHP cycle are examined. The research is aimed at adding both porous materials and nanofluids for estimating the best ratio of nanofluid for enhanced solar collector and protecting sedimentation in porous media. By adding porous materials (copper foam with porosity of 95%) and 0.5% nanofluids together, high efficiency in solar parabolic collectors can be achieved. The novelty in this research is the addition of both nanofluids and porous materials and calculating the best ratio for preventing sedimentation and pressure drop in solar collector’s pipe. In this study, it was observed that, by adding 0.5% of AL2O3 nanofluid in working fluids, the energy efficiency of PTC rises to 74.19% and exergy efficiency is grown up to 32.6%. In SCCHP cycle, energy efficiency is 54.49% and exergy efficiency is 18.29%.

    In this research, parabolic solar collectors fully filled by porous media (copper foam with a porosity of 95) are investigated. In the next step, parabolic solar collectors in the SCCHP cycle were simultaneously filled by porous media and different percentages of Al2O3 and CuO nanofluid. At this step, values of 0.1% to 0.6% of each nanofluid were added to the working fluid, and the efficiency of the energy and exergy of the collectors and the SCCHP cycle were determined. In this case, nanofluid and the porous media were used together in the solar collector and maximum efficiency achieved. 0.5% of both nanofluids were used to achieve the biggest efficiency enhancement.

    In the present study, as expected, the highest efficiency is for the parabolic solar collector fully filled by porous material (copper foam with a porosity of 95%) and 0.5% Al2O3. Results of the present study are as follows:(1)The average enhancement of collectors’ efficiency using porous media and nanofluids is 28%.(2)Solutions with 0.1 to 0.5% of nanofluids (CuO and Al2O3) are used to prevent collectors from sediment occurrence in porous media.(3)Collector of solar cogeneration cycles that is enhanced by both porous media and nanofluid has higher efficiency, and the stability of output temperature is more as well.(4)By using 0.6% of the nanofluids in the enhanced parabolic solar collectors with copper porous materials, sedimentation occurs and makes a high-pressure drop in the solar collector’s pipe which causes decrease in energy efficiency.(5)Average enhancement of SCCHP cycle efficiency is enhanced by both porous media and nanofluid 13%.

    Nomenclature

    :Solar radiation
    a:Heat transfer augmentation coefficient
    A:Solar collector area
    Bf:Basic fluid
    :Specific heat capacity of the nanofluid
    F:Constant of air dilution
    :Thermal conductivity of the nanofluid
    :Thermal conductivity of the basic fluid
    :Viscosity of the nanofluid
    :Viscosity of the basic fluid
    :Collector efficiency
    :Collector energy receives
    :Auxiliary boiler heat
    :Expander energy
    :Gas energy
    :Screw expander work
    :Cooling load, in kilowatts
    :Heating load, in kilowatts
    :Solar radiation energy on collector, in Joule
    :Sanitary hot water load
    Np:Nanoparticle
    :Energy efficiency
    :Heat exchanger efficiency
    :Sun exergy
    :Collector exergy
    :Natural gas exergy
    :Expander exergy
    :Cooling exergy
    :Heating exergy
    :Exergy efficiency
    :Steam mass flow rate
    :Hot water mass flow rate
    :Specific heat capacity of water
    :Power output form by the screw expander
    Tam:Average ambient temperature
    :Density of the mixture.

    Greek symbols

    ρ:Density
    ϕ:Nanoparticles volume fraction
    β:Ratio of the nanolayer thickness.

    Abbreviations

    CCHP:Combined cooling, heating, and power
    EES:Engineering equation solver.

    Data Availability

    For this study, data were generated by CARRIER software for the average electrical, heating, and cooling load of a residential building with 600 m2 in the city of Zahedan, Iran.

    Conflicts of Interest

    The authors declare that they have no conflicts of interest.

    Acknowledgments

    This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

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    Fig. 6. Configuration of Johnson (1958) hydraulic experiment.

    전체 수심 범위에서 선박 파고에 대한 방정식

    Equation for ship wave crests in the entire range of water depths

    Byeong Wook Lee a
    , Changhoon Lee b,
    *a Coastal Development and Ocean Energy Research Center, Korea Institute of Ocean Science & Technology, 385 Haeyang-ro, Busan, 49111, Republic of Korea
    b Department of Civil and Environmental Engineering, Sejong University, 209 Neungdong-ro, Gwangjin-gu, Seoul, 05006, Republic of Korea

    ABSTRACT

    An equation for ship wave crests y/x in the entire range of water depths is developed using the linear dispersion relation. In deep water, the developed equation is reduced to the equation of Kelvin (1906). The locations of ship wave crests in the x – and y -directions are obtained using a dimensionless constant C. The wave ray angle θc at the cusp locus is determined using the condition that θc is maximal at the cusp locus and the cusp locus angle is determined as αc=−tan−1(y/x)max. Numerical experiments are conducted using the FLOW-3D to simulate ship wave propagation. The cusp locus angles of the FLOW-3D are similar to both those of the present theory and Havelock (1908) theory in the entire range of the Froude number. Both the present theory and the FLOW-3D yield that, with the increase of ship speed, the Froude number increases and does the wavelength. For the Froude number equal to or greater than unity, the wavelength becomes infinitely large and the transverse waves disappear. The wavelengths of the FLOW-3D are slightly smaller than those of the present theory because the FLOW-3D considers the decrease of wavelength due to energy dissipation which happens because of viscosity of water and turbulence of high-speed particle velocities.

    Fig. 6. Configuration of Johnson (1958) hydraulic experiment.
    Fig. 6. Configuration of Johnson (1958) hydraulic experiment.
    Fig. 8. Comparison of ship wave crest patterns: (a) Fr ¼ 0:66 (Us ¼ 6:5m=s, kh � 0:724π), (b) Fr ¼ 0:86 (Us ¼ 8:5m=s, kh � 0:342π), (c) Fr ¼ 1:21 (Us ¼ 12:0m=s, kh � 0:003π). Line definition: red solid line ¼ present theory; yellow dashed line ¼ Kelvin theory; white dot ¼ FLOW-3D solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
    Fig. 8. Comparison of ship wave crest patterns: (a) Fr ¼ 0:66 (Us ¼ 6:5m=s, kh >= 0:724π), (b) Fr ¼ 0:86 (Us ¼ 8:5m=s, kh >= 0:342π), (c) Fr ¼ 1:21 (Us ¼ 12:0m=s, kh >= 0:003π). Line definition: red solid line ¼ present theory; yellow dashed line ¼ Kelvin theory; white dot ¼ FLOW-3D solution. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

    Keywords

    Ship wave crests
    Cusp locus angle
    Entire range of water depths
    Theoretical solution
    Numerical experiment

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    원문보기
    Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s.

    Optimization Algorithms and Engineering: Recent Advances and Applications

    Mahdi Feizbahr,1 Navid Tonekaboni,2Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4Show moreAcademic Editor: Mohammad YazdiReceived08 Apr 2021Revised18 Jun 2021Accepted17 Jul 2021Published11 Aug 2021

    Abstract

    Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.


    강의 식생은 거칠기를 증가시키고 평균 유속을 감소시키며, 유속 에너지를 감소시키고 강의 단면에서 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받으므로 홍수시 유동저항에 큰 영향을 미칩니다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건 및 식물에 따라 다르므로 모델은 유속, 흐름 깊이 및 운하를 따라 식생 유형의 영향을 고려하여 현재 속도를 시뮬레이션해야 합니다. 근관의 거칠기의 영향을 조사하기 위해 총 48개의 모델이 시뮬레이션되었습니다. 결과는 유속을 높임으로써 유속을 감소시키는 식생의 영향은 무시할 수 있는 반면, 해류가 더 낮은 유속일 때 유속을 감소시키는 식생의 영향은 분명히 상당함을 나타냈다.

    1. Introduction

    Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [1–14]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [15–27]. Consequently, it is necessary to study the effects of the passive factors on the active domain [28–36]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [38–41].

    One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [43–45]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [47, 48].

    Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity  is another form of current resistance. The reason for using the  ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

    To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

    The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where n, f, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

    Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.

    On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

    By using equation (6), equation (5) is converted as follows:

    Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the  ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

    Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [45, 55].

    One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [47, 57, 58] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [45, 59–61]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [49, 63–66] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where  is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

    FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where  are mass accelerations in the directions x, y, z and  are viscosity accelerations in the directions x, y, z and are obtained from the following equations:

    Shear stresses  in equation (11) are obtained from the following equations:

    The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

    Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

    Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

    In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).Table 1 The studied models.

    The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After  seconds, this model reached a convergence accuracy of .

    Figure 1 The simulated model and its boundary conditions.

    Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

    48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

    Any control and simulation system has some inputs that we should determine to test any technology [70–77]. Determination and true implementation of such parameters is one of the key steps of any simulation [23, 78–81] and computing procedure [82–86]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

    Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [87, 88]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

    Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

    Figure 3 Velocity profiles in positions 2 and 5.

    The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

    The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

    The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

    2. Modeling Results

    After analyzing the models, the results were shown in graphs (Figures 4–14 ). The total number of experiments in this study was 48 due to the limitations of modeling.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 4 Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

    Figure 5 Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

    Figure 6 Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

    Figure 7 Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

    Figure 8 Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 9 Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

    Figure 10 Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

    Figure 11 Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

    Figure 12 Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

    Figure 13 Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)(a)
    (a)(b)
    (b)(c)
    (c)(d)
    (d)Figure 14 Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

    To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

    According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

    According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

    According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

    According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5–10, which can be justified by increasing the speed and, of course, increasing the Froude number.

    With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 5–8 and 10, 11), which can be justified by increasing the speed and, of course, increasing the Froude number.

    According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

    According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

    Figure 15 Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

    According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

    Figure 16 Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

    According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

    Figure 17 Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

    According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

    Figure 18 Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

    According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.(a)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 19 Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

    According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.(a)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 20 Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

    According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [2, 7, 8, 15, 18, 89–94]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [95–99].(a)
    (a)(b)
    (b)(c)
    (c)(a)
    (a)(b)
    (b)(c)
    (c)Figure 21 Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

    3. Conclusion

    The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

    Nomenclature

    n:Manning’s roughness coefficient
    C:Chézy roughness coefficient
    f:Darcy–Weisbach coefficient
    V:Flow velocity
    R:Hydraulic radius
    g:Gravitational acceleration
    y:Flow depth
    Ks:Bed roughness
    A:Constant coefficient
    :Reynolds number
    ∂y/∂x:Depth of water change
    S0:Slope of the canal floor
    Sf:Slope of energy line
    Fr:Froude number
    D:Characteristic length of the canal
    G:Mass acceleration
    :Shear stresses.

    Data Availability

    All data are included within the paper.

    Conflicts of Interest

    The authors declare that they have no conflicts of interest.

    Acknowledgments

    This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

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    Stability and deformations of deposited layers in material extrusion additive manufacturing

    Conflict resolution in the multi-stakeholder stepped spillway design under uncertainty by machine learning techniques

    Md TusherMollah, Raphaël Comminal, Marcin P.Serdeczny, David B.Pedersen, Jon Spangenberg
    Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, Denmark

    Abstract

    This paper presents computational fluid dynamics simulations of the deposition flow during printing of multiple layers in material extrusion additive manufacturing. The developed model predicts the morphology of the deposited layers and captures the layer deformations during the printing of viscoplastic materials. The physics is governed by the continuity and momentum equations with the Bingham constitutive model, formulated as a generalized Newtonian fluid. The cross-sectional shapes of the deposited layers are predicted, and the deformation of layers is studied for different constitutive parameters of the material. It is shown that the deformation of layers is due to the hydrostatic pressure of the printed material, as well as the extrusion pressure during the extrusion. The simulations show that a higher yield stress results in prints with less deformations, while a higher plastic viscosity leads to larger deformations in the deposited layers. Moreover, the influence of the printing speed, extrusion speed, layer height, and nozzle diameter on the deformation of the printed layers is investigated. Finally, the model provides a conservative estimate of the required increase in yield stress that a viscoplastic material demands after deposition in order to support the hydrostatic and extrusion pressure of the subsequently printed layers.

    이 논문은 재료 압출 적층 제조에서 여러 레이어를 인쇄하는 동안 증착 흐름의 전산 유체 역학 시뮬레이션을 제공합니다. 개발된 모델은 증착된 레이어의 형태를 예측하고 점소성 재료를 인쇄하는 동안 레이어 변형을 캡처합니다.

    물리학은 일반화된 뉴턴 유체로 공식화된 Bingham 구성 모델의 연속성 및 운동량 방정식에 의해 제어됩니다. 증착된 층의 단면 모양이 예측되고 재료의 다양한 구성 매개변수에 대해 층의 변형이 연구됩니다. 층의 변형은 인쇄물의 정수압과 압출시 압출압력으로 인한 것임을 알 수 있다.

    시뮬레이션에 따르면 항복 응력이 높을수록 변형이 적은 인쇄물이 생성되는 반면 플라스틱 점도가 높을수록 증착된 레이어에서 변형이 커집니다. 또한 인쇄 속도, 압출 속도, 층 높이 및 노즐 직경이 인쇄된 층의 변형에 미치는 영향을 조사했습니다.

    마지막으로, 이 모델은 후속 인쇄된 레이어의 정수압 및 압출 압력을 지원하기 위해 증착 후 점소성 재료가 요구하는 항복 응력의 필요한 증가에 대한 보수적인 추정치를 제공합니다.

    Stability and deformations of deposited layers in material extrusion additive manufacturing
    Stability and deformations of deposited layers in material extrusion additive manufacturing

    Keywords

    Viscoplastic MaterialsMaterial Extrusion Additive Manufacturing (MEX-AM)Multiple-Layers DepositionComputational Fluid Dynamics (CFD)Deformation Control

    Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.

    Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses

    Triangular Macroroughnesses 대한 잠긴 수압 점프의 유동장 수치 시뮬레이션

    by Amir Ghaderi 1,2,Mehdi Dasineh 3,Francesco Aristodemo 2 andCostanza Aricò 4,*1Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, Iran2Department of Civil Engineering, University of Calabria, Arcavacata, 87036 Rende, Italy3Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran4Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy*Author to whom correspondence should be addressed.Academic Editor: Anis YounesWater2021, 13(5), 674; https://doi.org/10.3390/w13050674

    Abstract

    The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered.

    Keywords: submerged hydraulic jump; triangular macroroughnesses; TKE; bed shear stress coefficient; velocity; FLOW-3D model

    수중 유압 점프는 강한 난류, 공기 동반 및 에너지 손실로 지정된 초임계에서 아임계 흐름으로의 급격한 변화입니다. 최근 연구에도 불구하고, 특히 삼각형 거시적 거칠기의 경우, 평활 및 거친 베드에서의 수압 점프 특성, 거친 베드에서 잠긴 수압 점프의 공동 영역에서 난류, 평균 속도 및 유동 패턴이 완전히 이해되지 않았습니다.

    이 논문의 목적은 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 두께를 포함하여 서브머지드 점프의 특성에 대한 삼각형 거시 거칠기의 영향을 FLOW-3D 모델을 통해 수치적으로 조사하는 것이었습니다.

    내부 층의 층 전단 응력 계수, 난류 운동 에너지(TKE) 및 에너지 손실, 다양한 거시 거칠기 배열 및 다양한 입구 Froude 수(1.7 < Fr1 < 9.3). 현재 수치 시뮬레이션의 정확성과 신뢰성을 검증하기 위해 문헌 실험 데이터를 고려했습니다.

     Introduction

    격렬한 난류 혼합과 기포 동반이 있는 수압 점프는 초임계에서 아임계 흐름으로의 변화 과정으로 간주됩니다[1]. 자유 및 수중 유압 점프는 일반적으로 게이트, 배수로 및 둑과 같은 수력 구조 아래의 에너지 손실에 적합합니다. 매끄러운 베드에서 유압 점프의 특성은 널리 연구되었습니다[2,3,4,5,6,7,8,9].

    베드의 거칠기 요소가 매끄러운 베드와 비교하여 수압 점프의 특성에 어떻게 영향을 미치는지 예측하기 위해 거시적 거칠기에 대한 자유 및 수중 수력 점프에 대해 여러 실험 및 수치 연구가 수행되었습니다. Ead와 Rajaratnam[10]은 사인파 거대 거칠기에 대한 수리학적 점프의 특성을 조사하고 무차원 분석을 통해 수면 프로파일과 배출을 정규화했습니다.

    Tokyayet al. [11]은 두 사인 곡선 거대 거칠기에 대한 점프 길이 비율과 에너지 손실이 매끄러운 베드보다 각각 35% 더 작고 6% 더 높다는 것을 관찰했습니다. Abbaspur et al. [12]는 6개의 사인파형 거대 거칠기에 대한 수력학적 점프의 특성을 연구했습니다. 그 결과, 꼬리수심과 점프길이는 평상보다 낮았고 Froude 수는 점프길이에 큰 영향을 미쳤습니다.

    Shafai-Bejestan과 Neisi[13]는 수압 점프에 대한 마름모꼴 거대 거칠기의 영향을 조사했습니다. 결과는 마름모꼴 거시 거칠기를 사용하면 매끄러운 침대와 비교하여 꼬리 수심과 점프 길이를 감소시키는 것으로 나타났습니다. Izadjoo와 Shafai-Bejestan[14]은 다양한 사다리꼴 거시 거칠기에 대한 수압 점프를 연구했습니다.

    그들은 전단응력계수가 평활층보다 10배 이상 크고 점프길이가 50% 감소하는 것을 관찰하였습니다. Nikmehr과 Aminpour[15]는 Flow-3D 모델 버전 11.2[16]를 사용하여 사다리꼴 블록이 있는 거시적 거칠기에 대한 수력학적 점프의 특성을 조사했습니다. 결과는 거시 거칠기의 높이와 거리가 증가할수록 전단 응력 계수뿐만 아니라 베드 근처에서 속도가 감소하는 것으로 나타났습니다.

    Ghaderi et al. [17]은 다양한 형태의 거시 거칠기(삼각형, 정사각형 및 반 타원형)에 대한 자유 및 수중 수력 점프 특성을 연구했습니다. 결과는 Froude 수의 증가에 따라 자유 및 수중 점프에서 전단 응력 계수, 에너지 손실, 수중 깊이, 미수 깊이 및 상대 점프 길이가 증가함을 나타냅니다.

    자유 및 수중 점프에서 가장 높은 전단 응력과 에너지 손실은 삼각형의 거시 거칠기가 존재할 때 발생했습니다. Elsebaie와 Shabayek[18]은 5가지 형태의 거시적 거칠기(삼각형, 사다리꼴, 2개의 측면 경사 및 직사각형이 있는 정현파)에 대한 수력학적 점프의 특성을 연구했습니다. 결과는 모든 거시적 거칠기에 대한 에너지 손실이 매끄러운 베드에서보다 15배 이상이라는 것을 보여주었습니다.

    Samadi-Boroujeni et al. [19]는 다양한 각도의 6개의 삼각형 거시 거칠기에 대한 수력 점프를 조사한 결과 삼각형 거시 거칠기가 평활 베드에 비해 점프 길이를 줄이고 에너지 손실과 베드 전단 응력 계수를 증가시키는 것으로 나타났습니다.

    Ahmed et al. [20]은 매끄러운 베드와 삼각형 거시 거칠기에서 수중 수력 점프 특성을 조사했습니다. 결과는 부드러운 침대와 비교할 때 잠긴 깊이와 점프 길이가 감소했다고 밝혔습니다. 표 1은 다른 연구자들이 제시한 과거의 유압 점프에 대한 실험 및 수치 연구의 세부 사항을 나열합니다.

    Table 1. Main characteristics of some past experimental and numerical studies on hydraulic jumps.

    ReferenceShape Bed-Channel Type-
    Jump Type    		Channel Dimension (m)Roughness (mm)Fr1Investigated Flow
    Properties
    Ead and Rajaratnam [10]-Smooth and rough beds-Rectangular channel-Free jumpCL1 = 7.60
    CW2 = 0.44
    CH3 = 0.60    		-Corrugated sheets (RH4 = 13 and 22)4–10-Upstream and tailwater depths-Jump length-Roller length-Velocity-Water surface profile
    Tokyay et al. [11]-Smooth and rough beds-Rectangular channel-Free jumpCL = 10.50
    CW = 0.253
    CH = 0.432    		-Two sinusoidal corrugated (RH = 10 and 13)5–12-Depth ratio-Jump length-Energy loss
    Izadjoo and Shafai-Bejestan [14]-Smooth and rough beds-Two rectangular-channel-Free jumpCL = 1.2, 9
    CW = 0.25, 0.50
    CH = 0.40    		Baffle with trapezoidal cross section
    (RH: 13 and 26)    		6–12-Upstream and tailwater depths-Jump length-Velocity-Bed shear stress coefficient
    Abbaspour et al. [12]-Horizontal bed with slope 0.002-Rectangular channel—smooth and rough beds-Free jumpCL = 10
    CW = 0.25
    CH = 0.50    		-Sinusoidal bed (RH = 15,20, 25 and 35)3.80–8.60-Water surface profile-Depth ratio-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
    Shafai-Bejestan and Neisi [13]-Smooth and rough beds-Rectangular channel-Free jumpCL = 7.50
    CW = 0.35
    CH = 0.50    		Lozenge bed4.50–12-Sequent depth-Jump length
    Elsebaie and Shabayek [18]-Smooth and rough beds-Rectangular channel-With side slopes of 45 degrees for two trapezoidal and triangular macroroughnesses and of 60 degrees for other trapezoidal macroroughnesses-Free jumpCL = 9
    CW = 0.295
    CH = 0.32    		-Sinusoidal-Triangular-Trapezoidal with two side-Rectangular-(RH = 18 and corrugation wavelength = 65)50-Water surface profile-Sequent depth-Jump length-Bed shear stress coefficient
    Samadi-Boroujeni et al. [19]-Rectangular channel-Smooth and rough beds-Free jumpCL = 12
    CW = 0.40
    CH = 0.40    		-Six triangular corrugated (RH = 2.5)6.10–13.10-Water surface profile-Sequent depth-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
    Ahmed et al. [20]-Smooth and rough beds-Rectangular channel-Submerged jumpCL = 24.50
    CW = 0.75
    CH = 0.70    		-Triangular corrugated sheet (RH = 40)1.68–9.29-Conjugated and tailwater depths-Submerged ratio-Deficit depth-Relative jump length-Jump length-Relative roller jump length-Jump efficiency-Bed shear stress coefficient
    Nikmehr and Aminpour [15]-Horizontal bed with slope 0.002-Rectangular channel-Rough bed-Free jumpCL = 12
    CW = 0.25
    CH = 0.50    		-Trapezoidal blocks (RH = 2, 3 and 4)5.01–13.70-Water surface profile-Sequent depth-Jump length-Roller length-Velocity
    Ghaderi et al. [17]-Smooth and rough beds-Rectangular channel-Free and submerged jumpCL = 4.50
    CW = 0.75
    CH = 0.70    		-Triangular, square and semi-oval macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Horizontal velocity distributions-Bed shear stress coefficient-Sequent depth ratio and submerged depth ratio-Jump length-Energy loss
    Present studyRectangular channel
    Smooth and rough beds
    Submerged jump    		CL = 4.50
    CW = 0.75
    CH = 0.70    		-Triangular macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Longitudinal profile of streamlines-Flow patterns in the cavity region-Horizontal velocity profiles-Streamwise velocity distribution-Bed shear stress coefficient-TKE-Thickness of the inner layer-Energy loss

    CL1: channel length, CW2: channel width, CH3: channel height, RH4: roughness height.

    이전에 논의된 조사의 주요 부분은 실험실 접근 방식을 기반으로 하며 사인파, 마름모꼴, 사다리꼴, 정사각형, 직사각형 및 삼각형 매크로 거칠기가 공액 깊이, 잠긴 깊이, 점프 길이, 에너지 손실과 같은 일부 자유 및 수중 유압 점프 특성에 어떻게 영향을 미치는지 조사합니다.

    베드 및 전단 응력 계수. 더욱이, 저자[17]에 의해 다양한 형태의 거시적 거칠기에 대한 수력학적 점프에 대한 이전 발표된 논문을 참조하면, 삼각형의 거대조도는 가장 높은 층 전단 응력 계수 및 에너지 손실을 가지며 또한 가장 낮은 잠긴 깊이, tailwater를 갖는 것으로 관찰되었습니다.

    다른 거친 모양, 즉 정사각형 및 반 타원형과 부드러운 침대에 비해 깊이와 점프 길이. 따라서 본 논문에서는 삼각형 매크로 거칠기를 사용하여(일정한 거칠기 높이가 T = 4cm이고 삼각형 거칠기의 거리가 I = 4, 8, 12, 16 및 20cm인 다른 T/I 비율에 대해), 특정 캐비티 영역의 유동 패턴, 난류 운동 에너지(TKE) 및 흐름 방향 속도 분포와 같은 연구가 필요합니다.

    CFD(Computational Fluid Dynamics) 방법은 자유 및 수중 유압 점프[21]와 같은 복잡한 흐름의 모델링 프로세스를 수행하는 중요한 도구로 등장하며 수중 유압 점프의 특성은 CFD 시뮬레이션을 사용하여 정확하게 예측할 수 있습니다 [22,23 ].

    본 논문은 초기에 수중 유압 점프의 주요 특성, 수치 모델에 대한 입력 매개변수 및 Ahmed et al.의 참조 실험 조사를 제시합니다. [20], 검증 목적으로 보고되었습니다. 또한, 본 연구에서는 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 내부 층의 두께, 베드 전단 응력 계수, TKE 및 에너지 손실과 같은 특성을 조사할 것입니다.

    Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.
    Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.

    Table 2. Effective parameters in the numerical model.

    Bed TypeQ
    (l/s)    		I
    (cm)    		T (cm)d (cm)y1
    (cm)    		y4
    (cm)    		Fr1= u1/(gy1)0.5SRe1= (u1y1)/υ
    Smooth30, 45––51.62–3.839.64–32.101.7–9.30.26–0.5039,884–59,825
    Triangular macroroughnesses30, 454, 8, 12, 16, 20451.62–3.846.82–30.081.7–9.30.21–0.4439,884–59,825
    Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).
    Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).

    Table 3. Main flow variables for the numerical and physical models (Ahmed et al. [20]).

    ModelsBed TypeQ (l/s)d (cm)y1 (cm)u1 (m/s)Fr1
    Numerical and PhysicalSmooth4551.62–3.831.04–3.701.7–9.3
    T/I = 0.54551.61–3.831.05–3.711.7–9.3
    T/I = 0.254551.60–3.841.04–3.711.7–9.3
    Figure 3. The boundary conditions governing the simulations.
    Figure 3. The boundary conditions governing the simulations.
    Figure 4. Sketch of mesh setup.
    Figure 4. Sketch of mesh setup.

    Table 4. Characteristics of the computational grids.

    MeshNested Block Cell Size (cm)Containing Block Cell Size (cm)
    10.551.10
    20.651.30
    30.851.70

    Table 5. The numerical results of mesh convergence analysis.

    ParametersAmounts
    fs1 (-)7.15
    fs2 (-)6.88
    fs3 (-)6.19
    K (-)5.61
    E32 (%)10.02
    E21 (%)3.77
    GCI21 (%)3.03
    GCI32 (%)3.57
    GCI32/rp GCI210.98
    Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
    Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
    Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
    Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
    Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
    Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
    Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
    Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
    Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
    Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
    Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
    Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
    Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
    Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
    Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
    Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
    Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
    Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
    Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
    Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
    Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
    Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
    Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
    Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
    Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
    Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
    Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).
    Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).

    Conclusions

    • 본 논문에서는 유선의 종방향 프로파일, 공동 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 내부 층의 두께, 베드 전단 응력 계수, 난류 운동 에너지(TKE)를 포함하는 수중 유압 점프의 특성을 제시하고 논의했습니다. ) 및 삼각형 거시적 거칠기에 대한 에너지 손실. 이러한 특성은 FLOW-3D® 모델을 사용하여 수치적으로 조사되었습니다. 자유 표면을 시뮬레이션하기 위한 VOF(Volume of Fluid) 방법과 난류 RNG k-ε 모델이 구현됩니다. 본 모델을 검증하기 위해 평활층과 삼각형 거시 거칠기에 대해 수치 시뮬레이션과 실험 결과를 비교했습니다. 본 연구의 다음과 같은 결과를 도출할 수 있다.
    • 개발 및 개발 지역의 삼각형 거시 거칠기의 흐름 패턴은 수중 유압 점프 조건의 매끄러운 바닥과 비교하여 더 작은 영역에서 동일합니다. 삼각형의 거대 거칠기는 거대 거칠기 사이의 공동 영역에서 또 다른 시계 방향 와류의 형성으로 이어집니다.
    • T/I = 1, 0.5 및 0.33과 같은 거리에 대해 속도 벡터 분포는 캐비티 영역에서 시계 방향 소용돌이를 표시하며, 여기서 속도의 크기는 평균 유속보다 훨씬 작습니다. 삼각형 거대 거칠기(T/I = 0.25 및 0.2) 사이의 거리를 늘리면 캐비티 영역에 크기가 다른 두 개의 소용돌이가 형성됩니다.
    • 삼각형 거시조도 사이의 거리가 충분히 길면 흐름이 다음 조도에 도달할 때까지 속도 분포가 회복됩니다. 그러나 짧은 거리에서 흐름은 속도 분포의 적절한 회복 없이 다음 거칠기에 도달합니다. 따라서 거시 거칠기 사이의 거리가 감소함에 따라 마찰 계수의 증가율이 감소합니다.
    • 삼각형의 거시적 거칠기에서, 잠수 점프의 지정된 섹션에서 최대 속도는 자유 점프보다 높은 값으로 이어집니다. 또한, 수중 점프에서 두 가지 유형의 베드(부드러움 및 거친 베드)에 대해 깊이 및 와류 증가로 인해 베드로부터의 최대 속도 거리는 감소합니다. 잠수 점프에서 경계층 두께는 자유 점프보다 얇습니다.
    • 매끄러운 베드의 난류 영역은 게이트로부터의 거리에 따라 생성되고 자유 표면 롤러 영역 근처에서 발생하는 반면, 거시적 거칠기에서는 난류가 게이트 근처에서 시작되어 더 큰 강도와 제한된 스위프 영역으로 시작됩니다. 이는 반시계 방향 순환의 결과입니다. 거시 거칠기 사이의 공간에서 자유 표면 롤러 및 시계 방향 와류.
    • 삼각 거시 거칠기에서 침지 점프의 베드 전단 응력 계수와 에너지 손실은 유입구 Froude 수의 증가에 따라 증가하는 매끄러운 베드에서 발견된 것보다 더 큽니다. T/I = 0.50 및 0.20에서 최고 및 최저 베드 전단 응력 계수 및 에너지 손실이 평활 베드에 비해 거칠기 요소의 거리가 증가함에 따라 발생합니다.
    • 거의 거칠기 요소가 있는 삼각형 매크로 거칠기의 존재에 의해 주어지는 점프 길이와 잠긴 수심 및 꼬리 수심의 감소는 결과적으로 크기, 즉 길이 및 높이가 감소하는 정수조 설계에 사용될 수 있습니다.
    • 일반적으로 CFD 모델은 다양한 수력 조건 및 기하학적 배열을 고려하여 잠수 점프의 특성 예측을 시뮬레이션할 수 있습니다. 캐비티 영역의 흐름 패턴, 흐름 방향 및 수평 속도 분포, 베드 전단 응력 계수, TKE 및 유압 점프의 에너지 손실은 수치적 방법으로 시뮬레이션할 수 있습니다. 그러나 거시적 차원과 유동장 및 공동 유동의 변화에 ​​대한 다양한 배열에 대한 연구는 향후 과제로 남아 있다.

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    Fig. 12. Comparison of simulation results with experimental data for a flow rate of water = Ql=15 ml/hr and a flow rate of air = Qg =3 ml/hr.

    Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method

    Abstract

    This paper demonstrates that the Volume of Fluid (TruVOF) method in FLOW-3D (a general purpose CFD software) is an effective tool for studying droplet dynamics and mixing in microfluidic devices. The first example studied is a T-junction where flow patterns for both droplet generation and passive mixing are analyzed. The second example studied is a co-flowing device where the formation and breakup of bubbles is simulated. The effect of viscosity on bubble formation is also analyzed. For a T-junction the bubble size is corroborated with experimental data. Both the bubble size and frequency are studied and corroborated with experimental data for a co-flowing device. The third example studied is the electrowetting phenomenon observed in a small water droplet resting on a dielectric material. The steady-state contact angle is plotted against the voltage applied. The results are compared with both the Young-Lippmann curve and experimental results. 

    이 논문은 FLOW-3D (범용 CFD 소프트웨어)의 유체 부피 (TruVOF) 방법이 미세 유체 장치에서 액적 역학 및 혼합을 연구하는데 효과적인 도구임을 보여줍니다.

    연구된 첫 번째 예는 액적 생성 및 수동 혼합에 대한 흐름 패턴이 분석되는 T- 접합입니다. 연구된 두 번째 예는 기포의 형성 및 분해가 시뮬레이션 되는 동시 유동 장치입니다.

    기포 형성에 대한 점도의 영향도 분석됩니다. T 접합의 경우 기포 크기는 실험 데이터로 확증됩니다. 기포 크기와 빈도 모두 공동 유동 장치에 대한 실험 데이터로 연구되고 확증됩니다.

    연구된 세 번째 예는 유전 물질 위에 놓인 작은 물방울에서 관찰 된 전기 습윤 현상입니다. 정상 상태 접촉각은 적용된 전압에 대해 플롯됩니다. 결과는 Young-Lippmann 곡선 및 실험 결과와 비교됩니다.

    Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method Fig 1
    Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method Fig 1
    Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method Fig 2
    Simulation of Droplet Dynamics and Mixing in Microfluidic Devices using a VOF-Based Method Fig 2

    References

    Formation of bubbles in a simple co-flowing micro-channel

    SaveAlertResearch FeedFormation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up.

    SaveAlertResearch FeedCreating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits,

    SaveAlertResearch FeedFLOW DEVELOPMENT OF CO-FLOWING STREAMS IN RECTANGULAR MICRO-CHANNELS

    SaveAlertResearch FeedA microfluidic system for controlling reaction networks in time.

    SaveAlertResearch FeedElectrowetting: from basics to applications

    SaveAlertResearch FeedVolume of fluid (VOF) method for the dynamics of free boundaries

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    Fig.4　Schematic of a package structure

    Three-Dimensional Flow Analysis of a Thermosetting Compound during Mold Filling

    Junichi Saeki and Tsutomu Kono
    Production Engineering Research Laboratory, Hitachi Ltd.
    292, Y shida-cho, Totsuka-ku, Yokohama, 244-0817 Japan

    Abstract

    Thermosetting molding compounds are widely used for encapsulating semiconductor devices and electronic modules. In recent years, the number of electronic parts encapsulated in an electronic module has increased, in order to meet the requirements for high performance. As a result, the configuration of inserted parts during molding has become very complicated. Meanwhile, package thickness has been reduced in response to consumer demands for miniaturization. These trends have led to complicated flow patterns of molten compounds in a mold cavity, increasing the difficulty of predicting the occurrence of void formation or gold-wire deformation.

    A method of three-dimensional (3-D) flow analysis of thermosetting compounds has been developed with the objective of minimizing the trial term before mass production and of enhancing the quality of molded products. A constitutive equation model was developed to describe isothermal viscosity changes as a function of time and temperature. This isothermal model was used for predicting non-isothermal viscosity changes. In addition, an empirical model was developed for calculating the amount of wire deformation as a function of viscosity, wire configuration, and other parameters. These models were integrated with FLOW-3D® software, which is used for multipurpose 3-D flow analysis.

    The mold-filling dynamics of an epoxy compound were analyzed using the newly developed modeling software during transfer molding of an actual high performance electronic module. The changes in the 3-D distributions of parameters such as temperature, viscosity, velocity, and pressure were compared with the flow front patterns. The predicted results of cavity filling behavior corresponded well with actual short shot data. As well, the predicted amount of gold-wire deformation at each LSI chip with a substrate connection also corresponded well with observed data obtained by X-ray inspection of the molded product.

    Korea Abstract

    열경화성 몰딩 컴파운드는 반도체 장치 및 전자 모듈을 캡슐화하는 데 널리 사용됩니다. 최근에는 고성능에 대한 요구 사항을 충족시키기 위해 전자 모듈에 캡슐화되는 전자 부품의 수가 증가하고 있습니다.

    그 결과 성형시 삽입 부품의 구성이 매우 복잡해졌습니다. 한편, 소비자의 소형화 요구에 부응하여 패키지 두께를 줄였다. 이러한 경향은 몰드 캐비티에서 용융된 화합물의 복잡한 흐름 패턴을 야기하여 보이드 형성 또는 금선 변형의 발생을 예측하기 어렵게합니다.

    열경화성 화합물의 3 차원 (3-D) 유동 분석 방법은 대량 생산 전에 시험 기간을 최소화하고 성형 제품의 품질을 향상시킬 목적으로 개발되었습니다. 시간과 온도의 함수로서 등온 점도 변화를 설명하기 위해 구성 방정식 모델이 개발되었습니다. 이 등온 모델은 비등 온 점도 변화를 예측하는 데 사용되었습니다.

    또한 점도, 와이어 구성 및 기타 매개 변수의 함수로 와이어 변형량을 계산하기위한 경험적 모델이 개발되었습니다. 이 모델은 다목적 3D 흐름 분석에 사용되는 FLOW-3D® 소프트웨어와 통합되었습니다.

    실제 고성능 전자 모듈의 트랜스퍼 몰딩 과정에서 새로 개발 된 모델링 소프트웨어를 사용하여 에폭시 화합물의 몰드 충전 역학을 분석했습니다. 온도, 점도, 속도 및 압력과 같은 매개 변수의 3D 분포 변화를 유동 선단 패턴과 비교했습니다.

    캐비티 충전 거동의 예측 결과는 실제 미 성형 데이터와 잘 일치했습니다. 또한, 기판 연결이 있는 각 LSI 칩에서 예상되는 금선 변형량은 성형품의 X-ray 검사에서 얻은 관찰 데이터와도 잘 일치했습니다.

    Fig.1 A system of three-dimensional flow analysis for thermosetting compounds
    Fig.1 A system of three-dimensional flow analysis for thermosetting compounds
    Fig.2 Procedure for determining viscosity changes of thermosetting compounds
    Fig.2 Procedure for determining viscosity changes of thermosetting compounds
    Fig.4　Schematic of a package structure
    Fig.4　Schematic of a package structure
    Fig.6 Calculated results of filling behavior and temperature distribution in the runner
    Fig.6 Calculated results of filling behavior and temperature distribution in the runner
    Fig.8 Comparison of cavity filling
    Fig.8 Comparison of cavity filling
    PDF View

    References

    1)J.Saeki et al. ,6th annual meeting of PPS, 12KN1(1990)
    2)J.Saeki et al. , JSME International Journal Series Ⅱ, 33,486(1990)
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    5) J.Saeki et al.,SEIKEI KAKOU,13,49(2001)

    The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

    Numerical investigation of flow characteristics over stepped spillways

    Güven, Aytaç
    Mahmood, Ahmed Hussein
    Water Supply (2021) 21 (3): 1344–1355.
    https://doi.org/10.2166/ws.2020.283Article history

    Abstract

    Spillways are constructed to evacuate flood discharge safely so that a flood wave does not overtop the dam body. There are different types of spillways, with the ogee type being the conventional one. A stepped spillway is an example of a nonconventional spillway. The turbulent flow over a stepped spillway was studied numerically by using the Flow-3D package. Different fluid flow characteristics such as longitudinal flow velocity, temperature distribution, density and chemical concentration can be well simulated by Flow-3D. In this study, the influence of slope changes on flow characteristics such as air entrainment, velocity distribution and dynamic pressures distribution over a stepped spillway was modelled by Flow-3D. The results from the numerical model were compared with an experimental study done by others in the literature. Two models of a stepped spillway with different discharge for each model were simulated. The turbulent flow in the experimental model was simulated by the Renormalized Group (RNG) turbulence scheme in the numerical model. A good agreement was achieved between the numerical results and the observed ones, which are exhibited in terms of graphics and statistical tables.

    배수로는 홍수가 댐 몸체 위로 넘치지 않도록 안전하게 홍수를 피할 수 있도록 건설되었습니다. 다른 유형의 배수로가 있으며, ogee 유형이 기존 유형입니다. 계단식 배수로는 비 전통적인 배수로의 예입니다. 계단식 배수로 위의 난류는 Flow-3D 패키지를 사용하여 수치적으로 연구되었습니다.

    세로 유속, 온도 분포, 밀도 및 화학 농도와 같은 다양한 유체 흐름 특성은 Flow-3D로 잘 시뮬레이션 할 수 있습니다. 이 연구에서는 계단식 배수로에 대한 공기 혼입, 속도 분포 및 동적 압력 분포와 같은 유동 특성에 대한 경사 변화의 영향을 Flow-3D로 모델링 했습니다.

    수치 모델의 결과는 문헌에서 다른 사람들이 수행한 실험 연구와 비교되었습니다. 각 모델에 대해 서로 다른 배출이 있는 계단식 배수로의 두 모델이 시뮬레이션되었습니다. 실험 모델의 난류 흐름은 수치 모델의 Renormalized Group (RNG) 난류 계획에 의해 시뮬레이션되었습니다. 수치 결과와 관찰 된 결과 사이에 좋은 일치가 이루어졌으며, 이는 그래픽 및 통계 테이블로 표시됩니다.

    HIGHLIGHTS

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    • A numerical model was developed for stepped spillways.
    • The turbulent flow was simulated by the Renormalized Group (RNG) model.
    • Both numerical and experimental results showed that flow characteristics are greatly affected by abrupt slope change on the steps.

    Keyword

    CFD, numerical modelling, slope change, stepped spillway, turbulent flow

    INTRODUCTION

    댐 구조는 물 보호가 생활의 핵심이기 때문에 물을 저장하거나 물을 운반하는 전 세계에서 가장 중요한 프로젝트입니다. 그리고 여수로는 댐의 가장 중요한 부분 중 하나로 분류됩니다. 홍수로 인한 파괴 나 피해로부터 댐을 보호하기 위해 여수로가 건설됩니다.

    수력 발전, 항해, 레크리에이션 및 어업의 중요성을 감안할 때 댐 건설 및 홍수 통제는 전 세계적으로 매우 중요한 문제로 간주 될 수 있습니다. 많은 유형의 배수로가 있지만 가장 일반적인 유형은 다음과 같습니다 : ogee 배수로, 자유 낙하 배수로, 사이펀 배수로, 슈트 배수로, 측면 채널 배수로, 터널 배수로, 샤프트 배수로 및 계단식 배수로.

    그리고 모든 여수로는 입구 채널, 제어 구조, 배출 캐리어 및 출구 채널의 네 가지 필수 구성 요소로 구성됩니다. 특히 롤러 압축 콘크리트 (RCC) 댐 건설 기술과 더 쉽고 빠르며 저렴한 건설 기술로 분류 된 계단식 배수로 건설과 관련하여 최근 수십 년 동안 많은 계단식 배수로가 건설되었습니다 (Chanson 2002; Felder & Chanson 2011).

    계단식 배수로 구조는 캐비테이션 위험을 감소시키는 에너지 소산 속도를 증가시킵니다 (Boes & Hager 2003b). 계단식 배수로는 다양한 조건에서 더 매력적으로 만드는 장점이 있습니다.

    계단식 배수로의 흐름 거동은 일반적으로 낮잠, 천이 및 스키밍 흐름 체제의 세 가지 다른 영역으로 분류됩니다 (Chanson 2002). 유속이 낮을 때 nappe 흐름 체제가 발생하고 자유 낙하하는 낮잠의 시퀀스로 특징 지워지는 반면, 스키밍 흐름 체제에서는 물이 외부 계단 가장자리 위의 유사 바닥에서 일관된 흐름으로 계단 위로 흐릅니다.

    또한 주요 흐름에서 3 차원 재순환 소용돌이가 발생한다는 것도 분명합니다 (예 : Chanson 2002; Gonzalez & Chanson 2008). 계단 가장자리 근처의 의사 바닥에서 흐름의 방향은 가상 바닥과 가상으로 정렬됩니다. Takahashi & Ohtsu (2012)에 따르면, 스키밍 흐름 체제에서 주어진 유속에 대해 흐름은 계단 가장자리 근처의 수평 계단면에 영향을 미치고 슈트 경사가 감소하면 충돌 영역의 면적이 증가합니다. 전이 흐름 체제는 나페 흐름과 스키밍 흐름 체제 사이에서 발생합니다. 계단식 배수로를 설계 할 때 스키밍 흐름 체계를 고려해야합니다 (예 : Chanson 1994, Matos 2000, Chanson 2002, Boes & Hager 2003a).

    CFD (Computational Fluid Dynamics), 즉 수력 공학의 수치 모델은 일반적으로 물리적 모델에 소요되는 총 비용과 시간을 줄여줍니다. 따라서 수치 모델은 실험 모델보다 빠르고 저렴한 것으로 분류되며 동시에 하나 이상의 목적으로 사용될 수도 있습니다. 사용 가능한 많은 CFD 소프트웨어 패키지가 있지만 가장 널리 사용되는 것은 FLOW-3D입니다. 이 연구에서는 Flow 3D 소프트웨어를 사용하여 유량이 서로 다른 두 모델에 대해 계단식 배수로에서 공기 농도, 속도 분포 및 동적 압력 분포를 시뮬레이션합니다.

    Roshan et al. (2010)은 서로 다른 수의 계단 및 배출을 가진 계단식 배수로의 두 가지 물리적 모델에 대한 흐름 체제 및 에너지 소산 조사를 연구했습니다. 실험 모델의 기울기는 각각 19.2 %, 12 단계와 23 단계의 수입니다. 결과는 23 단계 물리적 모델에서 관찰 된 흐름 영역이 12 단계 모델보다 더 수용 가능한 것으로 간주되었음을 보여줍니다. 그러나 12 단계 모델의 에너지 손실은 23 단계 모델보다 더 많았습니다. 그리고 실험은 스키밍 흐름 체제에서 23 단계 모델의 에너지 소산이 12 단계 모델보다 약 12 ​​% 더 적다는 것을 관찰했습니다.

    Ghaderi et al. (2020a)는 계단 크기와 유속이 다른 정련 매개 변수의 영향을 조사하기 위해 계단식 배수로에 대한 실험 연구를 수행했습니다. 그 결과, 흐름 체계가 냅페 흐름 체계에서 발생하는 최소 scouring 깊이와 같은 scouring 구멍 치수에 영향을 미친다는 것을 보여주었습니다. 또한 테일 워터 깊이와 계단 크기는 최대 scouring깊이에 대한 실제 매개 변수입니다. 테일 워터의 깊이를 6.31cm에서 8.54 및 11.82cm로 늘림으로써 수세 깊이가 각각 18.56 % 및 11.42 % 증가했습니다. 또한 이 증가하는 테일 워터 깊이는 scouring 길이를 각각 31.43 % 및 16.55 % 감소 시킵니다. 또한 유속을 높이면 Froude 수가 증가하고 흐름의 운동량이 증가하면 scouring이 촉진됩니다. 또한 결과는 중간의 scouring이 횡단면의 측벽보다 적다는 것을 나타냅니다. 계단식 배수로 하류의 최대 scouring 깊이를 예측 한 후 실험 결과와 비교하기 위한 실험식이 제안 되었습니다. 그리고 비교 결과 제안 된 공식은 각각 3.86 %와 9.31 %의 상대 오차와 최대 오차 내에서 scouring 깊이를 예측할 수 있음을 보여주었습니다.

    Ghaderi et al. (2020b)는 사다리꼴 미로 모양 (TLS) 단계의 수치 조사를 했습니다. 결과는 이러한 유형의 배수로가 확대 비율 LT / Wt (LT는 총 가장자리 길이, Wt는 배수로의 폭)를 증가시키기 때문에 더 나은 성능을 갖는 것으로 관찰되었습니다. 또한 사다리꼴 미로 모양의 계단식 배수로는 더 큰 마찰 계수와 더 낮은 잔류 수두를 가지고 있습니다. 마찰 계수는 다양한 배율에 대해 0.79에서 1.33까지 다르며 평평한 계단식 배수로의 경우 대략 0.66과 같습니다. 또한 TLS 계단식 배수로에서 잔류 수두의 비율 (Hres / dc)은 약 2.89이고 평평한 계단식 배수로의 경우 약 4.32와 같습니다.

    Shahheydari et al. (2015)는 Flow-3D 소프트웨어, RNG k-ε 모델 및 VOF (Volume of Fluid) 방법을 사용하여 배출 계수 및 에너지 소산과 같은 자유 표면 흐름의 프로파일을 연구하여 스키밍 흐름 체제에서 계단식 배수로에 대한 흐름을 조사했습니다. 실험 결과와 비교했습니다. 결과는 에너지 소산 율과 방전 계수율의 관계가 역으로 실험 모델의 결과와 잘 일치 함을 보여 주었다.

    Mohammad Rezapour Tabari & Tavakoli (2016)는 계단 높이 (h), 계단 길이 (L), 계단 수 (Ns) 및 단위 폭의 방전 (q)과 같은 다양한 매개 변수가 계단식 에너지 ​​소산에 미치는 영향을 조사했습니다. 방수로. 그들은 해석에 FLOW-3D 소프트웨어를 사용하여 계단식 배수로에서 에너지 손실과 임계 흐름 깊이 사이의 관계를 평가했습니다. 또한 유동 난류에 사용되는 방정식과 표준 k-ɛ 모델을 풀기 위해 유한 체적 방법을 적용했습니다. 결과에 따르면 스텝 수가 증가하고 유량 배출량이 증가하면 에너지 손실이 감소합니다. 얻은 결과를 다른 연구와 비교하고 경험적, 수학적 조사를 수행하여 결국 합격 가능한 결과를 얻었습니다.

    METHODOLOGY

    ListenReadSpeaker webReader: ListenFor all numerical models the basic principle is very similar: a set of partial differential equations (PDE) present the physical problems. The flow of fluids (gas and liquid) are governed by the conservation laws of mass, momentum and energy. For Computational Fluid Dynamics (CFD), the PDE system is substituted by a set of algebraic equations which can be worked out by using numerical methods (Versteeg & Malalasekera 2007). Flow-3D uses the finite volume approach to solve the Reynolds Averaged Navier-Stokes (RANS) equation, by applying the technique of Fractional Area/Volume Obstacle Representation (FAVOR) to define an obstacle (Flow Science Inc. 2012). Equations (1) and (2) are RANS and continuity equations with FAVOR variables that are applied for incompressible flows.

    formula

    (1)

    formula

    (2)where  is the velocity in xi direction, t is the time,  is the fractional area open to flow in the subscript directions,  is the volume fraction of fluid in each cell, p is the hydrostatic pressure,  is the density, is the gravitational force in subscript directions and  is the Reynolds stresses.

    Turbulence modelling is one of three key elements in CFD (Gunal 1996). There are many types of turbulence models, but the most common are Zero-equation models, One-equation models, Two-equation models, Reynolds Stress/Flux models and Algebraic Stress/Flux models. In FLOW-3D software, five turbulence models are available. The formulation used in the FLOW-3D software differs slightly from other formulations that includes the influence of the fractional areas/volumes of the FAVORTM method and generalizes the turbulence production (or decay) associated with buoyancy forces. The latter generalization, for example, includes buoyancy effects associated with non-inertial accelerations.

    The available turbulence models in Flow-3D software are the Prandtl Mixing Length Model, the One-Equation Turbulent Energy Model, the Two-Equation Standard  Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (Flow Science Inc. 2012).In this research the RNG model was selected because this model is more commonly used than other models in dealing with particles; moreover, it is more accurate to work with air entrainment and other particles. In general, the RNG model is classified as a more widely-used application than the standard k-ɛ model. And in particular, the RNG model is more accurate in flows that have strong shear regions than the standard k-ɛ model and it is defined to describe low intensity turbulent flows. For the turbulent dissipation  it solves an additional transport equation:

    formula

    (3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is

    formula

    (4)where u, v and w are the x, y and z coordinates of the fluid velocity; ⁠, ⁠,  and ⁠, are FLOW-3D’s FAVORTM defined terms;  and  are turbulence due to shearing and buoyancy effects, respectively. R and  are related to the cylindrical coordinate system. The default values of RMTKE, CDIS1 and CNU differ, being 1.39, 1.42 and 0.085 respectively. And CDIS2 is calculated from turbulent production (⁠⁠) and turbulent kinetic energy (⁠⁠).The kinematic turbulent viscosity is the same in all turbulence transport models and is calculated from

    formula

    (5)where ⁠: is the turbulent kinematic viscosity.  is defined as the numerical challenge between the RNG and the two-equation k-ɛ models, found in the equation below. To avoid an unphysically large result for  in Equation (3), since this equation could produce a value for  very close to zero and also because the physical value of  may approach to zero in such cases, the value of  is calculated from the following equation:

    formula

    (6)where ⁠: the turbulent length scale.

    VOF and FAVOR are classifications of volume-fraction methods. In these two methods, firstly the area should be subdivided into a control volume grid or a small element. Each flow parameter like velocity, temperature and pressure values within the element are computed for each element containing liquids. Generally, these values represent the volumetric average of values in the elements.Numerous methods have been used recently to solve free infinite boundaries in the various numerical simulations. VOF is an easy and powerful method created based on the concept of a fractional intensity of fluid. A significant number of studies have confirmed that this method is more flexible and efficient than others dealing with the configurations of a complex free boundary. By using VOF technology the Flow-3D free surface was modelled and first declared in Hirt & Nichols (1981). In the VOF method there are three ingredients: a planner to define the surface, an algorithm for tracking the surface as a net mediator moving over a computational grid, and application of the boundary conditions to the surface. Configurations of the fluids are defined in terms of VOF function, F (x, y, z, t) (Hirt & Nichols 1981). And this VOF function shows the volume of flow per unit volume

    formula

    (7)

    formula

    (8)

    formula

    (9)where  is the density of the fluid, is a turbulent diffusion term,  is a mass source,  is the fractional volume open to flow. The components of velocity (u, v, w) are in the direction of coordinates (x, y, z) or (r, ⁠).  in the x-direction is the fractional area open to flow,  and  are identical area fractions for flow in the y and z directions. The R coefficient is based on the selection of the coordinate system.

    The FAVOR method is a different method and uses another volume fraction technique, which is only used to define the geometry, such as the volume of liquid in each cell used to determine the position of fluid surfaces. Another fractional volume can be used to define the solid surface. Then, this information is used to determine the boundary conditions of the wall that the flow should be adapted for.

    Case study

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    In this study, the experimental results of Ostad Mirza (2016) was simulated. In a channel composed of two 4 m long modules, with a transparent sidewall of height 0.6 m and 0.5 m width. The upstream chute slope (i.e. pseudo-bottom angle) Ɵ1 = 50°, the downstream chute slope Ɵ2 = 30° or 18.6°, the step heights h = 0.06 m, the total number of steps along the 50° chute 41 steps, the total number of steps along the 30° chute 34 steps and the total number of steps along the 18.6° chute 20 steps.

    The flume inflow tool contained a jetbox with a maximum opening set to 0.12 meters, designed for passing the maximum unit discharge of 0.48 m2/s. The measurements of the flow properties (i.e. air concentration and velocity) were computed perpendicular to the pseudo-bottom as shown in Figure 1 at the centre of twenty stream-wise cross-sections, along the stepped chute, (i.e. in five steps up on the slope change and fifteen steps down on the slope change, namely from step number −09 to +23 on 50°–30° slope change, or from −09 to +15 on 50°–18.6° slope change, respectively).

    Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).
    Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

    Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

    Pressure sensors were arranged with the x/l values for different slope change as shown in Table 1, where x is the distance from the step edge, along the horizontal step face, and l is the length of the horizontal step face. The location of pressure sensors is shown in Table 1.Table 1

    Location of pressure sensors on horizontal step faces

    Θ(°)L(m)x/l (–)
    50.0 0.050 0.35 0.64 – – – 
    30.0 0.104 0.17 0.50 0.84 – – 
    18.6 0.178 0.10 0.30 0.50 0.7 0.88 
    Location of pressure sensors on horizontal step faces
    Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.
    Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

    Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

    Numerical model set-up

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    A 3D numerical model of hydraulic phenomena was simulated based on an experimental study by Ostad Mirza (2016). The water surcharge and flow pressure over the stepped spillway was computed for two models of a stepped spillway with different discharge for each model. In this study, the package was used to simulate the flow parameters such as air entrainment, velocity distribution and dynamic pressures. The solver uses the finite volume technique to discretize the computational domain. In every test run, one incompressible fluid flow with a free surface flow selected at 20̊ was used for this simulation model. Table 2 shows the variables used in test runs.Table 2

    Variables used in test runs

    Test no.Θ1 (°)Θ2 (°)h(m)d0q (m3s−1)dc/h (–)
    1 50 18.6 0.06 0.045 0.1 2.6 
    2 50 18.6 0.06 0.082 0.235 4.6 
    3 50 30.0 0.06 0.045 0.1 2.6 
    4 50 30.0 0.06 0.082 0.235 4.6 
    Table 2 Variables used in test runs

    For stepped spillway simulation, several parameters should be specified to get accurate simulations, which is the scope of this research. Viscosity and turbulent, gravity and non-inertial reference frame, air entrainment, density evaluation and drift-flux should be activated for these simulations. There are five different choices in the ‘viscosity and turbulent’ option, in the viscosity flow and Renormalized Group (RNG) model. Then a dynamical model is selected as the second option, the ‘gravity and non-inertial reference frame’. Only the z-component was inputted as a negative 9.81 m/s2 and this value represents gravitational acceleration but in the same option the x and y components will be zero. Air entrainment is selected. Finally, in the drift-flux model, the density of phase one is input as (water) 1,000 kg/m3 and the density of phase two (air) as 1.225 kg/m3. Minimum volume fraction of phase one is input equal to 0.1 and maximum volume fraction of phase two to 1 to allow air concentration to reach 90%, then the option allowing gas to escape at free surface is selected, to obtain closer simulation.

    The flow domain is divided into small regions relatively by the mesh in Flow-3D numerical model. Cells are the smallest part of the mesh, in which flow characteristics such as air concentration, velocity and dynamic pressure are calculated. The accuracy of the results and simulation time depends directly on the mesh block size so the cell size is very important. Orthogonal mesh was used in cartesian coordinate systems. A smaller cell size provides more accuracy for results, so we reduced the number of cells whilst including enough accuracy. In this study, the size of cells in x, y and z directions was selected as 0.015 m after several trials.

    Figure 3 shows the 3D computational domain model 50–18.6 slope change, that is 6.0 m length, 0.50 m width and 4.23 m height. The 3D model of the computational domain model 50–30 slope changes this to 6.0 m length, 0.50 m width and 5.068 m height and the size of meshes in x, y, and z directions are 0.015 m. For the 50–18.6 slope change model: both total number of active and passive cells = 4,009,952, total number of active cells = 3,352,307, include real cells (used for solving the flow equations) = 3,316,269, open real cells = 3,316,269, fully blocked real cells equal to zero, external boundary cells were 36,038, inter-block boundary cells = 0 (Flow-3D report). For 50–30 slope change model: both total number of active and passive cells = 4,760,002, total number of active cells equal to 4,272,109, including real cells (used for solving the flow equations) were 3,990,878, open real cells = 3,990,878 fully blocked real cells = zero, external boundary cells were 281,231, inter-block boundary cells = 0 (Flow-3D report).

    The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.
    Figure3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

    Figure 3VIEW LARGEDOWNLOAD SLIDE

    The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

    When solving the Navier-Stokes equation and continuous equations, boundary conditions should be applied. The most important work of boundary conditions is to create flow conditions similar to physical status. The Flow-3D software has many types of boundary condition; each type can be used for the specific condition of the models. The boundary conditions in Flow-3D are symmetry, continuative, specific pressure, grid overlay, wave, wall, periodic, specific velocity, outflow, and volume flow rate.

    There are two options to input finite flow rate in the Flow-3D software either for inlet discharge of the system or for the outlet discharge of the domain: specified velocity and volume flow rate. In this research, the X-minimum boundary condition, volume flow rate, has been chosen. For X-maximum boundary condition, outflow was selected because there is nothing to be calculated at the end of the flume. The volume flow rate and the elevation of surface water was set for Q = 0.1 and 0.235 m3/s respectively (Figure 2).

    The bottom (Z-min) is prepared as a wall boundary condition and the top (Z-max) is computed as a pressure boundary condition, and for both (Y-min) and (Y-max) as symmetry.

    RESULTS AND DISCUSSION

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    The air concentration distribution profiles in two models of stepped spillway were obtained at an acquisition time equal to 25 seconds in skimming flow for both upstream and downstream of a slope change 50°–18.6° and 50°–30° for different discharge as in Table 2, and as shown in Figure 4 for 50°–18.6° slope change and Figure 5 for 50°–30° slope change configuration for dc/h = 4.6. The simulation results of the air concentration are very close to the experimental results in all curves and fairly close to that predicted by the advection-diffusion model for the air bubbles suggested by Chanson (1997) on a constant sloping chute.

    Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.
    Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

    Figure 4VIEW LARGEDOWNLOAD SLIDE

    Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

    Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.
    Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

    Figure 5VIEW LARGEDOWNLOAD SLIDE

    Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

    Figure 6VIEW LARGEDOWNLOAD SLIDE

    Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.
    Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

    Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

    Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.
    Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

    Figure 7VIEW LARGEDOWNLOAD SLIDE

    Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

    But as is shown in all above mentioned figures it is clear that at the pseudo-bottom the CFD results of air concentration are less than experimental ones until the depth of water reaches a quarter of the total depth of water. Also the direction of the curves are parallel to each other when going up towards the surface water and are incorporated approximately near the surface water. For all curves, the cross-section is separate between upstream and downstream steps. Therefore the (-) sign for steps represents a step upstream of the slope change cross-section and the (+) sign represents a step downstream of the slope change cross-section.

    The dimensionless velocity distribution (V/V90) profile was acquired at an acquisition time equal to 25 seconds in skimming flow of the upstream and downstream slope change for both 50°–18.6° and 50°–30° slope change. The simulation results are compared with the experimental ones showing that for all curves there is close similarity for each point between the observed and experimental results. The curves increase parallel to each other and they merge near at the surface water as shown in Figure 6 for slope change 50°–18.6° configuration and Figure 7 for slope change 50°–30° configuration. However, at step numbers +1 and +5 in Figure 7 there are few differences between the simulated and observed results, namely the simulation curves ascend regularly meaning the velocity increases regularly from the pseudo-bottom up to the surface water.

    Figure 8 (50°–18.6° slope change) and Figure 9 (50°–30° slope change) compare the simulation results and the experimental results for the presented dimensionless dynamic pressure distribution for different points on the stepped spillway. The results show a good agreement with the experimental and numerical simulations in all curves. For some points, few discrepancies can be noted in pressure magnitudes between the simulated and the observed ones, but they are in the acceptable range. Although the experimental data do not completely agree with the simulated results, there is an overall agreement.

    Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
    Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

    Figure 8VIEW LARGEDOWNLOAD SLIDE

    Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

    Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
    Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

    Figure 9VIEW LARGEDOWNLOAD SLIDE

    Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

    The pressure profiles were acquired at an acquisition time equal to 70 seconds in skimming flow on 50°–18.6°, where p is the measured dynamic pressure, h is step height and ϒ is water specific weight. A negative sign for steps represents a step upstream of the slope change cross-section and a positive sign represents a step downstream of the slope change cross-section.

    Figure 10 shows the experimental streamwise development of dimensionless pressure on the 50°–18.6° slope change for dc/h = 4.6, x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute compared with the numerical simulation. It is obvious from Figure 10 that the streamwise development of dimensionless pressure before slope change (steps number −1, −2 and −3) both of the experimental and simulated results are close to each other. However, it is clear that there is a little difference between the results of the streamwise development of dimensionless pressure at step numbers +1, +2 and +3. Moreover, from step number +3 to the end, the curves get close to each other.

    Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.
    Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

    Figure 10VIEW LARGEDOWNLOAD SLIDE

    Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

    Figure 11 compares the experimental and the numerical results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute. It is apparent that the outcomes of the experimental work are close to the numerical results, however, the results of the simulation are above the experimental ones before the slope change, but the results of the simulation descend below the experimental ones after the slope change till the end.

    Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.
    Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

    Figure 11VIEW LARGEDOWNLOAD SLIDE

    Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

    CONCLUSION

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    In this research, numerical modelling was attempted to investigate the effect of abrupt slope change on the flow properties (air entrainment, velocity distribution and dynamic pressure) over a stepped spillway with two different models and various flow rates in a skimming flow regime by using the CFD technique. The numerical model was verified and compared with the experimental results of Ostad Mirza (2016). The same domain of the numerical model was inputted as in experimental models to reduce errors as much as possible.

    Flow-3D is a well modelled tool that deals with particles. In this research, the model deals well with air entrainment particles by observing their results with experimental results. And the reason for the small difference between the numerical and the experimental results is that the program deals with particles more accurately than the laboratory. In general, both numerical and experimental results showed that near to the slope change the flow bulking, air entrainment, velocity distribution and dynamic pressure are greatly affected by abrupt slope change on the steps. Although the extent of the slope change was relatively small, the influence of the slope change was major on flow characteristics.

    The Renormalized Group (RNG) model was selected as a turbulence solver. For 3D modelling, orthogonal mesh was used as a computational domain and the mesh grid size used for X, Y, and Z direction was equal to 0.015 m. In CFD modelling, air concentration and velocity distribution were recorded for a period of 25 seconds, but dynamic pressure was recorded for a period of 70 seconds. The results showed that there is a good agreement between the numerical and the physical models. So, it can be concluded that the proposed CFD model is very suitable for use in simulating and analysing the design of hydraulic structures.

    이 연구에서 수치 모델링은 두 가지 다른 모델과 다양한 유속을 사용하여 스키밍 흐름 영역에서 계단식 배수로에 대한 유동 특성 (공기 혼입, 속도 분포 및 동적 압력)에 대한 급격한 경사 변화의 영향을 조사하기 위해 시도되었습니다. CFD 기술. 수치 모델을 검증하여 Ostad Mirza (2016)의 실험 결과와 비교 하였다. 오차를 최대한 줄이기 위해 실험 모형과 동일한 수치 모형을 입력 하였다.

    Flow-3D는 파티클을 다루는 잘 모델링 된 도구입니다. 이 연구에서 모델은 실험 결과를 통해 결과를 관찰하여 공기 혼입 입자를 잘 처리합니다. 그리고 수치와 실험 결과의 차이가 작은 이유는 프로그램이 실험실보다 입자를 더 정확하게 다루기 때문입니다. 일반적으로 수치 및 실험 결과는 경사에 가까워지면 유동 벌킹, 공기 혼입, 속도 분포 및 동적 압력이 계단의 급격한 경사 변화에 크게 영향을받는 것으로 나타났습니다. 사면 변화의 정도는 상대적으로 작았지만 사면 변화의 영향은 유동 특성에 큰 영향을 미쳤다.

    Renormalized Group (RNG) 모델이 난류 솔버로 선택되었습니다. 3D 모델링의 경우 계산 영역으로 직교 메쉬가 사용되었으며 X, Y, Z 방향에 사용 된 메쉬 그리드 크기는 0.015m입니다. CFD 모델링에서 공기 농도와 속도 분포는 25 초 동안 기록되었지만 동적 압력은 70 초 동안 기록되었습니다. 결과는 수치 모델과 물리적 모델간에 좋은 일치가 있음을 보여줍니다. 따라서 제안 된 CFD 모델은 수력 구조물의 설계 시뮬레이션 및 해석에 매우 적합하다는 결론을 내릴 수 있습니다.

    DATA AVAILABILITY STATEMENT

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    All relevant data are included in the paper or its Supplementary Information.

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    © 2021 The Authors
    This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).

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    Figure 1. Steady-state shear stress a as a function of shear rate y in Sn-Pb alloy [10).

    Numerical Modelling of Semi-Solid Flow under Processing Conditions

    처리조건에서의 반고체유동의 수치모델링

    David H. Kirkwood and Philip J. Ward
    Department of Engineering Materials, University of Sheffield, Sheffield I UK

    Keywords: semi-solid alloys, thixotropy, flow modelling.

    Abstract

    During the industrial process of semi-solid forming (or thixoforming) of alloy slurries, typically the operation of die filling takes around 0.1s.
    During this time period the alloy slug is transformed from a solid-like structure capable of maintaining its shape, into a liquid-like slurry able
    to fill a complex die cavity: this involves a decrease in viscosity of some 6 orders of magnitUde. Many attempts to measure thixotropic breakdown experimentally in alloy slurries have relied on the use of concentric cylindrical viscometers in which viscosity changes have been followed after shear rate changes over times above 1s to in excess of 1000 s, which have little relevance to actual processing conditions and therefore to modelling of flow in industrial practice. The present paper is an attempt to abstract thixotropic breakdown rates from rapid compression tests between parallel plates moving together at velocities of around 1mis, similar to industrial conditions. From this analysis, a model of slurry flow has been developed in which rapid thixotropic breakdown of the slurry occurs at high shear rates.

    합금 슬러리의 반고체 성형 (또는 틱소 성형)의 산업 공정 동안, 일반적으로 다이 충진 작업은 약 0.1 초가 걸립니다.
    이 기간 동안 합금 슬러그는 모양을 유지할 수있는 고체와 같은 구조에서 액체와 같은 슬러리로 변형됩니다.
    복잡한 다이 캐비티를 채우기 위해 : 이것은 약 6 차의 마그 니트 점도 감소를 포함합니다. 합금 슬러리에서 실험적으로 요 변성 파괴를 측정하려는 많은 시도는 전단 속도가 1 초 이상에서 1000 초 이상으로 변화 한 후 점도 변화가 뒤 따르는 동심원 원통형 점도계의 사용에 의존하여 실제 가공 조건과는 거의 관련이 없습니다. 따라서 산업 현장에서 흐름 모델링에. 본 논문은 산업 조건과 유사하게 약 1mis의 속도로 함께 이동하는 평행 판 사이의 빠른 압축 테스트에서 요 변성 파괴 율을 추상화하려는 시도입니다. 이 분석으로부터 슬러리의 급속한 요 변성 분해가 높은 전단 속도에서 발생하는 슬러리 흐름 모델이 개발되었습니다.

    Introduction

    기존의 다이캐스팅을 위한 다이 설계는 과거에 예비 테스트 및 조정과 함께 축적 된 실무 경험의 문제였으며, 단기 실행, 랩, 다공성 등과 같은 결함을 제거하기 위해 다이 캐스트 제품을 검사했습니다. 이것은 모두 비용이 많이 드는 절차입니다.

    시간과 비용, 그리고 프로세스의 컴퓨터 모델링은 이를 줄이거 나 없애기 위해 많은 운영자에 의해 개발되었습니다. 반고체 가공 (thixoforming)에서는 반고체 합금 슬러리의 전단이 내부 구조를 파괴하여 충전 작업 중 시간이 지남에 따라 점도가 낮아짐으로 발생하는 비 뉴턴 점도로 인해 모델링 문제가 더욱 어려워집니다.

    시스템 전체에서 균일하지 않습니다. 충전 중에 발생하는 추가 응고로 인해 문제가 더욱 복잡해집니다. 빠른 충전으로 인해 이 단계에서 매우 작은 것으로 간주되기 때문에 현재 분석에서는 무시되었습니다.

    우리 모델의 또 다른 한계는 슬러리가 균질한 물질로 거동 한다는 가정이며, 이는 어느 지점에서나 단일 점도로 설명될 수 있습니다. 이것은 빠른 전단의 고려 사항과 정상적인 요 변형성 조건 내에서 0.6 미만의 고형분을 분별하는 것으로 제한합니다.

    <중략>……

    Figure 1. Steady-state shear stress a as a function of shear rate y in Sn-Pb alloy [10).
    Figure 1. Steady-state shear stress a as a function of shear rate y in Sn-Pb alloy [10).
    Figure 2. Equilibrium viscosity as a function of shear rate in Sn-Pb alloy, fraction solid:0.36, fitted to Cross Model.
    Figure 2. Equilibrium viscosity as a function of shear rate in Sn-Pb alloy, fraction solid:0.36, fitted to Cross Model.
    Figure 3. Cheng Diagram: shear stress vs. shear rate.
    Figure 3. Cheng Diagram: shear stress vs. shear rate.
    Figure 4. Reciprocal of experimental breakdown time vs. y 1.3 for Sn-Pb alloy
    Figure 4. Reciprocal of experimental breakdown time vs. y 1.3 for Sn-Pb alloy
    Figure 5. Relaxation time, T, as a function of shear rate; see also figure 4, Fs =0.36.
    Figure 5. Relaxation time, T, as a function of shear rate; see also figure 4, Fs =0.36.
    Figure 6. Experimental and modelled results for compression test on AI-A356 alloy at two temperatures.
    Figure 6. Experimental and modelled results for compression test on AI-A356 alloy at two temperatures.
    Table 1. Calculated parameters for the breakdown in compression tests [20].
    Table 1. Calculated parameters for the breakdown in compression tests [20].
    Figure 7. Drop-forge results from Yurko and Flemings [7].
    Figure 7. Drop-forge results from Yurko and Flemings [7].
    Figure 8. Prediction of FLOW-3D®.
    Figure 8. Prediction of FLOW-3D®.

    Conclusions

    y에서 전단 된 반고체 슬러리의 틱소 트로픽 분해에 대한 속도 방정식은 다음과 같은 형식으로 제안됩니다. T = l / (a ​​+ uym), 여기서 T는 급속 분해 또는 유사 정상 상태 구조에 대한 특성 시간이며, 밴드 m은 상수입니다. 이 관계는 제한된 범위의 전단 속도에서 Sn-Pb 합금의 전단 속도 점프에 의해 실험적으로 확인되었습니다.

    이 파괴율 방정식은 AI-Si 합금의 반고체 슬러그에 대한 빠른 압축 테스트에서 실험적으로 얻은 힘-변위 곡선을 시뮬레이션하기 위해 FLOW-3D® (버전 8.2 : FlowScience Inc.)에 도입되었습니다. 담금 시간과 다른 압축 속도에서. 이 분석의 결과는 모든 경우에 요 변성 거동이 관련되어 있음을 나타내지만, 5 분 동안 담근 후 (산업 관행에서와 같이) 구조가 크게 분해되었으며 초기에는 낮은 전단 속도 영역에서 흐름이 뉴턴에 가깝습니다.

    파괴율은 100 S-I 이상의 전단율에서 극적으로 증가하는 것으로 가정 됩니다. 이 예측은 높은 전단 속도에서 더 세심한 작업에 의해 테스트되어야 하지만 평균 전단 속도가 1300 sol까지 생성된 드롭 단조 실험에 의해 뒷받침되는 것으로 보입니다 [7].

    References

    [I] T.Y Liu, H.Y. Atkinson, PJ. Ward, D.H. Kirkwood: Metall.Mater.TransA, 34A (2003), 409/17.
    [2] A. Zavaliangos and A. Lawley: J. Mater. Eng. Perfonn., 4 (1995),40/47.
    [3] M.R. Barkhudarov, e.L. Bronisz, e.w. Hirt: ProcAth Int. Conf. onSemi-solid Processing of Alloys and Composites,1996, Sheffield,p.llO.
    [4] W.R.Loue, M.Suery, J.L.Querbes: Proc.2ndInt.Conf.on Semi-solidProcessing of Alloys and Composites,1992, Cambridge MA , pp266-75.
    [5] P.Kapranos, D.H.Kirkwood, M.R. Barkhudarov: Proc.5th Int. Conf.on Semi-solid Processing of Alloys and Composites, Golden, Colorado,1998. pp.II-19.
    [6] T.Y. Liu, H.Y. Atkinson, P. Kapranos, D.H. Kirkwood, S.G. Hogg:Metall. Mater. Trans A, 34A (2003), 1545/54.
    [7] J.A. Yurko and M.e. Flemings: Metall. Mater. Trans A, 33A (2002),2737/46.
    [8] M. Modigell and J. Koke: Mechanics of Time Dependent Materials, 3(1999), 15/30.
    [9] Y. Laxmanan and M.e. Flemings: Metall. Trans. A, IIA( 1980),1927/36.
    [IO]A.R.A Mclelland, N.G. Henderson, H.Y. Atkinson, D.H. Kirkwood:Mater. Sci. Eng., A232 (1997), 110/18.
    [II] H.A. Barnes: 1. Non-Newtonian Fluid Mech., 81 (1999),133n8.
    [12]A.N. Alexandrou, E. Due , Y. Entov: 1. Non-Newtonian Fluid Mech.,96 (2001), 383/403.
    [13]C.L. Martin, P. Kumar and S. Brown: Acta Mat. Mater., 42 (1994),3603/14.
    [14]C. Quaak, L. Katgennan and W.H. Kool: Proc. 4th Conf. on Semi-solid Processing of Alloys and Composites, 1996, Sheffield, pp.35/39.
    [15]D.C-H. Cheng: Int. Journal Cosmetic Science, 9 (1987), pp.151/91.
    [16]An Introduction to Rheology: H.A. Barnes, J.F. Hutton and K Walters,Elsevier, Amsterdam, 1989.
    [17]A.M. de Figueredo, A. Kato and M.e. Flemings: Proc.6th Int. Conf.on Semi-solid Processing of Alloys and Composites, 2000, Turin,477/82.
    [18]1.y’ Chen and Z. Fan: Mater. Sci. Tech., 18 (2002), 237/42.
    [19]Z. Fan: Int. Mater. Rev., 47 (2002), No.2, 49/85.
    [20]D.H. Kirkwood and P.J. Ward: Proc. 8th Int. Conf. on Semi-solid Processing of Alloys and Composites, 2004, Cyprus. To be published.

    Full Text View
    Mixing Tank with FLOW-3D

    CFD Stirs Up Mixing 일반

    CFD (전산 유체 역학) 전문가가 필요하고 때로는 실행하는데 몇 주가 걸리는 믹싱 시뮬레이션의 시대는 오래 전입니다. 컴퓨팅 및 관련 기술의 엄청난 도약에 힘 입어 Ansys, Comsol 및 Flow Science와 같은 회사는 엔지니어의 데스크톱에 사용하기 쉬운 믹싱 시뮬레이션을 제공하고 있습니다.

    “병렬화 및 고성능 컴퓨팅의 발전과 템플릿화는 비전문 화학 엔지니어에게 정확한 CFD 시뮬레이션을 제공했습니다.”라고 펜실베이니아 주 피츠버그에있는 Ansys Inc.의 수석 제품 마케팅 관리자인 Bill Kulp는 말합니다 .

    흐름 개선을위한 실용적인 지침이 필요하십니까? 다운로드 화학 처리의 eHandbook을 지금 흐름 도전 싸우는 방법!

    예를 들어, 회사는 휴스턴에있는 Nalco Champion과 함께 프로젝트를 시작했습니다. 이 프로젝트는 시뮬레이션 전문가가 아닌 화학 엔지니어에게 Ansys Fluent 및 ACT (분석 제어 기술) 템플릿 기반 시뮬레이션 앱에 대한 액세스 권한을 부여합니다. 새로운 화학 물질을위한 프로세스를 빠르고 효율적으로 확장합니다.

    Giving Mixing Its Due

    “화학 산업은 CFD와 같은 계산 도구를 사용하여 많은 것을 얻을 수 있지만 혼합 프로세스는 단순하다고 가정하기 때문에 간과되는 경우가 있습니다. 그러나 최신 수치 기법을 사용하여 우수한 성능을 달성하는 흥미로운 방법이 많이 있습니다.”라고 Flow Science Inc. , Santa Fe, NM의 CFD 엔지니어인 Ioannis Karampelas는 말합니다 .

    이러한 많은 기술이 회사의 Flow-3D Multiphysics 모델링 소프트웨어 패키지와 전용 포스트 프로세서 시각화 도구 인 FlowSight에 포함되어 있습니다.

    “모든 상업용 CFD 패키지는 어떤 형태의 시각화 도구와 번들로 제공되지만 FlowSight는 매우 강력하고 사용하기 쉽고 이해하기 쉽게 설계되었습니다. 예를 들어, 프로세스를 재 설계하려는 엔지니어는 다양한 설계 변경의 효과를 평가하기 위해 매우 직관적인 시각화 도구가 필요합니다.”라고 그는 설명합니다.

    이 접근 방식은 실험 측정을 얻기 어려운 공정 (예 : 쉽게 측정 할 수없는 매개 변수 및 독성 물질의 존재로 인해 본질적으로 위험한 공정)을 더 잘 이해하고 최적화하는데 특히 효과적입니다.

    동일한 접근 방식은 또한 믹서 관련 장비 공급 업체가 고객 요구에 맞게 제품을보다 정확하게 개발하고 맞춤화하는 데 도움이되었습니다. “이는 불필요한 프로토 타이핑 비용이나 잠재적 인 과도한 엔지니어링을 방지합니다. 두 가지 모두 일부 공급 업체의 문제였습니다.”라고 Karampelas는 말합니다.

    CFD 기술 자체는 계속해서 발전하고 있습니다. 예를 들어, 수치 알고리즘의 관점에서 볼 때 구형 입자의 상호 작용이 열 전달을 적절하게 모델링하는 데 중요한 다양한 문제에 대해 이산 요소 모델링을 쉽게 적용 할 수있는 반면, LES 난류 모델은 난류 흐름 패턴을 정확하게 시뮬레이션하는 데 이상적입니다.

    컴퓨팅 리소스에 대한 비용과 수요에도 불구하고 Karampelas는 난류 모델의 전체 제품군을 제공 할 수있는 것이 중요하다고 생각합니다. 특히 LES는 이미 대부분의 학계와 일부 산업 (예 : 전력 공학)에서 선택하는 방법이기 때문입니다. .

    그럼에도 불구하고 CFD의 사용이 제한적이거나 비실용적 일 수있는 경우는 확실히 있습니다. 여기에는 나노 입자에서 벌크 유체 증발을 모델링하는 것과 같이 관심의 규모가 다른 규모에 따라 달라질 수있는 문제와 중요한 물리적 현상이 아직 알려지지 않았거나 제대로 이해되지 않았거나 아마도 매우 복잡한 문제 (예 : 모델링)가 포함됩니다. 음 펨바 효과”라고 Karampelas는 경고합니다.

    반면에 더욱 강력한 하드웨어와 업데이트 된 수치 알고리즘의 출현은 CFD 소프트웨어를 사용하여 과다한 설계 및 최적화 문제를 해결하기위한 최적의 접근 방식이 될 것이라고 그는 믿습니다.

    “복잡한 열교환 시스템 및 새로운 혼합 기술과 같이 점점 더 복잡한 공정을 모델링 할 수있는 능력은 가까운 장래에 가능할 수있는 일을 간단히 보여줍니다. 수치적 방법 사용의 주요 이점은 설계자가 상상력에 의해서만 제한되어 소규모 믹서에서 대규모 반응기 및 증류 컬럼에 이르기까지 다양한 화학 플랜트 공정을 최적화 할 수있는 길을 열어 준다는 것입니다. 실험적 또는 경험적 접근 방식은 항상 관련성이 있지만 CFD가 미래의 엔지니어를위한 선택 도구가 될 것이라고 확신합니다.”라고 그는 결론을 내립니다.


    Seán Ottewell은 Chemical Processing의 편집장입니다. sottewell@putman.net으로 이메일을 보낼 수 있습니다 .

    기사 원문 : https://www.chemicalprocessing.com/articles/2017/cfd-stirs-up-mixing/

    Fig. 3. Nylon 11 impact sequence onto a preheated substrate

    Impact Modeling of Thermally Sprayed Polymer Particles

    Ivosevic, M., Cairncross, R. A., Knight, R., Philadelphia / USA

    열 스프레이는 전통적으로 금속, 카바이드 및 세라믹 코팅을 증착하는 데 사용되어 왔지만 최근에는 HVOF (High Velocity Oxy-Fuel) 열 스프레이 공정의 높은 운동 에너지로 인해 용융 점도가 높은 폴리머의 무용제 처리도 가능하다는 사실이 밝혀졌습니다. , 유해한 휘발성 유기 용매가 필요하지 않습니다. 이 작업의 주된 목표는 지식 기반을 개발하고 HVOF 연소 스프레이 공정에 의해 분사되는 폴리머 입자의 충격 거동에 대한 질적 이해를 개선하는 것이 었습니다. 고분자 입자의 HVOF 분사 중 입자 가속, 가열 및 충격 변형의 수치 모델이 개발되었습니다. Volume-of-Fluid (VoF) 전산 유체 역학 패키지 인 Flow3D®는 입자가 강철 기판과 충돌하는 동안 유체 역학 및 열 전달을 모델링하는 데 사용되었습니다. 입자 가속 및 열 전달 모델을 사용하여 예측 된 방사형 온도 프로파일은 저온, 고점도 코어 및 고온, 저점도 표면을 가진 폴리머 입자를 시뮬레이션하기 위해 온도 의존 점도 모델과 함께 Flow3D®의 초기 조건으로 사용되었습니다. 이 접근법은 얇은 디스크 내에서 크고 거의 반구형 인 코어를 나타내는 변형 된 입자를 예측했으며 광학 현미경을 사용하여 만든 열 스프레이 스 플랫의 실험 관찰과 일치했습니다.

    폴리머 증착에 열 분무 공정을 사용하는 주요 이점은 다음과 같습니다. (i) 휘발성 유기 화합물 (VOCs)을 사용하지 않는 무용제 코팅; (ii) 거의 모든 환경 조건에서 큰 물체를 코팅 할 수있는 능력; (iii) 용융 점도가 높은 폴리머 코팅을 적용하는 능력; 및 (iv) 일반적으로 정전기 분말 코팅 및 용제 기반 페인트에 필요한 오븐 건조 또는 경화와 같은 증착 후 처리없이 “즉시 사용 가능한”코팅을 생산할 수있는 능력. 이러한 공정에 비해 주요 단점은 다음과 같습니다. (i) 낮은 증착 효율, (ii) 낮은 품질의 표면 마감 및 (iii) 높은 공정 복잡성 (종종 폴리머 용융 및 분해 온도에 의해 정의되는 좁은 공정 창). 폴리머 증착에 세 가지 열 스프레이 공정이 사용 된 것으로 알려졌습니다 [1].

    • 기존의 화염 분사.
    • HVOF 연소 스프레이.
    • 플라즈마 스프레이.

    HVOF 및 플라즈마 스프레이 공정에 의해 분사되는 폴리머의 수는 제한되어 있으며 HVOF 및 플라즈마 스프레이 폴리머 코팅의 상업적 응용은 아직 개발 단계에 있습니다 [1]. 폴리머의 HVOF 스프레이는 화염 스프레이 [최대 ~ 100m / s]에 비해 상당히 높은 입자 속도 [최대 1,000m / s]로 인해 주로 주목을 받았습니다. 이는 특히 고 분자량 폴리머 및 높은 (> 5 vol. %) 세라믹 강화 함량을 갖는 폴리머 / 세라믹 복합재를 포함하여 용융 점도가 높은 코팅의 증착에있어 중요한 이점입니다.

    Fig. 1. Nylon 11 splats deposited onto a room temperature glass slide.
    Fig. 1. Nylon 11 splats deposited onto a room temperature glass slide.
    Fig. 2. Nylon 11 splats deposited onto a preheated glass slide (200 °C).
    Fig. 2. Nylon 11 splats deposited onto a preheated glass slide (200 °C).
    Fig. 3. Nylon 11 impact sequence onto a preheated substrate
    Fig. 3. Nylon 11 impact sequence onto a preheated substrate, (I) partially melted particle before impact, (II) “fried-egg” shaped splat, (III) post-deposition flow of a fully molten droplet, (IV) droplet shrinkage during cooling.
    Fig. 5. Predicted velocities of Nylon 11 particles in an HVOF jet (total O2 + H2 gas flow rate of 1.86 g/s at Φ = 0.83).
    Fig. 5. Predicted velocities of Nylon 11 particles in an HVOF jet (total O2 + H2 gas flow rate of 1.86 g/s at Φ = 0.83).
    Fig. 7. Simulated deformation of a Nylon 11 droplet with a radial temperature gradient and temperaturedependent viscosity during impact.
    Fig. 7. Simulated deformation of a Nylon 11 droplet with a radial temperature gradient and temperaturedependent viscosity during impact.
    논문 원문 보기 바로가기
    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.

    Coupled CFD-Response Surface Method (RSM) Methodology for Optimizing Jettability Operating Conditions

    분사성 작동 조건을 최적화하기 위한 결합된 CFD-Response Surface Method(RSM)

    Nuno Couto 1, Valter Silva 1,2,* , João Cardoso 2, Leo M. González-Gutiérrez 3 and Antonio Souto-Iglesias 41
    INEGI-FEUP, Faculty of Engineering, Porto University, 4200-465 Porto, Portugal;
    nunodiniscouto@hotmail.com
    2 VALORIZA, Polytechnic Institute of Portalegre, 7300-110 Portalegre, Portugal; jps.cardoso@ipportalegre.pt
    3 CEHINAV, DMFPA, ETSIN, Universidad Politécnica de Madrid, 28040 Madrid, Spain; leo.gonzalez@upm.es
    4 CEHINAV, DACSON, ETSIN, Universidad Politécnica de Madrid, 28040 Madrid, Spain;
    antonio.souto@upm.es

    • Correspondence: valter.silva@ipportalegre.pt; Tel.: +351-245-301-592

    소개

    물방울 생성에 대한 이해는 여러 산업 응용 분야에서 매우 중요합니다 [ 1 ]. 잉크젯 프린팅 프로세스는 일반적으로 10 ~ 100 μm [ 1 ] 범위의 독특하고 작은 액적 크기를 특징으로 하며 연속적 또는 충동적 흐름을 사용하여 얻을 수 있습니다 (마지막 방식은 주문형 드롭 (DoD)이라고도 함). 잉크젯).

    여러 장점 덕분에 DoD 방법은 산업 환경에서 상당한 수용을 얻고 있습니다 [ 2 ].DoD는 복잡한 프로세스이며 유체 속성, 노즐 형상 및 구동 파형 [ 1 , 3 ]의 세 가지 주요 범주로 분류되는 여러 매개 변수에 따라 달라집니다 .그러나 길이와 시간 척도가 모두 마이크로 오더 [ 4 ] 이기 때문에 실험을하기가 어렵습니다 .

    결과적으로 실험 설정은 항상 비용이 많이 들고 복잡하며 CFD (전산 유체 역학)와 같은 고급 수치 접근 방식이 엄격한 요구 사항입니다 [ 5 , 6 ]. VOF (volume-of-fluid) 접근 방식은 액체 분해 및 액적 생성에 대한 다상 공정을 시뮬레이션하기위한 적절한 대안으로 밝혀졌으며 과거 연구에서 그대로 사용되었습니다 [ 7 , 8], 인쇄 프로세스의 맥락에서 전자는 여전히 현재 연구의 주제입니다. 

    또한 VOF 체계를 사용하면 단일 운동량 방정식 세트를 해결하고 도메인 전체에 걸쳐 각 유체의 체적 분율을 추적하여 명확하게 정의된 인터페이스로 둘 이상의 혼합 불가능한 유체를 효과적으로 시뮬레이션 할 수 있습니다. Feng [ 9 ]는 VOF 접근 방식을 사용하여 일시적인 유체 인터페이스 변형 및 중단을 효과적으로 추적하는 패키지 FLOW-3D를 사용하여 낙하 배출 중 복잡한 유체 역학 프로세스를 시뮬레이션하는 선구자 작업 중 하나를 수행했습니다.

    주요 목표는 볼륨 및 속도와 같은 민감한 변수를 더 잘 이해하면서 장치 개발에서 일반적인 설계 규칙을 구현하는 것이 었습니다. 이러한 종류의 공정과 관련된 주요 질문 중 하나는 안정적인 액적 형성을 위한 작동 범위의 정의입니다.

    Fromm [ 10 ]은 Reynolds 수와 Weber 수의 제곱근 비율이 2보다 작으면 안정적인 방울을 생성 할 수 없다는 것을 확인했습니다. 이 무차원 값은 나중에 Z 번호로 알려졌으며 분사 가능성 범위 [ 11 ]를 정의합니다 . 문헌에서 분사 가능성을 위한 Z 간격은 1 ~ 10 [ 12 ], 4 ~ 14 [ 13 ] 또는 0.67 ~ 50 [ 14]을 찾을 수 있습니다. 

    이것은 Z 값 만으로는 분사 가능성 조건을 나타낼 수 없음을 분명히 의미합니다. 실제로, 다른 속성을 가진 유체는 다른 인쇄 품질을 나타내면서 동일한 Z 값을 나타낼 수 있습니다. 액적 생성 공정과 해당 분사 성은 주로 전체 공정 품질에 큰 영향을 미치는 매개 변수 세트에 의해 결정됩니다. 

    토대 메커니즘을 더 잘 이해하려면 확장 된 작동 조건 및 매개 변수 세트를 고려하여 여러 실험 또는 수치 실행을 수행해야 합니다. DoE (design-of-experiment) 접근 방식과 같은 체계적인 접근 방식이 없으면 이것은 달성하기 매우 어려운 작업이 될 수 있습니다. 최적화 문제를 해결하기 위해 반응 표면 방법을 사용하여 처음으로 체계화된 접근 방식이 개발된 Box and Wilson [ 15 ] 의 선구자 기사 이후 ,이 입증된 방법론은 많은 화학 및 산업 공정[ 16 ] 및 기타 관련 학계에 성공적으로 적용되었습니다.

    예를 들어 Silva와 Rouboa [ 17 ]는 직접 메탄올 연료 전지의 출력 밀도에 영향을 미치는 관련 매개 변수를 식별하기 위해 반응 표면 방법론 (RSM)을 사용했습니다. 많은 실제 산업 응용 분야에서 실험 연구는 작동 매개 변수를 조절하기 어렵 기 때문에 제한적이지만 주로 설정을 개발하거나 실험을 실행하는 데 드는 비용이 높기 때문입니다. 

    따라서 솔루션은 주요 시스템 응답을 시뮬레이션하고 예측할 수 있는 효과적인 수학적 모델의 개발에 의존합니다. DoE와 같은 최적화 방법론을 수치 모델과 결합하면 비용이 많이 들고 시간이 많이 걸리는 실험을 피하고 다양한 입력 조합을 사용하여 최적의 조건을 얻을 수 있습니다 [ 16 ]. 

    실바와 루 보아 [ 18] CFD 프레임 워크 하에서 개발 된 2D Eulerian-Eulerian 바이오 매스 가스화 모델에서 얻은 결과를 RSM과 결합하여 다양한 응용 분야에서 합성 가스를 생성하기 위한 최적의 작동 조건을 찾습니다. 

    저자는 입력 요인으로 인한 최상의 응답과 최소한의 변동을 모두 보장하는 작동 조건을 찾을 수 있었습니다. Frawley et al. [ 19 ] CFD 및 DoE 기술 (특히 RSM)을 결합하여 파이프의 팔꿈치에서 고체 입자 침식에 대한 다양한 주요 요인의 영향을 조사하여 침식 예측 모델을 개발할 수 있습니다.우리가 아는 한, DoD 잉크젯 프로세스의 개선 및 더 나은 이해에 적용되는 DoE 접근법 (실험적으로 또는 모든 종류의 수치 모델과 결합)을 구현하는 연구는 없습니다. 선도 기업이 이러한 접근 방식을 적용 할 가능성이 있지만 관련 결과는 민감할 수 있으므로 더 넓은 커뮤니티에서 사용할 수 없습니다. 이 사실은 DoD 잉크젯 공정에서 액적 생성에 대한 여러 매개 변수의 영향을 평가하기 위한 이러한 종류의 연구로서 현재 논문의 영향을 증가 시킬 수 있습니다.

    CFD 프레임 워크 내에서 VOF 접근 방식을 사용하여 여러 컴퓨터 실험의 설계를 개발하고 RSM을 분석 도구로 사용했습니다. 충분한 수치 정확도와 수용 가능한 시간 계산 시뮬레이션의 균형을 맞추기 위해 메쉬 수렴 연구가 수행되었습니다. 설계 목적을 위해 점도, 표면 장력, 입구 속도 및 노즐 직경이 입력 요인으로 선택되었습니다. 응답은 break-up 시간과 break-up 길이였습니다.

    Figure 1. Schematic of the computational domain
    Figure 1. Schematic of the computational domain
    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.
    Figure 2. Ink fraction contours for mesh 1 through 4 (left to right) at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs.
    Figure 3. Comparison between surface tensions at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 3. Comparison between surface tensions at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 4. Comparison between viscosity values at the following four time steps: (a) 6 μs, (b) 12 μs, (c) 18 μs, and (d) 24 μs.
    Figure 4. Comparison between viscosity values at the following four time steps: (a) 6 μs, (b) 12 μs, (c) 18 μs, and (d) 24 μs.
    Figure 5. Comparison between different nozzle diameters at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 5. Comparison between different nozzle diameters at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 6. Comparison between different inlet velocities at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 6. Comparison between different inlet velocities at the following four time steps: (a) 6 µs, (b) 12 µs, (c) 18 µs, and (d) 24 µs
    Figure 8. Contour response plots for break-up time as a function of (a) surface tension and viscosity, (b) nozzle diameter and viscosity, (c) inlet velocity and viscosity, (d) nozzle diameter and surface tension, (e) inlet velocity and surface tension, and (f) inlet velocity and nozzle diameter.
    Figure 8. Contour response plots for break-up time as a function of (a) surface tension and viscosity, (b) nozzle diameter and viscosity, (c) inlet velocity and viscosity, (d) nozzle diameter and surface tension, (e) inlet velocity and surface tension, and (f) inlet velocity and nozzle diameter.
    Figure 12. Break-up length as a function of the We–Ca space (obtained from the 25 runs).
    Figure 12. Break-up length as a function of the We–Ca space (obtained from the 25 runs).
    논문 원문 바로가기

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    FIG. 2. Sequence of images showing capillary-driven neck evolution and droplet formation for low-viscosity fluids

    Computational analysis of self-similar capillary-driven thinning and pinch-off dynamics during dripping using the volume-of-fluid method

    낙하 형성 및 분리는 표면 장력 구동 흐름으로 인해 가늘어지는 유체 목의 형성을 포함하여 큰 위상 변화를 수반하며, 목의 pinch-off에서 Laplace pressure와 같은 속성은 유한한 시간 특이성을 나타냅니다. 드롭 형성 중에 발생하는 큰 위상 변형과 비선형성을 정확하게 시뮬레이션하는 것은 일반적으로 pinch-off 순간에 가까운 작은 특징을 해결하기 위해서는 고해상도 및 정확도가 필요하기 때문에 수치 시뮬레이션이 계산적으로 요구됩니다.

    필요한 질량 및 계산 시간을 보존하고 인터페이스를 추적하는 데 내재된 이점에도 불구하고, 초기 실무자들이 물 점도가 10배 이상인 유체에 대한 수렴 문제를 보고했기 때문에 낙하 형성 연구에 VOF(Volume-of-fluid) 방법을 활용하는 연구는 거의 없습니다.

    이 기여에서, 우리는 FLOW-3D에 구현된 VOF 방법을 사용하여 물 점도보다 4배 더 높은 점도 값을 포함하여 뉴턴 유체에 대한 드리프트의 원형 자유 표면 흐름을 시뮬레이션합니다. 우리는 이 연구의 일부로 수행된 실험에 대해 시뮬레이션된 목 모양, 목 진화 속도 및 헤어짐 길이를 벤치마킹합니다.

    핀치오프 역학은 관성, 점성 및 모세관 응력의 복잡한 상호 작용에 의해 결정되며, 여기서 실험과 시뮬레이션 모두에서 대조되는 자기 유사 스케일링 법칙은 종종 역학에 대해 설명합니다. 우리는 시뮬레이션된 반지름 진화 프로파일이 축 대칭 흐름에 대한 뉴턴 유체에 대해 실험적으로 관찰되고 이론적으로 예측되는 핀치오프 역학과 일치함을 보여준다. 또한, 우리는 가는 목 안에서 법칙, 속도 및 변형 필드의 스케일링에 대한 사전 요인을 결정하고, 우리는 실험과 비교할 수 있는 중단 시간과 길이뿐만 아니라 사전 요인을 VOF 방법을 사용하여 시뮬레이션할 수 있음을 보여줍니다.

    experimental setup, as shown schematically in Fig. 1(a), includes a dispensing system
    experimental setup, as shown schematically in Fig. 1(a), includes a dispensing system
    A numerical simulation of drop formation from a cylindrical nozzle at a constant flow rate is performed. (c) Graphical representation of the VOF approach
    A numerical simulation of drop formation from a cylindrical nozzle at a constant flow rate is performed. (c) Graphical representation of the VOF approach
    FIG. 2. Sequence of images showing capillary-driven neck evolution and droplet formation for low-viscosity fluids
    FIG. 2. Sequence of images showing capillary-driven neck evolution and droplet formation for low-viscosity fluids. (a) A sequence of simulated images of water (0 wt. % glycerol) shows neck formation and subsequent thinning and pinch-off dynamics including the formation of the satellite drop. (b) A sequence of images shows neck radius evolution and drop detachment for the low viscosity fluid composed of 50 wt. % glycerol in water. The time step between images is 500 µs, and the scale bar represents a length of 1 mm for the two cases shown. The color bar shows the velocity field in units of cm/s. The addition of glycerol seems to exercise a relatively minor influence on pinch-off dynamics despite a five-fold increase in viscosity.
    FIG. 3. Computed evolution of the minimum radius of the water neck during the drop formation and detachment process
    FIG. 3. Computed evolution of the minimum radius of the water neck during the drop formation and detachment process. The instantaneous neck radius of water and the inertio-capillary fit are shown. The inset shows a self-similar nature of neck thinning dynamics close to a pinch-off moment. The characteristic cone angle of 18.1◦ as predicted by Day et al.50 and visualized in experiments52 is captured well using the VOF method.
    FIG. 5. Glycerol thinning image sequence and break-up length visualization for three cases
    FIG. 5. Glycerol thinning image sequence and break-up length visualization for three cases. (a) Glycerol thinning is shown through a sequence of snapshots with a time step ∆t = 5 ms and reveals quite different dynamics compared to previously seen for low viscosity fluids. The length of a filament changes significantly when the glycerol content increases above 70 wt. %. (b) Final lengths of the simulated liquid filaments before pinch-off for three cases of glycerol + water mixtures (0 wt. %, 70 wt. %, and 100 wt. %).
    FIG. 8. Comparison of experiments and simulations for the case of a drop formation for 80 wt. % glycerol and water mixture
    FIG. 8. Comparison of experiments and simulations for the case of a drop formation for 80 wt. % glycerol and water mixture. (a) A set of images obtained from experiments (upper row) and simulations (bottom row) with a time step of 1 ms show good agreement. The simulated drop profiles shown in the bottom row are colored by the velocity magnitude [ranging from 0 (dark blue) to 100 cm/s (red) and colored online], and velocity vectors are shown in the images. (b) Radius evolution with time of liquid filament formed during the drop formation process is shown on a log-log plot for the two cases.
    논문 원문 링크

    FLOW-3D 튜토리얼 V12

    FLOW-3D 튜토리얼 V12

    빠른 시작

    이 튜토리얼 매뉴얼은 FLOW-3D 를 처음 사용하는 사용자에게 그래픽 사용자 인터페이스(GUI)의 주요 구성 요소를 쉽게 익히도록 하고, 다양한 시뮬레이션의 설정 및 실행 방법을 안내하기 위한 것입니다.

    이 매뉴얼에 있는 실습과정은 FLOW-3D의 기본 사항을 다루기 위한 것입니다. 이 매뉴얼에서 제시하는 문제는 다양한 주제를 설명하고, 발생할 수 있는 많은 질문을 해결하기 위해 선정되었습니다. 이 매뉴얼의 실습과정은 FLOW-3D를 실행하는 컴퓨터에 앉아 사용하는 것이 가장 좋습니다.

    CFD 사용 철학에 대한 간단한 섹션 다음에는 중요 파일과 시뮬레이션 파일을 실행하는 방법이 소개되어 있습니다. 이 소개 섹션 다음에는 모델 설정, 시뮬레이션 실행 및 포스트 프로세스, Simulation Manager 탐색 방법에 대한 설명이 있습니다. 이러한 각 단계에 대한 자세한 내용은 모델 설정, 컴퓨팅 결과 및 후처리 장에서 확인할 수 있습니다.

    1.CFD 사용에 대한 철학

    CFD (Computational Fluid Dynamics)는 유체 흐름(질량, 운동량 및 에너지 보존)에 대한 지배 방정식의 컴퓨터 솔루션입니다. 지정된 지배방정식은 이론 장에 설명된 Numerical방법을 사용하여 이산화되고 계산됩니다.

    CFD 소프트웨어를 사용하는 것은 여러 면에서 실험을 설정하는 것과 유사합니다. 실제 상황을 시뮬레이션하기 위해 실험을 올바르게 설정하지 않으면, 그 결과는 실제 상황을 반영하지 않습니다. 같은 방법으로 수치 모델이 실제 상황을 정확하게 나타내지 않으면, 그 결과는 실제 상황을 반영하지 않습니다. 사용자는 어떤 것이 중요한지, 어떻게 표현해야 하는지를 결정해야 합니다. 시작하기 전에 다음과 같은 질문을 하는 것이 중요합니다.

    • CFD 계산에서 무엇을 알고 싶습니까?
    • 중요한 현상을 포착하기 위해 규모와 Mesh는 어떻게 설계되어야 하는가?
    • 실제 물리적 상황을 가장 잘 나타내는 경계 조건은 무엇입니까?
    • 어떤 종류의 유체를 사용해야합니까?
    • 이 문제에 어떤 유체 특성이 중요합니까?
    • 다른 어떤 물리적 현상이 중요합니까?
    • 초기 유체 상태는 어떻게 됩니까?
    • 어떤 단위 시스템을 사용해야합니까?

    모델링 되는 문제가 실제 상황을 가능한 한 유사하게 나타내는지 확인하는 것이 중요합니다. 사용자는 복잡한 시뮬레이션 작업을 해결 가능한 부분으로 나누는 것이 좋습니다.

    복잡한 물리 효과를 추가하기 전에, 간단하고 쉽게 이해할 수 있는 근사값으로 점차적으로 시작하여 프로세스 진행하십시오. 간단한 손 계산(베르누이 방정식, 에너지 균형, 파동
    전파, 경계층 성장 등)은 물리 및 매개 변수를 선택하는데 도움이 되고, 결과와 비교할 수 있는 점검항목을 제공합니다.

    CFD의 장단점을 이해하면 분석을 진행하는데 도움이 될 수 있습니다. CFD는 다음과 같은 경우 탁월한 분석 옵션입니다.

    • 기하 구조, 물리학 또는 필요한 상세 수준으로 인해 표준 엔지니어링 계산이 유용하지 않은 경우가 많습니다.
    • 실제 실험은 비용이 많이 소요됩니다.
    • 실험에서 수집할 수 있는 것보다 유체흐름에 대한 자세한 정보가 필요한 경우 유용합니다.
    • 위험하거나 적대적인 조건, 확장이 잘되지 않는 프로세스 등으로 인해 정확한 실험 측정을 하기가 어려운 경우
    • 복잡한 흐름 정보에 대한 커뮤니케이션

    CFD는 다음과 같은 경우에 덜 효과적입니다.

    • 솔루션이 계산 리소스가 매우 많이 소요되거나, 도메인 크기를 줄이기 위한 가정 또는 해결되지 않은 물리적 현상을 설명하기 위한 반 임계 모델이 필요한 경우
    • CFD 시뮬레이션에 대한 입력이 되는 중요한 물리적 현상이 알려지지 않은 경우
    • 물리적 현상이 잘 이해되지 않거나 매우 복잡한 경우

    CFD를 사용할 때 명심해야 할 몇 가지 중요한 참고 사항이 있습니다.

    • CFD는 규정된 초기 및 경계 조건에 따라 지정된 지배 방정식의 수치해석 솔루션입니다. 따라서 모델 설정, 즉 어떤 방정식을 풀어야 하는지, 재료 특성, 초기 조건 및 경계 조건이, 가능한 한 물리적 상황과 최대한 일치해야 합니다.
    • 방정식의 수치 해는 일반적으로 어떤 종류의 근사치를 필요로 합니다. 물리적 모델에 대한 가정과 해결방법을 검토한 후 사용하는 것이 좋습니다.
    • 디지털 컴퓨터는 숫자가 유한 정밀도로 이진수로 표시되는 방식으로 인해 반올림 오류가 발생합니다. 이는 문제를 악화시키기 때문에 매우 근소한 숫자의 차이를 계산해야 하는 상황을 피하십시오. 이러한 상황의 예는 시뮬레이션 도메인이 원점에서 멀리 떨어져 있을 때입니다.

     

    2.중요한 파일

    FLOW-3D 시뮬레이션과 관련된 많은 파일이 있습니다. 가장 중요한 것들이 아래에 설명되어 있습니다. 모든 prepin.* 파일의 명칭에서 prepin는 파일 형식을 의미하며, 별표시* 위치는 시뮬레이션 이름을 의미합니다. (예 : prepin.example_simulation.)

    • ·prepin.*: 시뮬레이션용 입력 파일입니다. 시뮬레이션 설정을 설명하는 모든 입력 변수가 포함되어 있습니다.
    • ·prpgrf.*: 이것은 전 처리기 출력 파일입니다. 여기에는 계산된 초기 조건이 포함되며 시뮬레이션을 실행하기 전에 설정을 확인하는 데 사용될 수 있습니다.
    • ·flsgrf.*: 솔버 출력 파일입니다. 시뮬레이션의 최종 결과가 포함됩니다.
    • ·prperr.*, report.*, prpout.*: 이 파일들은 Preprocessor Diagnostic Files.
    • ·hd3err.*, hd3msg.*, hd3out.*: 이 파일들은 Solver Diagnostic Files.

    모든 시뮬레이션 파일은 단일 폴더에 함께 유지하므로, 설명이 될 수 있는 시뮬레이션 이름을 사용하는 것이 좋습니다. 그러나 매우 긴 파일 이름은 운영 체제에 따라 문제가 될 수 있습니다.

    노트

    • 시뮬레이션 이름이 inp(즉, 입력 파일이 있다면 prepin.inp) 출력 및 진단 파일은 모두 .dat이름을 갖습니다. 예: flsgrf.dat.
    • 모든 입력 파일은 네트워크 위치의 컴퓨터 대신 로컬 디렉토리에 저장하는 것이 좋습니다. 이것은 솔버가 더 빠르게 실행되고 GUI의 응답 속도가 빨라지며 실행중인 시뮬레이션을 방해하는 네트워크 문제 가능성을 제거합니다.

    3.시뮬레이션 관리자

    FLOW-3D 시뮬레이션 관리자의 탭은 주로 시뮬레이션을 실행할 수 있도록 시뮬레이션 환경을 구성하고 실행 시뮬레이션에 대한 상태 정보를 표시하는데 사용됩니다.

    작업 공간 (Workspaces)

    작업 공간(Workspaces)은 Simulation Manager의 필수 부분이며 파일을 FLOW-3D에서 처리하는 방식입니다. 기본적으로 시뮬레이션을 포함하고 구성하는 폴더입니다. 몇 가지 예를 들면 시뮬레이션과 또 다른 작업 공간인 검증 사례를 포함하도록 할 수 있습니다:

    포트폴리오의 작업 공간

    새로운 작업 공간 만들기

    이 튜토리얼에서는 작성하려는 시뮬레이션을 포함할 작업 공간(Workspaces)을 작성하십시오.

    1.File -> New workspace로 이동

    2.작업 공간 이름으로 Tutorial를 입력하십시오.

    3.기본 위치는 현재 사용자의 홈 디렉토리에 있습니다. 다른 곳에서 찾을 수 있지만 기본 위치가 우리의 목적에 적합합니다.

    4.하위 디렉토리를 사용하여 작업 공간 이름 만들기 확인란을 선택합니다. 이렇게 하면 파일 시스템에서 작업 공간에 대한 새로운 하위 디렉토리가 만들어져 시뮬레이션 파일을 훨씬 쉽게 구성할 수 있습니다.

    새로운 작업 공간 만들기

    5.확인을 눌러 새 작업 공간을 작성하십시오. 이제 포트폴리오에 표시됩니다.

    새로운 작업 공간 만들기

    작업 공간 닫기

    포트폴리오를 정리하고 탐색하기 쉽도록 필요 없는 작업공간을 닫는 것이 편리합니다. 작업 공간을 닫으면 포트폴리오에서 해당 작업 공간만 제거됩니다. 그러나, 컴퓨터에서 작업 공간을 삭제하지는 않습니다.

    작업 공간을 닫으려면

    1.기존 작업 공간을 마우스 오른쪽 버튼으로 클릭하고 작업 Close Workspace를 선택하십시오. 또는 포트폴리오에서 작업 공간을 선택 (왼쪽 클릭) 하고 Delete 키를 누를 수 있습니다.

    2.작업 공간을 닫을 것인지 묻는 메세지가 표시됩니다. 예를 선택하십시오.

    3.포트폴리오는 더 이상 닫힌 작업 공간을 포함하지 않습니다.

    기존 작업 공간 열기

    오래된 작업 공간을 열어야 할 때가 있을 것입니다. 예를 들어, 새 프로젝트에 유사한 시뮬레이션을 작성하기 전에 기존 시뮬레이션의 설정을 검토할 수 있습니다. 기존 작업 공간을 열려면

    1.File -> Open Workspace…를 선택하십시오

    2.작업 공간 파일이 있는 디렉토리를 찾으십시오. Tutorial.FLOW-3D_Workspace.

    작업 공간 열기

    3.작업 공간을 로드 하려면 OK을 누르십시오.

    작업 공간에서 시뮬레이션 작업

    작업 공간을 사용하는 방법을 알았으니, 여기에 시뮬레이션을 추가해 봅시다.

    Example를 추가하십시오

    작업 공간에 작업 시뮬레이션을 추가하는 가장 간단한 방법은 포함된 예제 시뮬레이션 중 하나를 추가하는 것입니다. FLOW-3D의 다양한 기능을 사용하는
    방법을 보여주기 위해 설계된 간단하고 빠른 시뮬레이션입니다. 기존 작업 공간에 예제를 추가하려면 다음을 수행하십시오.

    1.포트폴리오에서 원하는 작업 공간을 강조 표시하십시오

    2.File -> Add example…을 선택하십시오. 또는 작업공간을 마우스 오른쪽 버튼으로 클릭하고 예제 추가…를 선택할 수 있습니다.

    3.예제 대화 상자에서 예제를 선택하고 열기를 누르십시오. 자연 대류(Natural Convection) 예제를 선택했습니다.

    시뮬레이션 예제 추가

    4.새 시뮬레이션 대화 상자가 열립니다.

    5.디렉토리가 작업 공간 위치에 있는지 확인하는 것이 좋으므로 기본 시뮬레이션 이름과 위치를 잘 확인하는 것이 좋습니다. FLOW-3D는 모든 시뮬레이션 파일을 이 작업 공간 디렉토리의 별도 하위 디렉토리에 배치하여 파일 구성을 쉽게 만들어 줍니다.

    6.시뮬레이션을 위한 단위 시스템을 선택하십시오. 표준 단위 시스템이 권장되지만 각 단위를 독립적으로 선택하기 위해 사용자 지정 단위 시스템을 선택할 수 있습니다.

    7.확인을 눌러 새 시뮬레이션을 작업 공간에 추가하십시오.

    작업 공간에서의 시뮬레이션

    작업 공간에서 시뮬레이션 제거

    작업 공간에서 시뮬레이션을 제거해야 하는 경우가 있습니다 (이는 작업 공간에서 시뮬레이션을 제거만 하며, 컴퓨터에서 시뮬레이션을 삭제하지는 않습니다). 작업 공간에서 시뮬레이션을 제거하려면 다음을 수행하십시오.

    1.작업 공간에서 기존 시뮬레이션을 마우스 오른쪽 버튼으로 클릭하고 (이 경우 이전 섹션에서 추가 한 예제 사용) 시뮬레이션 제거를 선택하십시오. 또는 작업 공간에서 시뮬레이션을 선택 (왼쪽 클릭)하고 Delete 키를 누를 수 있습니다.

    2.작업 공간에는 더 이상 시뮬레이션이 포함되지 않습니다.

    모든 작업 공간 및 디스크에서 시뮬레이션 삭제

    작업 공간에서 시뮬레이션을 제거하는 것 외에도 디스크에서 모든 시뮬레이션 파일을 삭제해야 할 수도 있습니다. 작업 공간에서 시뮬레이션을 제거하고 디스크에서 시뮬레이션
    파일을 삭제하려면 다음을 수행하십시오.

    1.작업 공간에서 기존 시뮬레이션을 마우스 오른쪽 단추로 클릭하고 (이 경우 이전 섹션에서 추가 한 예제 사용) 모든 작업 공간 및 디스크에서 시뮬레이션
    삭제를     선택하십시오.

    2.시뮬레이션 디렉토리에서 삭제할 파일을 선택할 수 있는 창이 나타납니다. 삭제할 파일을 선택한 다음 확인을 눌러 해당 파일을 삭제하거나 취소를 눌러 작업을 중단하십시오.

    3.OK를 선택한 경우 선택한 작업 공간은 더 이상 시뮬레이션을 포함하지 않습니다. 선택한 작업 공간의 모든 시뮬레이션 파일은 디렉토리에서 삭제됩니다.

    경고

    이 작업은 취소할 수 없으므로 계속하기 확인 후 파일을 삭제해야 합니다.

    작업 공간에 기존 시뮬레이션 추가

    기존 시뮬레이션을 작업 공간에 추가하려면 다음을 수행하십시오.

    1.열린 작업 공간을 마우스 오른쪽 버튼으로 클릭하고 기존 시뮬레이션 추가…를 선택합니다. 작업 공간을 선택한 다음 File->Add Existing Simulation… 을 선택할 수도 있습니다.

    2.prepin.*파일 위치로 이동하여 열기를 선택하십시오.

    작업 공간에 기존 시뮬레이션 추가

    3.시뮬레이션이 이제 작업 공간에 나타납니다.

    작업 공간에 새로운 시뮬레이션 추가

    대부분의 경우 기존 시뮬레이션을 사용하는 대신 새 시뮬레이션을 작성하게 됩니다. 작업 공간에 새로운 시뮬레이션을 추가하려면:

    1.기존 작업 공간을 마우스 오른쪽 버튼으로 클릭하고 새 시뮬레이션 추가…를 선택하십시오.

    2.시뮬레이션 이름을 입력하라는 message가 표시됩니다. 이 예제에서는 heat transfer example 불러오십시오.

    3.그런 다음 드롭다운 목록을 사용하여 시뮬레이션을 위한 단위 시스템을 결정합니다. 사용 가능한 옵션은 질량, 길이, 시간, 전기요금
    각각 g, cm, s, coul기준의 Kg, m, s, CGS입니다. 또한 엔지니어링 단위도 사용할 수 있으며, slug, ft, s의 기초 단위가 있지만, 전기
    충전을 위한 단위는 없습니다. 이러한 옵션 중 어느 것도 해당되지 않는 경우, 질량, 길이, 시간 및 전기요금에 대한 기준 등을 사용자 정의하여 사용자 지정 단위 시스템을 사용할 수 있습니다.

    4.온도 단위는 드롭다운 목록을 사용하여 지정해야 합니다. 사용 가능한 옵션은 SI 및 CGS 단위의 경우 Celsius 및
    Kelvin, 엔지니어링 단위의 경우 Fahrenheit 및 Rankine입니다. Custom units(사용자 정의 단위) 옵션을 선택한 경우, 사용 가능한 온도 단위는 질량
    및 길이에 대해 선택한 기본 단위에 따라 변경됩니다.

    노트

    새 시뮬레이션의 시뮬레이션 단위는 신중하게 선택하십시오. 일단 설정하면 단위를 변경할 수 없습니다.

    5.이 시뮬레이션에 사용된 템플릿이 기본 템플릿이 됩니다. 템플릿은 포함된 설정을 새 시뮬레이션에 적용하는 저장된 값 세트입니다. 다른 템플릿을 사용해야하는 경우
    찾아보기 아이콘 (     browse_icon_v12)을 클릭하여 사용 가능한 템플릿 목록에서 선택하십시오.

    6.기본 시뮬레이션 이름과 위치는 디렉토리가 작업 공간 위치에 있는지 확인하는 것이 좋습니다. FLOW-3D는 모든 시뮬레이션 파일을 이 작업 공간 디렉토리의 별도 하위 디렉토리에 배치하여 파일 구성을 훨씬 쉽게 만듭니다. 시뮬레이션을 다른 위치에 저장하려면 찾아보기 아이콘 ( browse_icon_v12)을 사용하여 원하는 위치로 이동하십시오.

    7.확인을 클릭하여 작업 공간에 새 시뮬레이션을 추가하십시오.

    heat transfer example

    새로운 시뮬레이션 추가

    다른 옵션

    우리는 지금 이러한 옵션을 사용하지 않는 동안, 이 시뮬레이션을 마우스 오른쪽 버튼으로 클릭하여 추가 옵션에 대한 액세스를 제공합니다.

    일반적으로 사용되는 Add Simulation Copy… 그리고 Add Restart Simulation…을 추가합니다. 첫 번째 옵션은 기존 시뮬레이션의 사본을
    작성하고, 두 번째 옵션은 기존 시뮬레이션을 복사하고 원래 시뮬레이션의 결과를 다시 시작 시뮬레이션의 초기 조건으로 사용하도록 다시 시작 옵션을 구성합니다.

    추가 정보

    재시작 시뮬레이션에 대한 자세한 내용은 도움말에서 모델 설정 장의 재시작 섹션을 참조하십시오.

    전처리 및 시뮬레이션 실행

    시뮬레이션 전처리

    시뮬레이션 전처리는 초기 조건을 계산하고 입력 파일에서 일부 진단 테스트를 실행합니다. 문제가 올바르게 구성되었는지 확인하거나 전 처리기의 진단 정보가 필요한 경우에
    유용합니다. 시뮬레이션을 실행하기 전에 전처리할 필요가 없습니다. 시뮬레이션을 전처리 하려면

    1.작업 공간에서 시뮬레이션을 마우스 오른쪽 버튼으로 클릭하고 Preprocess Simulation->Local을 선택합니다. 이 경우 입력 파일 heat transfer example이 아직 완전히 정의되지 않았으므로 작업 공간에서 예제 문제를 선택하십시오.

    2.전처리 프로세스가 시작되고 Simulation Manager 하단의 텍스트 창에 일부 정보가 인쇄된 후 성공적으로 완료됩니다. 포트폴리오에서 시뮬레이션 이름 옆의 아이콘도 시뮬레이션이 성공적으로 처리되었음을 나타내도록 변경됩니다.

    추가 정보

    자세한 내용은 도움말의 컴퓨팅 결과 장의 전처리 섹션을 참조하십시오.

    시뮬레이션 실행

    시뮬레이션을 실행하면 입력 파일에 정의된 문제에 대한 지배 방정식(물리적 모델, 형상, 초기 조건, 경계 조건 등)이 해석됩니다. 시뮬레이션을 실행하려면

    1.작업 공간에서 시뮬레이션을 마우스 오른쪽 버튼으로 클릭하고 Run Simulation->Local을 선택하십시오. 이 경우 입력 파일 heat transfer example이 아직 완전히
    정의되지 않았으므로 작업 공간에서 예제 문제를 선택하십시오.

    2.솔버가 시작되고 시뮬레이션 관리자 하단의 텍스트 창에 일부 정보가 인쇄되고 플롯이 업데이트 된 후 성공적으로 완료됩니다. 포트폴리오에서 시뮬레이션 이름 옆의
    아이콘도 시뮬레이션이 성공적으로 실행되었음을 나타내도록 변경됩니다. 또한 솔버가 실행되는 동안 큐에 시뮬레이션이 나타나는 것을 볼 수 있으며, 완료되면 사라집니다    .

    추가 정보

    시뮬레이션 실행 및 진단 읽기에 대한 자세한 내용은 도움말의 컴퓨팅 결과 장에서 솔버 실행 섹션을 참조하십시오.

    작업 공간에서 모든 시뮬레이션 실행

    작업 공간을 마우스 오른쪽 버튼으로 클릭하고 Simulate Workspace->Local을 선택하여 작업 공간에서 모든 시뮬레이션을 실행할 수도 있습니다.

    추가 정보

    자세한 내용은 컴퓨팅 결과 장에서 솔버 실행 섹션을 참조하십시오.

    대기열

    사전 처리 또는 실행에 작업이 제출되면 큐의 맨 아래에 시뮬레이션이 자동으로 추가됩니다. 그런 다음 솔버에 사용 가능한 라이센스 및 계산 리소스가 있으면 시뮬레이션이 사전 처리되거나 실행됩니다. 대기열에 있지만 아직 전처리 또는 실행되지 않은 시뮬레이션은 대기열 맨 아래의 컨트롤을 사용하여 대기열에서 다시 정렬하거나 대기열에서 제거할 수 있습니다.

    추가 정보

    자세한 내용은 컴퓨팅 결과 장을 참조하십시오.

    파일 시스템에서 파일 찾기

    어떤 이유로 구조물 파일에 액세스해야 하는 경우 (아마 *.STL 폴더에 파일을 배치해야 함) 표시된 파일 경로를 시뮬레이션 입력 파일로 클릭하여 파일 시스템의 해당 위치로 이동할 수 있습니다.

    파일 링크

    4.모델 설정

    Model Setup(모델 설정) 탭은 시뮬레이션 관리자에서 현재 선택한 시뮬레이션에 대한 입력 매개 변수를 정의하는 곳입니다. 여기에는 전역설정, 물리학 모델, 유체,
    기하학, 메싱, 구성요소 특성, 초기 조건, 경계 조건, 출력 옵션 및 숫자가 포함된다.

    이 섹션은 물에 잠긴 모래(위; 파랑)의 바닥에서 가열된 구리 블록(위; 빨간색)에 의해 발생하는 열 기둥(아래)을 보여주는 간단한 시뮬레이션 설정 방법을 안내합니다.

    예제 문제

    이 튜토리얼은 방법이나 모델이 어떻게 작동하는지, 옵션을 선택한 이유 등에 대한 포괄적인 논의를 의도한 것이 아니며, 이 특정 시뮬레이션을 설정하기 위해 수행해야 할 사항에
    대한 간략한 개요일 뿐입니다. 여기서 행해지는 것에 대한 방법/모델과 추론의 세부사항은 사용 설명서의 다른 장에서 확인할 수 있습니다.

    시작하려면 새 작업 공간을 작성하고 새 시뮬레이션을 추가하십시오. 이를 수행하는 방법에 대한 지침은 새 작업 공간 작성 및 작업 공간에 새 시뮬레이션 추가를 참조하십시오.

    탐색

    모델 설정은 주로 빨간색으로 표시된 처음 9 개의 아이콘의 탐색을 통해 수행됩니다. 각 아이콘은 시뮬레이션의 특정 측면을 구성하기 위한 위젯을 엽니다. Global에서 시작하여 Numerics로 끝나는 다음 섹션은 각 위젯의 목적을 보여줍니다.

    시뮬레이션의 다양한 측면을 정의하기위한 탐색 아이콘

    통제 수단

    다음은 FLOW-3D 사용자 인터페이스의 그래픽 디스플레이 영역에서 사용되는 마우스 컨트롤입니다.

    행동

    버튼/키

    동작

    기술

    회전

    왼쪽

    길게 클릭

    마우스 왼쪽 버튼을 클릭 한 채로 Meshing & Geometry 창에서
    마우스를 움직입니다. 그에 따라 모델이 회전합니다.

    줌

    중간 버튼/스크롤
    휠

    스크롤/클릭 한
    상태

    마우스를 앞뒤로 움직여 확대/축소하려면 가운데 휠을 굴리거나 마우스 가운데 버튼을 클릭
    한 상태로 유지하십시오.

    팬

    우측

    길게 클릭

    마우스 오른쪽 버튼을 클릭 한 채로 창에서 마우스를 움직입니다. 모델이 마우스와 함께 움직입니다.

    객체에 초점 설정

    해당 없음

    객체 위에 커서를 놓기

    커서를 개체 위로 가져 가면 마우스 오른쪽 버튼 클릭 메뉴를
    통해 추가 조작을 위해 개체가 활성화됩니다. 개체가 활성화되면 강조 표시됩니다. Meshing & Geometry 탭에서 Tools->    Mouse Hover
    Selection     환경 설정 이 활성화된 경우에만
    수행됩니다.

    선택

    왼쪽

    더블 클릭

    객체를 두 번 클릭하면 마우스 오른쪽 버튼 메뉴를 통해 추가
    조작을 위해 객체를 선택하고 활성화합니다. Meshing
    & Geometry         탭에서 Tools    ->Mouse Hover Selection 환경 설정 이
    비활성화 된 경우에만 활성화됩니다.

    액세스 객체 속성

    우측

    딸깍 하는 소리

    강조 표시된 객체를 마우스 오른쪽 버튼으로 클릭하면 객체
    식별, 표시/숨기기, 활성화/비활성화, 투명도 조정 등의 옵션 목록이 표시됩니다.

    커서 좌표 반환 (프로브)

    왼쪽

    Shift + 클릭

    Shift 키를 누르면 커서가 대상으로 바뀝니다. Shift 키를 누른 상태에서 클릭하면 화면의 왼쪽 하단에 표시된 표면의 좌표가 표시됩니다.

    피벗 점 배치

    왼쪽

    cntrl + 클릭

    Ctrl 키를 누르고 있으면 커서가 피벗 아이콘으로 바뀝니다. Ctrl 키를 누른 상태에서 클릭하여 피벗 점을 설정하십시오. 뷰가
    피벗 점을 중심으로 회전합니다. 토글 사용자 정의 피벗 피벗 점을 끕니다.
    보기 창 위의 버튼을 누릅니다.

    도움이
    되는 툴바 옵션도 있습니다. 옵션의 목적을 찾으려면 아이콘 위로 마우스를 가져갑니다.

    메시 및 지오메트리 탭의 컨트롤

    글로벌

    이 매뉴얼에 대한 시뮬레이션을 만들려면 원하는 작업 공간을 마우스 오른쪽 단추로 클릭하고 새 시뮬레이션 추가…를 선택하십시오. 매뉴얼 섹션의 새 시뮬레이션 추가 작업 공간에 설명된 대로 이름을 ‘heat transfer example’로 지정하고 작업 공간에 추가하십시오. SI와 Kelvin을 각각 단위 시스템과 온도로 선택합니다. 일단 설정되면
    시뮬레이션을 위한 단위는 변경할 수 없다는 점을 기억하십시오.

    글로벌 아이콘 f3d_global_icon을 클릭하여 글로벌 위젯을 여십시오. 여기에서 정의된 단위가 표시되고 시뮬레이션 완료 시간이 설정됩니다. 이 시뮬레이션의 경우 완료 시간을 200 초로 설정하십시오. 시뮬레이션에 대한 중요한 세부 정보는 여기 노트 필드에도 추가할 수 있습니다.

    글로벌 탭 예를 들어 문제

    추가 정보

    자세한 내용은 모델 설정 장의 전역 섹션을 참조하십시오.

    물리

    물리 f3d_models_icon아이콘을 클릭하여 물리 위젯을 엽니다.

    모델 선택을위한 물리 위젯

    이 문제의 경우, 하나의 유체, 자유 표면, 경계 및 비압축/제한 압축의 기본 설정이 모두 정확합니다.

    관련 물리 메커니즘(즉, 추가 지배 방정식 또는 지배 방정식 용어)은 물리 위젯에서 정의됩니다. 모델을 활성화하려면 해당 모델의 아이콘을 마우스 왼쪽 버튼으로 클릭하고 ‘활성화‘를 선택하십시오. 이 시뮬레이션을 위해서는 다음 모델을 활성화해야 합니다.

    ·Density evaluation(밀도 평가): 이 모델은 열 기둥을 생성하는 밀도 변화를 설명합니다. 다른 양(예: 온도 또는 스칼라)의 함수로 평가된 밀도를 선택하고 Include volumetric thermal expansion 상자를 선택하십시오.

    문제 평가를위한 밀도 평가 모델

    ·Gravity and non-inertial reference frame(중력 및 비 관성 기준 프레임): 중력을 나타내는 힘이 추가되므로 Z 중력 성분에 -9.81을 입력하십시오.

    예를 들어 중력 모델

    ·
    Heat transfer(열 전달): 이 모델은 유체와 고체 물체 사이의 열 전달을 설명합니다. 이 시뮬레이션의 경우 First order for the Fluid internal Energy advection를 선택하고 Fluid to solid heat transfer를 활성화하려면 확인란을 선택하십시오. 나머지 옵션은 기본값으로 두어야합니다.

    열전달 모델 예 : 문제

    ·
    Viscosity and turbulence(점성 및 난류): 이 모델은 유체의 점성 응력을 설명합니다. Viscous flow 옵션을 선택하고 나머지 옵션은 기본값으로 두십시오.

    예를 들어 문제의 점도 모델

    추가 정보

    자세한 내용은 모델 설정 장의 물리 섹션을 참조하십시오.

    유체

    유체의 속성은 모델 설정 탭의 유체 위젯에 정의되어 있습니다. 유체 위젯은 수직 도구 모음에서 Fluids f3d_fluids_icon f3d_fluids_icon아이콘을 클릭하여 액세스할 수 있습니다. 먼저 유체 옵션 1 이 속성 옵션으로 선택되어 있는지 확인하십시오. 유체 1의 속성은 수동으로 입력할 수 있지만 일반적인 유체의 속성을 설정하는 빠른 방법은 재료 속성로드 버튼Matdatbas을 클릭하여 재료 데이터베이스에서 유체를 로드하는 것입니다. 다음으로, 원하는 재료를 탐색하십시오. 이 경우 Fluids->Liquids->Water_at_20_C를 선택하고 Load를 클릭하십시오.

    이 시뮬레이션에는 데이터베이스에 없는 특성인 체적 열 팽창 계수가 필요합니다. 밀도 하위 탭에서 207e-6을 입력하십시오. 최종 속성 세트는 다음과 같아야 합니다.

    유체 특성 (예 : 문제)

    추가 정보

    자세한 내용은 모델 설정 장의 유체 섹션을 참조하십시오.

    Geometry(기하)

    기하형상 f3d_geometry_icon아이콘을 클릭하여 물리 위젯을 엽니다.

    이 시뮬레이션을 위해 생성해야 하는 두 가지 형상은 구리 블록과 모래층이 있습니다. 둘 다 프리미티브를 사용하여 작성합니다. 보다 현실적인 시뮬레이션은 Primitives, Stereolithography(STL) Geometry File (s)/또는 Raster File (s)을 사용하여 지오메트리를 정의할 수 있습니다.

    구리 블록을 만들려면 먼저 지정된 상자 형상 아이콘을 클릭하여 작성합니다. 구리 블록을 x 및 y 방향 원점에서 +/- 2cm 연장하고 z 방향으로 0-4cm 연장합니다. 나머지 옵션은 그대로 두고 블럭을 솔리드로 만들고 새 구성 요소에 추가합니다.

    예제 문제에 대한 구리 블록 정의

    하위 구성 요소 정의를 마치고 구성 요소 정의로 이동하려면 확인을 선택하십시오. 자동으로 열린 구성요소 추가 대화상자에서 Type as General(솔리드)을 그대로 두고 Name(이름) 필드에 Copper block을 입력한 다음 OK(확인)를 선택하여 구성요소 정의를 완료하십시오.

    상자아이콘을 다시 클릭하여 베드 하위 구성 요소를 작성하십시오. 아래 표시된 범위를 사용하고 컴포넌트에 추가 선택 사항을 새 컴포넌트(2)로 설정하십시오.

    예를 들어 침대 문제 정의

    하위 구성 요소 정의를 마치고 구성 요소 정의로 이동하려면 확인을 선택하십시오. 대화 형으로 이름 필드에서Bed를 입력한 후 구성요소 정의를 마칩니다. 최종 형상은 다음과 같이 표시됩니다.

    예제 문제에 대한 형상 정의

    새 구성 요소를 추가하면 가로 및 세로 방향으로 그래픽 표시 창에 길이 스케일이 자동으로 생성됩니다. 이 눈금자 도구를 사용하여 생성된 기하학적 객체의 범위를 빠르게 측정할 수 있습니다.

    노트

    표시 영역에는 지오메트리 모양 정의만 표시되므로 객체가 솔리드인지 구멍인지에 대한 정보는 표시되지 않습니다. 즐겨 찾기옵션을 사용하여 Mesh 후에 나중에 수행할 수 있습니다.

    추가 정보

    자세한 내용은 도움말 모델 설정 장의 형상 섹션을 참조하십시오.

    구성 요소 속성

    열전달 모델은 고체 구성 요소의 전도 방정식을 해결하기 위해 재료 특성이 필요합니다. 이러한 속성은 이 아이콘f3d_geometry_icon을 클릭하여 구성 요소 속성 위젯에서 설정합니다.

    구성 요소 특성 위젯

    각 구성 요소에는 솔리드 특성 및 표면 특성이 정의 되어 있어야합니다. 구리 블록에 대해 이를 설정하려면 먼저 형상 위젯에서 구성 요소 1: copper block 요소를 선택하십시오. 그런 다음 컴포넌트 특성 위젯에서 솔리드 특성을 선택하고 다음과 같이 특성을 정의하십시오.

    구리 블록 고체 특성

    여기에서 두 번째 구성 요소(베드)에 대해 설명된 구성 요소 특성 정의를 위한 대체 방법을 사용할 수 있습니다. 이 방법에서는 구성 요소 2: 베드 구성 요소를 클릭하고 재료 필드 옆에 있는 재료 특성로드 Matdatbas 아이콘을 선택하여 시작합니다. 다음으로 재료를 탐색합니다. 이 경우 Solids->Sands->Sand_Quartz 를 선택하고 Load를 선택하십시오.

    베드 솔리드 속성

    추가 정보

    l 자세한 내용은 모델 설정 장의 유체 섹션을 참조하십시오.

    l 주어진 물리적 모델에 필요한 속성에 대한 자세한 내용은 모델 참조 장을 참조하십시오.

    Meshing(메싱)

    Mesh는 Mesh 위젯에서 생성 및 정의되며, 위젯을 통해 액세스 할 수 있습니다. 이 f3d_mesh_icon아이콘을 눌러 add_icon새 Mesh를 추가합니다. Mesh의 범위를 형상에 빠르게 적용하려면 형상에 맞추기 라디오 버튼을 선택하고 오프셋 라디오 버튼을 백분율로 유지합니다. 블록 속성에서 셀 크기를 0.004로 설정하십시오.

    메시 블록을 형상에 맞추기

    Mesh 상단은 z 방향으로 위쪽으로 확장해야 합니다. Z-Direciton 탭을 선택하고 Mesh Plane 2에 0.2를 입력합니다.

    z 높이 조정

    이 시뮬레이션은 2D가 될 것입니다. 동일한 프로세스에 따라 Y 방향 범위를 -0.005 및 0.005 로 설정하십시오. 그리고 합계 셀을 1로 설정하십시오.

    y 메쉬 평면 조정

    최종 Mesh는 그래픽 디스플레이 창 바로 위의 Mesh->Flow Mesh->View 모드 드롭 다운 메뉴에서 옵션을 변경하여 다른 방식으로 볼 수 있습니다. 그리드 라인 마다 그리드 선을 표시합니다 옵션은 Mesh Plane의 옵션만 표시됩니다 Plane Mesh 및 개요 옵션은 Mesh의 범위를 보여줍니다.

    또한 솔버가 Mesh의 최종 지오메트리를 인식하는 방법은 FAVOR TM 알고리즘을 사용하여 형상 정의를 면적 분수 및 부피 분수로 변환합니다. 이렇게 하려면 즐겨 찾기아이콘을 클릭한 다음 생성을 선택하십시오.

    호의

    잠시 후 회색 영역이 고체 물질을 나타내는 아래와 같은 형상을 표시해야 합니다.

    선호하는 결과

    추가 정보

    l Mesh에 대한 자세한 내용은 모델 설정 장의 Mesh 섹션을 참조하십시오.

    l FAVORTM 및 FAVORize
    옵션에 대한 자세한 내용은 모델 설정 즐겨 찾기장의 Reviewing the FAVORized Geometry and Mesh 섹션을 참조하십시오.

    경계 조건

    FLOW-3D는 구성 요소 유형 및 활성 물리적 모델에 기초한 구성 요소에 적절한 경계 조건을 자동으로 적용합니다. 그러나 경계 조건 위젯에서 Mesh 블록면의 경계 조건은 각 Mesh 블록에 대해 수동으로 설정해야 합니다(f3d_bc_icon ).

    이 매뉴얼의 경우 경계 조건 중 3 가지가 경계조건( X Min , X Max, Z Max 경계)을 기본 대칭 조건조건부터 변경해야 합니다.

    ·X Min :

    o경계 조건 위젯의 경계 섹션 아래에 있는 X Min 목록을 클릭하십시오. Type에서 경계 유형을 Velocity로 설정하고 X 속도에 대해 0.001을 입력하십시오.

    XMIN 경계 조건

    ·다음으로, 유체 분율 사용에서 유체 표고 사용으로 드롭다운 상자를 변경하고 유체 높이를 0.15로 설정하십시오.

    ·마지막으로 온도를 298K로 설정하십시오.

    XMIN 경계 조건

    ·
    X Max :

    o경계 조건 위젯의 경계 섹션 아래에 있는 X 최대 목록을 클릭하십시오. 경계 유형을 압력으로 설정하고 압력에 대해 0을 입력하십시오.

    o다음으로, 유체 분율 사용에서 유체 높이 사용으로 드롭다운 상자를 변경하고 유체 높이를 0.15로 설정하십시오.

    o마지막으로 온도를 298K로 맞춥니다.

    oXMAX 경계 조건

    ·
    Z 최대 :

    o경계 조건 위젯의 경계 섹션 아래에 있는 Z 최대 목록을 클릭하십시오. 경계 유형을 압력으로 설정하고 압력에 대해 0을 입력하십시오.

    o다음으로 유체 분율을 0.0으로 설정하십시오.

    o마지막으로 온도를 298K로 맞춘다.

    ZMAX 경계 조건

    추가 정보

    자세한 내용은 모델 설정 장의 Mesh 경계 조건 섹션을 참조하십시오.

    초기 조건

    도메인 내부의 솔리드 객체(구성 요소)와 유체 모두에 대해 초기 조건을 설정해야 합니다.

    ·
    구성 요소 :이 시뮬레이션에서 솔리드 객체에 필요한 유일한 초기 조건은 초기 온도입니다. 이것은 각 구성 요소에 대한 위젯에 설정되어 있는 구성 요소 속성에 대해 수행한 것과 유사한 방식으로 구성 요소를 등록합니다. 구성 요소 속성을 설정할 때 이전과 동일한 방법으로 구성 요소 1의 초기 온도를 350K로 설정하고 구성 요소 2의 초기 온도를 298K로 설정하십시오.

    유체 초기 조건

    유체: 유체의 초기 조건을 설정하기 위해 조금 더 설정해야 합니다. 이 경우 유체 구성, 온도, 속도 및 압력 분포를 모두 설정해야 합니다. 유체 초기 조건은 초기 위젯을 설정하고 초기 f3d_initial_icon를 클릭하면 열립니다.

    f3d_initial_icon 아이콘을 선택한 후 유체 목록에서 압력을 선택하고 온도를 298K로 설정합니다. x, y, z 속도를 0.0으로 설정하십시오.

    유체 초기 조건

    다음으로, 높이/볼륨 목록과 유체 높이 사용 드롭다운 버튼을 선택합니다. 유체 높이를 0.15로 설정하십시오.

    유체 초기 조건 계속

    추가 정보

    자세한 내용은 모델 설정 장의 초기 조건 섹션을 참조하십시오.

    출력

    FLOW-3D 옵션에는 결과 파일에 기록될 데이터와 출력 위젯에서 발견된 빈도를 제어하는 7가지 데이터 유형이 있습니다. 출력 f3d_output_icon 아이콘을 클릭합니다.

    다른 데이터 유형은 다음과 같습니다.

    ·Restart: 모든 흐름 변수. 기본 출력 주기는 시뮬레이션 시간의 1/10입니다.

    ·Selected: 사용자가 선택한 흐름 변수 만. 기본 출력 주기는 시뮬레이션 시간의 1/100입니다.

    ·History: 하나의 변수와 시간의 변화를 보여주는 데이터. 예는 시간 단계 크기, 평균 운동 에너지, 배플에서의 유속 등을 포함합니다. 기본 출력 주기 = 시뮬레이션 시간의 1/100.

    ·Short print: hd3msg.*파일에 텍스트 진단 데이터가 기록 됩니다. 기본 출력 주기는 시뮬레이션 시간의 1/100입니다.

    ·Long print : hd3out.*파일에 텍스트 진단 데이터가 기록 됩니다. 기본 출력 주기는 시뮬레이션 시간의 1/10입니다.

    ·Solidification: 응고 모델이 활성화 된 경우에만 사용 가능합니다.

    ·FSI TSE: 변형 가능한 솔리드에 대한 추가 출력 옵션.

    일반적으로 이 시뮬레이션에는 기본 출력 속도가 적합합니다. 그러나 Selected Data의 일부 추가 구성은 유용합니다. Selected data interval을 0.5로 설정한 다음 Fluid 온도, Fluid velocity, Macroscopic density 및 Wall 온도 옆에 있는 상자를 선택합니다. 그러면 이러한 값이 0.5초마다 출력됩니다.

    출력 탭 설정

    추가 정보

    자세한 내용은 모델 설정 장의 출력 섹션을 참조하십시오.

    Numerics

    기본 Numerics 옵션은 대부분의 시뮬레이션에서 잘 작동하므로 기본 옵션에서 벗어나야 하는 충분한 이유가 없는 경우에는 현재 그대로 두는 것이 가장 좋습니다.

    이것으로 모델 설정 섹션에서 시작된 예제 문제의 설정을 마칩니다. 이제 실행할 준비가 되었으므로 전처리 및 시뮬레이션 실행의 단계에 따라 시뮬레이션을 실행하십시오.

    추가 정보

    자세한 내용은 모델 설정 장의 Numerics 옵션 섹션을 참조하십시오.

    일반 시뮬레이션 설정 점검 목록

    시뮬레이션을 설정하는 데 필요한 단계에 대한 개략적인 개요가 아래에 나와 있습니다. 이 목록은 포괄적인 목록이 아닙니다. 일반적인 단계, 고려해야 할 몇 가지 중요한 사항 및 권장되는 설정 순서를 간단히 설명하는 안내서일 뿐입니다.

    시작하기 전에

    1.물리적 문제의 다이어그램을 그리기 및 주석 달기 : 이 다이어그램에는 기하학적 치수, 유체의 위치, 관련 힘, 움직이는 물체의 속도, 관련 열 전달 메커니즘 등이 포함되어야 합니다. 완성된 다이어그램은 문제에 대한 모든 관련 엔지니어링 정보로 인한 물리적 문제에 대한 이미지여야 합니다.

    2.모델링 접근법 결정: 주석이 달린 다이어그램을 가이드로 사용하여 문제점에 접근하는 방법을 결정 : 문제가 되는 유체의 수, 혼화 가능한 경우, 하나 이상의 유체에서 방정식을 풀어야하는 경우 및 압축성이 중요한지 파악하여 시작하십시오. 그런 다음 어떤 물리적 메커니즘이 중요한지 결정하십시오. 이러한 각 옵션 (예: 유체 유형, 열 전달 메커니즘 등)에 대한 관련 엔지니어링 정보를 다이어그램에 추가하십시오. 물리적 메커니즘이 포함되거나 무시된 이유를 정당화하려고 합니다. 이를 통해 시뮬레이션 프로세스 초기에 오류를 수정하는 데 시간이 거의 걸리지 않는 초기에 실수를 잡을 수 있습니다.

    3.다이어그램에 계산 영역을 그리고, 계산 영역의 가장자리에 있는 물리적 상황 설명 : 경계의 물리적 상황을 가장 잘 나타내는 경계 조건 유형을 기록합니다. 사용 가능한 경계 조건 유형이 경계의 물리적 상황에 대한 합리적인 근사치가 아닌 경우 이 경계를 다른 곳으로 이동해야 합니다.

    모델 설정 : 일반

    1.문제, 시뮬레이션의 목적, 사례 번호 등을 설명하는 메모를 추가하십시오. 메모는 향후 사용자 또는 나중에 참조할 수 있도록 설정을 설명하고 정당화하는 데 도움이 됩니다. 시뮬레이션의 목적, 분석 방법 등을 논의해야합니다.

    2.사용할 솔버와 프로세서 수를 선택하십시오.

    3.단위 시스템 선택: 소규모 문제를 모델링 할 때는 작은 단위 (예 : mm-gm-msec)를 사용하고 규모가 큰 문제는 큰 단위 (예 : SI)를 사용하십시오. 이를 통해 기계 정밀도로 인한 반올림 오류를 방지할 수 있습니다.

    4.유체 수, 인터페이스 추적 옵션 및 유량 모드를 선택하십시오. 주석이 달린 다이어그램을 이 단계의 지침으로 사용하십시오. 유체의 수는 질량, 운동량 및 에너지 보존을 관장하는 방정식이 유체 분율 f> 0″ width=”44″ height=”17″ border=”0″><!--[endif]--></span>(</span>유체<span lang= 1을 나타내는) 또는 유체 분획 f \ geq 0(유체 1 및 유체 2)이 있는 영역에서 해결되는지 여부를 나타냅니다. 인터페이스
    추적 옵션은 유체 분율의 변화가 급격한지 또는 확산되어야 하는지 여부를 정의하는 반면, 흐름 모드는 f = 0두 유체 문제에서 처리되는 영역을 정의합니다.

    5.마감 조건 정의: 시뮬레이션 종료 시점을 선택합니다. 시간, 채우기 비율 또는 기타 정상 상태 측정을 기반으로 할 수 있습니다.

    6.기존 결과에서 시뮬레이션을 다시 시작하는 방법 정의 (선택 사항): 기존 결과 파일에서 시뮬레이션을 다시 시작할 때 다시 시작 옵션이 적용됩니다. 재시작 옵션은 재시작 소스 파일에서 가져온 정보와 시뮬레이션의 초기 조건을 사용하여 재설정되는 정보를 정의합니다.

    모델 설정 : 물리

    1.주석이 달린 다이어그램을 기반으로 관련 실제 모델 활성화

    모델 설정 : 유체

    1.유체의 속성 정의 1: 주석이 달린 다이어그램을 가이드로 사용하여 활성 물리적 모델에 대한 적절한 물리적 속성을 정의하십시오.

    2.유체 2의 속성 정의 (사용하는 경우): 주석이 달린 다이어그램을 가이드로 사용하여 활성 물리적 모델에 적절한 물리적 속성을 정의하십시오.

    3.인터페이스의 속성 정의: f = 1과 f = 0의 영역 사이의 인터페이스 속성을 정의하십시오. 여기에는 표면 장력, 상 변화 및 확산에 대한 특성이 포함됩니다.

    모델 설정 : Mesh 및 형상

    1.모든 STL 파일의 오류 점검: ADmesh, netfabb Studio 또는 유사한 프로그램을 사용하여 모든 STL 파일의 오류를 점검하십시오. 이는 모델 설정에 시간을 소비하기 전에 형상
    정의와 관련된 문제를 파악하는 데 도움이 됩니다.

    2.모든 하위 구성 요소 및 구성 요소 가져 오기 및 정의 : 주석이 달린 다이어그램에 설명 된 대로 실제 사례와 일치하도록 3D 솔리드 형상을 정의합니다. 최종 결과는 물리적 형상의 정확한 복제본이어야 합니다. 각 부분에 설명적인 이름을 사용하고 대량 소스가 될 구성 요소를 포함하십시오.

    3.모든 구성 요소의 속성 정의: 주석이 달린 다이어그램에 그려진 내용을 기반으로 각 구성 요소의 모든 재료 속성, 표면 속성, 모션 속성 등을 정의합니다. 경계 조건이 정의될 때까지 질량 소스 특성을 정의하기를 기다리십시오.

    4.스프링과 로프 및 각각에 대한 관련 속성을 정의합니다.

    5.주석이 달린 다이어그램에 설명된 시뮬레이션 도메인과 일치하도록 Mesh를 정의하십시오. 도메인의 모서리가 다이어그램에서 식별된 위치에 있는지 확인하십시오. 또한 인터페이스 (셀이 있는 셀과 셀이 f = 1다른 셀 이 있는 셀)를 식별하려면 세 개의 셀이 필요합니다.f = 0 ). 최소 5 개의 셀이 예상되는 가장 얇은 연속 영역에 맞도록 충분히 작은 셀을 사용하십시오. f = 1 과 f = 0 .

    6.지오메트리를 정의하는 모든 배플 정의

    7.경계 조건, 질량 소스, 질량 모멘텀 소스, 밸브 및 벤트 정의: 경계 조건 (질량 소스, 질량 모멘텀 소스, 밸브 및 벤트 포함)은 모든 방정식을 풀기 위해 주어진 위치에서 솔루션을 규정합니다. 주석이 달린 다이어그램을 사용하여 각 경계 (또는 소스 등)에 지정된 내용이 유동 솔루션, 열 전달 솔루션, 전위 등에 대한 현실과 일치하는지 확인하십시오.

    8.유체 및 구성 요소의 초기 조건을 정의합니다. 초기 조건은 모든 방정식 (유량 솔루션, 열 전달 솔루션, 전위 등)에 대해 모든 영역에서 솔루션을 규정합니다.t = 0 .주석이
    달린 다이어그램을 사용하여 초기 조건에 지정된 내용이 현재 현실에 대한 근사치인지 확인하십시오. 유체 영역뿐만 아니라 구성 요소의 초기 조건을 설정해야 합니다.

    9.모든 측정 장치 정의 (샘플링 볼륨, 플럭스 표면 및 히스토리 프로브)

    모델 설정 : 출력

    1.출력 기준 (시간, 채우기 비율 또는 응고된 비율)을 선택하십시오.

    2.재시작 데이터에 추가할 출력을 선택하십시오.

    3.선택한 데이터에 기록할 정보를 선택하십시오.

    4.재시작, 선택, 히스토리, 짧은 인쇄 및 긴 인쇄 데이터의 출력 속도 정의 : 기본 속도는 재시작 및 긴 인쇄 데이터의 경우 (10개 출력)/(시뮬레이션 종료 시간) 및 선택한 기록, 짧은 인쇄 데이터의 경우 (100개 출력)/(시뮬레이션 종료 시간)입니다.

    모델 설정 : 숫자

    1.기본값이 아닌 필수 숫자 옵션을 선택 FLOW-3D의 숫자 옵션은 고급 사용자를 대상으로 하며, 지배 방정식을 해결하는 데 사용되는 숫자 근사치 및 방법을 상당히 제어할 수 있습니다. 이러한 옵션 중 일부를 잘못 사용하면 솔루션에 문제가 발생할 수 있으므로 일반적으로 이 옵션의 기능을 먼저 이해하고 조정의 정당성을 갖추지 않고는 이러한 설정을 조정하지 않습니다.

    5.FLOW-3D에서 후 처리

    이 섹션에서는 FLOW-3D에 통합된 포스트 프로세서를 사용하는 방법에 대해 설명합니다. 보다 강력한 외부 포스트프로세서 FlowSight에 대한 튜토리얼은 FlowSight 설명서를 참조하십시오. 또한 이 섹션에서는 Flow Over A Weir 예제 문제를 실행하여 생성된 결과 파일을 사용합니다. 이 예제 문제를 실행하는 방법에 대한 지침은 예제 추가 및 시뮬레이션 사전 처리 및 실행을 참조합니다.

    FlowSight 사용에 대한 기본 참조는 FlowSight의 Help->helpLocal Help 메뉴에서 액세스하는 FlowSight 사용자 설명서입니다.

    추가 정보

    기존 플롯

    기존 플롯은 솔버가 자동으로 생성하는 사전 정의된 플롯입니다. 사용자 정의 플롯은 아래의 사용자 정의 플롯 섹션에 설명되어 있습니다.

    1.분석 탭을 클릭하십시오. FLOW-3D 결과 대화 상자가 표시됩니다; 메세지가 나타나지 않으면 (분석 탭이 열림) 결과 파일 열기를 선택하여 동일한 대화 상자를 엽니다.

    2.기존 라디오 버튼을 선택하십시오. 데이터 파일 경로 상자에 두 가지 유형의 파일이 표시됩니다 (있는 경우). 이름이 prpplt.*있는 파일 에는 전처리 flsplt.*기에 의해 자동으로 작성된 플롯이 포함되고 이름이 있는 파일에는 입력 파일에 사전 지정된 플롯 뿐만 아니라 후 처리기에 의해 자동으로 작성된 플롯이 포함됩니다.

    3. 확인을 선택 flsplt.Flow_Over_A_Weir하고 클릭하십시오. 그러면 디스플레이 탭이 자동으로 열립니다.

    기존 결과 대화 상자

    4.사용 가능한 플롯 목록이 오른쪽에 나타납니다. 목록에서 해당 플롯의 이름을 클릭하면 특정 플롯을 볼 수 있습니다. 플롯 26 이 아래에 나와 있습니다.

    기존 플롯보기

    커스텀 플롯

    1.분석 탭으로 돌아갑니다. 대화 상자를 열려면 결과 파일 열기를 선택하십시오.

    2.전체 출력 파일을 보려면 사용자 정의 단일 선택 단추를 선택하십시오. 전체 출력 파일에는 prpgrf.*파일과 파일이 포함됩니다 flsgrf.*. 시뮬레이션이 실행되었으므로 전 처리기 출력 파일이 삭제되어 flsgrf파일에 통합되었습니다.

    3.flsgrf.Flow_Over_A_Weir대화 상자 에서 파일을 선택하고 확인을 클릭하십시오.

    FLOW-3D 결과 대화 상자

    이제 분석 탭이 표시됩니다. 시뮬레이션 결과를 시각화 하는 방법에는 여러 가지가 있습니다. 사용 가능한 플롯 유형은 다음과 같습니다.

    ·Custom : 이 매뉴얼 의 FLSINP 파일을 사용하여 플롯합니다. 사용자 정의 섹션의 출력 코드를 사용하여 출력 플롯을 수동으로 수정하는 데 사용할 수 있습니다. 이것은 고급 옵션입니다.

    ·프로브 : 개별 셀, 경계, 구성 요소 및 도메인 전체(전역) 변수 대 시간에 대한 그래픽 및 텍스트 출력을 표시합니다. 자세한 내용은 프로브 플롯 및 프로브 : 특정 시점의 데이터와 시간 을 참조하십시오.

    ·1-D : 셀 데이터는 X, Y 또는 Z 방향의 셀 라인을 따라 볼 수 있습니다. 플롯 제한은 공간 및 시간에 모두 적용할 수 있습니다. 자세한 내용은 1-D 플롯 및 1-D : 라인을 따른 데이터 대 시간 을 참조하십시오.

    ·2-D : 셀 데이터는 XY, YZ 또는 XZ 평면에서 볼 수 있습니다. 플롯 제한은 공간 및 시간에 모두 적용할 수 있습니다. 속도 벡터 및 입자를 추가할 수 있습니다. 자세한 내용은 2 차원 플롯 및 2 차원 : 평면의 데이터와 시간의 데이터 를 참조하십시오.

    ·3-D : 유체와 고체의 표면 플롯을 생성하고 셀 데이터로 채색 할 수 있습니다. 속도 벡터, 입자 (있는 경우) 및 유선과 같은 추가 정보를 추가할 수 있습니다. 플롯 제한은 공간 및 시간에 모두 적용할 수 있습니다. 자세한 내용은 3D 플롯 및 3D : 표면의 데이터 대 시간 을 참조하십시오.

    ·텍스트 출력 : cell-by-cell 재시작, 선택 및 응고 데이터를 텍스트 파일에 쓸 수 있습니다. 자세한 내용은 텍스트 출력 및 텍스트 : ASCII 형식의 공간 데이터 출력 대 시간 을 참조하십시오.

    ·중립 파일 : 재시작 및 선택된 데이터는 별도의 텍스트 파일에 정의 된 지정된 지점(보간 또는 셀 중심)에서 출력 될 수 있습니다. 자세한 내용은 중립 파일 : 사용자 정의 좌표에서의 공간 데이터 출력 대 시간 을 참조하십시오.

    ·FSI TSE : 유한 요소 유체 / 고체 상호 작용 및 열 응력 진화 물리학 패키지에서 출력됩니다. 자세한 내용은 FSI / TSE : 표면의 구조 데이터와 시간 을 참조하십시오.

    3 차원 도표

    1.Analyze -> 3-D 탭을 선택하십시오.

    2.Iso-surface = Fraction of fluid를 선택하십시오. 이것은 표면을 그리는 데 사용되는 변수입니다. 선택한 등면 변수에 대한 등고선 값 기준을 충족하는 모든 셀을 통해 표면이 그려집니다. 유체의 분율이 기본값이며 유체 표면이 표시됩니다.

    등 면형

    3.색상 변수 = 압력을 선택하십시오. 이 선택은 등위면의 색을 지정하는 데 사용되는 변수를 결정합니다 (이 경우 유체 표면은 압력에 의해 색이 그려집니다).

    색상 변수 유형

    4.Component iso-surface overlay = Solid volume을 선택하십시오. 솔리드 볼륨 은 유체와 함께 솔리드 구성 요소를 표시합니다. 이전 단계에서는 체적 분수의 보완을 등위면으로 선택하여 이 작업을 수행했지만 이 옵션을 사용하면 유체와 고체 표면을 동시에 플롯 할 수 있습니다.

    등표면 옵션

    5.이동 시간 프레임의 최소 및 최대 위치들 (0 내지 1.25 초)에 슬라이더 위치.

    시간대 옵션

    6.렌더 버튼을 클릭하여 디스플레이 탭으로 전환하고 t = 0.0에서 1.25 초 사이에 일련의 11 플롯을 생성하여 압력에 의해 채색된 유체 표면과 위어 구조를 보여줍니다. 데이터 다시 시작 이 선택되었으므로 11 개의 플롯이 있습니다.

    7.사용 가능한 플롯이 사용 가능한 시간 프레임 목록에 나열됩니다. 다음을 클릭하여 시간 프레임 사이를 이동하거나 시간 프레임을 두 번 클릭하여 표시하십시오. 첫 번째 및 마지막 시간 프레임은 다음과 같아야 합니다.

    위어 구조 렌더링

    8.Analyze -> 3-D 탭으로 돌아가서 Data Source 그룹에서 Selected data 라디오 버튼을 선택하십시오.

    데이터 소스

    9.시간 프레임 선택기의 두 슬라이더가 모두 오른쪽에 있으므로 마지막 시간 프레임 만 생성됩니다. 사용 가능한 시간 프레임이 많고 렌더링하는데 시간이 오래 걸리므로 선택한 데이터를 선택하면 인터페이스에서 자동으로 수행됩니다. 사용 가능한 모든 시간 프레임을 렌더링 하려면 왼쪽 슬라이더를 Time Frame Min = 0 으로 이동하십시오.

    10. 렌더링 버튼을 클릭하십시오. 몇 초 안에 뷰가 디스플레이 창으로 전환되고 101 개의 플롯이 사용 가능한 시간 프레임 목록에 나열됩니다. 시간 프레임 사이를 이동하려면 다음을 반복해서 클릭하십시오.

    대칭 흐름 표시

    위어 중심 아래로 대칭 평면을 사용하여 시뮬레이션을 설정했으므로 위어 구조의 절반만 시뮬레이션되고 표시됩니다. 프리젠테이션 목적으로 대칭 모델의 두 반쪽을 모두 표시할
    수 있습니다.

    1.아래와 같이 Analyze -> 3-D 탭으로 돌아가서 Open Symmetry Boundaries 확인란을 선택하십시오.

    열린 대칭 경계

    2.렌더링을 클릭하십시오. 유체 표면이 디스플레이 탭의 대칭 경계에서 열린 상태로 나타납니다.

    3.화면 위의 도구 모음 메뉴에서 도구 -> 대칭을 선택하십시오.

    4.대화 상자에서 Y 방향 확인란을 선택하여 Y = 0 평면에서 결과를 미러링합니다.

    대조

    5.적용 및 닫기를 선택하십시오.

    6.마지막 시간 프레임을 두 번 클릭하십시오. 디스플레이는 아래와 같이 전체 위어 구조를 보여줍니다.

    전체 위어 구조

    3 차원 애니메이션 만들기

    다음 단계는 3 차원 유체 표면의 애니메이션을 만드는 것입니다. 애니메이션은 사용 가능한 시간 프레임 목록의 프레임에서 만든 동영상입니다. 애니메이션의 시각적 효과를 향상시키려면 모든 프레임에 공통 색상 스케일을 적용하는 것이 좋습니다.

    1.분석 -> 3-D 탭으로 돌아갑니다.

    2.윤곽 제한 그룹 상자에서 전역 라디오 버튼을 모두 선택하십시오.

    윤곽 제한

    3.렌더 를 클릭 하여 다시 그리고 디스플레이 탭으로 돌아갑니다.

    4.도구 -> 대칭 -> Y 방향 -> 적용 선택을 반복하여 Y = 0 평면에서 결과를 반영합니다.

    5.선택 도구 -> 애니메이션 -> 러버 밴드 캡처를 다음과 같이 선택 확인 Mesh지가 나타납니다 그것을 읽은 후.

    러버 밴드 캡처

    6.마우스 왼쪽 버튼을 클릭 한 상태에서 드래그하여 애니메이션을 적용할 화면 부분을 선택하십시오. 선택한 영역 주위에 선택 상자가 나타납니다.

    X, Y, 너비 및 높이 상자

    7.디스플레이 창 위에서 빨간색 캡처 버튼을 선택하십시오. 애니메이션을 시작하는 대화 상자가 나타납니다.

    8.애니메이션의 기본 이름은 out.avi입니다. 아래에 표시된 것처럼 보다 구체적인 이름이 권장됩니다.

    9.기본 프레임 속도는 초당 10 프레임입니다. 이 시뮬레이션의 마감 시간은 1.25 초이고, 일정한 시간 간격으로 100 개의 플롯이 있으므로 ‘실제‘속도는 초당 80 프레임입니다. 너무 빠를 수 있으므로 대신 5 를 입력 하고 확인을 누르십시오.

    AVI 캡처

    10. 각 시간 프레임이 표시 창에 렌더링 되고 비트 맵 파일이 시뮬레이션 디렉토리에 작성됩니다. 이 프로세스가 완료되면 다음 대화 상자가 나타납니다.

    생성 된 이미지 소스 파일

    1. 프로세스의 다음 단계를 시작하려면 확인 버튼을 클릭하십시오. 새로운 프로세스 (BMP2VAI.exe)가 시작되고 압축 방법을 선택할 수 있는 새로운 비디오 압축 창이 나타납니다. 다른 창 뒤에 숨겨져 있으면 앞으로 가져옵니다.
    2. 애니메이션의 기본 압축은 압축되지 않습니다. 파일 크기가 너무 커서 뷰어에 로드 할 수 없으므로 대부분의 애니메이션에는 권장되지 않습니다. Windows를 사용하는 경우 Microsoft Video 1을, Linux를 사용하는 경우 Cinepak을 선택하십시오. 여기에서 선택하는 것은 컴퓨터에서 사용할 수 있는 비디오 코덱과 비디오를 표시하는 데 사용하는 기계에서 사용할 수 있는 것입니다.
    3. 애니메이션 속도가 데이터 속도에 의해 제한되지 않도록 데이터 속도 확인란을 선택 취소하십시오.
    비디오 압축

    1. 압축 프로세스를 시작하려면 확인을 클릭하십시오. 압축이 완료되면 다음 대화 상자가 나타납니다.
    AVI 파일 생성

    1. 확인을 클릭하십시오. 애니메이션 프로세스가 완료되었습니다.
    2. Windows 탐색기에서 .avi 파일을 찾는 가장 빠른 방법 은 시뮬레이션 관리자 탭으로 이동하여 시뮬레이션 입력 파일 링크를 클릭하는 것 입니다.
    3. .avi파일 을 두 번 클릭하여 애니메이션을 재생 하십시오. 이전에 선택한 압축 형식을 읽을 수 있는 올바른 코덱이 설치되어 있지 않으면 오픈 소스 다중 코덱 비디오 플레이어 설치를 고려하십시오.

    2 차원 도표

    1.Analyze -> 2-D 탭을 선택하십시오. 이 시뮬레이션의 결과를 보는 데 가장 유용한 평면은 평면 Y = 0.0에있는 위어 중심선의 XZ 평면입니다.

    2.XZ 평면 라디오 버튼을 선택하십시오.

    3.Y 제한 슬라이더를 모두 Y = 0.25 (Y = 0.0에 가장 가까운 셀 중심 y 좌표)로 드래그 합니다. 또한 동일한 위치가 J = 2 로 식별되어 해당 셀이 도메인에서 두 번째임을 나타냅니다. 첫 번째 셀 (J = 1) 은 Mesh 외부에 있으며 경계
    조건 속성을 계산하는 데 사용됩니다. 기본     윤곽 변수는 압력이며 기본 속도 벡터는 기본적으로 선택됩니다. 솔리드 형상은 모든 2D 플롯과 함께 자동으로 표시되므로 3D 플롯과 같이 활성화 할 필요가 없습니다.

    4.벡터 옵션을 클릭하고 X = 2 및 Z = 2를 입력하십시오. 벡터는 이제 다른 모든 셀에 플롯 됩니다. 벡터 옵션을 적용하려면 확인을 선택하십시오.

    벡터 옵션

    5.Y = 0 평면에서 2 차원 압력 플롯의 시간 시퀀스를 생성하려면 렌더링을 클릭하십시오. T = 0.0 초 (왼쪽) 인 다음과 유사한 그래픽이 나타납니다. T = 0.125 초 (중간); 그리고 T = 1.25 초 (오른쪽).

    2D 결과

    6.디스플레이 화면의 오른쪽 상단에 있는 형식 버튼을 선택하십시오.

    형식 옵션

    7.선 색상, 벡터 길이 및 화살촉 크기 변경과 같은 다양한 옵션을 시험해보십시오. 변경 사항을 보려면 적용을 선택하십시오. 완료되면 재설정 및 확인을 선택하여
    기본 설정으로 돌아가서 대화 상자를 닫습니다. 모든 플롯에 대해 선호하는 옵션 세트가 있는 경우     저장 버튼을 선택하여 저장할 수 있습니다.

    1 차원 도표

    1. 분석 -> 1-D 탭을 선택하십시오. 이 탭에서는 하나 이상의 플롯 시간에서 셀 행을 따라 압력, 유체 깊이, 유체 상승 및 속도와 같은 셀별 출력 변수의 꺾은 선형
      차트 플롯을 사용할 수 있습니다.
    2. 데이터 소스 로 선택을 선택합니다. 사용 가능한 변수는 이제 더 빈번한 플로팅을 위해 선택된 변수 만 표시합니다.
    3. 자유 변수 표고를 데이터 변수 로 선택하십시오. 유압 데이터는 출력 탭에서 선택되었으므로 사용할 수 있습니다.
    ID 그래픽을 위해 선택된 데이터

    1. 이 시뮬레이션의 흐름 방향은 주로 x 축과 평행하므로 X 방향을 선택하십시오.
    2. Y 방향 슬라이더를 0.25(J = 2)로 이동하여 Y 방향에서 흐름 중심선에 가장 가까운 셀이 표시됩니다.
    3. 기본적으로 전체 X 범위가 표시됩니다. 플롯의 범위를 제한하려는 경우 X 방향 슬라이더를 이동할 수 있습니다. Z 방향 슬라이더의 위치는 주어진 x, y 위치에서 z 셀의 각 열에 대해 하나의 자유 표면 높이만 기록되므로 중요하지 않습니다. 시간 프레임 슬라이더는 0초와 1.25초여야 합니다.
    흘러가는 방향

    1. 렌더링을 클릭하십시오. t = 0.0에서 t = 1.25s까지의 시리즈 플롯이 디스플레이 탭의 플롯 목록에 나열됩니다. 이러한 플롯을 볼 수 있는 여러 가지 모드가
      있습니다. 기본 모드는       단일 모드이며 형식 버튼 아래의 드롭 다운 상자에 표시됩니다.
    기본 단일 모드

    1. 다양한 시간에 유체 표면 높이의 플롯을 비교하려면 드롭 다운 상자에서 오버레이 모드를 선택하십시오.
    2. 오른쪽 창에서 플롯 1, 13 및 101 을 선택하려면 클릭하십시오. 플롯 이름에는 또한 기록된 시간이 표시됩니다 (t = 0.0, 0.15s 및 1.25 초). 출력은 아래와 같이 나타납니다.
    자유 표면 고도

    1. 이 플롯을 비트 맵 또는 포스트 스크립트 파일에 저장하려면 출력 버튼을 선택하십시오.
    2. 확인 화면에 플롯 오버레이 플롯을 캡처하는 확인란을 (그리고 단 하나의 출력 파일을).
    3. 쓰기 버튼을 선택하여 이미지 파일을 만듭니다.
    4. 결과 이미지 파일은 시뮬레이션 디렉토리에 있으며 (시뮬레이션 관리자 탭 에서이 파일을 찾는 방법을 기억하십시오) 이름이 지정한 plots_on_screen.bmp됩니다.
    출력 사진

    프로브 플롯

    1.
    분석 -> 프로브 탭을 선택하십시오. 시간 기록 플롯은이 탭에서 변수 대 시간의 라인 그래프 또는 텍스트 출력으로 생성됩니다. FLOW-3D 에는 데이터 소스 그룹에서 선택되는 세 가지 유형의 시간 종속 데이터가 있습니다.

    ·공간 데이터 : 재시작 및 선택된 데이터 소스. 단일 x, y, z 셀 중심 좌표의 시간 종속 값이 표시됩니다. 값은 시간과 관련하여 통합되거나 시간과 관련하여 차별화되거나 이동 평균 (시간)으로 통합될 수 있습니다.

    ·일반 history 데이터 :. 글로벌 수량은 시간에 따라 다릅니다. 일반적인 양은 평균 운동 에너지, 시간 단계 및 대류 볼륨 오류입니다. 또한 이 데이터 유형에는 모델 설정 -> 메싱 및 지오메트리 탭에서 이러한 옵션을 선택한 경우 지정된 측정 위치(배플, 샘플링 볼륨, 히스토리 프로브)의 모든 데이터와 이동 또는 정지 상태의 솔리드 및 스프링/로프를
    위한 통합 출력이 포함됩니다.

    ·Mesh-dependent data : 메쉬 경계에서 시간에 따른 수량(계산 또는 사용자 지정)입니다. 일반적인 수량은 경계에서의 유량 및 경계에서의 지정된 유체 높이입니다.

    2.데이터 원본에서 일반 기록 라디오 버튼을 선택합니다. X, Y 및 Z 데이터 점 슬라이더가 회색으로 바뀝니다. 이는 일반 기록 데이터가 특정 셀과 연결되어 있지 않기 때문입니다.

    3.목록에서 질량  평균 유체 평균 운동 에너지를 선택하십시오.

    그래픽 데이터 출력

    4. 단위를 선택하여 플로팅 단위 대화 상자를 엽니다.

    5. 플롯에 단위 표시를 선택하십시오.

    6. SI, CGS, slugs/feet/seconds 또는 pounds/inches/seconds를 선택하여 원하는 단위 시스템으로 결과를 변환하고 출력합니다. 장치를 표시하고 변환하려면 모델 설정 -> 일반 탭에서 장치 시스템을 선택해야 합니다. 이전 단계에서 이 항목을 확인했으며, 지오메트리 및 유체 특성은 centimeters/grams/seconds 시스템에서 지정되었습니다.

    플로팅 단위

    7.Plotting Units 대화 상자를 닫으려면 OK를 선택하십시오.

    8.데이터의 그래픽 출력을 생성하려면 렌더를 선택하십시오. 출력은 시간에 따른 영역의 모든 유체에 대한 질량 평균 평균 운동 에너지를 보여줍니다. 이전 단계에서 선택한 사항에 따라 단위 레이블과 함께 그림이 나타납니다. 플롯은 총 운동 에너지가 일부 평균값 주위에서 진동하고 있음을 나타냅니다. 진동이 작아짐에 따라 시뮬레이션은 정상 상태 흐름에 접근합니다.

    프로브 MKE 출력

    9.분석 -> 프로브 탭으로 돌아갑니다.

    10. 출력 양식 그룹에서 텍스트를 선택하여 그래프를 텍스트 데이터로 출력한 다음 렌더링을 다시 선택하십시오.

    출력 형태

    11. 나타나는 텍스트 대화 상자에서 다른 이름으로 저장 버튼을 선택하여 출력을 텍스트 파일로 저장할 수 있습니다.

    12. 출력 창을 닫으려면 계속을 선택하십시오.

    텍스트 출력

    1.Analyze -> Text Output 탭을 선택하십시오.

    2.텍스트 출력 은 셀별 데이터 ( 다시 시작 또는 선택됨 ) 만 출력 할 수 있고 (구성 요소, 측정 스테이션 또는 글로벌 데이터 없음) 둘 이상의 셀을 선택할 수 있다는 점을 제외하고 프로브 탭 과 동일한 방식으로 작동합니다. 각 플롯 시간에 대한 출력 데이터. 셀은 슬라이더를 사용하여 3D 블록에서 선택됩니다. 기본 공간 범위는 전체 도메인으로 설정됩니다.

    3.직접 텍스트 데이터를 출력해보십시오.

     

    FLOW-3D 및TruVOF는 미국 및 기타 국가에서 등록 상표입니다.

    FLOW-3D CAST Bibliography

    FLOW-3D CAST bibliography

    아래는 FSI의 금속 주조 참고 문헌에 수록된 기술 논문 모음입니다. 이 모든 논문에는 FLOW-3D CAST 해석 결과가 수록되어 있습니다. FLOW-3D CAST를 사용하여 금속 주조 산업의 응용 프로그램을 성공적으로 시뮬레이션하는 방법에 대해 자세히 알아보십시오.

    Below is a collection of technical papers in our Metal Casting Bibliography. All of these papers feature FLOW-3D CAST results. Learn more about how FLOW-3D CAST can be used to successfully simulate applications for the Metal Casting Industry.

    33-20     Eric Riedel, Martin Liepe Stefan Scharf, Simulation of ultrasonic induced cavitation and acoustic streaming in liquid and solidifying aluminum, Metals, 10.4; 476, 2020. doi.org/10.3390/met10040476

    20-20   Wu Yue, Li Zhuo and Lu Rong, Simulation and visual tester verification of solid propellant slurry vacuum plate casting, Propellants, Explosives, Pyrotechnics, 2020. doi.org/10.1002/prep.201900411

    17-20   C.A. Jones, M.R. Jolly, A.E.W. Jarfors and M. Irwin, An experimental characterization of thermophysical properties of a porous ceramic shell used in the investment casting process, Supplimental Proceedings, pp. 1095-1105, TMS 2020 149th Annual Meeting and Exhibition, San Diego, CA, February 23-27, 2020. doi.org/10.1007/978-3-030-36296-6_102

    12-20   Franz Josef Feikus, Paul Bernsteiner, Ricardo Fernández Gutiérrez and Michal Luszczak , Further development of electric motor housings, MTZ Worldwide, 81, pp. 38-43, 2020. doi.org/10.1007/s38313-019-0176-z

    09-20   Mingfan Qi, Yonglin Kang, Yuzhao Xu, Zhumabieke Wulabieke and Jingyuan Li, A novel rheological high pressure die-casting process for preparing large thin-walled Al–Si–Fe–Mg–Sr alloy with high heat conductivity, high plasticity and medium strength, Materials Science and Engineering: A, 776, art. no. 139040, 2020. doi.org/10.1016/j.msea.2020.139040

    07-20   Stefan Heugenhauser, Erhard Kaschnitz and Peter Schumacher, Development of an aluminum compound casting process – Experiments and numerical simulations, Journal of Materials Processing Technology, 279, art. no. 116578, 2020. doi.org/10.1016/j.jmatprotec.2019.116578

    05-20   Michail Papanikolaou, Emanuele Pagone, Mark Jolly and Konstantinos Salonitis, Numerical simulation and evaluation of Campbell running and gating systems, Metals, 10.1, art. no. 68, 2020. doi.org/10.3390/met10010068

    102-19   Ferencz Peti and Gabriela Strnad, The effect of squeeze pin dimension and operational parameters on material homogeneity of aluminium high pressure die cast parts, Acta Marisiensis. Seria Technologica, 16.2, 2019. doi.org/0.2478/amset-2019-0010

    94-19   E. Riedel, I. Horn, N. Stein, H. Stein, R. Bahr, and S. Scharf, Ultrasonic treatment: a clean technology that supports sustainability incasting processes, Procedia, 26th CIRP Life Cycle Engineering (LCE) Conference, Indianapolis, Indiana, USA, May 7-9, 2019. 

    93-19   Adrian V. Catalina, Liping Xue, Charles A. Monroe, Robin D. Foley, and John A. Griffin, Modeling and Simulation of Microstructure and Mechanical Properties of AlSi- and AlCu-based Alloys, Transactions, 123rd Metalcasting Congress, Atlanta, GA, USA, April 27-30, 2019. 

    84-19   Arun Prabhakar, Michail Papanikolaou, Konstantinos Salonitis, and Mark Jolly, Sand casting of sheet lead: numerical simulation of metal flow and solidification, The International Journal of Advanced Manufacturing Technology, pp. 1-13, 2019. doi.org/10.1007/s00170-019-04522-3

    72-19   Santosh Reddy Sama, Eric Macdonald, Robert Voigt, and Guha Manogharan, Measurement of metal velocity in sand casting during mold filling, Metals, 9:1079, 2019. doi.org/10.3390/met9101079

    71-19   Sebastian Findeisen, Robin Van Der Auwera, Michael Heuser, and Franz-Josef Wöstmann, Gießtechnische Fertigung von E-Motorengehäusen mit interner Kühling (Casting production of electric motor housings with internal cooling), Geisserei, 106, pp. 72-78, 2019 (in German).

    58-19     Von Malte Leonhard, Matthias Todte, and Jörg Schäffer, Realistic simulation of the combustion of exothermic feeders, Casting, No. 2, pp. 28-32, 2019. In English and German.

    52-19     S. Lakkum and P. Kowitwarangkul, Numerical investigations on the effect of gas flow rate in the gas stirred ladle with dual plugs, International Conference on Materials Research and Innovation (ICMARI), Bangkok, Thailand, December 17-21, 2018. IOP Conference Series: Materials Science and Engineering, Vol. 526, 2019. doi.org/10.1088/1757-899X/526/1/012028

    47-19     Bing Zhou, Shuai Lu, Kaile Xu, Chun Xu, and Zhanyong Wang, Microstructure and simulation of semisolid aluminum alloy castings in the process of stirring integrated transfer-heat (SIT) with water cooling, International Journal of Metalcasting, Online edition, pp. 1-13, 2019. doi.org/10.1007/s40962-019-00357-6

    31-19     Zihao Yuan, Zhipeng Guo, and S.M. Xiong, Skin layer of A380 aluminium alloy die castings and its blistering during solution treatment, Journal of Materials Science & Technology, Vol. 35, No. 9, pp. 1906-1916, 2019. doi.org/10.1016/j.jmst.2019.05.011

    25-19     Stefano Mascetti, Raul Pirovano, and Giulio Timelli, Interazione metallo liquido/stampo: Il fenomeno della metallizzazione, La Metallurgia Italiana, No. 4, pp. 44-50, 2019. In Italian.

    20-19     Fu-Yuan Hsu, Campbellology for runner system design, Shape Casting: The Minerals, Metals & Materials Series, pp. 187-199, 2019. doi.org/10.1007/978-3-030-06034-3_19

    19-19     Chengcheng Lyu, Michail Papanikolaou, and Mark Jolly, Numerical process modelling and simulation of Campbell running systems designs, Shape Casting: The Minerals, Metals & Materials Series, pp. 53-64, 2019. doi.org/10.1007/978-3-030-06034-3_5

    18-19     Adrian V. Catalina, Liping Xue, and Charles Monroe, A solidification model with application to AlSi-based alloys, Shape Casting: The Minerals, Metals & Materials Series, pp. 201-213, 2019. doi.org/10.1007/978-3-030-06034-3_20

    17-19     Fu-Yuan Hsu and Yu-Hung Chen, The validation of feeder modeling for ductile iron castings, Shape Casting: The Minerals, Metals & Materials Series, pp. 227-238, 2019. doi.org/10.1007/978-3-030-06034-3_22

    04-19   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, Vol. 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

    02-19   Jingying Sun, Qichi Le, Li Fu, Jing Bai, Johannes Tretter, Klaus Herbold and Hongwei Huo, Gas entrainment behavior of aluminum alloy engine crankcases during the low-pressure-die-casting-process, Journal of Materials Processing Technology, Vol. 266, pp. 274-282, 2019. doi.org/10.1016/j.jmatprotec.2018.11.016

    92-18   Fast, Flexible… More Versatile, Foundry Management Technology, March, 2018. 

    82-18   Xu Zhao, Ping Wang, Tao Li, Bo-yu Zhang, Peng Wang, Guan-zhou Wang and Shi-qi Lu, Gating system optimization of high pressure die casting thin-wall AlSi10MnMg longitudinal loadbearing beam based on numerical simulation, China Foundry, Vol. 15, no. 6, pp. 436-442, 2018. doi: 10.1007/s41230-018-8052-z

    80-18   Michail Papanikolaou, Emanuele Pagone, Konstantinos Salonitis, Mark Jolly and Charalampos Makatsoris, A computational framework towards energy efficient casting processes, Sustainable Design and Manufacturing 2018: Proceedings of the 5th International Conference on Sustainable Design and Manufacturing (KES-SDM-18), Gold Coast, Australia, June 24-26 2018, SIST 130, pp. 263-276, 2019. doi.org/10.1007/978-3-030-04290-5_27

    64-18   Vasilios Fourlakidis, Ilia Belov and Attila Diószegi, Strength prediction for pearlitic lamellar graphite iron: Model validation, Metals, Vol. 8, No. 9, 2018. doi.org/10.3390/met8090684

    51-18   Xue-feng Zhu, Bao-yi Yu, Li Zheng, Bo-ning Yu, Qiang Li, Shu-ning Lü and Hao Zhang, Influence of pouring methods on filling process, microstructure and mechanical properties of AZ91 Mg alloy pipe by horizontal centrifugal casting, China Foundry, vol. 15, no. 3, pp.196-202, 2018. doi.org/10.1007/s41230-018-7256-6

    47-18   Santosh Reddy Sama, Jiayi Wang and Guha Manogharan, Non-conventional mold design for metal casting using 3D sand-printing, Journal of Manufacturing Processes, vol. 34-B, pp. 765-775, 2018. doi.org/10.1016/j.jmapro.2018.03.049

    42-18   M. Koru and O. Serçe, The Effects of Thermal and Dynamical Parameters and Vacuum Application on Porosity in High-Pressure Die Casting of A383 Al-Alloy, International Journal of Metalcasting, pp. 1-17, 2018. doi.org/10.1007/s40962-018-0214-7

    41-18   Abhilash Viswanath, S. Savithri, U.T.S. Pillai, Similitude analysis on flow characteristics of water, A356 and AM50 alloys during LPC process, Journal of Materials Processing Technology, vol. 257, pp. 270-277, 2018. doi.org/10.1016/j.jmatprotec.2018.02.031

    29-18   Seyboldt, Christoph and Liewald, Mathias, Investigation on thixojoining to produce hybrid components with intermetallic phase, AIP Conference Proceedings, vol. 1960, no. 1, 2018. doi.org/10.1063/1.5034992

    28-18   Laura Schomer, Mathias Liewald and Kim Rouven Riedmüller, Simulation of the infiltration process of a ceramic open-pore body with a metal alloy in semi-solid state to design the manufacturing of interpenetrating phase composites, AIP Conference Proceedings, vol. 1960, no. 1, 2018. doi.org/10.1063/1.5034991

    41-17   Y. N. Wu et al., Numerical Simulation on Filling Optimization of Copper Rotor for High Efficient Electric Motors in Die Casting Process, Materials Science Forum, Vol. 898, pp. 1163-1170, 2017.

    12-17   A.M.  Zarubin and O.A. Zarubina, Controlling the flow rate of melt in gravity die casting of aluminum alloys, Liteynoe Proizvodstvo (Casting Manufacturing), pp 16-20, 6, 2017. In Russian.

    10-17   A.Y. Korotchenko, Y.V. Golenkov, M.V. Tverskoy and D.E. Khilkov, Simulation of the Flow of Metal Mixtures in the Mold, Liteynoe Proizvodstvo (Casting Manufacturing), pp 18-22, 5, 2017. In Russian.

    08-17   Morteza Morakabian Esfahani, Esmaeil Hajjari, Ali Farzadi and Seyed Reza Alavi Zaree, Prediction of the contact time through modeling of heat transfer and fluid flow in compound casting process of Al/Mg light metals, Journal of Materials Research, © Materials Research Society 2017

    04-17   Huihui Liu, Xiongwei He and Peng Guo, Numerical simulation on semi-solid die-casting of magnesium matrix composite based on orthogonal experiment, AIP Conference Proceedings 1829, 020037 (2017); doi.org/10.1063/1.4979769.

    100-16  Robert Watson, New numerical techniques to quantify and predict the effect of entrainment defects, applied to high pressure die casting, PhD Thesis: University of Birmingham, 2016.

    88-16   M.C. Carter, T. Kauffung, L. Weyenberg and C. Peters, Low Pressure Die Casting Simulation Discovery through Short Shot, Cast Expo & Metal Casting Congress, April 16-19, 2016, Minneapolis, MN, Copyright 2016 American Foundry Society.

    61-16   M. Koru and O. Serçe, Experimental and numerical determination of casting mold interfacial heat transfer coefficient in the high pressure die casting of a 360 aluminum alloy, ACTA PHYSICA POLONICA A, Vol. 129 (2016)

    59-16   R. Pirovano and S. Mascetti, Tracking of collapsed bubbles during a filling simulation, La Metallurgia Italiana – n. 6 2016

    43-16   Kevin Lee, Understanding shell cracking during de-wax process in investment casting, Ph.D Thesis: University of Birmingham, School of Engineering, Department of Chemical Engineering, 2016.

    35-16   Konstantinos Salonitis, Mark Jolly, Binxu Zeng, and Hamid Mehrabi, Improvements in energy consumption and environmental impact by novel single shot melting process for casting, Journal of Cleaner Production, doi.org/10.1016/j.jclepro.2016.06.165, Open Access funded by Engineering and Physical Sciences Research Council, June 29, 2016

    20-16   Fu-Yuan Hsu, Bifilm Defect Formation in Hydraulic Jump of Liquid Aluminum, Metallurgical and Materials Transactions B, 2016, Band: 47, Heft 3, 1634-1648.

    15-16   Mingfan Qia, Yonglin Kanga, Bing Zhoua, Wanneng Liaoa, Guoming Zhua, Yangde Lib,and Weirong Li, A forced convection stirring process for Rheo-HPDC aluminum and magnesium alloys, Journal of Materials Processing Technology 234 (2016) 353–367

    112-15   José Miguel Gonçalves Ledo Belo da Costa, Optimization of filling systems for low pressure by FLOW-3D, Dissertação de mestrado integrado em Engenharia Mecânica, 2015.

    89-15   B.W. Zhu, L.X. Li, X. Liu, L.Q. Zhang and R. Xu, Effect of Viscosity Measurement Method to Simulate High Pressure Die Casting of Thin-Wall AlSi10MnMg Alloy Castings, Journal of Materials Engineering and Performance, Published online, November 2015, doi.org/10.1007/s11665-015-1783-8, © ASM International.

    88-15   Peng Zhang, Zhenming Li, Baoliang Liu, Wenjiang Ding and Liming Peng, Improved tensile properties of a new aluminum alloy for high pressure die casting, Materials Science & Engineering A651(2016)376–390, Available online, November 2015.

    83-15   Zu-Qi Hu, Xin-Jian Zhang and Shu-Sen Wu, Microstructure, Mechanical Properties and Die-Filling Behavior of High-Performance Die-Cast Al–Mg–Si–Mn Alloy, Acta Metall. Sin. (Engl. Lett.), doi.org/10.1007/s40195-015-0332-7, © The Chinese Society for Metals and Springer-Verlag Berlin Heidelberg 2015.

    82-15   J. Müller, L. Xue, M.C. Carter, C. Thoma, M. Fehlbier and M. Todte, A Die Spray Cooling Model for Thermal Die Cycling Simulations, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

    81-15   M. T. Murray, L.F. Hansen, L. Chilcott, E. Li and A.M. Murray, Case Studies in the Use of Simulation- Improved Yield and Reduced Time to Market, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

    80-15   R. Bhola, S. Chandra and D. Souders, Predicting Castability of Thin-Walled Parts for the HPDC Process Using Simulations, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

    76-15   Prosenjit Das, Sudip K. Samanta, Shashank Tiwari and Pradip Dutta, Die Filling Behaviour of Semi Solid A356 Al Alloy Slurry During Rheo Pressure Die Casting, Transactions of the Indian Institute of Metals, pp 1-6, October 2015

    74-15   Murat KORU and Orhan SERÇE, Yüksek Basınçlı Döküm Prosesinde Enjeksiyon Parametrelerine Bağlı Olarak Döküm Simülasyon, Cumhuriyet University Faculty of Science, Science Journal (CSJ), Vol. 36, No: 5 (2015) ISSN: 1300-1949, May 2015

    69-15   A. Viswanath, S. Sivaraman, U. T. S. Pillai, Computer Simulation of Low Pressure Casting Process Using FLOW-3D, Materials Science Forum, Vols. 830-831, pp. 45-48, September 2015

    68-15   J. Aneesh Kumar, K. Krishnakumar and S. Savithri, Computer Simulation of Centrifugal Casting Process Using FLOW-3D, Materials Science Forum, Vols. 830-831, pp. 53-56, September 2015

    59-15   F. Hosseini Yekta and S. A. Sadough Vanini, Simulation of the flow of semi-solid steel alloy using an enhanced model, Metals and Materials International, August 2015.

    44-15   Ulrich E. Klotz, Tiziana Heiss and Dario Tiberto, Platinum investment casting material properties, casting simulation and optimum process parameters, Jewelry Technology Forum 2015

    41-15   M. Barkhudarov and R. Pirovano, Minimizing Air Entrainment in High Pressure Die Casting Shot Sleeves, GIFA 2015, Düsseldorf, Germany

    40-15   M. Todte, A. Fent, and H. Lang, Simulation in support of the development of innovative processes in the casting industry, GIFA 2015, Düsseldorf, Germany

    19-15   Bruce Morey, Virtual casting improves powertrain design, Automotive Engineering, SAE International, March 2015.

    15-15   K.S. Oh, J.D. Lee, S.J. Kim and J.Y. Choi, Development of a large ingot continuous caster, Metall. Res. Technol. 112, 203 (2015) © EDP Sciences, 2015, doi.org/10.1051/metal/2015006, www.metallurgical-research.org

    14-15   Tiziana Heiss, Ulrich E. Klotz and Dario Tiberto, Platinum Investment Casting, Part I: Simulation and Experimental Study of the Casting Process, Johnson Matthey Technol. Rev., 2015, 59, (2), 95, doi.org/10.1595/205651315×687399

    138-14 Christopher Thoma, Wolfram Volk, Ruben Heid, Klaus Dilger, Gregor Banner and Harald Eibisch, Simulation-based prediction of the fracture elongation as a failure criterion for thin-walled high-pressure die casting components, International Journal of Metalcasting, Vol. 8, No. 4, pp. 47-54, 2014. doi.org/10.1007/BF03355594

    107-14  Mehran Seyed Ahmadi, Dissolution of Si in Molten Al with Gas Injection, ProQuest Dissertations And Theses; Thesis (Ph.D.), University of Toronto (Canada), 2014; Publication Number: AAT 3637106; ISBN: 9781321195231; Source: Dissertation Abstracts International, Volume: 76-02(E), Section: B.; 191 p.

    99-14   R. Bhola and S. Chandra, Predicting Castability for Thin-Walled HPDC Parts, Foundry Management Technology, December 2014

    92-14   Warren Bishenden and Changhua Huang, Venting design and process optimization of die casting process for structural components; Part II: Venting design and process optimization, Die Casting Engineer, November 2014

    90-14   Ken’ichi Kanazawa, Ken’ichi Yano, Jun’ichi Ogura, and Yasunori Nemoto, Optimum Runner Design for Die-Casting using CFD Simulations and Verification with Water-Model Experiments, Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, IMECE2014, November 14-20, 2014, Montreal, Quebec, Canada, IMECE2014-37419

    89-14   P. Kapranos, C. Carney, A. Pola, and M. Jolly, Advanced Casting Methodologies: Investment Casting, Centrifugal Casting, Squeeze Casting, Metal Spinning, and Batch Casting, In Comprehensive Materials Processing; McGeough, J., Ed.; 2014, Elsevier Ltd., 2014; Vol. 5, pp 39–67.

    77-14   Andrei Y. Korotchenko, Development of Scientific and Technological Approaches to Casting Net-Shaped Castings in Sand Molds Free of Shrinkage Defects and Hot Tears, Post-doctoral thesis: Russian State Technological University, 2014. In Russian.

    69-14   L. Xue, M.C. Carter, A.V. Catalina, Z. Lin, C. Li, and C. Qiu, Predicting, Preventing Core Gas Defects in Steel Castings, Modern Casting, September 2014

    68-14   L. Xue, M.C. Carter, A.V. Catalina, Z. Lin, C. Li, and C. Qiu, Numerical Simulation of Core Gas Defects in Steel Castings, Copyright 2014 American Foundry Society, 118th Metalcasting Congress, April 8 – 11, 2014, Schaumburg, IL

    51-14   Jesus M. Blanco, Primitivo Carranza, Rafael Pintos, Pedro Arriaga, and Lakhdar Remaki, Identification of Defects Originated during the Filling of Cast Pieces through Particles Modelling, 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V), 6th European Conference on Computational Fluid Dynamics (ECFD VI), E. Oñate, J. Oliver and A. Huerta (Eds)

    47-14   B. Vijaya Ramnatha, C.Elanchezhiana, Vishal Chandrasekhar, A. Arun Kumarb, S. Mohamed Asif, G. Riyaz Mohamed, D. Vinodh Raj , C .Suresh Kumar, Analysis and Optimization of Gating System for Commutator End Bracket, Procedia Materials Science 6 ( 2014 ) 1312 – 1328, 3rd International Conference on Materials Processing and Characterisation (ICMPC 2014)

    42-14  Bing Zhou, Yong-lin Kang, Guo-ming Zhu, Jun-zhen Gao, Ming-fan Qi, and Huan-huan Zhang, Forced convection rheoforming process for preparation of 7075 aluminum alloy semisolid slurry and its numerical simulation, Trans. Nonferrous Met. Soc. China 24(2014) 1109−1116

    37-14    A. Karwinski, W. Lesniewski, P. Wieliczko, and M. Malysza, Casting of Titanium Alloys in Centrifugal Induction Furnaces, Archives of Metallurgy and Materials, Volume 59, Issue 1, doi.org/10.2478/amm-2014-0068, 2014.

    26-14    Bing Zhou, Yonglin Kang, Mingfan Qi, Huanhuan Zhang and Guoming Zhu, R-HPDC Process with Forced Convection Mixing Device for Automotive Part of A380 Aluminum Alloy, Materials 2014, 7, 3084-3105; doi.org/10.3390/ma7043084

    20-14  Johannes Hartmann, Tobias Fiegl, Carolin Körner, Aluminum integral foams with tailored density profile by adapted blowing agents, Applied Physics A, doi.org/10.1007/s00339-014-8377-4, March 2014.

    19-14    A.Y. Korotchenko, N.A. Nikiforova, E.D. Demjanov, N.C. Larichev, The Influence of the Filling Conditions on the Service Properties of the Part Side Frame, Russian Foundryman, 1 (January), pp 40-43, 2014. In Russian.

    11-14 B. Fuchs and C. Körner, Mesh resolution consideration for the viability prediction of lost salt cores in the high pressure die casting process, Progress in Computational Fluid Dynamics, Vol. 14, No. 1, 2014, Copyright © 2014 Inderscience Enterprises Ltd.

    08-14 FY Hsu, SW Wang, and HJ Lin, The External and Internal Shrinkages in Aluminum Gravity Castings, Shape Casting: 5th International Symposium 2014. Available online at Google Books

    103-13  B. Fuchs, H. Eibisch and C. Körner, Core Viability Simulation for Salt Core Technology in High-Pressure Die Casting, International Journal of Metalcasting, July 2013, Volume 7, Issue 3, pp 39–45

    94-13    Randall S. Fielding, J. Crapps, C. Unal, and J.R.Kennedy, Metallic Fuel Casting Development and Parameter Optimization Simulations, International Conference on Fast reators and Related Fuel Cycles (FR13), 4-7 March 2013, Paris France

    90-13  A. Karwińskia, M. Małyszaa, A. Tchórza, A. Gila, B. Lipowska, Integration of Computer Tomography and Simulation Analysis in Evaluation of Quality of Ceramic-Carbon Bonded Foam Filter, Archives of Foundry Engineering, doi.org/10.2478/afe-2013-0084, Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences, ISSN, (2299-2944), Volume 13, Issue 4/2013

    88-13  Litie and Metallurgia (Casting and Metallurgy), 3 (72), 2013, N.V.Sletova, I.N.Volnov, S.P.Zadrutsky, V.A.Chaikin, Modeling of the Process of Removing Non-metallic Inclusions in Aluminum Alloys Using the FLOW-3D program, pp 138-140. In Russian.

    85-13    Michał Szucki,Tomasz Goraj, Janusz Lelito, Józef S. Suchy, Numerical Analysis of Solid Particles Flow in Liquid Metal, XXXVII International Scientific Conference Foundryman’ Day 2013, Krakow, 28-29 November 2013

    84-13  Körner, C., Schwankl, M., Himmler, D., Aluminum-Aluminum compound castings by electroless deposited zinc layers, Journal of Materials Processing Technology (2014), doi.org/10.1016/j.jmatprotec.2013.12.01483-13.

    77-13  Antonio Armillotta & Raffaello Baraggi & Simone Fasoli, SLM tooling for die casting with conformal cooling channels, The International Journal of Advanced Manufacturing Technology, doi.org/10.1007/s00170-013-5523-7, December 2013.

    64-13   Johannes Hartmann, Christina Blümel, Stefan Ernst, Tobias Fiegl, Karl-Ernst Wirth, Carolin Körner, Aluminum integral foam castings with microcellular cores by nano-functionalization, J Mater Sci, doi.org/10.1007/s10853-013-7668-z, September 2013.

    46-13  Nicholas P. Orenstein, 3D Flow and Temperature Analysis of Filling a Plutonium Mold, LA-UR-13-25537, Approved for public release; distribution is unlimited. Los Alamos Annual Student Symposium 2013, 2013-07-24 (Rev.1)

    42-13   Yang Yue, William D. Griffiths, and Nick R. Green, Modelling of the Effects of Entrainment Defects on Mechanical Properties in a Cast Al-Si-Mg Alloy, Materials Science Forum, 765, 225, 2013.

    39-13  J. Crapps, D.S. DeCroix, J.D Galloway, D.A. Korzekwa, R. Aikin, R. Fielding, R. Kennedy, C. Unal, Separate effects identification via casting process modeling for experimental measurement of U-Pu-Zr alloys, Journal of Nuclear Materials, 15 July 2013.

    35-13   A. Pari, Real Life Problem Solving through Simulations in the Die Casting Industry – Case Studies, © Die Casting Engineer, July 2013.

    34-13  Martin Lagler, Use of Simulation to Predict the Viability of Salt Cores in the HPDC Process – Shot Curve as a Decisive Criterion, © Die Casting Engineer, July 2013.

    24-13    I.N.Volnov, Optimizatsia Liteynoi Tekhnologii, (Casting Technology Optimization), Liteyshik Rossii (Russian Foundryman), 3, 2013, 27-29. In Russian

    23-13  M.R. Barkhudarov, I.N. Volnov, Minimizatsia Zakhvata Vozdukha v Kamere Pressovania pri Litie pod Davleniem, (Minimization of Air Entrainment in the Shot Sleeve During High Pressure Die Casting), Liteyshik Rossii (Russian Foundryman), 3, 2013, 30-34. In Russian

    09-13  M.C. Carter and L. Xue, Simulating the Parameters that Affect Core Gas Defects in Metal Castings, Copyright 2012 American Foundry Society, Presented at the 2013 CastExpo, St. Louis, Missouri, April 2013

    08-13  C. Reilly, N.R. Green, M.R. Jolly, J.-C. Gebelin, The Modelling Of Oxide Film Entrainment In Casting Systems Using Computational Modelling, Applied Mathematical Modelling, http://dx.doi.org/10.1016/j.apm.2013.03.061, April 2013.

    03-13  Alexandre Reikher and Krishna M. Pillai, A fast simulation of transient metal flow and solidification in a narrow channel. Part II. Model validation and parametric study, Int. J. Heat Mass Transfer (2013), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.061.

    02-13  Alexandre Reikher and Krishna M. Pillai, A fast simulation of transient metal flow and solidification in a narrow channel. Part I: Model development using lubrication approximation, Int. J. Heat Mass Transfer (2013), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.060.

    116-12  Jufu Jianga, Ying Wang, Gang Chena, Jun Liua, Yuanfa Li and Shoujing Luo, “Comparison of mechanical properties and microstructure of AZ91D alloy motorcycle wheels formed by die casting and double control forming, Materials & Design, Volume 40, September 2012, Pages 541-549.

    107-12  F.K. Arslan, A.H. Hatman, S.Ö. Ertürk, E. Güner, B. Güner, An Evaluation for Fundamentals of Die Casting Materials Selection and Design, IMMC’16 International Metallurgy & Materials Congress, Istanbul, Turkey, 2012.

    103-12 WU Shu-sen, ZHONG Gu, AN Ping, WAN Li, H. NAKAE, Microstructural characteristics of Al−20Si−2Cu−0.4Mg−1Ni alloy formed by rheo-squeeze casting after ultrasonic vibration treatment, Transactions of Nonferrous Metals Society of China, 22 (2012) 2863-2870, November 2012. Full paper available online.

    109-12 Alexandre Reikher, Numerical Analysis of Die-Casting Process in Thin Cavities Using Lubrication Approximation, Ph.D. Thesis: The University of Wisconsin Milwaukee, Engineering Department (2012) Theses and Dissertations. Paper 65.

    97-12 Hong Zhou and Li Heng Luo, Filling Pattern of Step Gating System in Lost Foam Casting Process and its Application, Advanced Materials Research, Volumes 602-604, Progress in Materials and Processes, 1916-1921, December 2012.

    93-12  Liangchi Zhang, Chunliang Zhang, Jeng-Haur Horng and Zichen Chen, Functions of Step Gating System in the Lost Foam Casting Process, Advanced Materials Research, 591-593, 940, DOI: 10.4028/www.scientific.net/AMR.591-593.940, November 2012.

    91-12  Hong Yan, Jian Bin Zhu, Ping Shan, Numerical Simulation on Rheo-Diecasting of Magnesium Matrix Composites, 10.4028/www.scientific.net/SSP.192-193.287, Solid State Phenomena, 192-193, 287.

    89-12  Alexandre Reikher and Krishna M. Pillai, A Fast Numerical Simulation for Modeling Simultaneous Metal Flow and Solidification in Thin Cavities Using the Lubrication Approximation, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 63:2, 75-100, November 2012.

    82-12  Jufu Jiang, Gang Chen, Ying Wang, Zhiming Du, Weiwei Shan, and Yuanfa Li, Microstructure and mechanical properties of thin-wall and high-rib parts of AM60B Mg alloy formed by double control forming and die casting under the optimal conditions, Journal of Alloys and Compounds, http://dx.doi.org/10.1016/j.jallcom.2012.10.086, October 2012.

    78-12   A. Pari, Real Life Problem Solving through Simulations in the Die Casting Industry – Case Studies, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

    77-12  Y. Wang, K. Kabiri-Bamoradian and R.A. Miller, Rheological behavior models of metal matrix alloys in semi-solid casting process, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

    76-12  A. Reikher and H. Gerber, Analysis of Solidification Parameters During the Die Cast Process, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

    75-12 R.A. Miller, Y. Wang and K. Kabiri-Bamoradian, Estimating Cavity Fill Time, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

    65-12  X.H. Yang, T.J. Lu, T. Kim, Influence of non-conducting pore inclusions on phase change behavior of porous media with constant heat flux boundary, International Journal of Thermal Sciences, Available online 10 October 2012. Available online at SciVerse.

    55-12  Hejun Li, Pengyun Wang, Lehua Qi, Hansong Zuo, Songyi Zhong, Xianghui Hou, 3D numerical simulation of successive deposition of uniform molten Al droplets on a moving substrate and experimental validation, Computational Materials Science, Volume 65, December 2012, Pages 291–301.

    52-12 Hongbing Ji, Yixin Chen and Shengzhou Chen, Numerical Simulation of Inner-Outer Couple Cooling Slab Continuous Casting in the Filling Process, Advanced Materials Research (Volumes 557-559), Advanced Materials and Processes II, pp. 2257-2260, July 2012.

    47-12    Petri Väyrynen, Lauri Holappa, and Seppo Louhenkilpi, Simulation of Melting of Alloying Materials in Steel Ladle, SCANMET IV – 4th International Conference on Process Development in Iron and Steelmaking, Lulea, Sweden, June 10-13, 2012.

    46-12  Bin Zhang and Dave Salee, Metal Flow and Heat Transfer in Billet DC Casting Using Wagstaff® Optifill™ Metal Distribution Systems, 5th International Metal Quality Workshop, United Arab Emirates Dubai, March 18-22, 2012.

    45-12 D.R. Gunasegaram, M. Givord, R.G. O’Donnell and B.R. Finnin, Improvements engineered in UTS and elongation of aluminum alloy high pressure die castings through the alteration of runner geometry and plunger velocity, Materials Science & Engineering.

    44-12    Antoni Drys and Stefano Mascetti, Aluminum Casting Simulations, Desktop Engineering, September 2012

    42-12   Huizhen Duan, Jiangnan Shen and Yanping Li, Comparative analysis of HPDC process of an auto part with ProCAST and FLOW-3D, Applied Mechanics and Materials Vols. 184-185 (2012) pp 90-94, Online available since 2012/Jun/14 at www.scientific.net, © (2012) Trans Tech Publications, Switzerland, doi:10.4028/www.scientific.net/AMM.184-185.90.

    41-12    Deniece R. Korzekwa, Cameron M. Knapp, David A. Korzekwa, and John W. Gibbs, Co-Design – Fabrication of Unalloyed Plutonium, LA-UR-12-23441, MDI Summer Research Group Workshop Advanced Manufacturing, 2012-07-25/2012-07-26 (Los Alamos, New Mexico, United States)

    29-12  Dario Tiberto and Ulrich E. Klotz, Computer simulation applied to jewellery casting: challenges, results and future possibilities, IOP Conf. Ser.: Mater. Sci. Eng.33 012008. Full paper available at IOP.

    28-12  Y Yue and N R Green, Modelling of different entrainment mechanisms and their influences on the mechanical reliability of Al-Si castings, 2012 IOP Conf. Ser.: Mater. Sci. Eng. 33,012072.Full paper available at IOP.

    27-12  E Kaschnitz, Numerical simulation of centrifugal casting of pipes, 2012 IOP Conf. Ser.: Mater. Sci. Eng. 33 012031, Issue 1. Full paper available at IOP.

    15-12  C. Reilly, N.R Green, M.R. Jolly, The Present State Of Modeling Entrainment Defects In The Shape Casting Process, Applied Mathematical Modelling, Available online 27 April 2012, ISSN 0307-904X, 10.1016/j.apm.2012.04.032.

    12-12   Andrei Starobin, Tony Hirt, Hubert Lang, and Matthias Todte, Core drying simulation and validation, International Foundry Research, GIESSEREIFORSCHUNG 64 (2012) No. 1, ISSN 0046-5933, pp 2-5

    10-12  H. Vladimir Martínez and Marco F. Valencia (2012). Semisolid Processing of Al/β-SiC Composites by Mechanical Stirring Casting and High Pressure Die Casting, Recent Researches in Metallurgical Engineering – From Extraction to Forming, Dr Mohammad Nusheh (Ed.), ISBN: 978-953-51-0356-1, InTech

    07-12     Amir H. G. Isfahani and James M. Brethour, Simulating Thermal Stresses and Cooling Deformations, Die Casting Engineer, March 2012

    06-12   Shuisheng Xie, Youfeng He and Xujun Mi, Study on Semi-solid Magnesium Alloys Slurry Preparation and Continuous Roll-casting Process, Magnesium Alloys – Design, Processing and Properties, ISBN: 978-953-307-520-4, InTech.

    04-12 J. Spangenberg, N. Roussel, J.H. Hattel, H. Stang, J. Skocek, M.R. Geiker, Flow induced particle migration in fresh concrete: Theoretical frame, numerical simulations and experimental results on model fluids, Cement and Concrete Research, http://dx.doi.org/10.1016/j.cemconres.2012.01.007, February 2012.

    01-12   Lee, B., Baek, U., and Han, J., Optimization of Gating System Design for Die Casting of Thin Magnesium Alloy-Based Multi-Cavity LCD Housings, Journal of Materials Engineering and Performance, Springer New York, Issn: 1059-9495, 10.1007/s11665-011-0111-1, Volume 1 / 1992 – Volume 21 / 2012. Available online at Springer Link.

    104-11  Fu-Yuan Hsu and Huey Jiuan Lin, Foam Filters Used in Gravity Casting, Metall and Materi Trans B (2011) 42: 1110. doi:10.1007/s11663-011-9548-8.

    99-11    Eduardo Trejo, Centrifugal Casting of an Aluminium Alloy, thesis: Doctor of Philosophy, Metallurgy and Materials School of Engineering University of Birmingham, October 2011. Full paper available upon request.

    93-11  Olga Kononova, Andrejs Krasnikovs ,Videvuds Lapsa,Jurijs Kalinka and Angelina Galushchak, Internal Structure Formation in High Strength Fiber Concrete during Casting, World Academy of Science, Engineering and Technology 59 2011

    76-11  J. Hartmann, A. Trepper, and C. Körner, Aluminum Integral Foams with Near-Microcellular Structure, Advanced Engineering Materials 2011, Volume 13 (2011) No. 11, © Wiley-VCH

    71-11  Fu-Yuan Hsu and Yao-Ming Yang Confluence Weld in an Aluminum Gravity Casting, Journal of Materials Processing Technology, Available online 23 November 2011, ISSN 0924-0136, 10.1016/j.jmatprotec.2011.11.006.

    65-11     V.A. Chaikin, A.V. Chaikin, I.N.Volnov, A Study of the Process of Late Modification Using Simulation, in Zagotovitelnye Proizvodstva v Mashinostroenii, 10, 2011, 8-12. In Russian.

    54-11  Ngadia Taha Niane and Jean-Pierre Michalet, Validation of Foundry Process for Aluminum Parts with FLOW-3D Software, Proceedings of the 2011 International Symposium on Liquid Metal Processing and Casting, 2011.

    51-11    A. Reikher and H. Gerber, Calculation of the Die Cast parameters of the Thin Wall Aluminum Cast Part, 2011 Die Casting Congress & Tabletop, Columbus, OH, September 19-21, 2011

    50-11   Y. Wang, K. Kabiri-Bamoradian, and R.A. Miller, Runner design optimization based on CFD simulation for a die with multiple cavities, 2011 Die Casting Congress & Tabletop, Columbus, OH, September 19-21, 2011

    48-11 A. Karwiński, W. Leśniewski, S. Pysz, P. Wieliczko, The technology of precision casting of titanium alloys by centrifugal process, Archives of Foundry Engineering, ISSN: 1897-3310), Volume 11, Issue 3/2011, 73-80, 2011.

    46-11  Daniel Einsiedler, Entwicklung einer Simulationsmethodik zur Simulation von Strömungs- und Trocknungsvorgängen bei Kernfertigungsprozessen mittels CFD (Development of a simulation methodology for simulating flow and drying operations in core production processes using CFD), MSc thesis at Technical University of Aalen in Germany (Hochschule Aalen), 2011.

    44-11  Bin Zhang and Craig Shaber, Aluminum Ingot Thermal Stress Development Modeling of the Wagstaff® EpsilonTM Rolling Ingot DC Casting System during the Start-up Phase, Materials Science Forum Vol. 693 (2011) pp 196-207, © 2011 Trans Tech Publications, July, 2011.

    43-11 Vu Nguyen, Patrick Rohan, John Grandfield, Alex Levin, Kevin Naidoo, Kurt Oswald, Guillaume Girard, Ben Harker, and Joe Rea, Implementation of CASTfill low-dross pouring system for ingot casting, Materials Science Forum Vol. 693 (2011) pp 227-234, © 2011 Trans Tech Publications, July, 2011.

    40-11  A. Starobin, D. Goettsch, M. Walker, D. Burch, Gas Pressure in Aluminum Block Water Jacket Cores, © 2011 American Foundry Society, International Journal of Metalcasting/Summer 2011

    37-11 Ferencz Peti, Lucian Grama, Analyze of the Possible Causes of Porosity Type Defects in Aluminum High Pressure Diecast Parts, Scientific Bulletin of the Petru Maior University of Targu Mures, Vol. 8 (XXV) no. 1, 2011, ISSN 1841-9267

    31-11  Johannes Hartmann, André Trepper, Carolin Körner, Aluminum Integral Foams with Near-Microcellular Structure, Advanced Engineering Materials, 13: n/a. doi: 10.1002/adem.201100035, June 2011.

    27-11  A. Pari, Optimization of HPDC Process using Flow Simulation Case Studies, Die Casting Engineer, July 2011

    26-11    A. Reikher, H. Gerber, Calculation of the Die Cast Parameters of the Thin Wall Aluminum Die Casting Part, Die Casting Engineer, July 2011

    21-11 Thang Nguyen, Vu Nguyen, Morris Murray, Gary Savage, John Carrig, Modelling Die Filling in Ultra-Thin Aluminium Castings, Materials Science Forum (Volume 690), Light Metals Technology V, pp 107-111, 10.4028/www.scientific.net/MSF.690.107, June 2011.

    19-11 Jon Spangenberg, Cem Celal Tutum, Jesper Henri Hattel, Nicolas Roussel, Metter Rica Geiker, Optimization of Casting Process Parameters for Homogeneous Aggregate Distribution in Self-Compacting Concrete: A Feasibility Study, © IEEE Congress on Evolutionary Computation, 2011, New Orleans, USA

    16-11  A. Starobin, C.W. Hirt, H. Lang, and M. Todte, Core Drying Simulation and Validations, AFS Proceedings 2011, © American Foundry Society, Presented at the 115th Metalcasting Congress, Schaumburg, Illinois, April 2011.

    15-11  J. J. Hernández-Ortega, R. Zamora, J. López, and F. Faura, Numerical Analysis of Air Pressure Effects on the Flow Pattern during the Filling of a Vertical Die Cavity, AIP Conf. Proc., Volume 1353, pp. 1238-1243, The 14th International Esaform Conference on Material Forming: Esaform 2011; doi:10.1063/1.3589686, May 2011. Available online.

    10-11 Abbas A. Khalaf and Sumanth Shankar, Favorable Environment for Nondentric Morphology in Controlled Diffusion Solidification, DOI: 10.1007/s11661-011-0641-z, © The Minerals, Metals & Materials Society and ASM International 2011, Metallurgical and Materials Transactions A, March 11, 2011.

    08-11 Hai Peng Li, Chun Yong Liang, Li Hui Wang, Hong Shui Wang, Numerical Simulation of Casting Process for Gray Iron Butterfly Valve, Advanced Materials Research, 189-193, 260, February 2011.

    04-11  C.W. Hirt, Predicting Core Shooting, Drying and Defect Development, Foundry Management & Technology, January 2011.

    76-10  Zhizhong Sun, Henry Hu, Alfred Yu, Numerical Simulation and Experimental Study of Squeeze Casting Magnesium Alloy AM50, Magnesium Technology 2010, 2010 TMS Annual Meeting & Exhibition, February 14-18, 2010, Seattle, WA.

    68-10  A. Reikher, H. Gerber, K.M. Pillai, T.-C. Jen, Natural Convection—An Overlooked Phenomenon of the Solidification Process, Die Casting Engineer, January 2010

    54-10    Andrea Bernardoni, Andrea Borsi, Stefano Mascetti, Alessandro Incognito and Matteo Corrado, Fonderia Leonardo aveva ragione! L’enorme cavallo dedicato a Francesco Sforza era materialmente realizzabile, A&C – Analisis e Calcolo, Giugno 2010. In  Italian.

    48-10  J. J. Hernández-Ortega, R. Zamora, J. Palacios, J. López and F. Faura, An Experimental and Numerical Study of Flow Patterns and Air Entrapment Phenomena During the Filling of a Vertical Die Cavity, J. Manuf. Sci. Eng., October 2010, Volume 132, Issue 5, 05101, doi:10.1115/1.4002535.

    47-10  A.V. Chaikin, I.N. Volnov, and V.A. Chaikin, Development of Dispersible Mixed Inoculant Compositions Using the FLOW-3D Program, Liteinoe Proizvodstvo, October, 2010, in Russian.

    42-10  H. Lakshmi, M.C. Vinay Kumar, Raghunath, P. Kumar, V. Ramanarayanan, K.S.S. Murthy, P. Dutta, Induction reheating of A356.2 aluminum alloy and thixocasting as automobile component, Transactions of Nonferrous Metals Society of China 20(20101) s961-s967.

    41-10  Pamela J. Waterman, Understanding Core-Gas Defects, Desktop Engineering, October 2010. Available online at Desktop Engineering. Also published in the Foundry Trade Journal, November 2010.

    39-10  Liu Zheng, Jia Yingying, Mao Pingli, Li Yang, Wang Feng, Wang Hong, Zhou Le, Visualization of Die Casting Magnesium Alloy Steering Bracket, Special Casting & Nonferrous Alloys, ISSN: 1001-2249, CN: 42-1148/TG, 2010-04. In Chinese.

    37-10  Morris Murray, Lars Feldager Hansen, and Carl Reinhardt, I Have Defects – Now What, Die Casting Engineer, September 2010

    36-10  Stefano Mascetti, Using Flow Analysis Software to Optimize Piston Velocity for an HPDC Process, Die Casting Engineer, September 2010. Also available in Italian: Ottimizzare la velocita del pistone in pressofusione.  A & C, Analisi e Calcolo, Anno XII, n. 42, Gennaio 2011, ISSN 1128-3874.

    32-10  Guan Hai Yan, Sheng Dun Zhao, Zheng Hui Sha, Parameters Optimization of Semisolid Diecasting Process for Air-Conditioner’s Triple Valve in HPb59-1 Alloy, Advanced Materials Research (Volumes 129 – 131), Vol. Material and Manufacturing Technology, pp. 936-941, DOI: 10.4028/www.scientific.net/AMR.129-131.936, August 2010.

    29-10 Zheng Peng, Xu Jun, Zhang Zhifeng, Bai Yuelong, and Shi Likai, Numerical Simulation of Filling of Rheo-diecasting A357 Aluminum Alloy, Special Casting & Nonferrous Alloys, DOI: CNKI:SUN:TZZZ.0.2010-01-024, 2010.

    27-10 For an Aerospace Diecasting, Littler Uses Simulation to Reveal Defects, and Win a New Order, Foundry Management & Technology, July 2010

    23-10 Michael R. Barkhudarov, Minimizing Air Entrainment, The Canadian Die Caster, June 2010

    15-10 David H. Kirkwood, Michel Suery, Plato Kapranos, Helen V. Atkinson, and Kenneth P. Young, Semi-solid Processing of Alloys, 2010, XII, 172 p. 103 illus., 19 in color., Hardcover ISBN: 978-3-642-00705-7.

    09-10  Shannon Wetzel, Fullfilling Da Vinci’s Dream, Modern Casting, April 2010.

    08-10 B.I. Semenov, K.M. Kushtarov, Semi-solid Manufacturing of Castings, New Industrial Technologies, Publication of Moscow State Technical University n.a. N.E. Bauman, 2009 (in Russian)

    07-10 Carl Reilly, Development Of Quantitative Casting Quality Assessment Criteria Using Process Modelling, thesis: The University of Birmingham, March 2010 (Available upon request)

    06-10 A. Pari, Optimization of HPDC Process using Flow Simulation – Case Studies, CastExpo ’10, NADCA, Orlando, Florida, March 2010

    05-10 M.C. Carter, S. Palit, and M. Littler, Characterizing Flow Losses Occurring in Air Vents and Ejector Pins in High Pressure Die Castings, CastExpo ’10, NADCA, Orlando, Florida, March 2010

    04-10 Pamela Waterman, Simulating Porosity Factors, Foundry Management Technology, March 2010, Article available at Foundry Management Technology

    03-10 C. Reilly, M.R. Jolly, N.R. Green, JC Gebelin, Assessment of Casting Filling by Modeling Surface Entrainment Events Using CFD, 2010 TMS Annual Meeting & Exhibition (Jim Evans Honorary Symposium), Seattle, Washington, USA, February 14-18, 2010

    02-10 P. Väyrynen, S. Wang, J. Laine and S.Louhenkilpi, Control of Fluid Flow, Heat Transfer and Inclusions in Continuous Casting – CFD and Neural Network Studies, 2010 TMS Annual Meeting & Exhibition (Jim Evans Honorary Symposium), Seattle, Washington, USA, February 14-18, 2010

    60-09   Somlak Wannarumon, and Marco Actis Grande, Comparisons of Computer Fluid Dynamic Software Programs applied to Jewelry Investment Casting Process, World Academy of Science, Engineering and Technology 55 2009.

    59-09   Marco Actis Grande and Somlak Wannarumon, Numerical Simulation of Investment Casting of Gold Jewelry: Experiments and Validations, World Academy of Science, Engineering and Technology, Vol:3 2009-07-24

    56-09  Jozef Kasala, Ondrej Híreš, Rudolf Pernis, Start-up Phase Modeling of Semi Continuous Casting Process of Brass Billets, Metal 2009, 19.-21.5.2009

    51-09  In-Ting Hong, Huan-Chien Tung, Chun-Hao Chiu and Hung-Shang Huang, Effect of Casting Parameters on Microstructure and Casting Quality of Si-Al Alloy for Vacuum Sputtering, China Steel Technical Report, No. 22, pp. 33-40, 2009.

    42-09  P. Väyrynen, S. Wang, S. Louhenkilpi and L. Holappa, Modeling and Removal of Inclusions in Continuous Casting, Materials Science & Technology 2009 Conference & Exhibition, Pittsburgh, Pennsylvania, USA, October 25-29, 2009

    41-09 O.Smirnov, P.Väyrynen, A.Kravchenko and S.Louhenkilpi, Modern Methods of Modeling Fluid Flow and Inclusions Motion in Tundish Bath – General View, Proceedings of Steelsim 2009 – 3rd International Conference on Simulation and Modelling of Metallurgical Processes in Steelmaking, Leoben, Austria, September 8-10, 2009

    21-09 A. Pari, Case Studies – Optimization of HPDC Process Using Flow Simulation, Die Casting Engineer, July 2009

    20-09 M. Sirvio, M. Wos, Casting directly from a computer model by using advanced simulation software, FLOW-3D Cast, Archives of Foundry Engineering Volume 9, Issue 1/2009, 79-82

    19-09 Andrei Starobin, C.W. Hirt, D. Goettsch, A Model for Binder Gas Generation and Transport in Sand Cores and Molds, Modeling of Casting, Welding, and Solidification Processes XII, TMS (The Minerals, Metals & Minerals Society), June 2009

    11-09 Michael Barkhudarov, Minimizing Air Entrainment in a Shot Sleeve during Slow-Shot Stage, Die Casting Engineer (The North American Die Casting Association ISSN 0012-253X), May 2009

    10-09 A. Reikher, H. Gerber, Application of One-Dimensional Numerical Simulation to Optimize Process Parameters of a Thin-Wall Casting in High Pressure Die Casting, Die Casting Engineer (The North American Die Casting Association ISSN 0012-253X), May 2009

    7-09 Andrei Starobin, Simulation of Core Gas Evolution and Flow, presented at the North American Die Casting Association – 113th Metalcasting Congress, April 7-10, 2009, Las Vegas, Nevada, USA

    6-09 A.Pari, Optimization of HPDC PROCESS: Case Studies, North American Die Casting Association – 113th Metalcasting Congress, April 7-10, 2009, Las Vegas, Nevada, USA

    2-09 C. Reilly, N.R. Green and M.R. Jolly, Oxide Entrainment Structures in Horizontal Running Systems, TMS 2009, San Francisco, California, February 2009

    30-08 I.N.Volnov, Computer Modeling of Casting of Pipe Fittings, © 2008, Pipe Fittings, 5 (38), 2008. Russian version

    28-08 A.V.Chaikin, I.N.Volnov, V.A.Chaikin, Y.A.Ukhanov, N.R.Petrov, Analysis of the Efficiency of Alloy Modifiers Using Statistics and Modeling, © 2008, Liteyshik Rossii (Russian Foundryman), October, 2008

    27-08 P. Scarber, Jr., H. Littleton, Simulating Macro-Porosity in Aluminum Lost Foam Castings, American Foundry Society, © 2008, AFS Lost Foam Conference, Asheville, North Carolina, October, 2008

    25-08 FMT Staff, Forecasting Core Gas Pressures with Computer Simulation, Foundry Management and Technology, October 28, 2008 © 2008 Penton Media, Inc. Online article

    24-08 Core and Mold Gas Evolution, Foundry Management and Technology, January 24, 2008 (excerpted from the FM&T May 2007 issue) © 2008 Penton Media, Inc.

    22-08 Mark Littler, Simulation Eliminates Die Casting Scrap, Modern Casting/September 2008

    21-08 X. Chen, D. Penumadu, Permeability Measurement and Numerical Modeling for Refractory Porous Materials, AFS Transactions © 2008 American Foundry Society, CastExpo ’08, Atlanta, Georgia, May 2008

    20-08 Rolf Krack, Using Solidification Simulations for Optimising Die Cooling Systems, FTJ July/August 2008

    19-08 Mark Littler, Simulation Software Eliminates Die Casting Scrap, ECS Casting Innovations, July/August 2008

    13-08 T. Yoshimura, K. Yano, T. Fukui, S. Yamamoto, S. Nishido, M. Watanabe and Y. Nemoto, Optimum Design of Die Casting Plunger Tip Considering Air Entrainment, Proceedings of 10th Asian Foundry Congress (AFC10), Nagoya, Japan, May 2008

    08-08 Stephen Instone, Andreas Buchholz and Gerd-Ulrich Gruen, Inclusion Transport Phenomena in Casting Furnaces, Light Metals 2008, TMS (The Minerals, Metals & Materials Society), 2008

    07-08 P. Scarber, Jr., H. Littleton, Simulating Macro-Porosity in Aluminum Lost Foam Casting, AFS Transactions 2008 © American Foundry Society, CastExpo ’08, Atlanta, Georgia, May 2008

    06-08 A. Reikher, H. Gerber and A. Starobin, Multi-Stage Plunger Deceleration System, CastExpo ’08, NADCA, Atlanta, Georgia, May 2008

    05-08 Amol Palekar, Andrei Starobin, Alexander Reikher, Die-casting end-of-fill and drop forge viscometer flow transients examined with a coupled-motion numerical model, 68th World Foundry Congress, Chennai, India, February 2008

    03-08 Petri J. Väyrynen, Sami K. Vapalahti and Seppo J. Louhenkilpi, On Validation of Mathematical Fluid Flow Models for Simulation of Tundish Water Models and Industrial Examples, AISTech 2008, May 2008

    53-07   A. Kermanpur, Sh. Mahmoudi and A. Hajipour, Three-dimensional Numerical Simulation of Metal Flow and Solidification in the Multi-cavity Casting Moulds of Automotive Components, International Journal of Iron & Steel Society of Iran, Article 2, Volume 4, Issue 1, Summer and Autumn 2007, pages 8-15.

    36-07 Duque Mesa A. F., Herrera J., Cruz L.J., Fernández G.P. y Martínez H.V., Caracterización Defectológica de Piezas Fundida por Lost Foam Casting Mediante Simulación Numérica, 8° Congreso Iberoamericano de Ingenieria Mecanica, Cusco, Peru, 23 al 25 de Octubre de 2007 (in Spanish)

    27-07 A.Y. Korotchenko, A.M. Zarubin, I.A.Korotchenko, Modeling of High Pressure Die Casting Filling, Russian Foundryman, December 2007, pp 15-19. (in Russian)

    26-07 I.N. Volnov, Modeling of Casting Processes with Variable Geometry, Russian Foundryman, November 2007, pp 27-30. (in Russian)

    16-07 P. Väyrynen, S. Vapalahti, S. Louhenkilpi, L. Chatburn, M. Clark, T. Wagner, Tundish Flow Model Tuning and Validation – Steady State and Transient Casting Situations, STEELSIM 2007, Graz/Seggau, Austria, September 12-14 2007

    11-07 Marco Actis Grande, Computer Simulation of the Investment Casting Process – Widening of the Filling Step, Santa Fe Symposium on Jewelry Manufacturing Technology, May 2007

    09-07 Alexandre Reikher and Michael Barkhudarov, Casting: An Analytical Approach, Springer, 1st edition, August 2007, Hardcover ISBN: 978-1-84628-849-4. U.S. Order Form; Europe Order Form.

    07-07 I.N. Volnov, Casting Modeling Systems – Current State, Problems and Perspectives, (in Russian), Liteyshik Rossii (Russian Foundryman), June 2007

    05-07 A.N. Turchin, D.G. Eskin, and L. Katgerman, Solidification under Forced-Flow Conditions in a Shallow Cavity, DOI: 10.1007/s1161-007-9183-9, © The Minerals, Metals & Materials Society and ASM International 2007

    04-07 A.N. Turchin, M. Zuijderwijk, J. Pool, D.G. Eskin, and L. Katgerman, Feathery grain growth during solidification under forced flow conditions, © Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. DOI: 10.1016/j.actamat.2007.02.030, April 2007

    03-07 S. Kuyucak, Sponsored Research – Clean Steel Casting Production—Evaluation of Laboratory Castings, Transactions of the American Foundry Society, Volume 115, 111th Metalcasting Congress, May 2007

    02-07 Fu-Yuan Hsu, Mark R. Jolly and John Campbell, The Design of L-Shaped Runners for Gravity Casting, Shape Casting: 2nd International Symposium, Edited by Paul N. Crepeau, Murat Tiryakioðlu and John Campbell, TMS (The Minerals, Metals & Materials Society), Orlando, FL, Feb 2007

    30-06 X.J. Liu, S.H. Bhavnani, R.A. Overfelt, Simulation of EPS foam decomposition in the lost foam casting process, Journal of Materials Processing Technology 182 (2007) 333–342, © 2006 Elsevier B.V. All rights reserved.

    25-06 Michael Barkhudarov and Gengsheng Wei, Modeling Casting on the Move, Modern Casting, August 2006; Modeling of Casting Processes with Variable Geometry, Russian Foundryman, December 2007, pp 10-15. (in Russian)

    24-06 P. Scarber, Jr. and C.E. Bates, Simulation of Core Gas Production During Mold Fill, © 2006 American Foundry Society

    7-06 M.Y.Smirnov, Y.V.Golenkov, Manufacturing of Cast Iron Bath Tubs Castings using Vacuum-Process in Russia, Russia’s Foundryman, July 2006. In Russian.

    6-06 M. Barkhudarov, and G. Wei, Modeling of the Coupled Motion of Rigid Bodies in Liquid Metal, Modeling of Casting, Welding and Advanced Solidification Processes – XI, May 28 – June 2, 2006, Opio, France, eds. Ch.-A. Gandin and M. Bellet, pp 71-78, 2006.

    2-06 J.-C. Gebelin, M.R. Jolly and F.-Y. Hsu, ‘Designing-in’ Controlled Filling Using Numerical Simulation for Gravity Sand Casting of Aluminium Alloys, Int. J. Cast Met. Res., 2006, Vol.19 No.1

    1-06 Michael Barkhudarov, Using Simulation to Control Microporosity Reduces Die Iterations, Die Casting Engineer, January 2006, pp. 52-54

    30-05 H. Xue, K. Kabiri-Bamoradian, R.A. Miller, Modeling Dynamic Cavity Pressure and Impact Spike in Die Casting, Cast Expo ’05, April 16-19, 2005

    22-05 Blas Melissari & Stavros A. Argyropoulous, Measurement of Magnitude and Direction of Velocity in High-Temperature Liquid Metals; Part I, Mathematical Modeling, Metallurgical and Materials Transactions B, Volume 36B, October 2005, pp. 691-700

    21-05 M.R. Jolly, State of the Art Review of Use of Modeling Software for Casting, TMS Annual Meeting, Shape Casting: The John Campbell Symposium, Eds, M. Tiryakioglu & P.N Crepeau, TMS, Warrendale, PA, ISBN 0-87339-583-2, Feb 2005, pp 337-346

    20-05 J-C Gebelin, M.R. Jolly & F-Y Hsu, ‘Designing-in’ Controlled Filling Using Numerical Simulation for Gravity Sand Casting of Aluminium Alloys, TMS Annual Meeting, Shape Casting: The John Campbell Symposium, Eds, M. Tiryakioglu & P.N Crepeau, TMS, Warrendale, PA, ISBN 0-87339-583-2, Feb 2005, pp 355-364

    19-05 F-Y Hsu, M.R. Jolly & J Campbell, Vortex Gate Design for Gravity Castings, TMS Annual Meeting, Shape Casting: The John Campbell Symposium, Eds, M. Tiryakioglu & P.N Crepeau, TMS, Warrendale, PA, ISBN 0-87339-583-2, Feb 2005, pp 73-82

    18-05 M.R. Jolly, Modelling the Investment Casting Process: Problems and Successes, Japanese Foundry Society, JFS, Tokyo, Sept. 2005

    13-05 Xiaogang Yang, Xiaobing Huang, Xiaojun Dai, John Campbell and Joe Tatler, Numerical Modelling of the Entrainment of Oxide Film Defects in Filling of Aluminium Alloy Castings, International Journal of Cast Metals Research, 17 (6), 2004, 321-331

    10-05 Carlos Evaristo Esparza, Martha P. Guerro-Mata, Roger Z. Ríos-Mercado, Optimal Design of Gating Systems by Gradient Search Methods, Computational Materials Science, October 2005

    6-05 Birgit Hummler-Schaufler, Fritz Hirning, Jurgen Schaufler, A World First for Hatz Diesel and Schaufler Tooling, Die Casting Engineer, May 2005, pp. 18-21

    4-05 Rolf Krack, The W35 Topic—A World First, Die Casting World, March 2005, pp. 16-17

    3-05 Joerg Frei, Casting Simulations Speed Up Development, Die Casting World, March 2005, p. 14

    2-05 David Goettsch and Michael Barkhudarov, Analysis and Optimization of the Transient Stage of Stopper-Rod Pour, Shape Casting: The John Campbell Symposium, The Minerals, Metals & Materials Society, 2005

    36-04  Ik Min Park, Il Dong Choi, Yong Ho Park, Development of Light-Weight Al Scroll Compressor for Car Air Conditioner, Materials Science Forum, Designing, Processing and Properties of Advanced Engineering Materials, 449-452, 149, March 2004.

    32-04 D.H. Kirkwood and P.J Ward, Numerical Modelling of Semi-Solid Flow under Processing Conditions, steel research int. 75 (2004), No. 8/9

    30-04 Haijing Mao, A Numerical Study of Externally Solidified Products in the Cold Chamber Die Casting Process, thesis: The Ohio State University, 2004 (Available upon request)

    28-04 Z. Cao, Z. Yang, and X.L. Chen, Three-Dimensional Simulation of Transient GMA Weld Pool with Free Surface, Supplement to the Welding Journal, June 2004.

    23-04 State of the Art Use of Computational Modelling in the Foundry Industry, 3rd International Conference Computational Modelling of Materials III, Sicily, Italy, June 2004, Advances in Science and Technology,  Eds P. Vincenzini & A Lami, Techna Group Srl, Italy, ISBN: 88-86538-46-4, Part B, pp 479-490

    22-04 Jerry Fireman, Computer Simulation Helps Reduce Scrap, Die Casting Engineer, May 2004, pp. 46-49

    21-04 Joerg Frei, Simulation—A Safe and Quick Way to Good Components, Aluminium World, Volume 3, Issue 2, pp. 42-43

    20-04 J.-C. Gebelin, M.R. Jolly, A. M. Cendrowicz, J. Cirre and S. Blackburn, Simulation of Die Filling for the Wax Injection Process – Part II Numerical Simulation, Metallurgical and Materials Transactions, Volume 35B, August 2004

    14-04 Sayavur I. Bakhtiyarov, Charles H. Sherwin, and Ruel A. Overfelt, Hot Distortion Studies In Phenolic Urethane Cold Box System, American Foundry Society, 108th Casting Congress, June 12-15, 2004, Rosemont, IL, USA

    13-04 Sayavur I. Bakhtiyarov and Ruel A. Overfelt, First V-Process Casting of Magnesium, American Foundry Society, 108th Casting Congress, June 12-15, 2004, Rosemont, IL, USA

    5-04 C. Schlumpberger & B. Hummler-Schaufler, Produktentwicklung auf hohem Niveau (Product Development on a High Level), Druckguss Praxis, January 2004, pp 39-42 (in German).

    3-04 Charles Bates, Dealing with Defects, Foundry Management and Technology, February 2004, pp 23-25

    1-04 Laihua Wang, Thang Nguyen, Gary Savage and Cameron Davidson, Thermal and Flow Modeling of Ladling and Injection in High Pressure Die Casting Process, International Journal of Cast Metals Research, vol. 16 No 4 2003, pp 409-417

    2-03 J-C Gebelin, AM Cendrowicz, MR Jolly, Modeling of the Wax Injection Process for the Investment Casting Process – Prediction of Defects, presented at the Third International Conference on Computational Fluid Dynamics in the Minerals and Process Industries, December 10-12, 2003, Melbourne, Australia, pp. 415-420

    29-03 C. W. Hirt, Modeling Shrinkage Induced Micro-porosity, Flow Science Technical Note (FSI-03-TN66)

    28-03 Thixoforming at the University of Sheffield, Diecasting World, September 2003, pp 11-12

    26-03 William Walkington, Gas Porosity-A Guide to Correcting the Problems, NADCA Publication: 516

    22-03 G F Yao, C W Hirt, and M Barkhudarov, Development of a Numerical Approach for Simulation of Sand Blowing and Core Formation, in Modeling of Casting, Welding, and Advanced Solidification Process-X”, Ed. By Stefanescu et al pp. 633-639, 2003

    21-03 E F Brush Jr, S P Midson, W G Walkington, D T Peters, J G Cowie, Porosity Control in Copper Rotor Die Castings, NADCA Indianapolis Convention Center, Indianapolis, IN September 15-18, 2003, T03-046

    12-03 J-C Gebelin & M.R. Jolly, Modeling Filters in Light Alloy Casting Processes,  Trans AFS, 2002, 110, pp. 109-120

    11-03 M.R. Jolly, Casting Simulation – How Well Do Reality and Virtual Casting Match – A State of the Art Review, Intl. J. Cast Metals Research, 2002, 14, pp. 303-313

    10-03 Gebelin., J-C and Jolly, M.R., Modeling of the Investment Casting Process, Journal of  Materials Processing Tech., Vol. 135/2-3, pp. 291 – 300

    9-03 Cox, M, Harding, R.A. and Campbell, J., Optimised Running System Design for Bottom Filled Aluminium Alloy 2L99 Investment Castings, J. Mat. Sci. Tech., May 2003, Vol. 19, pp. 613-625

    8-03 Von Alexander Schrey and Regina Reek, Numerische Simulation der Kernherstellung, (Numerical Simulation of Core Blowing), Giesserei, June 2003, pp. 64-68 (in German)

    7-03 J. Zuidema Jr., L Katgerman, Cyclone separation of particles in aluminum DC Casting, Proceedings from the Tenth International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, Destin, FL, May 2003, pp. 607-614

    6-03 Jean-Christophe Gebelin and Mark Jolly, Numerical Modeling of Metal Flow Through Filters, Proceedings from the Tenth International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, Destin, FL, May 2003, pp. 431-438

    5-03 N.W. Lai, W.D. Griffiths and J. Campbell, Modelling of the Potential for Oxide Film Entrainment in Light Metal Alloy Castings, Proceedings from the Tenth International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, Destin, FL, May 2003, pp. 415-422

    21-02 Boris Lukezic, Case History: Process Modeling Solves Die Design Problems, Modern Casting, February 2003, P 59

    20-02 C.W. Hirt and M.R. Barkhudarov, Predicting Defects in Lost Foam Castings, Modern Casting, December 2002, pp 31-33

    19-02 Mark Jolly, Mike Cox, Ric Harding, Bill Griffiths and John Campbell, Quiescent Filling Applied to Investment Castings, Modern Casting, December 2002 pp. 36-38

    18-02 Simulation Helps Overcome Challenges of Thin Wall Magnesium Diecasting, Foundry Management and Technology, October 2002, pp 13-15

    17-02 G Messmer, Simulation of a Thixoforging Process of Aluminum Alloys with FLOW-3D, Institute for Metal Forming Technology, University of Stuttgart

    16-02 Barkhudarov, Michael, Computer Simulation of Lost Foam Process, Casting Simulation Background and Examples from Europe and the USA, World Foundrymen Organization, 2002, pp 319-324

    15-02 Barkhudarov, Michael, Computer Simulation of Inclusion Tracking, Casting Simulation Background and Examples from Europe and the USA, World Foundrymen Organization, 2002, pp 341-346

    14-02 Barkhudarov, Michael, Advanced Simulation of the Flow and Heat Transfer of an Alternator Housing, Casting Simulation Background and Examples from Europe and the USA, World Foundrymen Organization, 2002, pp 219-228

    8-02 Sayavur I. Bakhtiyarov, and Ruel A. Overfelt, Experimental and Numerical Study of Bonded Sand-Air Two-Phase Flow in PUA Process, Auburn University, 2002 American Foundry Society, AFS Transactions 02-091, Kansas City, MO

    7-02 A Habibollah Zadeh, and J Campbell, Metal Flow Through a Filter System, University of Birmingham, 2002 American Foundry Society, AFS Transactions 02-020, Kansas City, MO

    6-02 Phil Ward, and Helen Atkinson, Final Report for EPSRC Project: Modeling of Thixotropic Flow of Metal Alloys into a Die, GR/M17334/01, March 2002, University of Sheffield

    5-02 S. I. Bakhtiyarov and R. A. Overfelt, Numerical and Experimental Study of Aluminum Casting in Vacuum-sealed Step Molding, Auburn University, 2002 American Foundry Society, AFS Transactions 02-050, Kansas City, MO

    4-02 J. C. Gebelin and M. R. Jolly, Modelling Filters in Light Alloy Casting Processes, University of Birmingham, 2002 American Foundry Society AFS Transactions 02-079, Kansas City, MO

    3-02 Mark Jolly, Mike Cox, Jean-Christophe Gebelin, Sam Jones, and Alex Cendrowicz, Fundamentals of Investment Casting (FOCAST), Modelling the Investment Casting Process, Some preliminary results from the UK Research Programme, IRC in Materials, University of Birmingham, UK, AFS2001

    49-01   Hua Bai and Brian G. Thomas, Bubble formation during horizontal gas injection into downward-flowing liquid, Metallurgical and Materials Transactions B, Vol. 32, No. 6, pp. 1143-1159, 2001. doi.org/10.1007/s11663-001-0102-y

    45-01 Jan Zuidema; Laurens Katgerman; Ivo J. Opstelten;Jan M. Rabenberg, Secondary Cooling in DC Casting: Modelling and Experimental Results, TMS 2001, New Orleans, Louisianna, February 11-15, 2001

    43-01 James Andrew Yurko, Fluid Flow Behavior of Semi-Solid Aluminum at High Shear Rates,Ph.D. thesis; Massachusetts Institute of Technology, June 2001. Abstract only; full thesis available at http://dspace.mit.edu/handle/1721.1/8451 (for a fee).

    33-01 Juang, S.H., CAE Application on Design of Die Casting Dies, 2001 Conference on CAE Technology and Application, Hsin-Chu, Taiwan, November 2001, (article in Chinese with English-language abstract)

    32-01 Juang, S.H. and C. M. Wang, Effect of Feeding Geometry on Flow Characteristics of Magnesium Die Casting by Numerical Analysis, The Preceedings of 6th FADMA Conference, Taipei, Taiwan, July 2001, Chinese language with English abstract

    26-01 C. W. Hirt., Predicting Defects in Lost Foam Castings, December 13, 2001

    21-01 P. Scarber Jr., Using Liquid Free Surface Areas as a Predictor of Reoxidation Tendency in Metal Alloy Castings, presented at the Steel Founders’ Society of American, Technical and Operating Conference, October 2001

    20-01 P. Scarber Jr., J. Griffin, and C. E. Bates, The Effect of Gating and Pouring Practice on Reoxidation of Steel Castings, presented at the Steel Founders’ Society of American, Technical and Operating Conference, October 2001

    19-01 L. Wang, T. Nguyen, M. Murray, Simulation of Flow Pattern and Temperature Profile in the Shot Sleeve of a High Pressure Die Casting Process, CSIRO Manufacturing Science and Technology, Melbourne, Victoria, Australia, Presented by North American Die Casting Association, Oct 29-Nov 1, 2001, Cincinnati, To1-014

    18-01 Rajiv Shivpuri, Venkatesh Sankararaman, Kaustubh Kulkarni, An Approach at Optimizing the Ingate Design for Reducing Filling and Shrinkage Defects, The Ohio State University, Columbus, OH, Presented by North American Die Casting Association, Oct 29-Nov 1, 2001, Cincinnati, TO1-052

    5-01 Michael Barkhudarov, Simulation Helps Overcome Challenges of Thin Wall Magnesium Diecasting, Diecasting World, March 2001, pp. 5-6

    2-01 J. Grindling, Customized CFD Codes to Simulate Casting of Thermosets in Full 3D, Electrical Manufacturing and Coil Winding 2000 Conference, October 31-November 2, 20

    20-00 Richard Schuhmann, John Carrig, Thang Nguyen, Arne Dahle, Comparison of Water Analogue Modelling and Numerical Simulation Using Real-Time X-Ray Flow Data in Gravity Die Casting, Australian Die Casting Association Die Casting 2000 Conference, September 3-6, 2000, Melbourne, Victoria, Australia

    15-00 M. Sirvio, Vainola, J. Vartianinen, M. Vuorinen, J. Orkas, and S. Devenyi, Fluid Flow Analysis for Designing Gating of Aluminum Castings, Proc. NADCA Conf., Rosemont, IL, Nov 6-8, 1999

    14-00 X. Yang, M. Jolly, and J. Campbell, Reduction of Surface Turbulence during Filling of Sand Castings Using a Vortex-flow Runner, Conference for Modeling of Casting, Welding, and Advanced Solidification Processes IX, Aachen, Germany, August 2000

    13-00 H. S. H. Lo and J. Campbell, The Modeling of Ceramic Foam Filters, Conference for Modeling of Casting, Welding, and Advanced Solidification Processes IX, Aachen, Germany, August 2000

    12-00 M. R. Jolly, H. S. H. Lo, M. Turan and J. Campbell, Use of Simulation Tools in the Practical Development of a Method for Manufacture of Cast Iron Camshafts,” Conference for Modeling of Casting, Welding, and Advanced Solidification Processes IX, Aachen, Germany, August, 2000

    14-99 J Koke, and M Modigell, Time-Dependent Rheological Properties of Semi-solid Metal Alloys, Institute of Chemical Engineering, Aachen University of Technology, Mechanics of Time-Dependent Materials 3: 15-30, 1999

    12-99 Grun, Gerd-Ulrich, Schneider, Wolfgang, Ray, Steven, Marthinusen, Jan-Olaf, Recent Improvements in Ceramic Foam Filter Design by Coupled Heat and Fluid Flow Modeling, Proc TMS Annual Meeting, 1999, pp. 1041-1047

    10-99 Bongcheol Park and Jerald R. Brevick, Computer Flow Modeling of Cavity Pre-fill Effects in High Pressure Die Casting, NADCA Proceedings, Cleveland T99-011, November, 1999

    8-99 Brad Guthrie, Simulation Reduces Aluminum Die Casting Cost by Reducing Volume, Die Casting Engineer Magazine, September/October 1999, pp. 78-81

    7-99 Fred L. Church, Virtual Reality Predicts Cast Metal Flow, Modern Metals, September, 1999, pp. 67F-J

    19-98 Grun, Gerd-Ulrich, & Schneider, Wolfgang, Numerical Modeling of Fluid Flow Phenomena in the Launder-integrated Tool Within Casting Unit Development, Proc TMS Annual Meeting, 1998, pp. 1175-1182

    18-98 X. Yang & J. Campbell, Liquid Metal Flow in a Pouring Basin, Int. J. Cast Metals Res, 1998, 10, pp. 239-253

    15-98 R. Van Tol, Mould Filling of Horizontal Thin-Wall Castings, Delft University Press, The Netherlands, 1998

    14-98 J. Daughtery and K. A. Williams, Thermal Modeling of Mold Material Candidates for Copper Pressure Die Casting of the Induction Motor Rotor Structure, Proc. Int’l Workshop on Permanent Mold Casting of Copper-Based Alloys, Ottawa, Ontario, Canada, Oct. 15-16, 1998

    10-98 C. W. Hirt, and M.R. Barkhudarov, Lost Foam Casting Simulation with Defect Prediction, Flow Science Inc, presented at Modeling of Casting, Welding and Advanced Solidification Processes VIII Conference, June 7-12, 1998, Catamaran Hotel, San Diego, California

    9-98 M. R. Barkhudarov and C. W. Hirt, Tracking Defects, Flow Science Inc, presented at the 1st International Aluminum Casting Technology Symposium, 12-14 October 1998, Rosemont, IL

    5-98 J. Righi, Computer Simulation Helps Eliminate Porosity, Die Casting Management Magazine, pp. 36-38, January 1998

    3-98 P. Kapranos, M. R. Barkhudarov, D. H. Kirkwood, Modeling of Structural Breakdown during Rapid Compression of Semi-Solid Alloy Slugs, Dept. Engineering Materials, The University of Sheffield, Sheffield S1 3JD, U.K. and Flow Science Inc, USA, Presented at the 5th International Conference Semi-Solid Processing of Alloys and Composites, Colorado School of Mines, Golden, CO, 23-25 June 1998

    1-98 U. Jerichow, T. Altan, and P. R. Sahm, Semi Solid Metal Forming of Aluminum Alloys-The Effect of Process Variables Upon Material Flow, Cavity Fill and Mechanical Properties, The Ohio State University, Columbus, OH, published in Die Casting Engineer, p. 26, Jan/Feb 1998

    8-97 Michael Barkhudarov, High Pressure Die Casting Simulation Using FLOW-3D, Die Casting Engineer, 1997

    15-97 M. R. Barkhudarov, Advanced Simulation of the Flow and Heat Transfer Process in Simultaneous Engineering, Flow Science report, presented at the Casting 1997 – International ADI and Simulation Conference, Helsinki, Finland, May 28-30, 1997

    14-97 M. Ranganathan and R. Shivpuri, Reducing Scrap and Increasing Die Life in Low Pressure Die Casting through Flow Simulation and Accelerated Testing, Dept. Welding and Systems Engineering, Ohio State University, Columbus, OH, presented at 19th International Die Casting Congress & Exposition, November 3-6, 1997

    13-97 J. Koke, Modellierung und Simulation der Fließeigenschaften teilerstarrter Metallegierungen, Livt Information, Institut für Verfahrenstechnik, RWTH Aachen, October 1997

    10-97 J. P. Greene and J. O. Wilkes, Numerical Analysis of Injection Molding of Glass Fiber Reinforced Thermoplastics – Part 2 Fiber Orientation, Body-in-White Center, General Motors Corp. and Dept. Chemical Engineering, University of Michigan, Polymer Engineering and Science, Vol. 37, No. 6, June 1997

    9-97 J. P. Greene and J. O. Wilkes, Numerical Analysis of Injection Molding of Glass Fiber Reinforced Thermoplastics. Part 1 – Injection Pressures and Flow, Manufacturing Center, General Motors Corp. and Dept. Chemical Engineering, University of Michigan, Polymer Engineering and Science, Vol. 37, No. 3, March 1997

    8-97 H. Grazzini and D. Nesa, Thermophysical Properties, Casting Simulation and Experiments for a Stainless Steel, AT Systemes (Renault) report, presented at the Solidification Processing ’97 Conference, July 7-10, 1997, Sheffield, U.K.

    7-97 R. Van Tol, L. Katgerman and H. E. A. Van den Akker, Horizontal Mould Filling of a Thin Wall Aluminum Casting, Laboratory of Materials report, Delft University, presented at the Solidification Processing ’97 Conference, July 7-10, 1997, Sheffield, U.K.

    6-97 M. R. Barkhudarov, Is Fluid Flow Important for Predicting Solidification, Flow Science report, presented at the Solidification Processing ’97 Conference, July 7-10, 1997, Sheffield, U.K.

    22-96 Grun, Gerd-Ulrich & Schneider, Wolfgang, 3-D Modeling of the Start-up Phase of DC Casting of Sheet Ingots, Proc TMS Annual Meeting, 1996, pp. 971-981

    9-96 M. R. Barkhudarov and C. W. Hirt, Thixotropic Flow Effects under Conditions of Strong Shear, Flow Science report FSI96-00-2, to be presented at the “Materials Week ’96” TMS Conference, Cincinnati, OH, 7-10 October 1996

    4-96 C. W. Hirt, A Computational Model for the Lost Foam Process, Flow Science final report, February 1996 (FSI-96-57-R2)

    3-96 M. R. Barkhudarov, C. L. Bronisz, C. W. Hirt, Three-Dimensional Thixotropic Flow Model, Flow Science report, FSI-96-00-1, published in the proceedings of (pp. 110- 114) and presented at the 4th International Conference on Semi-Solid Processing of Alloys and Composites, The University of Sheffield, 19-21 June 1996

    1-96 M. R. Barkhudarov, J. Beech, K. Chang, and S. B. Chin, Numerical Simulation of Metal/Mould Interfacial Heat Transfer in Casting, Dept. Mech. & Process Engineering, Dept. Engineering Materials, University of Sheffield and Flow Science Inc, 9th Int. Symposium on Transport Phenomena in Thermal-Fluid Engineering, June 25-28, 1996, Singapore

    11-95 Barkhudarov, M. R., Hirt, C.W., Casting Simulation Mold Filling and Solidification-Benchmark Calculations Using FLOW-3D, Modeling of Casting, Welding, and Advanced Solidification Processes VII, pp 935-946

    10-95 Grun, Gerd-Ulrich, & Schneider, Wolfgang, Optimal Design of a Distribution Pan for Level Pour Casting, Proc TMS Annual Meeting, 1995, pp. 1061-1070

    9-95 E. Masuda, I. Itoh, K. Haraguchi, Application of Mold Filling Simulation to Die Casting Processes, Honda Engineering Co., Ltd., Tochigi, Japan, presented at the Modelling of Casting, Welding and Advanced Solidification Processes VII, The Minerals, Metals & Materials Society, 1995

    6-95 K. Venkatesan, Experimental and Numerical Investigation of the Effect of Process Parameters on the Erosive Wear of Die Casting Dies, presented for Ph.D. degree at Ohio State University, 1995

    5-95 J. Righi, A. F. LaCamera, S. A. Jones, W. G. Truckner, T. N. Rouns, Integration of Experience and Simulation Based Understanding in the Die Design Process, Alcoa Technical Center, Alcoa Center, PA 15069, presented by the North American Die Casting Association, 1995

    2-95 K. Venkatesan and R. Shivpuri, Numerical Simulation and Comparison with Water Modeling Studies of the Inertia Dominated Cavity Filling in Die Casting, NUMIFORM, 1995

    1-95 K. Venkatesan and R. Shivpuri, Numerical Investigation of the Effect of Gate Velocity and Gate Size on the Quality of Die Casting Parts, NAMRC, 1995.

    15-94 D. Liang, Y. Bayraktar, S. A. Moir, M. Barkhudarov, and H. Jones, Primary Silicon Segregation During Isothermal Holding of Hypereutectic AI-18.3%Si Alloy in the Freezing Range, Dept. of Engr. Materials, U. of Sheffield, Metals and Materials, February 1994

    13-94 Deniece Korzekwa and Paul Dunn, A Combined Experimental and Modeling Approach to Uranium Casting, Materials Division, Los Alamos National Laboratory, presented at the Symposium on Liquid Metal Processing and Casting, El Dorado Hotel, Santa Fe, New Mexico, 1994

    12-94 R. van Tol, H. E. A. van den Akker and L. Katgerman, CFD Study of the Mould Filling of a Horizontal Thin Wall Aluminum Casting, Delft University of Technology, Delft, The Netherlands, HTD-Vol. 284/AMD-Vol. 182, Transport Phenomena in Solidification, ASME 1994

    11-94 M. R. Barkhudarov and K. A. Williams, Simulation of ‘Surface Turbulence’ Fluid Phenomena During the Mold Filling Phase of Gravity Castings, Flow Science Technical Note #41, November 1994 (FSI-94-TN41)

    10-94 M. R. Barkhudarov and S. B. Chin, Stability of a Numerical Algorithm for Gas Bubble Modelling, University of Sheffield, Sheffield, U.K., International Journal for Numerical Methods in Fluids, Vol. 19, 415-437 (1994)

    16-93 K. Venkatesan and R. Shivpuri, Numerical Simulation of Die Cavity Filling in Die Castings and an Evaluation of Process Parameters on Die Wear, Dept. of Industrial Systems Engineering, Presented by: N.A. Die Casting Association, Cleveland, Ohio, October 18-21, 1993

    15-93 K. Venkatesen and R. Shivpuri, Numerical Modeling of Filling and Solidification for Improved Quality of Die Casting: A Literature Survey (Chapters II and III), Engineering Research Center for Net Shape Manufacturing, Report C-93-07, August 1993, Ohio State University

    1-93 P-E Persson, Computer Simulation of the Solidification of a Hub Carrier for the Volvo 800 Series, AB Volvo Technological Development, Metals Laboratory, Technical Report No. LM 500014E, Jan. 1993

    13-92 D. R. Korzekwa, M. A. K. Lewis, Experimentation and Simulation of Gravity Fed Lead Castings, in proceedings of a TMS Symposium on Concurrent Engineering Approach to Materials Processing, S. N. Dwivedi, A. J. Paul and F. R. Dax, eds., TMS-AIME Warrendale, p. 155 (1992)

    12-92 M. A. K. Lewis, Near-Net-Shaiconpe Casting Simulation and Experimentation, MST 1992 Review, Los Alamos National Laboratory

    2-92 M. R. Barkhudarov, H. You, J. Beech, S. B. Chin, D. H. Kirkwood, Validation and Development of FLOW-3D for Casting, School of Materials, University of Sheffield, Sheffield, UK, presented at the TMS/AIME Annual Meeting, San Diego, CA, March 3, 1992

    1-92 D. R. Korzekwa and L. A. Jacobson, Los Alamos National Laboratory and C.W. Hirt, Flow Science Inc, Modeling Planar Flow Casting with FLOW-3D, presented at the TMS/AIME Annual Meeting, San Diego, CA, March 3, 1992

    12-91 R. Shivpuri, M. Kuthirakulathu, and M. Mittal, Nonisothermal 3-D Finite Difference Simulation of Cavity Filling during the Die Casting Process, Dept. Industrial and Systems Engineering, Ohio State University, presented at the 1991 Winter Annual ASME Meeting, Atlanta, GA, Dec. 1-6, 1991

    3-91 C. W. Hirt, A FLOW-3D Study of the Importance of Fluid Momentum in Mold Filling, presented at the 18th Annual Automotive Materials Symposium, Michigan State University, Lansing, MI, May 1-2, 1991 (FSI-91-00-2)

    11-90 N. Saluja, O.J. Ilegbusi, and J. Szekely, On the Calculation of the Electromagnetic Force Field in the Circular Stirring of Metallic Melts, accepted in J. Appl. Physics, 1990

    10-90 N. Saluja, O. J. Ilegbusi, and J. Szekely, On the Calculation of the Electromagnetic Force Field in the Circular Stirring of Metallic Molds in Continuous Castings, presented at the 6th Iron and Steel Congress of the Iron and Steel Institute of Japan, Nagoya, Japan, October 1990

    9-90 N. Saluja, O. J. Ilegbusi, and J. Szekely, Fluid Flow in Phenomena in the Electromagnetic Stirring of Continuous Casting Systems, Part I. The Behavior of a Cylindrically Shaped, Laboratory Scale Installation, accepted for publication in Steel Research, 1990

    8-89 C. W. Hirt, Gravity-Fed Casting, Flow Science Technical Note #20, July 1989 (FSI-89-TN20)

    6-89 E. W. M. Hansen and F. Syvertsen, Numerical Simulation of Flow Behaviour in Moldfilling for Casting Analysis, SINTEF-Foundation for Scientific and Industrial Research at the Norwegian Institute of Technology, Trondheim, Norway, Report No. STS20 A89001, June 1989

    1-88 C. W. Hirt and R. P. Harper, Modeling Tests for Casting Processes, Flow Science report, Jan. 1988 (FSI-88-38-01)

    2-87 C. W. Hirt, Addition of a Solidification/Melting Model to FLOW-3D, Flow Science report, April 1987 (FSI-87-33-1)

    Sediment Transport Model

    Sediment Transport Model

    Sediment Transport Model

    FLOW-3D의 침전물 이송 모델을 사용하여 세굴 및 침전물을 평가할 수 있으며, 여기서 3차원 유량 구성 요소가 세굴 프로세스를 주도하고 있습니다. Flow-3D의 유체역학 모델은 유체물리학을 설명하는 정전기적이지 않은 레이놀즈-평균화된 Navier-Stokes 방정식을 완벽하게 해결합니다. 유체역학적 솔버는 침전물 운반 모듈과 완전히 결합되어 있어 침전물 운반 및 비접착 토양의 부유식 침식, 인포테인먼트 및 침식을 시뮬레이션합니다(Wei et al., 2014). 베드로드, 인포테인먼트 및 정착 프로세스에 사용되는 모든 경험적 관계는 완전히 사용자 정의 가능하며, 최대 10개의 침전물 종(곡물 크기, 질량 밀도, 임계 전단 응력 등 서로 다른 특성을 가진)을 정의할 수 있습니다. FLOW-3D는 짧은 경과 시간 척도에 대한 국부적 스쿠어를 시뮬레이션하는 데 이상적입니다.

    FLOW-3D‘s Sediment Transport model can be used to evaluate scour and deposition, where three-dimensional flow components are driving the scouring process. FLOW-3D’s hydrodynamic model solves the full unsteady non-hydrostatic Reynolds-averaged Navier-Stokes equations that describe the flow physics. The hydrodynamic solver is fully coupled with a sediment transport module that simulates bedload and suspended sediment transport, entrainment and erosion for non-cohesive soils (Wei et al., 2014). All empirical relationships used in bedload, entrainment and settling processes are fully customizable, and up to 10 different sediment species (with different properties such as grain size, mass density and critical shear stress) can be defined. FLOW-3D is ideal for simulating local scour over short episodic time scales.

    Modeling Capabilities
    – Unsteady 3D mobile bed modeling
    – Bedload and suspended sediment transport
    – Non-cohesive sediment
    – 10 individual grain size fractions
    – Suspended sediment settling and entrainment
    – Critical angle of repose    		Applications
    – River and coastal morphodynamics
    – Bridge pier and abutment scour
    – Local scour at hydraulic structures
    – Sedimentation basins
    – Reservoir flushing

    Sediment Transport Model

    Sentral Transport 모델은 8.0 버전(Brethour, 2009년)에서 처음 도입되었으며, 11.1 버전(Wei et al., 2014년), 가장 최근에는 12.0 버전(Flow Science, 2019년)에서 광범위한 개정을 거쳤습니다. 숫자 모델에서 시뮬레이션된 물리적 프로세스의 개략도가 아래에 나와 있습니다.

    The Sediment Transport model was first introduced in version 8.0 (Brethour, 2009), and has gone through extensive revisions in version 11.1 (Wei et al., 2014), and most recently in version 12.0 (Flow Science, 2019). A schematic of the physical processes simulated in the numerical model is illustrated below.

    The different processes modeled by the Sediment Transport Model.

    수치 모델에서 침전물은 포장된 Bed로서 일시 중단된 상태로 존재할 수 있습니다. 포장된 Bed는 PRIPT™ 기법을 사용하여 복잡한 솔리드 경계(Hirt 및 Sicilian, 1985)에 표현된 지울 수 없는 솔리드 객체입니다. 이것은 유체역학 용해기의 고체 물체를 나타내는 데 사용되는 방법과 동일합니다. 포장된 Bed의 형태학적 변화는 침전물 질량의 보존에 의해 좌우됩니다.

    In the numerical model, sediment can exist as packed bed and in a suspended state. A packed bed is an erodible solid object that is represented using the FAVOR™ technique for complex solid boundaries (Hirt and Sicilian, 1985). This is the same method used to represent solid objects in the hydrodynamic solver. The morphological change in the packed bed is governed by the conservation of sediment mass.

    형태학적 변경은 모형에 숫자로 표시되는 여러 가지 물리적 프로세스에 의해 제어됩니다. 이러한 프로세스에는 베드로드 운송, 인포테인먼트 및 증착이 포함됩니다. 베드로드 이송은 침전물이 서스펜션에 전달되지 않고 채널을 따라 횡방향으로 이동하는 물리적 과정입니다. 인포테인먼트란 난류 에디가 패킹 베드 상단의 곡물을 제거하고 일시 중단된 상태로 전환하는 과정입니다. 포장이란 곡물이 현수막에서 안착되어 포장된 침대에 퇴적하는 과정입니다. 수치 모델에서 이것은 일시 중단된 상태에서 포장된 베드 상태로의 전환입니다.

    The morphological changes are governed by several different physical processes that are represented numerically in the model. These processes include bedload transport, entrainment and deposition. Bedload transport is the physical process of sediment moving laterally along the channel without being carried into suspension. Entrainment is the process by which turbulent eddies remove the grains from the top of the packed bed and transition to the suspended state. Packing is the process of grains settling out of suspension and depositing onto the packed bed. In the numerical model, this is the transition from the suspended to the packed bed state.

    인포테인먼트 및 패킹의 상대적 비율은 포장된 베드와 부유 상태 사이의 침전물 질량 교환을 제어합니다. 이 모델은 Meyer-Peter Müler(1948), Nielsen(1992) 또는 Van Rijn(1984)의 방정식을 사용하여 베드 인터페이스가 포함된 각 메시 셀에서 베드로드 전송을 계산합니다. 메쉬 셀에서 이웃의 각 메쉬 셀로 이동하는 곡물의 양을 결정하기 위해 하위 메쉬 방법이 사용됩니다. 인포테인먼트에서 곡물의 리프팅 속도는 Winterwerp 등(1992)의 방정식을 사용하여 계산됩니다. 안착 속도는 Soulsby(1997년)를 사용하여 계산됩니다. 베드 인터페이스가 포함된 메시 셀에서 인터페이스의 위치, 방향 및 면적을 계산하여 베드 전단 응력, 무차원 전단 응력, 베드로드 전송 속도 및 인포테인먼트 속도를 결정합니다. 3D 난류 흐름의 베드 전단 응력은 표준 벽 함수를 사용하여 중간 곡물 크기에 비례하는 베드 표면 거칠기를 고려하여 평가됩니다.

    The relative rates of entrainment and packing control the exchange of sediment mass between the packed bed and suspended states. The model calculates bedload transport in each mesh cell containing the bed interface using the equation of Meyer-Peter Müller (1948), Nielsen (1992) or Van Rijn (1984). A sub-mesh method is employed to determine the amount of grains moving from the mesh cell into each mesh cell in its neighbor. The lifting velocity of grains in entrainment is calculated using the equation of Winterwerp et al. (1992). The settling velocity is calculated using Soulsby (1997). In the mesh cells containing the bed interface, location, orientation and area of the interface are calculated to determine the bed shear stress, dimensionless shear stress, bedload transport rates and entrainment rates. Bed shear stress in 3D turbulent flows is evaluated using the standard wall function with consideration of bed surface roughness that is proportional to the median grain size.

    부유된 침전물은 유체의 스칼라 질량 농도로 표시됩니다. 농도는 주어진 셀에서 균일한 것으로 가정되며 유체 셀 밀도 및 점도와 결합됩니다. 각 종에 대해, 부유 침전물 농도는 수송 방정식을 풀어서 계산됩니다.

    The suspended sediment is represented as a scalar mass concentration in the fluid. The concentration is assumed to be uniform in a given cell and is coupled with the fluid cell density and viscosity. For each species, the suspended sediment concentration is calculated by solving a transport equation.

    Validations

    다음 5가지 검증 사례는 실험 데이터와 FLOW-3D의 침전물 이송 모델의 시뮬레이션 결과를 비교합니다.

    마오(1986년)
    Mao는 수중 수평 파이프라인 아래 침대의 무서운 프로파일을 얻기 위해 실험 작업을 수행했습니다. 아래 그림은 FLOW-3D를 사용하여 얻은 결과와 실험 결과를 비교합니다.

    그림 A는 파이프라인 아래의 최대 scour깊이를 시간 경과에 따라 비교하는 반면, 그림 B ~ F는 스터디의 scour프로필(빨간색 점으로 표시됨)과 FLOW-3D 프로필을 오버레이합니다.
    Chatterjee et al. (1994)

    수평 제트 침수로 인해 국부적인 스쿠어 프로파일을 얻기 위한 실험 작업이 수행되었습니다. 아래 그림은 scour구멍 깊이와 둔부 높이에 대한 실험 대 FLOW-3D의 숫자 결과를 시간의 함수로 비교합니다. 이 애니메이션은 scour구멍과 둔부 높이가 최대 1시간 내에 안정된 상태에 도달한다는 것을 보여줍니다.

    Gladstone et al. (1998)

    In these experiments the propagation and deposition patterns of particle-laden flows were studied. The plot below compares experimental versus FLOW-3D simulation results from three different setups, labeled case A (100% 0.025mm size particles), case D (50% 0.069mm and 50% 0.025mm size particles), and case G (100% 0.069mm size particles).

    Faruque et al. (2006)

    이 논문에서, 저자들은 실험을 통해 3차원 벽면 제트기를 물에 잠기게 함으로써 국부적인 악취를 연구했습니다. 아래 표는 세 가지 서로 다른 테일워터 비율에 대한 scour 구멍의 3D 형태학적 변화에 대한 실험과 FLOW-3D 수치 결과를 비교합니다.

    Equilibrium bed elevation changes predicted by the numerical model for a cylindrical pier. (A) Isometric view of scour and deposition adjacent to the pier. (B) Comparison between numerical results (top) and physical model measurements (bottom).
    Equilibrium bed elevation changes predicted by the numerical model for the diamond pier. (A) Isometric view of scour and deposition adjacent to the pier. (B) Comparison between numerical results (top) and physical model measurements (bottom).

    In this paper, the authors studied local scour by submerged three-dimensional wall jets via experiments. The table below compares the experimental versus FLOW-3D numerical results for 3D morphological changes in the scour hole for three different tailwater ratios.

    References

    Brethour, J.M., Hirt, C.W., 2009, Drift Model for Two-Component Flows,  FSI-14-TN-83, Flow Science, Inc.

    Chatterjee, S.S., Ghosh, S.N., and Chatterjee M., 1994, Local scour due to submerged horizontal jet, Journal of Hydraulic Engineering, 120(8), pp. 973-992.

    Faruque, M.A.A., Sarathi, P., and Balachandar R., 2006, Clear Water Local Scour by Submerged Three-Dimensional Wall Jets : Effect of Tailwater Depth, Journal of Hydraulic Engineering, 132(6), pp. 575-580.

    Flow Science, 2019, FLOW-3D Version 12.0 User Manual, Santa Fe, NM: Flow Science, Inc. https://www.flow3d.com

    Fox, B. and Feurich, R., 2019, CFD Analysis of Local Scour at Bridge Piers, Federal Interagency Sedimentation and Hydrologic Modeling Conference (SEDHYD), Reno, NV.

    Gladstone, C., Phillips, J.C., and Sparks R.S.J., 1998, Experiments on bidisperse, constant-volume gravity currents: propagation and sediment deposition, Sedimentology 45, pp. 833-843.

    Hirt, C.W. and Sicilian, J.M., 1985, A porosity technique for the definition of obstacles in rectangular cell meshes, 4th International Conference on Numerical Ship Hydrodynamics, Washington, D.C.

    Khosronejad, A., Kang, S., & Sotiropoulos, F., 2012. Experimental and computational investigation of local scour around bridge piers, Advances in Water Resources, 37, pp. 73-85.

    Mao, Y., 1986. The interaction between a pipeline and an erodible bed, PhD thesis, Institute of Hydrodynamics and Hydraulic Engineering, Technical University of Denmark, Lyngby, Denmark.

    Meyer-Peter, E. and Müller, R., 1948, Formulas for bed-load transport, Proceedings of the 2nd Meeting of the International Association for Hydraulic Structures Research. pp. 39–64.

    Nielsen, P., 1992, Coastal bottom boundary layers and sediment transport (Vol. 4). World scientific.

    Soulsby, R., 1997, Dynamics of Marine Sands, Thomas Telford Publications, London.

    Van Rijn, L. C., 1984, Sediment Transport, Part I: Bed load transport, Journal of Hydraulic Engineering 110(10), pp. 1431-1456.

    Wei, G., Brethour, J.M., Grüenzner M., and Burnham, J., 2014, The Sediment Scour Model in FLOW-3D, Technical Note FSI-14-TN-99, Flow Science, Inc.

    Winterwerp, J.C., Bakker, W.T., Mastbergen, D.R. and Van Rossum, H., 1992, Hyperconcentrated sand-water mixture flows over erodible bed, Journal of Hydraulic Engineering, 118(11), pp. 1508–1525.

    Coating Application/코팅분야 응용

    해석 조건

    • Viscosity(점도) = 0.204 Pa-s
    • Density(밀도) = 965 kg/m^3
    • Surface tension(표면 장력) = 0.035N/m
    • Roll coating

    물리 모델

    • Surface tension(표면 장력) 모델
    • Viscosity(점도)
    • Moving Objects(운동)

    Classic Inlet Flooded Regime

    Revers Operating Regime

    Inlet Starved Operating Regime

    • 2D 시뮬레이션은 작동 코팅 윈도우의 빠른 평가를 제공
    • 계단식, 공기 유입, 기아 및 런백을 식별
    • 리빙(Ribbing)은 3D 분석이 필요

    해석 결과

    Electro (&magneto) hydro-dynamics

    Electro (&magneto) hydro-dynamics 사례

    • FLOW-3D models
    • Electrophoresis
    • Dielecrophoresis
    • Conductive fluid model
    • Electro-wetting
    • Electro-osmosis
    • Joules heating

    Electrophoresis

    • Electric charge / electrophoresis
    • Particle sorting

    Electro-wetting

    • Integrates effects of electrophoresis and dielectrophoresis
    • Induced charges manipulate fluid at micro/nano volumes
    • Electrowetting on dielectric (EWOD).

    Dielectrophoresis (DEP)

    DEP는 particle/fluid의 dielectric 특성이 주변 매체의 dielectric 특성과 다를 때만 발생한다.

    Inputs required:

    • Dielectric constant of the fluid and or particles
    • Dielectric constant of any components, that may influence the electric field
    • Define electric potential on the components or on the mesh boundaries
    • Permittivity of vacuum.

    섬세한 경계를 가진 두 개의 유체, 표면 장력, electric potential, fluid electric charge, dielectrophoresis, newtonian viscosity

    Electro osmosis

    Micro-pump example

    • Zeta potential
    • Electric field defined by the electric potential on the components or on the mesh boundaries.
    • Permittivity of vacuum
    • Flow rate control through device

    Inputs required:

    • Zeta potential
    • Electric field defined by the electric potential on the components or on the mesh boundaries.
    • Permittivity of vacuum
    • Flow rate control through device

    Electro-thermal effects (Joules heating)

    • 전류가 물질을 통해 흐를 때 그 저항성은 물질을 가열하게 하며, 이 효과를 joule heating이라고 한다.
    • 온도 구배 설정 속도 필드 및 장치의 유체 순환

    Magneto Hydrodynamics

    • 자력에 의해 입자가 유선으로부터 이탈한다.

    Xiaozheng Xue1, Ioannis H. Karampelas1, Chenxu Liu2 and Edward P. Furlani1,2
    1 Department of Chemical and Biological Engineering
    2 Department of Electrical Engineering
    SUNY at Buffalo
    FLOW-3D Americas User Conference , Toronto, 2014

    Magneto Hydrodynamics

    • 자기 제어로 유체 혼합 사용

    Use of magnetic field to align beads

    John Wendelbo MEng, MSc.
    Senior CFD Engineer, Flow Science
    john.wendelbo@flow3d.com

    FLOW-3D CAST Suites

    FLOW-3D CAST Suites

    FLOW-3D CAST v5 comes in Suites of relevant casting processes: 

    HIGH PRESSURE DIE CASTING SUITE

    Process Workspace

    High Pressure Die Casting

    Features

    Thermal Die Cycling
    – Cooling/heating channels
    – Spray cooling
    Filling
    – Shot sleeve with Plunger
    – Shot motion
    – Ladles, stoppers
    – Venting efficiency
    – PQ^2 analysis
    – HPDC machine database
    Solidification
    – Squeeze pins
    Cooling

    PERMANENT MOLD CASTING SUITE

    Process Workspaces

    Permanent Mold Casting
    Low Pressure Die Casting
    Tilt Pour Casting

    Features

    Thermal Die Cycling
    – Cooling/heating channels
    Filling
    – Tilt pouring
    Solidification
    – Squeeze pins
    Cooling

    SAND CASTING SUITE

    Process Workspaces

    Sand Casting
    Low Pressure Sand Casting

    Features

    Filling
    – Permeable molds
    – Moisture evaporation in molds
    – Gas generation in cores
    – Ladle model
    Solidification
    – Exothermic sleeves
    – Chills
    – Cast iron solidification
    Cooling

    LOST FOAM CASTING SUITE

    Process Workspaces

    Lost Foam
    Sand Casting
    Low Pressure Sand Casting

    Features

    Filling
    – Permeable molds
    – Moisture evaporation in molds
    – Gas generation in cores
    – Ladle model
    – Lost foam pattern evaporation models (Fast model and Full model)
    – Lost foam defect prediction
    Solidification
    – Exothermic sleeves
    – Chills
    – Cast iron solidification
    Cooling

     

    ALL SUITES INCLUDE THESE CORE FEATURES:

    Solver Engine

    • TruVOF – The most accurate filling simulation tool in the industry
    • Heat transfer and solidification
    • Shrinkage – Rapid Shrinkage model and Shrinkage with flow model
    • Temperature dependent properties
    • Multi-block meshing including conforming meshes
    • Turbulence models
    • Non-Newtonian viscosity (shear thinning/thickening, thixotropic)
    • Flow tracers
    • Active Simulation Control with Global Conditions
    • Surface tension model
    • Thermal stress analysis with warpage
    • General moving geometry w/6 DOF

    FlowSight

    • Multi-case analysis
    • Porosity analysis tool

    Defect Prediction Tools

    • Gas entrainment model
    • Thermal Modulus output
    • Hot Spot identification
    • Micro and macro porosity prediction
    • Surface defect prediction
    • Shrinkage
    • Cavitation and Cavitation Potential
    • Particle models (Inclusion modeling, collapsed bubble tracking)

    User Conveniences

    • Process-oriented workspaces
    • Configurable Simulation Monitor
    • Metal and solid material databases
    • Heat transfer database
    • Filter database
    • Remote solving queues
    • Quick Analyze/Display tool

    Computational Analysis of Drop Formation and Detachment

    Computational Analysis of Drop Formation and Detachment

    Introduction and Problem Statement

    신속, 반복, 작은 물방울의 생성 및 증착, 작은 형상의 프린팅 또는 패터닝 (예 : l = 10-3-1 mm), 스프레이로  균일한 두께의 박막 형성은 다양한 산업에 매우 중요합니다(1-5). 액체 이동과 액적 형성 / 증착 공정은 복잡한 자유 표면 흐름, 자연적인 모세관운동 형성, thinning, pinch-off를 수반한다 (1-5). 단순한 뉴턴 및 비탄성 유체에 대해 액적 생성 및 액적 이동을 분석하기위한 실험적, 이론적 및 1 차원 시뮬레이션 연구가 진행되었지만 프린팅 또는 패터닝에 대한 기계론적인 이해는 여전히 과제로 남아 있습니다. 현재의 계산에 대한 주된 목표는 뉴턴 유체의 pinch-off에 대한 기계론적 이해를 얻기 위해 FLOW-3D에 내장된 VOF(volume-of-fluid) 접근법으로 시험하는 것입니다. 전산해석은 모세관, 관성, 점성 응력의 복잡한 상호 작용을 포착하여 자기유사 모세관의 thinning and pinch-off를 결정합니다. 뉴턴 유체의 물방울 형성 ​​및 분리현상은  전산해석으로부터 얻어진 자기유사 모세관현상 이론, 보편적인 축소화 기법인 1D 시뮬레이션 (1-7)과 실험 (1, 2, 8-12)을 이용하여 설명될 수 있음을 보여준다. 이러한 우리가 진행한 원형흐름 시뮬레이션은 유한한 시간의 비선형 역학, 위성 낙하현상, 복잡한 형상의 프린팅과 같이 어려운 전산해석의 기반이 될 것 입니다.

    방울 형성의 전산 분석
    그림 1 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭 형성 및 분리에 대한 전산해석 : (a) 5개의 저점도 유체에 대한 물방울의 necking에 대한 반경이 시간변화에 따라 표시됩니다. 물방울 necking의 반지름이 오른쪽에서 왼쪽으로 시간에 따른 전개를 보여줍니다. 마찬가지로 스냅 샷은 necking의 반경이 오른쪽에서 왼쪽으로 줄어듭니다. 속도의 크기 (단위 : cm/s) 와 화살표의 방향에 대한 컬러 맵을 사용하면 변형장을 결정할 수 있으며 Fluid 5 (표 1 참조)의 경우에는 순식간에 신장이됩니다. 이미지 II에 캡처 된 pinch-off 하기 전에 형성된 원추형 necking은 실험을 통해 얻은 necking 모양과 유사합니다.

    Modeling Approach and Parameter Space

    표면 장력 및 중력 모델을 적용한 FLOW-3D 에서 균일한 메쉬 크기를 사용하여 노즐에서 드롭 형성 및 분리에 대한 시뮬레이션을 수행하였습니다. 유한 체적의 유체를 떨어뜨리거나 분리하는 일은 물방울의 성장과 드롭, 노즐에 연결되는 모세관 현상, 관성, 점도 및 중력에 대한 상호 작용을 수반합니다. 시뮬레이션에서 스테인레스 강 노즐 ( {{D} _ {0}} = 2 {{R} _ {0}} = 1.7 \, \ text {mm}) 에서 유한 체적의 뉴턴 유체가 발생합니다. 표면 장력이 중력을 겪으면 새로 형성된 액적 분리가 발생합니다 (mg> 2 \ pi \ sigma {{R} _ {0}}). 시뮬레이션은 유체점도의 영향을 설명하기 위해 두 그룹으로 나누어져 있습니다: 저점도 유체 (글리세롤 함량이 40 % 미만인 물과 글리세롤/물 혼합물) 및 점도가 높은 유체 (예 : 글리세롤과 글리세롤/물 혼합물 점도 > 100x 물 점도). 두 그룹의 유체 특성은 각각 표 1과 2에 나와 있습니다.

    계산 분석 드롭 형성 저점도

    그림 2 : FLOW-3D를 사용하여 시뮬레이션 한 저점도 유체의 드롭형성 및 분리에 대한 전산 해석 : 반경 플롯에서 4개의 고점도 뉴톤유체에 대해 necking 반경을 시간변화에 따라 표시합니다. 낙하 분리 중 모세관 현상이 스냅 샷으로 표시됩니다. 컬러 맵은 Fluid 8의 속도 크기 (단위 : cm/s)의 변화를 포착합니다 (표2 참조). 화살표는 성장하는 물방울과 얇아지는 물방울내에서 흐름방향을 나타냅니다. FLOW-3D 시뮬레이션으로 얻은 necking 모양은 고점도의 뉴턴유체에 대한 특징인 원통형 유체요소로 이어집니다.

     

    <표 1 : FLOW-3D를 사용하여 시뮬레이션 된 저점도 유체의 특성>
    Fluid PropertyFluid 1Fluid 2Fluid 3Fluid 4Fluid 5
    Viscosity [Pa · s]0.050.020.010.00750.005
    Surface Tension  [mN / m]6868686868
    Density [g / cm 3 ]11111
    Ohnesorge Number0.210.080.040.030.021
     저점도 유체 (표 1의 유체 2) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s)이며 속도벡터가 표시됩니다.

     

    <표 2 : FLOW-3D를 사용하여 시뮬레이션 된 고점도 유체의 특성>
    Fluid PropertyFluid 6Fluid 7Fluid 8Fluid 9
    Viscosity [Pa · s]1.50.80.50.25
    Surface Tension  [mN / m ]68686868
    Density [g / cm 3 ]1111
    Ohnesorge Number6.243.332.081.04

    고점도 유체 (표 2의 유체 8) 가 노즐에서 떨어지는 것을 시뮬레이션 합니다. 색상변수는 속도크기 (단위 : cm / s) 이며 속도 벡터가 표시됩니다.

    Discussion of the Simulation Results

    드롭 형성 및 분리는 표1과 표2에 열거 된 유체에 대해 FLOW-3D 를 사용하여 시뮬레이션 하였고, 시간 경과에 따른 necking 모양, 반경을 분석하였습니다. 물방울의 necking 모양과 저점도에서의 necking에 대한 역학(그림 1 참조)은 실험, 흐름 이론, 1D 시뮬레이션, 자기유사 관성에 대한 모세현상의 특성을 나타냅니다 (1, 2, 6, 7, 13) :

    (1)  \ displaystyle \ frac {{R (t)}} {{{{R} _ {0}}}} \ approx 0.8 R {{{{왼쪽} {R} {0} 3}}} 오른쪽}) ^ {{{{frac {1} {3}}} {{왼쪽 {{{{왼쪽}}} {2} {3}}}}

    여기서 R (t)가  necking의 순간 반경이고, R0는 노즐의 외부반경이며,  \ displaystyle \ sigma 는 표면 장력,  \ displaystyle \ rho 는 유체의 밀도 tC 는 pinch-off 시간이다. 마찬가지로, 이러한 더 높은 점도의 뉴턴유체에 대한 반경 변화데이터는 시간에 따른 반경의 감소를 나타내는 것이며,  Papageorgiou’s visco-capillary scaling (8, 9)은 아래의 식으로 표현된다.

    (2)  \ {0 \} {} {} {} {} {} {} {} {} {} {} {} {} { } ({{t} _ {p}} - t)

    모세관 속도(표면 장력과 점도의 비)의 측정 값은 McKinley와 Tripathi (8)에 의해 Capillary Break-Up Extensional Rheometer (CaBER)라고 불리는 상업적으로 이용 가능한 장비를 사용하여 얻은 값과 모세관 속도는 공칭 표면 장력과 점도를 사용하여 계산됩니다.

    FLOW-3D 는 물방울의 necking부분을 속도 벡터로 시각화하여 유체의 흐름을 나타낼 수 있습니다. 또한, 이는 그림 1과 같이 전단, 확장을 겪은 후 얇아지는 물방울이 흐르는 과정의 순간을 결정할 수 있는 가능성을 줍니다. 추가로, 낮은 점도의 뉴턴유체는 높은 점도의 뉴턴 유체에 비해 질적으로 다른 거동을 보여준다(그림 2참조). 낮은 점도의 뉴턴 유체에 대한 necking 프로파일은 이론(6,13)에 따라 자기 유사성이 됩니다.

    Conclusions, Outlook and Ongoing work

    우리의 예비결과는 FLOW-3D 기반의 전산해석이 액적 형성과 탈착의 기초가 되는 프로토타입의 자유 표면흐름을 시뮬레이션하는데 사용될 수 있음을 보여줍니다 . 시뮬레이션된 반경변화 프로파일이 실험적으로 관찰된 높은 유체 및 이론적으로 예측된 유체인 스케일링 법칙 및 pinch-off dynamics과 일치하는 것을 발견하였습니다.

    자주 사용되는 1D 또는 2D 모델과 달리 FLOW-3D 는 기본 응력 및 확장 유동장 (균일도 및 크기)의 강도와 얇은 액체 필라멘트 내 흐름에 대한 시각화를 나타낼 수 있습니다(그림1과 2 참조). 확장 유동장과 연관된 흐름 방향 속도 구배는 모세관현상이 나타나는 물방울의 얇은 부분 내에서 발생합니다. 유동학적으로 복잡한 유체에서 non Newtonian shear 및 신장, 점도뿐만 아니라 그외의 탄성 응력이 nonlinear pinch-off dynamics을 급격하게 변화시킵니다(2, 10-12). 우리는 현재 점탄성과 non-Newtonian 유동학을 사용하여 FLow-3D에 복합 유체의 처리 성능평가를 위한 강력한 연산 프로토콜을 개발하고 있습니다.

    References

    1. J. Eggers, Nonlinear dynamics and breakup of free-surface flows. Rev. Mod. Phys. 69, 865-929 (1997).
    2. G. H. McKinley, Visco-elasto-capillary thinning and break-up of complex fluids. Rheology Reviews, 1-48 (2005).
    3. B. Derby, Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution. Annual Review of Materials Research 40, 395-414 (2010).
    4. O. A. Basaran, H. Gao, P. P. Bhat, Nonstandard Inkjets. Annual Review of Fluid Mechanics 45, 85-113 (2013).
    5. S. Kumar, Liquid Transfer in Printing Processes: Liquid Bridges with Moving Contact Lines. Annual Review of Fluid Mechanics 47, 67-94 (2014).
    6. R. F. Day, E. J. Hinch, J. R. Lister, Self-similar capillary pinchoff of an inviscid fluid. Phys. Rev. Lett. 80, 704-707 (1998).
    7. J. Eggers, M. A. Fontelos, Singularities: Formation, Structure, and Propagation. (Cambridge University Press, Cambridge, UK, 2015), vol. 53.
    8. G. H. McKinley, A. Tripathi, How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer. J. Rheol. 44, 653-670 (2000).
    9. D. T. Papageorgiou, On the breakup of viscous liquid threads. Phys. Fluids 7, 1529-1544 (1995).
    10. J. Dinic, L. N. Jimenez, V. Sharma, Pinch-off dynamics and dripping-onto-substrate (DoS) rheometry of complex fluids. Lab on a Chip 17, 460-473 (2017).
    11. J. Dinic, Y. Zhang, L. N. Jimenez, V. Sharma, Extensional Relaxation Times of Dilute, Aqueous Polymer Solutions. ACS Macro Letters 4, 804-808 (2015).
    12. V. Sharma et al., The rheology of aqueous solutions of Ethyl Hydroxy-Ethyl Cellulose (EHEC) and its hydrophobically modified Analogue (hmEHEC): Extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 11, 3251-3270 (2015).
    13. J. R. Castrejón-Pita et al., Plethora of transitions during breakup of liquid filaments. Proc. Natl. Acad. Sci. U.S.A. 112, 4582-4587 (2015).

    [FLOW-3D 물리모델] Solidification 응고

    응고 모델은 열전달이 활성화되고(Physics → Heat Transfer → Fluid internal energy advection) 유체비열(Fluids → Fluid 1 → Thermal Properties → Specific heat)과 전도도(Fluids → Fluid 1 → Thermal Properties → Thermal Conductivity) 이 지정될 때 사용될 수 있다. 단지 유체 1만 상 변화를 겪을 수 있다.

    Solidification - Activate solidification

    응고모델을 활성화하기 위해 Fluids → Fluid 1 → Solidification Model 을 체크하고 물성 Fluids → Fluid 1 → Solidification Model 가지에서 Liquidus temperature, Solidus temperature, 그리고 Latent heat of fusion 를 지정한다. 가장 간단한 모델(Latent Heat Release Definition 에 펼쳐지는 메뉴에서 Linearly with constant 를 선택)에서, 잠열은 물체가 Liquidus 에서 Solidus 온도로 냉각될 때 선형적으로 방출된다. 고상에서의 상변화열을 포함하는, 잠열 방출의 더 자세한 모델을 위해 온도의 함수로 잠열방출을 정의하기 위해 Specific energy vs. temperature 또는 Solid fraction vs. temperature 선택을 사용한다. 이 지정에 대한 더 자세한 내용은 이론 매뉴얼의 Heat of Transformation 를 참조한다.

    solidification-fluid-properties

    응고는 유체의 강직성 및 유동저항을 뜻한다. 이 강직성은 두 가지로 모델링 된다. 낮은 고상율에 대해 즉 Fluids → Fluid 1 → Solidification Model → Solidified Fluid 1 Properties → Coherent Solid Fraction 의 coherency 점 밑에서는 점도는 고상율의 함수이다. 간섭 고상율보다 큰 고상율에 대해서는 고상율의 함수에 비례하는 항력계수를 갖는 Darcy 형태의 항력이 이용된다. 이 항력은 모멘텀 방정식에 (bx,by,bz) 로써 추가된다- Momentum Equations 를 보라. 이 항력의 계산은 Solidification Drag Model 에서 기술된다. 항력계수는 사용자가 유동저항에 양을 조절할 수 있는 Coefficient of Solidification Drag 인자를 포함한다. 항력계수는 FLOW-3D 출력에서 기록된 속도에 상응하는 지역 상 평균 속도에 의해 곱해진다.

    Fluid 1 Properties)을 지나면 항력은 무한대가 되고 계산격자 관련하여 유동이 있을 수 없다(단 예외로 Moving Solid Phase를 참조).

    Note

    모든 유체가 완전히 응고하면 모사를 정지시키기 위해 General → Finish condition → Solidified fluid fraction 를 이용한다. General → Finish condition → Finish fraction 은 모사를 중지하기 위한 고상율 값을 정한다.

    See also

    Macro-Segregation during Alloy Solidification and Solidification Drag Model.

     

    Drag in the Mushy Zone, Mushy영역 내 항력

     

    주조 시 mushy zone 은 액상과 고상이 혼합물로 존재하는 지역이다. 이 지역 혼합점도는 동축의 수지상 조직(과냉각된 액체 안에서 방사상으로 자라는 결정으로 된 구조) 이 액체 안에서 자유롭게 부유할 때 영향을 미친다.

    일단 수지상 조직의 간섭성이 발생하여 고정된 고상 망이 형성되면 액상이 고정된 다공 수지상 구조를 통과해야 하므로 추가의 유동손실이 발생한다. 다른 방법으로는 간섭점을 지난 액/고상 혼합물은 다공물질을 통한 유동 대신에 고점도의 유체로 간주될 수 있다. 점성유체로 간주하는 접근은 예를 들면 연속 이중 롤 주조 과정같이 고상이 계속 이동 및 변형할 때 유용하다.

     

    Solidification Drag Models in FLOW-3D, FLOW-3D 내 응고 항력모델

    응고에 의한 항력계수를 정의하기 위해 사용자는 우선 열전달 및 응고모델을 활성화 해야 한다. 이들은 Model Setup → Physics 탭 에서 활성화될 수 있다. 수축모델 또한 응고모델 창에서 활성화될 수 있다.

    Solidification model

    일단 Solidification 모델이 활성화되면 항력의 공식이 지정될 필요가 있다. Solidification대화의 밑 좌측 모퉁이에서 Porous media drag-based 와 Viscosity-based 의 항력공식 중의 선택을 한다.

      • Viscosity-based 공식은 점성 유체로 취급하며 Viscosity 영역 내Flow model for solidified metal 입력 밑에서 지정되는 순수 고상 점성을 갖는 고상화된 유체로 간주된다. 이 접근법은 경직성의 항력모델(즉, 응고 금속이 롤러 사이로 압착될 때)을 사용할 수 없는 경우의 모사에 이용된다. 이 점성은 고상율에 따라 선형으로 변한다.고상율이0일 때 점도는 유체1의 점도이다.고상율이1이면 점도는 Solidification 패널에서 지정된 값과 같다.
      • Porous media drag-based 공식은 응고상태를 결정하기 위해 고상율을 사용한다. 고상율이 Critical Solid Fraction 이거나 초과하면 이때 항력은 무한대가 된다-즉, 액상/고상 혼합물은 고체같이 거동한다. 고상율이 Coherent Solid Fraction 보다 작으면 항력은 0이다. 이 두 값 사이에서 유동은 mushy 지역에 있고 이를 통한 유동은 마치 다공질 내에서의 유동같이 처리된다. 또한 모델은 고상율이 Coherent Solid Fraction 보다 작을 때 자동적으로 용융 금속의 점도를 조절한다. 이 상태에서 고상결정은 점도를 올리지만 결합하지는 않는다(즉, 간섭 없음). 일단 유체가 Coherent Solid Fraction 에 도달하면 항력방정식이 고려되고 점도는 간섭성에 도달하기 전의 값으로 일정하게 된다. 임계 및 간섭 고상율은 사용자가 정의하며 논문이나 책 등에서 찾을 수 있다. 이 식에서는 Coefficient of Solidification Drag 가 정의되어야 한다. 이는 Solidification 창 또는 Fluid 1 → Solidification Model→Solidified Fluid 1 Properties tree → Other 트리를열어 Model Setup →Fluids 탭에서 될 수 있다.

    How to Calculate Permeability 투과성 계산법

    밑에 주어진 Darcy법칙은 수지상 구조를 위한 다공매질내의 수학적 유동기술이다.[Poi87].

    (19)\mathbf{u} = - \frac{K}{\mu} \nabla P

    여기서 u 는 수지상 구조 내 유동의 속도이고 ∇P 는 지역 압력구배, 그리고 K 는 mushy 구역의 특정 투수성이다. 이 방정식은 단지 유동이 거의 정상 상태이고, 관성효과가 없으며 유체의 체적율이 일정하고 균일하며 액체-액체의 상호작용 힘이 없을 때 유효하다. 투수성을 정의하는데 이용될 수 있는 대 여섯 개의 모델이 있으나 FLOW-3D 는 밑에 보여주는 Blake-Kozeny 을 이용한다. 다른 모델들은 코드와 함께 제공되는 소스코드를 사용자 사양에 맞게 수정하여 추가할 수 있다.

    (20)\mathbf{u} = -C_2 \left( \frac{\lambda_1^2 (1-f_s)^3}{\mu f_s^2} \right) \left( \nabla P - \rho \mathbf{g} \right)

    여기서

    C2 는 전형적으로 와 같은 비틀림

    fs 는 고상율이고

    λ1는 유동을 위한 특정 치수

    이 응용에서 수지상 가지 간격(DAS)이 이용된다.

    • 식 (11.19) 을 식(11.20) 에 적용하면 투수성을 위한 다음 식을 얻는다.

    (21)K = \lambda_1^2 \frac{(1-f_s)^3}{180f_s^2}

    수지상 가지 간격(DAS)에 대한 일반적인 값들은 밑에 주어져 있다.

    Range of Cooling Rates in Solidification Processes
    COOLING RATE, K/sPRODUCTION PROCESSESDENDRITE ARM SPACING, \mu m
    10^{-4} to 10^{-2}large castings5000 to 200
    10^{-2} to 10^3small castings, continuous castings, die castings, strip castings, coarse powder atomization200 to 5
    10^3 to 10^9fine powder atomization, melt spinning, spray deposition, electron beam or laser surface melting5 to 0.05

    Range of cooling rates in solidification processes [CF85]

     

    How FLOW-3D Defines the Coefficient of Solidification Drag FLOW-3D 가 응고 항력계수를 결정하는법

    FLOW-3D 는 액고상 변화를 모델링하기 위해 다공매질항력을 이용한다. 항력은 고상율의 함수이다. 사용자에게 두 수축모델이 이용 가능하다; 급속 수축 모델 과 완전 유동모델. 급속 수축 모델은 상변화와 연관된 체적변화를 고려하지 않으며 유체는 정지해 있다고 가정한다. 완전 유동모델은 상변화가 관련된 체적변화를 고려한다. 항력은 투수성에 역으로 비례하므로 다음과 같이 표현될 수 있다.

    (22)K = \frac{\mu}{\rho F_d}

    여기서, Fd 는 FLOW-3D 에서 사용된 항력계수이다. 이 항력계수는 지역 속도에 의해 곱해지고 모멘텀 방정식의 오른쪽에서 차감된다 (Momentum Equations 참조). 식 (11.22) 를 재정리하고 식 (11.21) 로부터의 투수성에 치환하면 다음을 얻는다.

    • The Coefficient of Solidification Drag: \text{TSDRG}=\frac{180 \mu}{\lambda_1^2\rho },
    • The drag force: F_d = \mbox{TSDRG} \frac{ f_s^2}{(1-f_s)^3}.

    See also

    Model Reference -> Solidification

     

    Macro-Segregation during Alloy Solidification 합금응고시 거시적 편절

    편절 모델은 대류와 확산에 의한 용질 이동에 따른 이원합금 요소에서의 변화를 모델링 하도록 되어 있다. 이 모델링은 Physics → Solidification 로 부터 될 수 있다.

    Solidification

    Activate binary alloy segregation model 을 체크하고 편절 모델을 활성화한다.

    여러 온도에서 평형에 있는2원합금 요소농도를 정의하는 상태도는 직선의 고상선 및 액상선을 가진다고 가정된다. 상태도는 입력데이터에 의해 구성되고 전처리 그림파일 prpplt 에 포함된다. Analyze → Existing 에서 이용 가능하다

    Macro-Segregation Model (under Fluids → Fluid 1 → Solidification Model)에 관련된 일부 유체물성 트리가 밑에 보여진다. 상태도는 Reference Solute Concentration 에서의 the Solidus 와 Liquidus Temperatures 값들에 의해 정의된다. 추가로 Concentration Variables 밑의 Partition coefficient 도 정의되어야 한다. 그렇지 않으면 Pure Solvent Melting Temperature 가 정의될 수 있다. Partition coefficient 와 Pure Solvent Melting Temperature 둘 다가 지정되면 용매 용융 온도는 상태도로부터 재 정의된다.

    Macro segregation fluid properties

     

    Eutectic Temperature 또는 Eutectic Concentration 는 융해작용을 정의하기 위해 지정될 수 있다. 또 이 두 변수가 다 지정되면 Eutectic Concentration 은 상태도에서 재 정의된다.

    Diffusion Coefficients 는 고상과 액상 사이의 용질의 확산계수 비율을 정의한다. 액체 내의 용질의 분자 확산계수는 Physics → Solidification 에서 specifying Solute diffusion coefficient 를 지정함으로써 정해진다. RMSEG 는 용질의 난류 확산계수 승수를 정의한다; 이는 입력파일에서 직접 지정된다.

    Density evaluation

    용질 재 분배에 의한 농도변화가 중요하면 Physics → Density evaluation → Density evaluated as a function of other quantities를 정하고 용질농도의 선형함수로써 금속농도를 정의하기 위해 Fluids → Segregation model 밑의 Solutal Expansion Coefficient 를 용질 확장계수로 지정한다. 이 경우 Reference Solute Concentration 이 기준농도로 사용될 것이다. 추가로 Fluids → Fluid 1 → Density Properties → Volumetric Thermal Expansion 은 액체 내 열부력 효과를 참작하기 위해 지정될 수 있다(또한 Buoyant Flow참조).

    초기 용질농도는 Meshing & Geometry → Initial → Global → Uniform alloy solute concentration 에서 지정될 수 있다. 불 균일한 초기 분포는 Alloy solute concentration 밑의 초기유체 구역 안에서 정의될 수 있다. 추가로 농도는 Initial Conditions: Region Values 에서 기술된 바와 같이 2차함수를 사용하는 부분을 편집하여 공간상의2차함수로 변화할 수 있다. 압력과속도 경계에서 용질 경계조건을 정하기 위해 Boundaries → Boundary face → Solute concentration 를 이용한다.

    액상 및 고상 구성은 후처리에서 데이터 변환을 이용하여 그려질 수 있다. 용융 응고금속은 금속 내 용융의 질량 분율을 저장하는 SLDEUT 를 그림으로써 가시화될 수 있다.

    액상 내 열구배가 크면 Physics → Heat Transfer → Second order monotonicity preserving 를 지정함으로써 더 나은 정확성을 위해 고차원 이류법을 사용한다.

     

    Heat Transfer

    mushy 지역에서의 유동손실은 수지상 가지 간격(DAS)의 함수인 Fluids → Fluid 1 → Solidification Model → Solidified Fluid 1 Properties → Coefficient of Solidification Drag 에 의해 조절된다. 후자는 이 모델에 의해 계산되지 않으므로 사용자는 Coefficient of Solidification Drag 를 지정해야 한다

    Note

    • 표준 응고모델 과는 달리 상태도상의 용융점을 지나 고상선을 외삽하여 정의되므로 여기서 응고선의 값은 음수일 수 있다.

    Microporosity Formation 미세다공형성

    Solidification

    미세다공모델은 단지 응고(Solidification참조)를 모델링할 때 사용될 수 있고 Physics → Solidification → Activate micro-porosity model 에서 활성화된다. 필요한 입력은 Fluids → Densities → Fluid 1 and Fluids → Solidification Properties → Solidified Fluid 1 Properties → Density 에서 정의되는 액체와 고상 유체밀도이며 고상유체밀도는 액체밀도보다 크다. 또한 Fluids → Fluid 1 → Solidification Model → Solidified Fluid 1 Properties 안에 있는 Critical Solid Fraction 은 1.0보다작게 설정되어야 한다.

    Square of the speed of sound at critical solid fraction 값이 정의될 수 있다. 이는 수축에 의해 mushy 지역에서 전개되는 커다란 음압에서의 응고유체의 압축성을 기술한다. Critical pressure at which gas pores can form 값은 모델이 Initial tab 탭에서 또는 재 시작 데이터에서 정의되는 유체내의 초기 압력과 결합되도록 한다.

    Intensification pressure 또한 다공 생성을 지연시키기 위해 응고 시 shot sleeve plunger 에 의해 형성되는 추가압력을 고려하기 위한 고압 주조모사를 위해 정의될 수 있다. Intensification pressure 가 클수록 더 적은 양의 다공이 주조 시 응고 과정에서 발생할 것이다.

    미세 다공 모델은 응고 모델의 활성화 이외의 어떤 다른 설정을 필요로 하지 않는다. 이는 완전 유동방정식이나 속도장이 0인 경우, 즉 순수한 열 문제에서도 함께 사용될 수 있다.

    이 모델은 후처리 과정의 공간 및 이력에서 사용 가능한 Percent micro-porosity 라고 불리는 추가 출력 양을 생성한다.

     

    Note

    A Flow Science technical note on modeling micro-porosity (TN66) can be found at http://users.flow3d.com/technical-notes/.

     

    Moving Solid Phase  이동고상

    MAIN VARIABLES:OBS:IFOB, UTOBS, VTOBS, WTOBS

    이동고상 선택은 연속주조 모델링을 가능하게 한다. Continuous Casting Phantom 요소는 응고된 이동 유체가 있는 지역에서 정의된다. 이는 지정된 영역을 차지하지만 정의에만 존재하므로 환영요소라고 한다. 이는 실제로 면적이나 체적을 차지하지 않으므로 체적이 없고 결과에서도 고체요소로 보이지 않는다. 이는 Meshing & Geometry → Geometry → Component → Component Type 옆 펼쳐지는 메뉴에서 정의된다.

    Moving solid phase selection

    다른 방법으로는 입력파일(prepin.*)에서 IFOB(N) 변수가 4로 지정되고 N 은 요소 번호이다. 이 파일은 File → Edit Simulation…. 을 선택하여 이용될 수 있다. 또한 입력파일에서 시간의 함수(TOBS(t) 에 의해 지정되는)일 수 있는 가상 요소의 속도성분 UTOBS(t,N), VTOBS(t,N) 그리고 WTOBS(t,N) 이 지정된다.

    Fluids → Fluid 1 → Solidification Properties → Solidified Fluid 1 Properties → Coherent Solid Fraction 에 의해 정의된 간섭 고상율 보다 큰 고상율에 대해서는 Darcy 형태의 항력 이 유체를 가상 요소의 속도로 움직이게 하는데 사용된다. 고상율이 Fluids → Fluid 1 → Solidification Properties → Solidified Fluid 1 Properties → Critical Solid Fraction 에서 지정된 경직점을 능가하게 되면 가상 요소의 속도를 따라 움직일 것이다.

    Note

    • 가상 요소는 요소 그림에 안 나타나나 Component number 를 그릴 때는 보여진다.가상 요소는 균일속도가 요소의 전체에 적용되므로 평평해야 한다.

    Solidification Shrinkage 응고수축

     

    체적 수축은 소재가 응고하고 응고소재의 밀도가 액체소재의 밀도보다 클 때 나타난다(즉, Fluids → Fluid 1 → Solidification Model → Solidified Fluid 1 Properties → Density > Fluids → Fluid 1 → Density Properties → Density). 수축모델은 그러므로 Solidification 모델이 활성화되어야 하고 고상/액상의 두 밀도가 정의되어야 한다. 수축은 단지 1유체의 뚜렷한 경계면 문제에서만 모델링 될 수 있다.

    두 가지 수축모델이 있다. Shrinkage model with flow effects 를 선택하면 완전 열 유체방정식을 해석한다(이론 매뉴얼의Solidification Shrinkage and Porosity Models 참조). 그러나 이 모델은 특히 장시간의 응고가 고려되면 컴퓨터 계산시간이 많이 소요된다. 다른 방법으로 사용자 Interface 에 Shrinkage model 이라고 불리는 단순모델이 있다.

    Activate simplified shrinkage model

     

    이 모델은 단지 열전달 방정식의 해석에 의존하며 특히 내재적 열전달 모델 (Numerics → Explicit/implicit options → Heat transfer → Implicit –Thermal solution 참조)과 사용시에 빨리 해석할 수 있다. 액체 체적 내로의 유동 통로가 없을 때 내부공동이 발생한다.

    이 두 모델에서 유입은 mushy 지역 유동에 대한 항력계수를 계산함으로써 정의된다. 격자 내 모든 점에서의 항력함수는 상수승수 Fluids → Solidification properties → Other → Coefficient of Solidification Drag (Solidification Drag Model 참조)를 가지는 지역 고상율의 함수로 계산된다. 항력함수의 역의 값은 공간 그림에서 가시화 될 수 있다: 이 그림을 위한 변수이름은 ‘drag coefficient’ 이다.

    Mushy 지역에서의 커다란 유동 손실에 따른 부분적 유입이 Shrinkage model with flow effects 에서 발생할 수 있지만 단순화된 Shrinkage model 은 완전 유입이 아니면 유입이 없게 된다. 후자는 유입 통로를 따라 지역 고상율이 Fluids → Fluid 1 → Solidification Model → Solidified Fluid 1 Properties → Critical Solid Fraction (디폴트는1.0)에서 정의된 임계값보다 커질 때 발생한다. 추가로 고립된 액체 내의 금속의 고상율이 Coherent Solid Fraction 에 도달할 때까지 단순모델에서의 유입은 고립부 상부로부터 발생한다. 그 후로는 유입이 고립부의 가장 뜨거운 부분에서부터 발생한다.

    모든 유체가 완전히 응고되면 모사가 정지하도록 General → Additional finish condition → Solidified fluid fraction 를 사용한다. 변수 Finish fraction 는 유체가 지정된 고상율에 도달할 때 모사가 정지하도록 하는데 사용될 수 있다.

    Solid fraction finish condition

    Note

    이송 방향을 결정하기 위해 단순 수축 모델에서 중력이 필요하며 좌표축 중 하나를 따라야합니다. 둘 이상의 중력 구성 요소가 0이 아닌 경우, 가장 큰 중력 구성 요소가 공급 방향을 결정하는 데 사용됩니다.

    See also

    Solidification and Solidification Drag Model.

     

    Salt dissolution model [소금 용해 모델]

    Introduction
    Dissolution of salt in liquid is of interest in several applications – from solution mining to food processing to medical applications. This article describes a new model in FLOW-3D1 version 10.0 for dissolving salt in fluids and tracking the solute in the brine.
    The dissolution of salt increases the density of the fluid and thus may affect the flow. In addition, as salt is dissolved, the flow domain increases. It is of interest, therefore, to predict these changes in the flow as well as the transport of the dissolved salt in the fluid.
    The model accounts for the basic physical phenomena, such as mass transfer at the interface between salt and fluid, the change of volume and shape of the solid salt, diffusion and convection of dissolved salt in fluid and, finally, the change in fluid density, viscosity and surface tension coefficient.

    Turbulent Flow Over a Backward-Facing Step Using the RNG Model

    Abstract
    Turbulent flow over a backward-facing step is one of the classical tests to validate turbulence models in CFD. In the present work, steady-state turbulent flow over a backward-facing step was simulated using FLOW-3D1 with the Renormalization-group (RNG) k-ε model to account for turbulent viscosity. The Reynolds number was computed using the step height h and the inlet free-stream velocity. The test case was run for two different Reynolds numbers: Reh=5100 and Reh=44,000.

    The numerical predictions were compared with the experimental results with the same flow configuration. Streamwise velocity profiles at different locations in the flow direction were in good agreement both qualitatively and quantitatively with the experimental results.

    One of the main objectives of this work is to study the sensitivity of the results to the turbulent mixing length parameter tlen in the RNG model. The steady-state velocity was used to compute the reattachment length behind the step for different values of tlen and compared with experimental data. A grid refinement study was performed to find the least mesh resolution needed to capture the essential flow physics of the problem.