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

[1] Aminoroayaie Yamini, O., Mousavi, S.H., Kavianpour, M.R., Movahedi, A. (2018). Numerical modeling of sediment scouring phenomenon around the offshore wind turbine pile in marine environment. Environmental Earth Sciences, 77: 1-15. https://doi.org/10.1007/s12665-018-7967-4

[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

[4] Stahlmann, A. (2013). Numerical and experimental modeling of scour at foundation structures for offshore wind turbines. In ISOPE International Ocean and Polar Engineering Conference. ISOPE, pp. ISOPE-I.

[5] Petersen, T.U., Sumer, B.M., Fredsøe, J. (2014). Edge scour at scour protections around offshore wind turbine foundations. In 7th International Conference on Scour and Erosion. CRC Press, pp. 587-592.

[6] Sumer, B.M., Fredsøe, J. (2001). Scour around pile in combined waves and current. Journal of Hydraulic Engineering, 127(5): 403-411. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:5(403)

[7] Jalal, H.K., Hassan, W.H. (2020). Effect of bridge pier shape on depth of scour. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 671(1): 012001. https://doi.org/10.1088/1757-899X/671/1/012001

[8] Hassan, W.H., Jalal, H.K. (2021). Prediction of the depth of local scouring at a bridge pier using a gene expression programming method. SN Applied Sciences, 3(2): 159. https://doi.org/10.1007/s42452-020-04124-9

[9] Jalal, H.K., Hassan, W.H. (2020). Three-dimensional numerical simulation of local scour around circular bridge pier using Flow-3D software. In IOP Conference Series: Materials Science and Engineering. IOP Publishing, 745(1): 012150. https://doi.org/10.1088/1757-899X/745/1/012150

[10] Hassan, W.H., Attea, Z.H., Mohammed, S.S. (2020). Optimum layout design of sewer networks by hybrid genetic algorithm. Journal of Applied Water Engineering and Research, 8(2): 108-124. https://doi.org/10.1080/23249676.2020.1761897

[11] Hassan, W.H., Hussein, H.H., Alshammari, M.H., Jalal, H.K., Rasheed, S.E. (2022). Evaluation of gene expression programming and artificial neural networks in PyTorch for the prediction of local scour depth around a bridge pier. Results in Engineering, 13: 100353. https://doi.org/10.1016/j.rineng.2022.100353

[12] Hassan, W.H., Hh, H., Mohammed, S.S., Jalal, H.K., Nile, B.K. (2021). Evaluation of gene expression programming to predict the local scour depth around a bridge pier. Journal of Engineering Science and Technology, 16(2): 1232-1243. https://doi.org/10.1016/j.rineng.2022.100353

[13] Nerland, C. (2010). Offshore wind energy: Balancing risk and reward. In Proceedings of the Canadian Wind Energy Association’s 2010 Annual Conference and Exhibition, Canada, p. 2000. 

[14] Hassan, W.H., Nile, B.K., Mahdi, K., Wesseling, J., Ritsema, C. (2021). A feasibility assessment of potential artificial recharge for increasing agricultural areas in the kerbala desert in Iraq using numerical groundwater modeling. Water, 13(22): 3167. https://doi.org/10.3390/w13223167

[15] Schendel, A., Welzel, M., Schlurmann, T., Hsu, T.W. (2020). Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coastal Engineering, 161: 103751. https://doi.org/10.1016/j.coastaleng.2020.103751

[16] Yakhot, V., Orszag, S.A. (1986). Renormalization group analysis of turbulence. I. Basic theory. Journal of Scientific Computing, 1(1): 3-51. https://doi.org/10.1007/BF01061452

[17] Mastbergen, D.R., Van Den Berg, J.H. (2003). Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology, 50(4): 625-637. https://doi.org/10.1046/j.1365-3091.2003.00554.x

[18] Soulsby, R. (1997). Dynamics of marine sands. https://doi.org/10.1680/doms.25844

[19] Van Rijn, L.C. (1984). Sediment transport, part I: Bed load transport. Journal of Hydraulic Engineering, 110(10): 1431-1456. https://doi.org/10.1061/(ASCE)0733-9429(1984)110:10(1431)

[20] Pang, A.L.J., Skote, M., Lim, S.Y., Gullman-Strand, J., Morgan, N. (2016). A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Applied Ocean Research, 57: 114-124. https://doi.org/10.1016/j.apor.2016.02.010

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

PDF 원문 보기
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

PDF Download

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.

REFERENCES

  1. S. L. Sing and W. Y. Yeong , “ Laser powder bed fusion for metal additive manufacturing: Perspectives on recent developments,” Virtual Phys. Prototyping. 15, 359–370 (2020).https://doi.org/10.1080/17452759.2020.1779999
    Google ScholarCrossref
  2. A. M. Khorasani , I. G. Jithin , J. K. Veetil , and A. H. Ghasemi , “ A review of technological improvements in laser-based powder bed fusion of metal printers,” Int. J. Adv. Manuf. Technol. 108, 191–209 (2020).https://doi.org/10.1007/s00170-020-05361-3
    Google ScholarCrossref
  3. Y. Qin , A. Brockett , Y. Ma , A. Razali , J. Zhao , C. Harrison , W. Pan , X. Dai , and D. Loziak , “ Micro-manufacturing: Research, technology outcomes and development issues,” Int. J. Adv. Manuf. Technol. 47, 821–837 (2010).https://doi.org/10.1007/s00170-009-2411-2
    Google ScholarCrossref
  4. B. Nagarajan , Z. Hu , X. Song , W. Zhai , and J. Wei , “ Development of micro selective laser melting: The state of the art and future perspectives,” Engineering. 5, 702–720 (2019).https://doi.org/10.1016/j.eng.2019.07.002
    Google ScholarCrossref
  5. Y. Wei , G. Chen , W. Li , Y. Zhou , Z. Nie , J. Xu , and W. Zhou , “ Micro selective laser melting of SS316L: Single tracks, defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 145, 107469 (2022).https://doi.org/10.1016/j.optlastec.2021.107469
    Google ScholarCrossref
  6. Y. Wei , G. Chen , W. Li , M. Li , Y. Zhou , Z. Nie , and J. Xu , “ Process optimization of micro selective laser melting and comparison of different laser diameter for forming different powder,” Opt. Laser Technol. 150, 107953 (2022).https://doi.org/10.1016/j.optlastec.2022.107953
    Google ScholarCrossref
  7. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Formation of SS316L single tracks in micro selective laser melting: Surface, geometry, and defects,” Adv. Mater. Sci. Eng. 2019, 9451406.https://doi.org/10.1155/2019/9451406
    Crossref
  8. B. Nagarajan , Z. Hu , S. Gao , X. Song , R. Huang , M. Seita , and J. Wei , “ Effect of in-situ laser remelting on the microstructure of SS316L fabricated by micro selective laser melting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 330–336.
    Google ScholarCrossref
  9. H. Zhiheng , B. Nagarajan , X. Song , R. Huang , W. Zhai , and J. Wei , “ Tailoring surface roughness of micro selective laser melted SS316L by in-situ laser remelting,” in Advanced Surface Enhancement, edited by Sho Itoh and Shashwat Shukla , Lecture Notes in Mechanical Engineering ( Springer Singapore, Singapore, 2020), pp. 337–343.
    Google Scholar
  10. J. Fu , Z. Hu , X. Song , W. Zhai , Y. Long , H. Li , and M. Fu , “ Micro selective laser melting of NiTi shape memory alloy: Defects, microstructures and thermal/mechanical properties,” Opt. Laser Technol. 131, 106374 (2020).https://doi.org/10.1016/j.optlastec.2020.106374
    Google ScholarCrossref
  11. E. Abele and M. Kniepkamp , “ Analysis and optimisation of vertical surface roughness in micro selective laser melting,” Surf. Topogr.: Metrol. Prop. 3, 034007 (2015).https://doi.org/10.1088/2051-672X/3/3/034007
    Google ScholarCrossref
  12. S. Qu , J. Ding , J. Fu , M. Fu , B. Zhang , and X. Song , “ High-precision laser powder bed fusion processing of pure copper,” Addit. Manuf. 48, 102417 (2021).https://doi.org/10.1016/j.addma.2021.102417
    Google ScholarCrossref
  13. Y. Wei , G. Chen , M. Li , W. Li , Y. Zhou , J. Xu , and Z. wei , “ High-precision laser powder bed fusion of 18Ni300 maraging steel and its SiC reinforcement composite materials,” J. Manuf. Process. 84, 750–763 (2022).https://doi.org/10.1016/j.jmapro.2022.10.049
    Google ScholarCrossref
  14. B. Liu , R. Wildman , T. Christopher , I. Ashcroft , and H. Richard , “ Investigation the effect of particle size distribution on processing parameters optimisation in selective laser melting process,” in 2011 International Solid Freeform Fabrication Symposium ( University of Texas at Austin, 2011).
    Google Scholar
  15. T. D. McLouth , G. E. Bean , D. B. Witkin , S. D. Sitzman , P. M. Adams , D. N. Patel , W. Park , J.-M. Yang , and R. J. Zaldivar , “ The effect of laser focus shift on microstructural variation of Inconel 718 produced by selective laser melting,” Mater. Des. 149, 205–213 (2018).https://doi.org/10.1016/j.matdes.2018.04.019
    Google ScholarCrossref
  16. Y. Qian , Y. Wentao , and L. Feng , “ Mesoscopic simulations of powder bed fusion: Research progresses and conditions,” Electromachining Mould 06, 46–52 (2017).https://doi.org/10.3969/j.issn.1009-279X.2017.06.012
    Google Scholar
  17. J. Fu , S. Qu , J. Ding , X. Song , and M. W. Fu , “ Comparison of the microstructure, mechanical properties and distortion of stainless Steel 316L fabricated by micro and conventional laser powder bed fusion,” Addit. Manuf. 44, 102067 (2021).https://doi.org/10.1016/j.addma.2021.102067
    Google ScholarCrossref
  18. N. T. Aboulkhair , I. Maskery , C. Tuck , I. Ashcroft , and N. M. Everitt , “ The microstructure and mechanical properties of selectively laser Melted AlSi10Mg: The effect of a conventional T6-like heat treatment,” Mater. Sci. Eng. A 667, 139–146 (2016).https://doi.org/10.1016/j.msea.2016.04.092
    Google ScholarCrossref
  19. S. Y. Chen , J. C. Huang , C. T. Pan , C. H. Lin , T. L. Yang , Y. S. Huang , C. H. Ou , L. Y. Chen , D. Y. Lin , H. K. Lin , T. H. Li , J. S. C. Jang , and C. C. Yang , “ Microstructure and mechanical properties of open-cell porous Ti-6Al-4V fabricated by selective laser melting,” J. Alloys Compd. 713, 248–254 (2017).https://doi.org/10.1016/j.jallcom.2017.04.190
    Google ScholarCrossref
  20. Y. Bai , Y. Yang , D. Wang , and M. Zhang , “ Influence mechanism of parameters process and mechanical properties evolution mechanism of Maraging steel 300 by selective laser melting,” Mater. Sci. Eng. A 703, 116–123 (2017).https://doi.org/10.1016/j.msea.2017.06.033
    Google ScholarCrossref
  21. Y. Bai , Y. Yang , Z. Xiao , M. Zhang , and D. Wang , “ Process optimization and mechanical property evolution of AlSiMg0.75 by selective laser melting,” Mater. Des. 140, 257–266 (2018).https://doi.org/10.1016/j.matdes.2017.11.045
    Google ScholarCrossref
  22. Y. Liu , M. Zhang , W. Shi , Y. Ma , and J. Yang , “ Study on performance optimization of 316L stainless steel parts by high-efficiency selective laser melting,” Opt. Laser Technol. 138, 106872 (2021).https://doi.org/10.1016/j.optlastec.2020.106872
    Google ScholarCrossref
  23. D. Gu , Y.-C. Hagedorn , W. Meiners , G. Meng , R. J. S. Batista , K. Wissenbach , and R. Poprawe , “ Densification behavior, microstructure evolution, and wear performance of selective laser melting processed commercially pure titanium,” Acta Mater. 60, 3849–3860 (2012).https://doi.org/10.1016/j.actamat.2012.04.006
    Google ScholarCrossref
  24. N. Read , W. Wang , K. Essa , and M. M. Attallah , “ Selective laser melting of AlSi10Mg alloy: Process optimisation and mechanical properties development,” Mater. Des. 65, 417–424 (2015).https://doi.org/10.1016/j.matdes.2014.09.044
    Google ScholarCrossref
  25. I. A. Roberts , C. J. Wang , R. Esterlein , M. Stanford , and D. J. Mynors , “ A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing,” Int. J. Mach. Tools Manuf. 49(12–13), 916–923 (2009).https://doi.org/10.1016/j.ijmachtools.2009.07.004
    Google ScholarCrossref
  26. K. Dai and L. Shaw , “ Finite element analysis of the effect of volume shrinkage during laser densification,” Acta Mater. 53(18), 4743–4754 (2005).https://doi.org/10.1016/j.actamat.2005.06.014
    Google ScholarCrossref
  27. K. Carolin , E. Attar , and P. Heinl , “ Mesoscopic simulation of selective beam melting processes,” J. Mater. Process. Technol. 211(6), 978–987 (2011).https://doi.org/10.1016/j.jmatprotec.2010.12.016
    Google ScholarCrossref
  28. F.-J. Gürtler , M. Karg , K.-H. Leitz , and M. Schmidt , “ Simulation of laser beam melting of steel powders using the three-dimensional volume of fluid method,” Phys. Procedia 41, 881–886 (2013).https://doi.org/10.1016/j.phpro.2013.03.162
    Google ScholarCrossref
  29. P. Meakin and R. Jullien , “ Restructuring effects in the rain model for random deposition,” J. Phys. France 48(10), 1651–1662 (1987).https://doi.org/10.1051/jphys:0198700480100165100
    Google ScholarCrossref
  30. J-m Wang , G-h Liu , Y-l Fang , and W-k Li , “ Marangoni effect in nonequilibrium multiphase system of material processing,” Rev. Chem. Eng. 32(5), 551–585 (2016).https://doi.org/10.1515/revce-2015-0067
    Google ScholarCrossref
  31. W. Ye , S. Zhang , L. L. Mendez , M. Farias , J. Li , B. Xu , P. Li , and Y. Zhang , “ Numerical simulation of the melting and alloying processes of elemental titanium and boron powders using selective laser alloying,” J. Manuf. Process. 64, 1235–1247 (2021).https://doi.org/10.1016/j.jmapro.2021.02.044
    Google ScholarCrossref
  32. U. S. Bertoli , A. J. Wolfer , M. J. Matthews , J.-P. R. Delplanque , and J. M. Schoenung , “ On the limitations of volumetric energy density as a design parameter for selective laser melting,” Mater. Des. 113, 331–340 (2017).https://doi.org/10.1016/j.matdes.2016.10.037
    Google ScholarCrossref
  33. W. E. King , H. D. Barth , V. M. Castillo , G. F. Gallegos , J. W. Gibbs , D. E. Hahn , C. Kamath , and A. M. Rubenchik , “ Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing,” J. Mater. Process. Technol. 214(12), 2915–2925 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.005
    Google ScholarCrossref
  34. L. Cao , “ Numerical simulation of the impact of laying powder on selective laser melting single-pass formation,” Int. J. Heat Mass Transfer 141, 1036–1048 (2019).https://doi.org/10.1016/j.ijheatmasstransfer.2019.07.053
    Google ScholarCrossref
  35. L. Huang , X. Hua , D. Wu , and F. Li , “ Numerical study of keyhole instability and porosity formation mechanism in laser welding of aluminum alloy and steel,” J. Mater. Process. Technol. 252, 421–431 (2018).https://doi.org/10.1016/j.jmatprotec.2017.10.011
    Google ScholarCrossref
  36. K. Q. Le , C. Tang , and C. H. Wong , “ On the study of keyhole-mode melting in selective laser melting process,” Int. J. Therm. Sci. 145, 105992 (2019).https://doi.org/10.1016/j.ijthermalsci.2019.105992
    Google ScholarCrossref
  37. J.-H. Cho and S.-J. Na , “ Theoretical analysis of keyhole dynamics in polarized laser drilling,” J. Phys. D: Appl. Phys. 40(24), 7638 (2007).https://doi.org/10.1088/0022-3727/40/24/007
    Google ScholarCrossref
  38. W. Ye , “ Mechanism analysis of selective laser melting and metallurgy process based on base element powder of titanium and boron,” Ph.D. dissertation ( Nanchang University, 2021).
    Google Scholar
  39. R. Ammer , M. Markl , U. Ljungblad , C. Körner , and U. Rüde , “ Simulating fast electron beam melting with a parallel thermal free surface lattice Boltzmann method,” Comput. Math. Appl. 67(2), 318–330 (2014).https://doi.org/10.1016/j.camwa.2013.10.001
    Google ScholarCrossref
  40. H. Chen , Q. Wei , S. Wen , Z. Li , and Y. Shi , “ Flow behavior of powder particles in layering process of selective laser melting: Numerical modeling and experimental verification based on discrete element method,” Int. J. Mach. Tools Manuf. 123, 146–159 (2017).https://doi.org/10.1016/j.ijmachtools.2017.08.004
    Google ScholarCrossref
  41. F. Verhaeghe , T. Craeghs , J. Heulens , and L. Pandelaers , “ A pragmatic model for selective laser melting with evaporation,” Acta Mater. 57(20), 6006–6012 (2009).https://doi.org/10.1016/j.actamat.2009.08.027
    Google ScholarCrossref
  42. C. H. Fu and Y. B. Guo , “ Three-dimensional temperature gradient mechanism in selective laser melting of Ti-6Al-4V,” J. Manuf. Sci. Eng. 136(6), 061004 (2014).https://doi.org/10.1115/1.4028539
    Google ScholarCrossref
  43. Y. Xiang , Z. Shuzhe , L. Junfeng , W. Zhengying , Y. Lixiang , and J. Lihao , “ Numerical simulation and experimental verification for selective laser single track melting forming of Ti6Al4V,” J. Zhejiang Univ. (Eng. Sci.) 53(11), 2102–2109 + 2117 (2019).https://doi.org/10.3785/j.issn.1008-973X.2019.11.007
    Google Scholar
  44. Q. He , H. Xia , J. Liu , X. Ao , and S. Lin , “ Modeling and numerical studies of selective laser melting: Multiphase flow, solidification and heat transfer,” Mater. Des. 196, 109115 (2020).https://doi.org/10.1016/j.matdes.2020.109115
    Google ScholarCrossref
  45. L. Cao , “ Mesoscopic-scale numerical simulation including the influence of process parameters on SLM single-layer multi-pass formation,” Metall. Mater. Trans. A 51, 4130–4145 (2020).https://doi.org/10.1007/s11661-020-05831-z
    Google ScholarCrossref
  46. L. Cao , “ Mesoscopic-scale numerical investigation including the influence of process parameters on LPBF multi-layer multi-path formation,” Comput. Model. Eng. Sci. 126(1), 5–23 (2021).https://doi.org/10.32604/cmes.2021.014693
    Google ScholarCrossref
  47. H. Yin and S. D. Felicelli , “ Dendrite growth simulation during solidification in the LENS process,” Acta Mater. 58(4), 1455–1465 (2010).https://doi.org/10.1016/j.actamat.2009.10.053
    Google ScholarCrossref
  48. P. Nie , O. A. Ojo , and Z. Li , “ Numerical modeling of microstructure evolution during laser additive manufacturing of a nickel-based superalloy,” Acta Mater. 77, 85–95 (2014).https://doi.org/10.1016/j.actamat.2014.05.039
    Google ScholarCrossref
  49. Z. Liu and H. Qi , “ Effects of substrate crystallographic orientations on crystal growth and microstructure formation in laser powder deposition of nickel-based superalloy,” Acta Mater. 87, 248–258 (2015).https://doi.org/10.1016/j.actamat.2014.12.046
    Google ScholarCrossref
  50. L. Wei , L. Xin , W. Meng , and H. Weidong , “ Cellular automaton simulation of the molten pool of laser solid forming process,” Acta Phys. Sin. 64(01), 018103–018363 (2015).https://doi.org/10.7498/aps.64.018103
    Google ScholarCrossref
  51. R. Acharya , J. A. Sharon , and A. Staroselsky , “ Prediction of microstructure in laser powder bed fusion process,” Acta Mater. 124, 360–371 (2017).https://doi.org/10.1016/j.actamat.2016.11.018
    Google ScholarCrossref
  52. M. R. Rolchigo and R. LeSar , “ Modeling of binary alloy solidification under conditions representative of additive manufacturing,” Comput. Mater. Sci. 150, 535–545 (2018).https://doi.org/10.1016/j.commatsci.2018.04.004
    Google ScholarCrossref
  53. S. Geng , P. Jiang , L. Guo , X. Gao , and G. Mi , “ Multi-scale simulation of grain/sub-grain structure evolution during solidification in laser welding of aluminum alloys,” Int. J. Heat Mass Transfer 149, 119252 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119252
    Google ScholarCrossref
  54. W. L. Wang , W. Q. Liu , X. Yang , R. R. Xu , and Q. Y. Dai , “ Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy,” J. Mater. Sci. Technol. 119, 11–24 (2022).https://doi.org/10.1016/j.jmst.2021.12.029
    Google ScholarCrossref
  55. Q. Xia , J. Yang , and Y. Li , “ On the conservative phase-field method with the N-component incompressible flows,” Phys. Fluids 35, 012120 (2023).https://doi.org/10.1063/5.0135490
    Google ScholarCrossref
  56. Q. Xia , G. Sun , J. Kim , and Y. Li , “ Multi-scale modeling and simulation of additive manufacturing based on fused deposition technique,” Phys. Fluids 35, 034116 (2023).https://doi.org/10.1063/5.0141316
    Google ScholarCrossref
  57. A. Hussein , L. Hao , C. Yan , and R. Everson , “ Finite element simulation of the temperature and stress fields in single layers built without-support in selective laser melting,” Mater. Des. 52, 638–647 (2013).https://doi.org/10.1016/j.matdes.2013.05.070
    Google ScholarCrossref
  58. J. Ding , P. Colegrove , J. Mehnen , S. Ganguly , P. M. Sequeira Almeida , F. Wang , and S. Williams , “ Thermo-mechanical analysis of wire and arc additive layer manufacturing process on large multi-layer parts,” Comput. Mater. Sci. 50(12), 3315–3322 (2011).https://doi.org/10.1016/j.commatsci.2011.06.023
    Google ScholarCrossref
  59. Y. Du , X. You , F. Qiao , L. Guo , and Z. Liu , “ A model for predicting the temperature field during selective laser melting,” Results Phys. 12, 52–60 (2019).https://doi.org/10.1016/j.rinp.2018.11.031
    Google ScholarCrossref
  60. X. Luo , M. Liu , L. Zhenhua , H. Li , and J. Shen , “ Effect of different heat-source models on calculated temperature field of selective laser melted 18Ni300,” Chin. J. Lasers 48(14), 1402005–1402062 (2021).https://doi.org/10.3788/CJL202148.1402005
    Google ScholarCrossref
  61. J. F. Li , L. Li , and F. H. Stott , “ Thermal stresses and their implication on cracking during laser melting of ceramic materials,” Acta Mater. 52(14), 4385–4398 (2004).https://doi.org/10.1016/j.actamat.2004.06.005
    Google ScholarCrossref
  62. P. Aggarangsi and J. L. Beuth , “ Localized preheating approaches for reducing residual stress in additive manufacturing,” paper presented at the 2006 International Solid Freeform Fabrication Symposium, The University of Texas in Austin on August 14–16, 2006.
  63. K. Dai and L. Shaw , “ Thermal and mechanical finite element modeling of laser forming from metal and ceramic powders,” Acta Mater. 52(1), 69–80 (2004).https://doi.org/10.1016/j.actamat.2003.08.028
    Google ScholarCrossref
  64. A. H. Nickel , D. M. Barnett , and F. B. Prinz , “ Thermal stresses and deposition patterns in layered manufacturing,” Mater. Sci. Eng. A 317(1–2), 59–64 (2001).https://doi.org/10.1016/S0921-5093(01)01179-0
    Google ScholarCrossref
  65. M. F. Zaeh and G. Branner , “ Investigations on residual stresses and deformations in selective laser melting,” Prod. Eng. 4(1), 35–45 (2010).https://doi.org/10.1007/s11740-009-0192-y
    Google ScholarCrossref
  66. P. Bian , J. Shi , Y. Liu , and Y. Xie , “ Influence of laser power and scanning strategy on residual stress distribution in additively manufactured 316L steel,” Opt. Laser Technol. 132, 106477 (2020).https://doi.org/10.1016/j.optlastec.2020.106477
    Google ScholarCrossref
  67. B. M. Marques , C. M. Andrade , D. M. Neto , M. C. Oliveira , J. L. Alves , and L. F. Menezes , “ Numerical analysis of residual stresses in parts produced by selective laser melting process,” Procedia Manuf. 47, 1170–1177 (2020).https://doi.org/10.1016/j.promfg.2020.04.167
    Google ScholarCrossref
  68. W. Mu , “ Numerical simulation of SLM forming process and research and prediction of forming properties,” MA thesis ( Anhui Jianzhu University, 2022).
    Google Scholar
  69. Y. Zhang , “ Multi-scale multi-physics modeling of laser powder bed fusion process of metallic materials with experiment validation,” Ph.D. dissertation ( Purdue University, 2018).
    Google Scholar
  70. Y. Qian , “ Mesoscopic simulation studies of key processing issues for powder bed fusion technology,” Ph.D. dissertation ( Tsinghua University, 2019).
    Google Scholar
  71. N. V. Brilliantov , S. Frank , J.-M. Hertzsch , and T. Pöschel , “ Model for collisions in granular gases,” Phys. Rev. E 53(5), 5382–5392 (1996).https://doi.org/10.1103/PhysRevE.53.5382
    Google ScholarCrossref
  72. Z. Xiao , “ Research on microscale selective laser melting process of high strength pure copper specimens,” MA thesis ( Hunan University, 2022).
    Google Scholar
  73. Z. Li , K. Mukai , M. Zeze , and K. C. Mills , “ Determination of the surface tension of liquid stainless steel,” J. Mater. Sci. 40(9–10), 2191–2195 (2005).https://doi.org/10.1007/s10853-005-1931-x
    Google ScholarCrossref
  74. R. Scardovelli and S. Zaleski , “ Analytical relations connecting linear interfaces and volume fractions in rectangular grids,” J. Comput. Phys. 164(1), 228–237 (2000).https://doi.org/10.1006/jcph.2000.6567
    Google ScholarCrossref
  75. D.-W. Cho , W.-I. Cho , and S.-J. Na , “ Modeling and simulation of arc: Laser and hybrid welding process,” J. Manuf. Process. 16(1), 26–55 (2014).https://doi.org/10.1016/j.jmapro.2013.06.012
    Google ScholarCrossref
    76.Flow3D. Version 11.1.0: User Manual ( FlowScience, Santa Fe, NM, USA, 2015).
  76. Y. Tian , L. Yang , D. Zhao , Y. Huang , and J. Pan , “ Numerical analysis of powder bed generation and single track forming for selective laser melting of ss316l stainless steel,” J. Manuf. Process. 58, 964–974 (2020).https://doi.org/10.1016/j.jmapro.2020.09.002
    Google ScholarCrossref
  77. C. Tang , K. Q. Le , and C. H. Wong , “ Physics of humping formation in laser powder bed fusion,” Int. J. Heat Mass Transfer 149, 119172 (2020).https://doi.org/10.1016/j.ijheatmasstransfer.2019.119172
    Google ScholarCrossref
  78. L. Cao , “ Mesoscopic-scale simulation of pore evolution during laser powder bed fusion process,” Comput. Mater. Sci. 179, 109686 (2020).https://doi.org/10.1016/j.commatsci.2020.109686
    Google ScholarCrossref
  79. R. Li , J. Liu , Y. Shi , W. Li , and W. Jiang , “ Balling behavior of stainless steel and nickel powder during selective laser melting process,” Int. J. Adv. Manuf. Technol. 59(9–12), 1025–1035 (2012).https://doi.org/10.1007/s00170-011-3566-1
    Google ScholarCrossref
  80. S. A. Khairallah and A. Anderson , “ Mesoscopic simulation model of selective laser melting of stainless steel powder,” J. Mater. Process. Technol. 214(11), 2627–2636 (2014).https://doi.org/10.1016/j.jmatprotec.2014.06.001
    Google ScholarCrossref
  81. J. Liu , D. Gu , H. Chen , D. Dai , and H. Zhang , “ Influence of substrate surface morphology on wetting behavior of tracks during selective laser melting of aluminum-based alloys,” J. Zhejiang Univ. Sci. A 19(2), 111–121 (2018).https://doi.org/10.1631/jzus.A1700599
    Google ScholarCrossref
  82. L. Li , J. Li , and T. Fan , “ Phase-field modeling of wetting and balling dynamics in powder bed fusion process,” Phys. Fluids 33, 042116 (2021).https://doi.org/10.1063/5.0046771
    Google ScholarCrossref
  83. X. Nie , Z. Hu , H. Zhu , Z. Hu , L. Ke , and X. Zeng , “ Analysis of processing parameters and characteristics of selective laser melted high strength Al-Cu-Mg alloys: from single tracks to cubic samples,” J. Mater. Process. Technol. 256, 69–77 (2018).https://doi.org/10.1016/j.jmatprotec.2018.01.030
    Google ScholarCrossref
원본 바로가기
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)

Download 

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.

Jmse 09 00886 g004 550

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.

Jmse 09 00886 g005 550

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.

Jmse 09 00886 g006 550

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.

Jmse 09 00886 g007 550

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.

Jmse 09 00886 g008 550

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.

Jmse 09 00886 g009 550

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.

Jmse 09 00886 g010a 550
Jmse 09 00886 g010b 550

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.

Jmse 09 00886 g011 550

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

Jmse 09 00886 g012 550

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.

Jmse 09 00886 g013 550

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.

Jmse 09 00886 g014 550

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

Jmse 09 00886 g015a 550
Jmse 09 00886 g015b 550

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.

Jmse 09 00886 g016 550

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

Jmse 09 00886 g017 550

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.

Jmse 09 00886 g018 550

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)

Jmse 09 00886 g019 550

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.

Jmse 09 00886 g020 550

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.

Jmse 09 00886 g021 550

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)

Jmse 09 00886 g022 550

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.

Jmse 09 00886 g023 550

Figure 23. The fitting curve between Seq/D and Fr.

Jmse 09 00886 g024 550

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.

Jmse 09 00886 g025 550

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.

References

  1. Sumer, B.M.; Fredsøe, J.; Christiansen, N. Scour Around Vertical Pile in Waves. J. Waterw. Port. Coast. Ocean Eng. 1992, 118, 15–31. [Google Scholar] [CrossRef]
  2. Rudolph, D.; Bos, K. Scour around a monopile under combined wave-current conditions and low KC-numbers. In Proceedings of the 6th International Conference on Scour and Erosion, Amsterdam, The Netherlands, 1–3 November 2006; pp. 582–588. [Google Scholar]
  3. Nielsen, A.W.; Liu, X.; Sumer, B.M.; Fredsøe, J. Flow and bed shear stresses in scour protections around a pile in a current. Coast. Eng. 2013, 72, 20–38. [Google Scholar] [CrossRef]
  4. Ahmad, N.; Bihs, H.; Myrhaug, D.; Kamath, A.; Arntsen, Ø.A. Three-dimensional numerical modelling of wave-induced scour around piles in a side-by-side arrangement. Coast. Eng. 2018, 138, 132–151. [Google Scholar] [CrossRef]
  5. Li, H.; Ong, M.C.; Leira, B.J.; Myrhaug, D. Effects of Soil Profile Variation and Scour on Structural Response of an Offshore Monopile Wind Turbine. J. Offshore Mech. Arct. Eng. 2018, 140, 042001. [Google Scholar] [CrossRef]
  6. Li, H.; Liu, H.; Liu, S. Dynamic analysis of umbrella suction anchor foundation embedded in seabed for offshore wind turbines. Géoméch. Energy Environ. 2017, 10, 12–20. [Google Scholar] [CrossRef]
  7. Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Vanem, E.; Carvalho, H.; Correia, J.A.F.D.O. Editorial: Advanced research on offshore structures and foundation design: Part 1. Proc. Inst. Civ. Eng. Marit. Eng. 2019, 172, 118–123. [Google Scholar] [CrossRef]
  8. Chavez, C.E.A.; Stratigaki, V.; Wu, M.; Troch, P.; Schendel, A.; Welzel, M.; Villanueva, R.; Schlurmann, T.; De Vos, L.; Kisacik, D.; et al. Large-Scale Experiments to Improve Monopile Scour Protection Design Adapted to Climate Change—The PROTEUS Project. Energies 2019, 12, 1709. [Google Scholar] [CrossRef][Green Version]
  9. Wu, M.; De Vos, L.; Chavez, C.E.A.; Stratigaki, V.; Fazeres-Ferradosa, T.; Rosa-Santos, P.; Taveira-Pinto, F.; Troch, P. Large Scale Experimental Study of the Scour Protection Damage Around a Monopile Foundation Under Combined Wave and Current Conditions. J. Mar. Sci. Eng. 2020, 8, 417. [Google Scholar] [CrossRef]
  10. Sørensen, S.P.H.; Ibsen, L.B. Assessment of foundation design for offshore monopiles unprotected against scour. Ocean Eng. 2013, 63, 17–25. [Google Scholar] [CrossRef]
  11. Prendergast, L.; Gavin, K.; Doherty, P. An investigation into the effect of scour on the natural frequency of an offshore wind turbine. Ocean Eng. 2015, 101, 1–11. [Google Scholar] [CrossRef][Green Version]
  12. Fazeres-Ferradosa, T.; Chambel, J.; Taveira-Pinto, F.; Rosa-Santos, P.; Taveira-Pinto, F.; Giannini, G.; Haerens, P. Scour Protections for Offshore Foundations of Marine Energy Harvesting Technologies: A Review. J. Mar. Sci. Eng. 2021, 9, 297. [Google Scholar] [CrossRef]
  13. Yang, Q.; Yu, P.; Liu, Y.; Liu, H.; Zhang, P.; Wang, Q. Scour characteristics of an offshore umbrella suction anchor foundation under the combined actions of waves and currents. Ocean Eng. 2020, 202, 106701. [Google Scholar] [CrossRef]
  14. Yu, P.; Hu, R.; Yang, J.; Liu, H. Numerical investigation of local scour around USAF with different hydraulic conditions under currents and waves. Ocean Eng. 2020, 213, 107696. [Google Scholar] [CrossRef]
  15. Sumer, B.M.; Christiansen, N.; Fredsøe, J. The horseshoe vortex and vortex shedding around a vertical wall-mounted cylinder exposed to waves. J. Fluid Mech. 1997, 332, 41–70. [Google Scholar] [CrossRef]
  16. Sumer, B.M.; Fredsøe, J. Scour around Pile in Combined Waves and Current. J. Hydraul. Eng. 2001, 127, 403–411. [Google Scholar] [CrossRef]
  17. Petersen, T.U.; Sumer, B.M.; Fredsøe, J. Time scale of scour around a pile in combined waves and current. In Proceedings of the 6th International Conference on Scour and Erosion, Paris, France, 27–31 August 2012. [Google Scholar]
  18. Petersen, T.U.; Sumer, B.M.; Fredsøe, J.; Raaijmakers, T.C.; Schouten, J.-J. Edge scour at scour protections around piles in the marine environment—Laboratory and field investigation. Coast. Eng. 2015, 106, 42–72. [Google Scholar] [CrossRef]
  19. Qi, W.; Gao, F. Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci. China Ser. E Technol. Sci. 2014, 57, 1030–1039. [Google Scholar] [CrossRef][Green Version]
  20. Larsen, B.E.; Fuhrman, D.R.; Baykal, C.; Sumer, B.M. Tsunami-induced scour around monopile foundations. Coast. Eng. 2017, 129, 36–49. [Google Scholar] [CrossRef][Green Version]
  21. Corvaro, S.; Marini, F.; Mancinelli, A.; Lorenzoni, C.; Brocchini, M. Hydro- and Morpho-dynamics Induced by a Vertical Slender Pile under Regular and Random Waves. J. Waterw. Port. Coast. Ocean Eng. 2018, 144, 04018018. [Google Scholar] [CrossRef]
  22. Schendel, A.; Welzel, M.; Schlurmann, T.; Hsu, T.-W. Scour around a monopile induced by directionally spread irregular waves in combination with oblique currents. Coast. Eng. 2020, 161, 103751. [Google Scholar] [CrossRef]
  23. Fazeres-Ferradosa, T.; Taveira-Pinto, F.; Romão, X.; Reis, M.; das Neves, L. Reliability assessment of offshore dynamic scour protections using copulas. Wind. Eng. 2018, 43, 506–538. [Google Scholar] [CrossRef]
  24. Fazeres-Ferradosa, T.; Welzel, M.; Schendel, A.; Baelus, L.; Santos, P.R.; Pinto, F.T. Extended characterization of damage in rubble mound scour protections. Coast. Eng. 2020, 158, 103671. [Google Scholar] [CrossRef]
  25. Tavouktsoglou, N.S.; Harris, J.M.; Simons, R.R.; Whitehouse, R.J.S. Equilibrium Scour-Depth Prediction around Cylindrical Structures. J. Waterw. Port. Coast. Ocean Eng. 2017, 143, 04017017. [Google Scholar] [CrossRef][Green Version]
  26. Ettema, R.; Melville, B.; Barkdoll, B. Scale Effect in Pier-Scour Experiments. J. Hydraul. Eng. 1998, 124, 639–642. [Google Scholar] [CrossRef]
  27. Umeda, S. Scour Regime and Scour Depth around a Pile in Waves. J. Coast. Res. Spec. Issue 2011, 64, 845–849. [Google Scholar]
  28. Umeda, S. Scour process around monopiles during various phases of sea storms. J. Coast. Res. 2013, 165, 1599–1604. [Google Scholar] [CrossRef]
  29. Baykal, C.; Sumer, B.; Fuhrman, D.R.; Jacobsen, N.; Fredsøe, J. Numerical simulation of scour and backfilling processes around a circular pile in waves. Coast. Eng. 2017, 122, 87–107. [Google Scholar] [CrossRef][Green Version]
  30. Miles, J.; Martin, T.; Goddard, L. Current and wave effects around windfarm monopile foundations. Coast. Eng. 2017, 121, 167–178. [Google Scholar] [CrossRef][Green Version]
  31. Miozzi, M.; Corvaro, S.; Pereira, F.A.; Brocchini, M. Wave-induced morphodynamics and sediment transport around a slender vertical cylinder. Adv. Water Resour. 2019, 129, 263–280. [Google Scholar] [CrossRef]
  32. Yu, T.; Zhang, Y.; Zhang, S.; Shi, Z.; Chen, X.; Xu, Y.; Tang, Y. Experimental study on scour around a composite bucket foundation due to waves and current. Ocean Eng. 2019, 189, 106302. [Google Scholar] [CrossRef]
  33. Carreiras, J.; Larroudé, P.; Seabra-Santos, F.; Mory, M. Wave Scour Around Piles. In Proceedings of the Coastal Engineering 2000, American Society of Civil Engineers (ASCE), Sydney, Australia, 16–21 July 2000; pp. 1860–1870. [Google Scholar]
  34. Raaijmakers, T.; Rudolph, D. Time-dependent scour development under combined current and waves conditions—Laboratory experiments with online monitoring technique. In Proceedings of the 4th International Conference on Scour and Erosion, Tokyo, Japan, 5–7 November 2008; pp. 152–161. [Google Scholar]
  35. Khalfin, I.S. Modeling and calculation of bed score around large-diameter vertical cylinder under wave action. Water Resour. 2007, 34, 357. [Google Scholar] [CrossRef][Green Version]
  36. Zanke, U.C.; Hsu, T.-W.; Roland, A.; Link, O.; Diab, R. Equilibrium scour depths around piles in noncohesive sediments under currents and waves. Coast. Eng. 2011, 58, 986–991. [Google Scholar] [CrossRef]
  37. Myrhaug, D.; Rue, H. Scour below pipelines and around vertical piles in random waves. Coast. Eng. 2003, 48, 227–242. [Google Scholar] [CrossRef]
  38. Myrhaug, D.; Ong, M.C.; Føien, H.; Gjengedal, C.; Leira, B.J. Scour below pipelines and around vertical piles due to second-order random waves plus a current. Ocean Eng. 2009, 36, 605–616. [Google Scholar] [CrossRef]
  39. Myrhaug, D.; Ong, M.C. Random wave-induced onshore scour characteristics around submerged breakwaters using a stochastic method. Ocean Eng. 2010, 37, 1233–1238. [Google Scholar] [CrossRef]
  40. Ong, M.C.; Myrhaug, D.; Hesten, P. Scour around vertical piles due to long-crested and short-crested nonlinear random waves plus a current. Coast. Eng. 2013, 73, 106–114. [Google Scholar] [CrossRef]
  41. Yakhot, V.; Orszag, S.A. Renormalization group analysis of turbulence. I. Basic theory. J. Sci. Comput. 1986, 1, 3–51. [Google Scholar] [CrossRef]
  42. Yakhot, V.; Smith, L.M. The renormalization group, the e-expansion and derivation of turbulence models. J. Sci. Comput. 1992, 7, 35–61. [Google Scholar] [CrossRef]
  43. Mastbergen, D.R.; Berg, J.V.D. Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology 2003, 50, 625–637. [Google Scholar] [CrossRef]
  44. Soulsby, R. Dynamics of Marine Sands; Thomas Telford Ltd.: London, UK, 1998. [Google Scholar] [CrossRef]
  45. Van Rijn, L.C. Sediment Transport, Part I: Bed Load Transport. J. Hydraul. Eng. 1984, 110, 1431–1456. [Google Scholar] [CrossRef][Green Version]
  46. Zhang, Q.; Zhou, X.-L.; Wang, J.-H. Numerical investigation of local scour around three adjacent piles with different arrangements under current. Ocean Eng. 2017, 142, 625–638. [Google Scholar] [CrossRef]
  47. Yu, Y.X.; Liu, S.X. Random Wave and Its Applications to Engineering, 4th ed.; Dalian University of Technology Press: Dalian, China, 2011. [Google Scholar]
  48. Pang, A.; Skote, M.; Lim, S.; Gullman-Strand, J.; Morgan, N. A numerical approach for determining equilibrium scour depth around a mono-pile due to steady currents. Appl. Ocean Res. 2016, 57, 114–124. [Google Scholar] [CrossRef]
  49. Higuera, P.; Lara, J.L.; Losada, I.J. Three-dimensional interaction of waves and porous coastal structures using Open-FOAM®. Part I: Formulation and validation. Coast. Eng. 2014, 83, 243–258. [Google Scholar] [CrossRef]
  50. Corvaro, S.; Crivellini, A.; Marini, F.; Cimarelli, A.; Capitanelli, L.; Mancinelli, A. Experimental and Numerical Analysis of the Hydrodynamics around a Vertical Cylinder in Waves. J. Mar. Sci. Eng. 2019, 7, 453. [Google Scholar] [CrossRef][Green Version]
  51. Flow3D User Manual, version 11.0.3; Flow Science, Inc.: Santa Fe, NM, USA, 2013.
  52. Khosronejad, A.; Kang, S.; Sotiropoulos, F. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour. 2012, 37, 73–85. [Google Scholar] [CrossRef]
  53. Stahlmann, A. Experimental and Numerical Modeling of Scour at Foundation Structures for Offshore Wind Turbines. Ph.D. Thesis, Franzius-Institute for Hydraulic, Estuarine and Coastal Engineering, Leibniz Universität Hannover, Hannover, Germany, 2013. [Google Scholar]
  54. Breusers, H.N.C.; Nicollet, G.; Shen, H. Local Scour Around Cylindrical Piers. J. Hydraul. Res. 1977, 15, 211–252. [Google Scholar] [CrossRef]
  55. Schendel, A.; Hildebrandt, A.; Goseberg, N.; Schlurmann, T. Processes and evolution of scour around a monopile induced by tidal currents. Coast. Eng. 2018, 139, 65–84. [Google Scholar] [CrossRef]
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Share and Cite

      

MDPI and ACS Style

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

AMA Style

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

Find Other Styles

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

For more information on the journal statistics, click here.

Multiple requests from the same IP address are counted as one view.

원본 다운로드
Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

레이저 보조 분말 기반 직접 에너지 증착에서 용융 풀 거동에 대한 감쇠 레이저 빔 강도 프로파일의 영향에 대한 열유체 모델링

Thermo-fluid modeling of influence of attenuated laser beam intensity profile on melt pool behavior in laser-assisted powder-based direct energy deposition

Mohammad Sattari, Amin Ebrahimi, Martin Luckabauer, Gert-willem R.B.E. Römer

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Professional

5Downloads (Pure)

Abstract

A numerical framework based on computational fluid dynamics (CFD), using the finite volume method (FVM) and volume of fluid (VOF) technique is presented to investigate the effect of the laser beam intensity profile on melt pool behavior in laser-assisted powder-based directed energy deposition (L-DED). L-DED is an additive manufacturing (AM) process that utilizes a laser beam to fuse metal powder particles. To assure high-fidelity modeling, it was found that it is crucial to accurately model the interaction between the powder stream and the laser beam in the gas region above the substrate. The proposed model considers various phenomena including laser energy attenuation and absorption, multiple reflections of the laser rays, powder particle stream, particle-fluid interaction, temperature-dependent properties, buoyancy effects, thermal expansion, solidification shrinkage and drag, and Marangoni flow. The latter is induced by temperature and element-dependent surface tension. The model is validated using experimental results and highlights the importance of considering laser energy attenuation. Furthermore, the study investigates how the laser beam intensity profile affects melt pool size and shape, influencing the solidification microstructure and mechanical properties of the deposited material. The proposed model has the potential to optimize the L-DED process for a variety of materials and provides insights into the capability of numerical modeling for additive manufacturing optimization.

Original languageEnglish
Title of host publicationFlow-3D World Users Conference
Publication statusPublished – 2023
EventFlow-3D World User Conference – Strasbourg, France
Duration: 5 Jun 2023 → 7 Jun 2023

Conference

ConferenceFlow-3D World User Conference
Country/TerritoryFrance
CityStrasbourg
Period5/06/23 → 7/06/23
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

원문보기
PDF View
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

Go to:

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

Go to:

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.

Go to:

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.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g001.jpg

Figure 1

A 3D model—impeller with four holes—variant B4.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g002.jpg

Figure 2

A 3D model—impeller with eight holes—variant B8.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g003.jpg

Figure 3

A 3D model—impeller with twelve holes—variant B12.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g004.jpg

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

Open in a separate window

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

Open in a separate window

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.

Open in a separate window

Go to:

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

Open in a separate window

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

Open in a separate window

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

Open in a separate window

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).

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g009.jpg

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

Open in a separate window

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.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g011.jpg

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.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g012.jpg

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.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g013.jpg

Figure 13

Gas bubble dispersion registered for different processing parameters (impeller variant B12).

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g014.jpg

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.

An external file that holds a picture, illustration, etc. Object name is materials-15-05273-g015.jpg

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

Open in a separate window

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.

Go to:

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.

Go to:

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.

Go to:

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.

Go to:

Institutional Review Board Statement

Not applicable.

Go to:

Informed Consent Statement

Not applicable.

Go to:

Data Availability Statement

Data are contained within the article.

Go to:

Conflicts of Interest

The authors declare no conflict of interest.

Go to:

Footnotes

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Go to:

References

1. Zhang L., Xuewei L., Torgerson A.T., Long M. Removal of Impurity Elements from Molten Aluminium: A Review. Miner. Process. Extr. Metall. Rev. 2011;32:150–228. doi: 10.1080/08827508.2010.483396. [CrossRef] [Google Scholar]

2. Saternus M. Impurities of liquid aluminium-methods on their estimation and removal. Met. Form. 2015;23:115–132. [Google Scholar]

3. Żak P.L., Kalisz D., Lelito J., Gracz B., Szucki M., Suchy J.S. Modelling of non-metallic particle motion process in foundry alloys. Metalurgija. 2015;54:357–360. [Google Scholar]

4. Kalisz D., Kuglin K. Efficiency of aluminum oxide inclusions rmoval from liquid steel as a result of collisions and agglomeration on ceramic filters. Arch. Foundry Eng. 2020;20:43–48. [Google Scholar]

5. Kuglin K., Kalisz D. Evaluation of the usefulness of rotors for aluminium refining. IOP Conf. Ser. Mater. Sci. Eng. 2021;1178:012036. doi: 10.1088/1757-899X/1178/1/012036. [CrossRef] [Google Scholar]

6. Saternus M., Merder T. Physical modeling of the impeller construction impact o the aluminium refining process. Materials. 2022;15:575. doi: 10.3390/ma15020575. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

7. Saternus M., Merder T. Physical modelling of aluminum refining process conducted in batch reactor with rotary impeller. Metals. 2018;8:726. doi: 10.3390/met8090726. [CrossRef] [Google Scholar]

8. Saternus M., Merder T., Pieprzyca J. The influence of impeller geometry on the gas bubbles dispersion in uro-200 reactor—RTD curves. Arch. Metall. Mater. 2015;60:2887–2893. doi: 10.1515/amm-2015-0461. [CrossRef] [Google Scholar]

9. Hernández-Hernández M., Camacho-Martínez J., González-Rivera C., Ramírez-Argáez M.A. Impeller design assisted by physical modeling and pilot plant trials. J. Mater. Process. Technol. 2016;236:1–8. doi: 10.1016/j.jmatprotec.2016.04.031. [CrossRef] [Google Scholar]

10. Mancilla E., Cruz-Méndez W., Garduño I.E., González-Rivera C., Ramírez-Argáez M.A., Ascanio G. Comparison of the hydrodynamic performance of rotor-injector devices in a water physical model of an aluminum degassing ladle. Chem. Eng. Res. Des. 2017;118:158–169. doi: 10.1016/j.cherd.2016.11.031. [CrossRef] [Google Scholar]

11. Michalek K., Socha L., Gryc K., Tkadleckova M., Saternus M., Pieprzyca J., Merder T. Modelling of technological parameters of aluminium melt refining in the ladle by blowing of inert gas through the rotating impeller. Arch. Metall. Mater. 2018;63:987–992. [Google Scholar]

12. Walek J., Michalek K., Tkadlecková M., Saternus M. Modelling of Technological Parameters of Aluminium Melt Refining in the Ladle by Blowing of Inert Gas through the Rotating Impeller. Metals. 2021;11:284. doi: 10.3390/met11020284. [CrossRef] [Google Scholar]

13. Michalek K., Gryc K., Moravka J. Physical modelling of bath homogenization in argon stirred ladle. Metalurgija. 2009;48:215–218. [Google Scholar]

14. Michalek K. The Use of Physical Modeling and Numerical Optimization for Metallurgical Processes. VSB; Ostrawa, Czech Republic: 2001. [Google Scholar]

15. Chen J., Zhao J. Light Metals. TMS; Warrendale, PA, USA: 1995. Bubble distribution in a melt treatment water model; pp. 1227–1231. [Google Scholar]

16. Saternus M. Model Matematyczny do Sterowania Procesem Rafinacji Ciekłych Stopów Aluminium Przy Zastosowaniu URO-200. Katowice, Poland: 2004. Research Project Nr 7 T08B 019 21. [Google Scholar]

17. Pietrewicz L., Wężyk W. Urządzenia do rafinacji gazowej typu URO-200 sześć lat produkcji i doświadczeń; Proceedings of the Aluminum Conference; Zakopane, Poland. 12–16 October 1998. [Google Scholar]

18. Flow3d User’s Guide. Flow Science, Inc.; Santa Fe, NM, USA: 2020. [Google Scholar]

19. Sinelnikov V., Szucki M., Merder T., Pieprzyca J., Kalisz D. Physical and numerical modeling of the slag splashing process. Materials. 2021;14:2289. doi: 10.3390/ma14092289. [PMC free article] [PubMed] [CrossRef] [Google Scholar]

20. White F. Fluid Mechanics. McGraw-Hill; New York, NY, USA: 2010. (McGraw-Hill Series in Mechanical Engineering). [Google Scholar]

21. Yang Z., Yang L., Cheng T., Chen F., Zheng F., Wang S., Guo Y. Fluid Flow Characteristic of EAF Molten Steel with Different Bottom-Blowing Gas Flow Rate Distributions. ISIJ. 2020;60:1957–1967. doi: 10.2355/isijinternational.ISIJINT-2019-794. [CrossRef] [Google Scholar]

22. Nichols B.D., Hirt C.W. Methods for calculating multi-dimensional, transient free surface flows past bodies; Proceedings of the First International Conference on Numerical Ship Hydrodynamics; Gaithersburg, MD, USA. 20–22 October 1975. [Google Scholar]

23. Hirt C.W., Nichols B.D. Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries. J. Comput. Phys. 1981;39:201–255. doi: 10.1016/0021-9991(81)90145-5. [CrossRef] [Google Scholar]

24. Szucki M., Suchy J.S., Lelito J., Malinowski P., Sobczyk J. Application of the lattice Boltzmann method for simulation of the mold filling process in the casting industry. Heat Mass Transf. 2017;53:3421–3431. doi: 10.1007/s00231-017-2069-5. [CrossRef] [Google Scholar]

25. Themelis N.J., Goyal P. Gas injection in steelmaking. Candian Metall. Trans. 1983;22:313–320. [Google Scholar]

26. Zhang L., Jing X., Li Y., Xu Z., Cai K. Mathematical model of decarburization of ultralow carbon steel during RH treatment. J. Univ. Sci. Technol. Beijing. 1997;4:19–23. [Google Scholar]

27. Chiti F., Paglianti A., Bujalshi W. A mechanistic model to estimate powder consumption and mixing time in aluminium industries. Chem. Eng. Res. Des. 2004;82:1105–1111. doi: 10.1205/cerd.82.9.1105.44156. [CrossRef] [Google Scholar]

28. Bouaifi M., Roustan M. Power consumption, mixing time and homogenization energy in dual-impeller agitated gas-liquid reactors. Chem. Eng. Process. 2011;40:87–95. doi: 10.1016/S0255-2701(00)00128-8. [CrossRef] [Google Scholar]

29. Kang J., Lee C.H., Haam S., Koo K.K., Kim W.S. Studies on the overall oxygen transfer rate and mixing time in pilot-scale surface aeration vessel. Environ. Technol. 2001;22:1055–1068. doi: 10.1080/09593332208618215. [PubMed] [CrossRef] [Google Scholar]

30. Moucha T., Linek V., Prokopov E. Gas hold-up, mixing time and gas-liquid volumetric mass transfer coefficient of various multiple-impeller configurations: Rushton turbine, pitched blade and techmix impeller and their combinations. Chem. Eng. Sci. 2003;58:1839–1846. doi: 10.1016/S0009-2509(02)00682-6. [CrossRef] [Google Scholar]

31. Szekely J. Flow phenomena, mixing and mass transfer in argon-stirred ladles. Ironmak. Steelmak. 1979;6:285–293. [Google Scholar]

32. Iguchi M., Nakamura K., Tsujino R. Mixing time and fluid flow phenomena in liquids of varying kinematic viscosities agitated by bottom gas injection. Metall. Mat. Trans. 1998;29:569–575. doi: 10.1007/s11663-998-0091-1. [CrossRef] [Google Scholar]

33. Hjelle O., Engh T.A., Rasch B. Removal of Sodium from Aluminiummagnesium Alloys by Purging with Cl2. Aluminium-Verlag GmbH; Dusseldorf, Germany: 1985. pp. 343–360. [Google Scholar]

34. Zhang L., Taniguchi S. Fundamentals of inclusion removal from liquid steel by bubble flotation. Int. Mat. Rev. 2000;45:59–82. doi: 10.1179/095066000101528313. [CrossRef] [Google Scholar]

원문 보기
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

[1]V. SinghDam breach modeling technologySpringer Science & Business Media (1996)Google Scholar[2]Wahl TL. 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. Experimental study of breach process of landslide dams by overtopping and its initiation mechanismsJ Hydrodynamics, 27 (6) (2015), pp. 872-883ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[11]G.G.D. Zhou, M. Zhou, M.S. Shrestha, D. Song, C.E. Choi, K.F.E. Cui, et al.Experimental investigation on the longitudinal evolution of landslide dam breaching and outburst floodsGeomorphology, 334 (2019), pp. 29-43ArticleDownload PDFView Record in ScopusGoogle Scholar[12]J. Zhang, Z.-x. Guo, S.-y. CaoYang F-g. Experimental study on scour and erosion of blocked damWater Sci Eng, 5 (2012), pp. 219-229ArticleDownload PDFView Record in ScopusGoogle Scholar[13]K. Höeg, A. Løvoll, K. VaskinnStability and breaching of embankment dams: Field tests on 6 m high damsInt J Hydropower Dams, 11 (2004), pp. 88-92View Record in ScopusGoogle Scholar[14]H. Hakimzadeh, V. Nourani, A.B. AminiGenetic programming simulation of dam breach hydrograph and peak outflow dischargeJ Hydrol Eng, 19 (4) (2014), pp. 757-768View Record in ScopusGoogle Scholar[15]A.R. Refaiy, N.M. AboulAtta, N.Y. Saad, D.A. El-MollaModeling the effect of downstream drain geometry on seepage through earth damsAin Shams Eng J, 12 (3) (2021), pp. 2511-2531ArticleDownload PDFView Record in ScopusGoogle Scholar[16]Y. Zhu, P.J. Visser, J.K. Vrijling, G. WangExperimental investigation on breaching of embankmentsScience China Technological Sci, 54 (1) (2011), pp. 148-155 View PDFCrossRefView Record in ScopusGoogle Scholar[17]M.-H. Yu, H.-Y. Wei, Y.-J. Liang, Y. ZhaoInvestigation of non-cohesive levee breach by overtopping flowJ Hydrodyn, 25 (4) (2013), pp. 572-579ArticleDownload PDFCrossRefView Record in ScopusGoogle Scholar[18]S. Wu, M. Yu, H. Wei, Y. Liang, J. ZengNon-symmetrical levee breaching processes in a channel bend due to overtoppingInt J Sedim Res, 33 (2) (2018), pp. 208-215ArticleDownload PDFView Record in ScopusGoogle Scholar[19]O. Saberi, G. ZenzNumerical investigation on 1D and 2D embankment dams failure due to overtopping flowInt J Hydraulic Engineering, 5 (2016), pp. 9-18View Record in ScopusGoogle Scholar[20]M. Guan, N.G. Wright, P.A. Sleigh2D Process-Based Morphodynamic Model for Flooding by Noncohesive Dyke BreachJ Hydraul Eng, 140 (7) (2014), p. 04014022, 10.1061/(ASCE)HY.1943-7900.0000861 View PDFView Record in ScopusGoogle Scholar[21]W. Wu, R. Marsooli, Z. HeDepth-Averaged Two-Dimensional Model of Unsteady Flow and Sediment Transport due to Noncohesive Embankment Break/BreachingJ Hydraul Eng, 138 (6) (2012), pp. 503-516View Record in ScopusGoogle Scholar[22]Z. Wang, D.S. BowlesThree-dimensional non-cohesive earthen dam breach model. Part 1: Theory and methodologyAdv Water Resour, 29 (10) (2006), pp. 1528-1545ArticleDownload PDFView Record in ScopusGoogle Scholar[23]Říha J, Duchan D, Zachoval Z, Erpicum S, Archambeau P, Pirotton M, et al. Performance of a shallow-water model for simulating flow over trapezoidal broad-crested weirs. J Hydrology Hydromechanics. 2019;67:322-8.Google Scholar[24]C.B. VreugdenhilNumerical methods for shallow-water flowSpringer Science & Business Media (1994)Google Scholar[25]L.A. Larocque, J. Imran, M.H. Chaudhry3D numerical simulation of partial breach dam-break flow using the LES and k–∊ turbulence modelsJ Hydraul Res, 51 (2) (2013), pp. 145-157 View PDFCrossRefView Record in ScopusGoogle Scholar[26]C. Yang, B. Lin, C. Jiang, Y. LiuPredicting near-field dam-break flow and impact force using a 3D modelJ Hydraul Res, 48 (6) (2010), pp. 784-792 View PDFCrossRefView Record in ScopusGoogle Scholar[27]FLOW-3D. Version 11.1.1 Flow Science, Inc., Santa Fe, NM. https://wwwflow3dcom.Google Scholar[28]C.W. Hirt, B.D. NicholsVolume of fluid (VOF) method for the dynamics of free boundariesJ Comput Phys, 39 (1) (1981), pp. 201-225ArticleDownload PDFGoogle Scholar[29]S.V. PatankarNumerical heat transfer and fluid flow, Hemisphere PublCorp, New York, 58 (1980), p. 288View Record in ScopusGoogle Scholar[30]M. Alemi, R. MaiaNumerical simulation of the flow and local scour process around single and complex bridge piersInt J Civil Eng, 16 (5) (2018), pp. 475-487 View PDFCrossRefView Record in ScopusGoogle Scholar

PDF 전체 원문 보기
Proceedings of the 6th International Conference on Civil, Offshore and Environmental Engineering (ICCOEE2020)

Numerical Simulation to Assess Floating Instability of Small Passenger Vehicle Under Sub-critical Flow

미 임계 흐름에서 소형 승용차의 부동 불안정성을 평가하기 위한 수치 시뮬레이션

Proceedings of the International Conference on Civil, Offshore and Environmental Engineering
ICCOEE 2021: ICCOEE2020 pp 258-265| Cite as

  • Ebrahim Hamid Hussein Al-Qadami
  • Zahiraniza Mustaffa
  • Eduardo Martínez-Gomariz
  • Khamaruzaman Wan Yusof
  • Abdurrasheed S. Abdurrasheed
  • Syed Muzzamil Hussain Shah

Conference paperFirst Online: 01 January 2021

  • 355Downloads

Part of the Lecture Notes in Civil Engineering book series (LNCE, volume 132)

Abstract

Parked vehicles can be directly affected by the floods and at a certain flow velocity and depth, vehicles can be easily swept away. Therefore, studying flooded vehicles stability limits is required. Herein, an attempt has been done to assess numerically the floating instability mode of a small passenger car with a scaled-down ratio of 1:10 using FLOW-3D. The 3D car model was placed inside a closed box and the six degrees of freedom numerical simulation was conducted. Later, numerical results validated experimentally and analytically. Results showed that buoyancy depths were 3.6 and 3.8 cm numerically and experimentally, respectively with a percentage difference of 5.4%. Further, the buoyancy forces were 8.95 N and 8.97 N numerically and analytically, respectively with a percentage difference of 0.2%. With this small difference, it can be concluded that the numerical modeling for such cases using FLOW-3D software can give an acceptable prediction on the vehicle stability limits.

주차된 차량은 홍수의 직접적인 영향을 받을 수 있으며 특정 유속과 깊이에서 차량을 쉽게 쓸어 버릴 수 있습니다. 따라서 침수 차량 안정성 한계를 연구해야 합니다. 여기에서는 FLOW-3D를 사용하여 축소 비율이 1:10 인 소형 승용차의 부동 불안정 모드를 수치 적으로 평가하려는 시도가 이루어졌습니다. 3D 자동차 모델은 닫힌 상자 안에 배치되었고 6 개의 자유도 수치 시뮬레이션이 수행되었습니다. 나중에 수치 결과는 실험적으로 그리고 분석적으로 검증되었습니다. 결과는 부력 깊이가 각각 5.4 %의 백분율 차이로 수치 및 실험적으로 3.6 및 3.8 cm임을 보여 주었다. 또한 부력은 수치적으로 8.95N과 분석적으로 8.97N이었고 백분율 차이는 0.2 %였다. 이 작은 차이로 인해 FLOW-3D 소프트웨어를 사용한 이러한 경우의 수치 모델링은 차량 안정성 한계에 대한 허용 가능한 예측을 제공 할 수 있다는 결론을 내릴 수 있습니다.

Keywords

Floating instability Small passenger car Numerical simulation FLOW-3D Subcritical flowe 

References

  1. 1.Hung, C.L.J., James, L.A., Carbone, G.J., Williams, J.M.: Impacts of combined land-use and climate change on streamflow in two nested catchments in the southeastern united states. Ecol. Eng. 143, 105665 (2020)CrossRefGoogle Scholar
  2. 2.Bui, D.T., Hoang, N.D., Martínez-Álvarez, F., Ngo, P.T.T., Hoa, P.V., Pham, T.D., Samui, P., Costache, R.: A novel deep learning neural network approach for predicting flash flood susceptibility: a case study at a high frequency tropical storm area. Sci. Total Environ. 701, 134413 (2020)CrossRefGoogle Scholar
  3. 3.Shah, S.M.H., Mustaffa, Z., Martínez-Gomariz, E., Yusof, K.W., Al-Qadami, E.H.H.: A review of safety guidelines for vehicles in floodwaters. Int. J. River Basin Manage. 1–17 (2019)Google Scholar
  4. 4.Shah, S.M.H., Mustaffa, Z., Yusof, K.W.: Disasters worldwide and floods in the malaysian region: a brief review. Indian J. Sci. Technol. 10(2), (2017)Google Scholar
  5. 5.Xia, J., Falconer, R.A., Lin, B., Tan, G.: Numerical assessment of flood hazard risk to people and vehicles in flash floods. Environ. Model Softw. 26(8), 987–998 (2011)CrossRefGoogle Scholar
  6. 6.Bonham, A.J., Hattersley, R.T.: Low level causeways. Technical report, University of New South Wales, Water Research Laboratory (1967)Google Scholar
  7. 7.Gordon, A.D., Stone, P.B.: Car stability on road causeways. Technical report No. 73/12, Institution (1973)Google Scholar
  8. 8.Keller, R.J., Mitsch, B.: Safety aspects of the design of roadways as floodways. Research Report No. 69, Urban Water Research Association of Australia, Melbourne (1993)Google Scholar
  9. 9.Shah, S.M.H., Mustaffa, Z., Martinez-Gomariz, E., Kim, D.K., Yusof, K.W.: Criterion of vehicle instability in floodwaters: past, present and future. Int. J. River Basin Manage. 1–23 (2019)Google Scholar
  10. 10.Teo, F.Y.: Study of the hydrodynamic processes Ofrivers and flood- plains with obstructions. Ph.D. thesis (2010). https://orca.cf.ac.uk/54161/1/U517543.pdf
  11. 11.Xia, J., Teo, F.Y., Lin, B., Falconer, R.A.: Formula of incipient velocity for flooded vehicles. Nat. Hazards 58(1), 1–14 (2011)CrossRefGoogle Scholar
  12. 12.Shu, C., Xia, J., Falconer, R.A., Lin, B.: Incipient velocity for partially submerged vehicles in floodwaters. J. Hydraul. Res. 49(6), 709–717 (2011)CrossRefGoogle Scholar
  13. 13.Toda, K., Ishigaki, T., Ozaki, T.: Experiments study on floating car in flooding. In: International Conference on Flood Resilience: Experiences in Asia and Europe (2013)Google Scholar
  14. 14.Xia, J., Falconer, R.A., Xiao, X., Wang, Y.: Criterion of vehicle stability in floodwaters based on theoretical and experimental studies. Nat. Hazards 70(2), 1619–1630 (2014)CrossRefGoogle Scholar
  15. 15.Martínez-Gomariz, E., Gómez, M., Russo, B., Djordjević, S.: A new experiments-based methodology to define the stability threshold for any vehicle exposed to flooding. Urban Water J. 14(9), 930–939 (2017)CrossRefGoogle Scholar
  16. 16.Smith, G.P., Modra, B.D., Tucker, T.A., Cox, R.J.: Vehicle stability testing for flood flows. Technical report 7, Water Research Laboratory, School of Civil and Environmental Engineering (2017)Google Scholar
  17. 17.Xia, J., Falconer, R.A., Lin, B., Tan, G.: Modelling flash flood risk in urban areas. In: Proceedings of the Institution of Civil Engineers-Water Management, vol. 164 (6), pp. 267–282. Thomas Telford Ltd, (2011)Google Scholar
  18. 18.Arrighi, C., Alcèrreca-Huerta, J.C., Oumeraci, H., Castelli, F.: Drag and lift contribution to the incipient motion of partly submerged flooded vehicles. J. Fluids Struct. 57, 170–184 (2015)CrossRefGoogle Scholar
  19. 19.Gómez, M., Martínez, E., Russo, B.: Experimental and numerical study of stability of vehicles exposed to flooding. In: Advances in Hydroinformatics, pp. 595–605. Springer, Singapore (2018). http://doi.org/10.1007/978-981-10-7218-5_42
  20. 20.Al-Qadami, E.H.H., Abdurrasheed, A.S.I., Mustaffa, Z., Yusof, K.W., Malek, M.A., Ab Ghani, A.: Numerical modelling of flow characteristics over sharp crested triangular hump. Results Eng. 4, 100052 (2019)Google Scholar
Full Text View
Figure 1 - General diagram of the forehead and body of the concentrated

Laboratory and Numerical Study of Dynamics Salty Density Current in The Reservoirs

저수지의 동적 염분 흐름의 실험 및 수치해석적 연구

Authors

1 Water resource expert Khuzestan Water and Power Authority
2 shahid chamran univercity of ahwaz

Since the characteristics of density current is affected by different parameters, the effect of discharge rate changes, gradient and the concentration of density current on speed of the forehead  and also the speed distribution in density current’s body have been investigated by physical and three-dimensional mathematical model (Flow-3d) in this research. For these purposes, different tests in the form of salty density current were done with three inflow discharge rates (0.7, 1 and 1.3 liters per second) and three different slopes (0, 1 and 2.2 percent). As well as to evaluate the effect of density changes on the flow characteristics, the concentration of 10, 15 and 20 grams per liter were used. In order to measure the speed of the forehead, velocity distribution in the body and its changes with flow, density and different slopes, video camera and ultrasound profiler speedometer were used in this study. Then, forehead speed and velocity distribution in the current’s body were achieved using six different turbulence models which are available on the software of “Flow-3D”. Comparing the results of physical and mathematical model showed that Eddy turbulence model and laminar flow mode have better accuracy in relation to other turbulent models. It should be noted that Reynolds number on experiments are at the range of  2000-4000.

밀도 흐름의 특성은 서로 다른 파라미터에 의해 영향을 받기 때문에 방출 속도 변화, 구배 및 밀도 흐름의 농도가 수두 속도에 미치는 영향과 밀도 흐름의 볼륨 속도 분포도 물리적 및 3차원 수학 모델(Flow-3d)에 의해 조사되었습니다.

이러한 목적을 위해 세 가지 유입 배출 속도(초당 0.7, 1 및 1.3L)와 세 가지 다른 경사도(0, 1, 2.2%)로 염분 밀도 흐름 형태의 다른 테스트가 수행되었습니다.

밀도 변화가 흐름 특성에 미치는 영향을 평가하기 위해 리터당 10, 15, 20g의 농도를 사용했습니다. 이 연구에서는 수두의 속도를 측정하기 위해 체내의 속도 분포와 흐름, 밀도 및 다양한 기울기와 함께 변화된 속도, 비디오 카메라 및 초음파 프로파일러 속도계를 사용했습니다.

그런 다음, “Flow-3D” 소프트웨어에서 사용할 수 있는 6가지 난류 모델을 사용하여 현재 볼륨의 수두 속도와 속도 분포를 달성했습니다.

물리적 모델과 수학적 모델의 결과를 비교한 결과, 에디 난류 모델과 층류 모드가 다른 난류 모델과 비교하여 더 나은 정확도를 가지고 있다는 것을 보여주었습니다.

레이놀즈 실험 번호는 2000-4000 범위라는 점에 유의해야 합니다.

Figure 1 - General diagram of the forehead and body of the concentrated
Figure 1 – General diagram of the forehead and body of the concentrated
Figure 2 - Dimensional profile of velocity distribution in concentrated flow (Graph and Altinacar, 1662)
Figure 2 – Dimensional profile of velocity distribution in concentrated flow (Graph and Altinacar, 1662)
Figure 1 - Schematic drawing of the physical model used
Figure 1 – Schematic drawing of the physical model used
Figure 0 - Sample of the concentrated flow created in the laboratory (front and body of concentrated flow)
Figure 0 – Sample of the concentrated flow created in the laboratory (front and body of concentrated flow)
Figure 6 - Mixing intensity values against Richardson number and comparing it with the results of other researchers
Figure 6 – Mixing intensity values against Richardson number and comparing it with the results of other researchers

Reference

1- حقی آبی، ا. 1383. بررسی اثر شیب کف بر پروفیل سرعت جریان غلیظ رساله دکتری رشته سازه های آبی ، دانشکده مهندسی علوم آب، دانشگاه شهید چمران اهواز.

2- کاهه، م. قمشی، م. و س، ح، موسوی جهرمی، 1391. بررسی آزمایشگاهی سرعت پیشروی جریان غلیظ بر روی سطوح زبر. علوم و مهندسی آبیاری، 35(1): 101-110.

3- کشتکار، ش. ایوب زاده، س ع. و ب، فیروزآبادی، 1389 . بررسی پروفیل سرعت و غلظت جریان گل آلود با استفاده از مدل فیزیکی. پژوهش‌های آبخیزداری،87(2): 43-36.

4- کوتی، ف. کاشفی پور، س، م. و م قمشی، 1391. تجزیه و تحلیل پروفیل های سرعت در جریان غلیظ. مجله ی علوم و فنون کشاورزی و منابع طبیعی، علوم آب و خاک، 59: 29-15.

5- Altinakar, M.S., Graf, W.H. and , E.J, Hopfinger. 1990. Weakly depositing turbidity current on a small slope. Journal of Hydraulic Research. 28(1): 55-80.

6- Baas, J.H. McCaffrey, W.D. Haughton P.D.W. and C, Choux. 2005. Coupling between suspended sediment distribution and turbulence structure in a laboratory turbidity current. Journal of Geophysics Research, 110: 20-32.

7- Barahmand, N. and A, Shamsai. 2010. Experimental and theoretical study of density jumps on smooth and rough beds”. Lakes and Reservoirs: Research and Management, 15(4): 285-307.

8- Britter, R.E. and P, Linden. 1980.The motion of the front of a gravity current traveling down an incline. Journal of Fluid Mechanics, 99(3): 531- 543.

9- Buckee, C. Kneller, B. and J, Peakall. 2001. Turbulence structure in steady solute-driven gravity currents Blackwell Oxford pp, 173-188.

10- Choux, C.M.A. Baas, J.H. McCaffrey, W.D. and P.D.W, Haughton. 2005. Comparison of spatio–temporal evolution of experimental particulate gravity flows at two different initial concentrations based on velocity grain size and density data. Sedimentary Geology, 179: 49-69.

11- FathiMoghadam, M. TorabiPoudeh, H. Ghomshi, M. and M, Shafaei. 2008. The density current head velocity in expansion reaches. Lakes & Reservoirs: Research & Management, 13(1): 63-68.

12- Ghomeshi, M. 1995. Reservoir sedimentationmodeling. Ph.D. Thesis. University of Wollongong. Australia.

  1. Graf, W.H. and M, S, Altinakar. 1998. Fluvial Hydraulics, Flow and Transport Processes in Channels of Simple Geometry. John Wiley and Sons, Ltd, England.

14- Ieong, K, K. Mok, K,M. and H, Yeh. 2006. Fluctuation of the front propagation speed of developed gravity current. Journal of Hydrodynamics, 18(3): 351-355.

15- LaRocca, M. Adduce, C. Sciortino, G. And A, B, Pinzon. 2008. Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom. Physics of Fluids, 20, 106603.

16- McCaffrey, W, D. Choux, C, M. Baas, J, H. And P, D, W, Haughton. 2003. Spatio-temporal evolution of velocity structure concentration and grainsize stratification within experimental particulate gravity currents. Marine and Petroleum Geology. 20: 851-860.

17- Sequeiros, O, E. Spinewine, B. Beaubouef, R, T. Sun, T. Garcia, H. M., and G, Parker. 2010. Characteristics of Velocity and Excess Density Profiles of Saline Underflows and Turbidity Currents Flowing over a Mobile Bed”. Journal of Hydraulic Engineering, 136(7): 167-180.

18- Turner, J, S. 1973. Buoyancy Effects in Fluids. Cambridge University Press London, U.K, pp. 178-181.

19- Yu, W, S. Lee, H, Y. And M, S, Hsu. 2000. Experiments on deposition behavior of fine in a reservoir. Journal of Hydraulic Engineering, 126(12): 912-920.

PDF View
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

ListenReadSpeaker webReader: Listen

  • 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

ListenReadSpeaker webReader: Listen

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

ListenReadSpeaker webReader: Listen

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

ListenReadSpeaker webReader: Listen

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

ListenReadSpeaker webReader: Listen

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

ListenReadSpeaker webReader: Listen

All relevant data are included in the paper or its Supplementary Information.

REFERENCES

Boes R. M. Hager W. H. 2003a Hydraulic design of stepped spillways. Journal of Hydraulic Engineering 129 (9), 671–679.
Google Scholar
Boes R. M. Hager W. H. 2003b Two-Phase flow characteristics of stepped spillways. Journal of Hydraulic Engineering 129 (9), 661–670.
Google Scholar
Chanson H. 1994 Hydraulics of skimming flows over stepped channels and spillways. Journal of Hydraulic Research 32 (3), 445–460.
Google Scholar
Chanson H. 1997 Air Bubble Entrainment in Free Surface Turbulent Shear Flows. Academic Press, London.
Google Scholar
Chanson H. 2002 The Hydraulics of Stepped Chutes and Spillways. Balkema, Lisse, The Netherlands.
Google Scholar
Felder S. Chanson H. 2011 Energy dissipation down a stepped spillway with nonuniform step heights. Journal of Hydraulic Engineering 137 (11), 1543–1548.
Google Scholar
Flow Science, Inc. 2012 FLOW-3D v10-1 User Manual. Flow Science, Inc., Santa Fe, CA.
Ghaderi A. Daneshfaraz R. Torabi M. Abraham J. Azamathulla H. M. 2020a Experimental investigation on effective scouring parameters downstream from stepped spillways. Water Supply 20 (5), 1988–1998.
Google Scholar
Ghaderi A. Abbasi S. Abraham J. Azamathulla H. M. 2020b Efficiency of trapezoidal labyrinth shaped stepped spillways. Flow Measurement and Instrumentation 72, 101711.
Google Scholar
Gonzalez C. A. Chanson H. 2008 Turbulence and cavity recirculation in air-water skimming flows on a stepped spillway. Journal of Hydraulic Research 46 (1), 65–72.
Google Scholar
Gunal M. 1996 Numerical and Experimental Investigation of Hydraulic Jumps. PhD Thesis, University of Manchester, Institute of Science and Technology, Manchester, UK.
Hirt C. W. Nichols B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39 (1), 201–225.
Google Scholar
Matos J. 2000 Hydraulic design of stepped spillways over RCC dams. In: Intl Workshop on Hydraulics of Stepped Spillways (H.-E. Minor & W. Hager, eds). Balkema Publ, Zurich, pp. 187–194.
Google Scholar
Mohammad Rezapour Tabari M. Tavakoli S. 2016 Effects of stepped spillway geometry on flow pattern and energy dissipation. Arabian Journal for Science & Engineering (Springer Science & Business Media BV) 41 (4), 1215–1224.
Google Scholar
Ostad Mirza M. J. 2016 Experimental Study on the Influence of Abrupt Slope Changes on Flow Characteristics Over Stepped Spillways. Communications du Laboratoire de Constructions Hydrauliques, No. 64 (A. J. Schleiss, ed.). Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
Roshan R. Azamathulla H. M. Marosi M. Sarkardeh H. Pahlavan H. Ab Ghani A. 2010 Hydraulics of stepped spillways with different numbers of steps. Dams and Reservoirs 20 (3), 131–136.
Google Scholar
Shahheydari H. Nodoshan E. J. Barati R. Moghadam M. A. 2015 Discharge coefficient and energy dissipation over stepped spillway under skimming flow regime. KSCE Journal of Civil Engineering 19 (4), 1174–1182.
Google Scholar
Takahashi M. Ohtsu I. 2012 Aerated flow characteristics of skimming flow over stepped chutes. Journal of Hydraulic Research 50 (4), 427–434.
Google Scholar
Versteeg H. K. Malalasekera W. 2007 An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Pearson Education, Harlow.
Google Scholar
© 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/).

Full Text View
Figure 3-3 E200U+ PMD sponge draining

CORRELATIONS BETWEEN NEUTRAL BUOYANCY TESTS AND CED

Abstract

NEUTRAL BUOYANCY 테스트는 표면 장력 장치의 기능 검증을 위해 Matra Marconi Space에서 잘 알려진 테스트 기능입니다. 새로운 Eurostar 3000 PMD를 검증하고 성능을 E2000 + PMD의 성능과 비교하기 위해 완전한 저수지가 중성 부력 테스트 벤치에서 테스트되었습니다. 또한, 일시적 및 고정 모세관 현상에 대한 우리의 지식을 연관시키고 개선하기 위해 수치 시뮬레이션이 수행되었습니다. 다양한 결과에 대한 토론과 상관 관계가 제시됩니다. 다양한 도구의 한계가 표시되고 E3000 개선의 간단한 예가 모델링됩니다.

Figure 2-2 Propellant position under acceleration
Figure 2-2 Propellant position under acceleration
Figure 2-3 E2000+ PMD
Figure 2-3 E2000+ PMD
Figure 3-1 Propellant position under acceleration
Figure 3-1 Propellant position under acceleration
Figure 3-2 Propellant position under acceleration
Figure 3-2 Propellant position under acceleration
Figure 3-3 E200U+ PMD sponge draining
Figure 3-3 E200U+ PMD sponge draining
Figure 3-5 Improved PMD sponge draining
Figure 3-5 Improved PMD sponge draining
Figure 4-1 E2000+ reservoir
Figure 4-1 E2000+ reservoir
논문 원문 바로가기
유압 헤드 계산에서는 유선이 평행하다고 가정

FLOW-3D Output variables(출력 변수)

Output variables(출력 변수)

FLOW-3D에서 주어진 시뮬레이션의 정확한 출력은 어떤 물리적 모델, 출력 위젯에 정의된 추가 출력 및 특정 구성 요소별 출력에 따라 달라집니다. 이 문서는 FLOW-3D의 출력에 대해 좀 더 복잡한 출력 변수 중 일부를 참조하는 역할을 합니다.

FLOW-3D Additional output
FLOW-3D Additional output

Distance Traveled by Fluid(유체로 이동 한 거리)

때로는 유체 입자가 이동한 거리가 중요한 경우도 있습니다. FLOW-3D에서 사용자는 모델 설정 ‣ 출력 위젯에서 유체가 이동한 거리에 대한 출력을 요청할 수 있습니다. 이 기능은 유체가 흐름 영역(경계 또는 질량 소스를 통해)에 들어간 시간 또는 유체가 도메인을 통해 이동한 거리를 계산합니다. 이 기능은 모든 시뮬레이션에도 사용할 수 있으며, 특별한 모델을 사용할 필요가 없으며, 흐름에도 영향을 미치지 않습니다. 이 모델을 사용하려면 출력 위젯으로 이동하고 추가 출력 섹션에서 “Distance traveled by fluid” 옆의 체크상자를 선택하십시오.

 노트

추가 출력 섹션은 출력 위젯의 모든 탭에서 사용할 수 있습니다.

유체 도착 시간

유체 도착 시간을 아는 것은 종종 유용합니다. 예를 들어 주조 시뮬레이션에서 주입 시간을 결정하는 데 사용할 수 있습니다. 제어 볼륨은 충전 프로세스 동안 여러 번 채워지고 비워지기 때문에 계산 셀이 채워지는 처음과 마지막 시간 모두 기록되고, 후 처리를 위해 저장될 수 있습니다. 이 작업은 출력 위젯과 추가 출력 섹션 내에서 유체 도착 시간 확인란을 선택하여 수행됩니다.

 노트

이 출력 옵션은 1 유체 자유 표면 흐름에만 사용할 수 있습니다.

유체 체류 시간

때로는 유체가 계산 영역 내에서 보내는 시간인 체류시간을 아는 것이 유용합니다. 이는 출력 ‣ Output ‣ Additional Output ‣ Fluid residence time 확인란을 선택하여 수행합니다. 여기서 S로 지정된 이 변수에 대한 전송 방정식은 단위 소스 항과 함께 Solve됩니다.

유체 체류 시간(Fluid residence time)
유체 체류 시간(Fluid residence time)

여기에서 t는 시간이며 u는 유체 속도입니다.

S의 단위는 시간이다. 계산 도메인에 들어가는 모든 유체에 대한 S의 초기값은 0입니다.

의 값은 항상 second order체계를 가진 데이터로부터 근사치를 구합니다.

이 출력 옵션은 1 유체 및 2 유체 유량 모두에 사용할 수 있습니다.

 노트

경계 조건 또는 소스에서 도메인으로 유입되는 유체가 이미 도메인에 있는 유체와 혼합될 때 체류가 감소하는 것처럼 보일 수 있습니다.

Wall Contact Time

벽면 접촉 시간 출력은 (1)개별 유체 요소가 특정 구성 요소와 접촉하는 시간 및 (2)특정 구성 요소가 유체와 접촉하는 시간을 추적합니다. 이 모델은 액체 금속이 모래 오염물과 접촉했을 때 오염과 상관 관계가 있는 proxy 변수를 제공하기 위한 것입니다. 이 출력은 최종 주조물에서 오염된 유체가 어디에 있는지 확인하는 데 사용될 수 있습니다. 접촉 시간 모델의 또 다른 해석은, 예를 들어, 용해를 통해 다소 일정한 비율로 화학물질을 방출하는 물에 잠긴 물체에 의한 강의 물의 오염입니다.

모델은 Model Setup ‣ Output ‣ Wall contact time 박스를 확인하여 활성화됩니다. 또한 Model Setup ‣ Output ‣ Geometry Data section의 각 구성요소에 대해 해당 구성요소를 계산에 포함하기 위해 반드시 설정해야 하는 Contact time flag가 있습니다.

 추가 정보

Wall Contact Time with Fluid and Component Properties: Contact Time with Fluid for more information on the input variables를 참조하십시오.

 노트

이 모델은 실제 구성 요소, 즉 고체, 다공성 매체, 코어 가스 및 충전 퇴적물 구성 요소로 제한됩니다. 접촉 시간은 유체 # 1과 관련해서만 계산됩니다.

2. 형상 데이터
2. 형상 데이터

Component wetted are

Fluid 1과 접촉하는 구성 요소의 표면 영역은 관심 구성 요소에 대한 Model Setup ‣ Output ‣ Geometry Data ‣ Wetted area 옵션을 활성화하여 History Data로 출력 될 수 있습니다.

구성 요소의 힘과 토크

Forces

Model Setup ‣ Output ‣ Geometry Data ‣ Forces 옵션을 활성화하면 부품에 대한 압력, 전단력, 탄성 및 벽 접착력을 History Data에 출력할 수 있습니다.

압력을 가지지 않은 셀(즉, 도메인 외부에 있거나 다른 구성 요소 안에 있는 셀)이 구성 요소 주변의 각 셀에 대한 압력 영역 제품을 합산하는 동안 어떻게 처리되는지를 제어하는 압력 계산에 대한 몇 가지 추가 옵션이 있습니다. 기본 동작은 이러한 셀에서 사용자 정의 기준 압력을 사용하는 것입니다. 지정되지 않은 경우 기준 압력은 초기 무효 압력인 PVOID로 기본 설정됩니다. 또는, 코드는 Reference pressure is code calculated 옵션을 선택하여 구성요소의 노출된 표면에 대한 평균 압력을 사용할 수 있습니다.

마지막으로, 일반 이동 물체의 경우, 규정된/제약을 받는 대로 물체를 이동시키는 힘을 나타내는 잔류 힘의 추가 출력이 있습니다.

Torques

Model Setup ‣ Output ‣ Force 옵션이 활성화되면 구성 요소의 토크가 계산되고 History Data에 출력됩니다. 토크는 힘-모멘트에 대한 기준점 X, 힘-모멘트에 대한 기준점 Y, 정지 구성 요소에 대한 힘-모멘트 입력에 대한 기준점 Z에 의해 지정된 지점에 대해 보고됩니다. 참조점의 기본 위치는 원점입니다.

General Moving Objects에는 몇 가지 추가 참고 사항이 있습니다. 첫째, 토크는 (1) 6-DOF 동작의 질량 위치 중심 또는 (2)고정축 및 고정점 회전의 회전 축/점에 대해 보고됩니다. 힘에서 행해지는 것과 마찬가지로, 규정된/제한된 바와 같이 물체를 이동시키는 토크를 나타내는 잔류 토크의 출력도 있습니다.

 노트

힘 및 토크 출력은 각 지오메트리 구성 요소의 일반 히스토리 데이터에 기록됩니다. 출력은 개별 힘/토크 기여 (예: 압력, 전단, 탄성, 벽 접착) 및 개별 기여도의 합으로 계산된 총 결합력/토크로 제공됩니다.

Buoyancy center and metacentric height (부력 중심 및 메타 중심 높이)

일반 이동 객체의 부력과 안정성에 대한 정보는 각 구성 요소에 대해 모델 설정 Setup 출력 ‣ 기하학적 데이터 ‣ 부력 중심 및 도량형 높이 옵션을 활성화하여 History Data에서 출력할 수 있습니다. 이렇게 하면 구성 요소의 중심 위치와 중심 높이가 출력됩니다.

  1. Advanced

FLOW-3D Advanced Output Option
FLOW-3D Advanced Output Option

Fluid vorticity & Q-criterion(유체 와동 및 Q 기준)

와동구성 요소뿐만 아니라 와동 구조를 위한 Q-criterion을 계산하고 내보내려면 Model Setup ‣ Output ‣ Advanced 탭에서 해당 확인란을 클릭하여 유체 와동 & Q-criterion을 활성화하십시오.

여기에서:

:  소용돌이 벡터의 다른 구성 요소

 Q-criterion은 속도 구배 텐서의 2차 불변성을 갖는 연결된 유체 영역으로 소용돌이를 정의합니다. 이는 전단 변형률과 와류 크기 사이의 국부적 균형을 나타내며, 와류 크기가 변형률의 크기보다 큰 영역으로 와류를 정의합니다.

Hydraulic Data and Total Hydraulic Head 3D

Hydraulic Data

깊이 기준 유압 데이터를 요청하려면 출력 ‣ 고급으로 이동한 후 유압 데이터 옆의 확인란을 선택하십시오(심층 평균 값과 중력을 -Z 방향으로 가정).

이 옵션은 FLOW-3D가 유압 시뮬레이션에 유용할 수 있는 추가 깊이 평균 데이터를 출력하도록 합니다.

  • Flow depth
  • Maximum flow depth
  • Free surface elevation
  • Velocity
  • Offset velocity
  • Froude number
  • Specific hydraulic head
  • Total hydraulic head

이 수량 각각에 대해 하나의 값 이 메쉬의 모든 (x, y) 위치에서 계산되고 수직 열의 모든 셀에 저장됩니다 (이 수량이 깊이 평균이기 때문에 z 방향으로 데이터의 변화가 없습니다). 변수는 정확도를 보장하기 위해주기마다 계산됩니다. 모든 경우에,  깊이 평균 속도, z- 방향  의 중력 가속도, 유체 깊이, 및 컬럼 내 유체의 최소 z- 좌표입니다.

  • 자유 표면 고도는 수직 기둥의 맨 위 유체 요소에 있는 자유 표면의 z-좌표로 계산됩니다.
  • The Froude number 은   

식으로 계산됩니다.

  • 유체 깊이는 깊이 평균 메쉬 열의 모든 유체의 합으로 계산됩니다.

특정 유압 헤드 

및 총 유압 헤드

변수는 다음에서 계산됩니다.  

 노트

  • 깊이 기준 유압 출력 옵션은 예리한 인터페이스가 있고 중력이 음의 z 방향으로 향할 때에만 유체 1에 유효합니다.
  • 유압 헤드 계산은 스트림 라인이 평행하다고 가정한다는 점을 유념해야 합니다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 이 문제가 발생할 수 있습니다. 이 경우, 유량 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산에서 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.

Total Hydraulic Head 3D(총 유압 헤드 3D)

또한 총 유압 헤드 3D 옵션을 확인하여 국부적(3D) 속도 필드, 플럭스 표면에서의 유압 에너지(배플 참조) 및 플럭스 기반 유압 헤드를 사용하여 유체 1의 총 헤드를 계산할 수 있다. 3D 계산은 국부 압력을 사용하여 수행되며(즉, 압력이 유체 깊이와 관련이 있다고 가정하지 않음) 원통 좌표와 호환됩니다.

 노트

  • 유압 헤드 계산은 스트림 라인이 평행하다고 가정한다는 점을 유념해야 한다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 문제가 발생할 수 있습니다. 이 경우, 플럭스 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산 시 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.
  • 3D 유압 헤드 계산은 입력 파일에 중력이 정의되지 않은 경우 중력 벡터의 크기를 1로 가정합니다.

Flux-averaged hydraulic head

특정 위치 (즉, 배플)의 플럭스 평균 유압 헤드는 다음과 같이 계산됩니다.

Flux-averaged hydraulic head
Flux-averaged hydraulic head

유압 헤드 계산에서는 유선이 평행하다고 가정합니다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치된 경우 (예: 아래에 표시된 것과 같이) 문제가 될 수 있습니다.

유압 헤드 계산에서는 유선이 평행하다고 가정




유압 헤드 계산에서는 유선이 평행하다고 가정

이 경우 플럭스 표면에 보고된 플럭스 평균 유압 헤드는 헤드 계산 시 흐름 방향이 무시되므로 예상보다 클 수 있습니다.

FLOW-3D에는 History Probes, Flux surface, Sampling Volumes의 세 가지 주요 측정 장치가 있습니다. 이러한 장치를 시뮬레이션에 추가하는 방법은 모델 설정 섹션에 설명되어 있습니다(측정 장치 참조). 이들의 출력은 기록 데이터 편집 시간 간격으로 flsgrf 파일의 일반 기록 데이터 카탈로그에 저장됩니다. 이러한 결과는 Analyze ‣ Probe 탭에서 Probe Plots을 생성하여 액세스할 수 있습니다.

히스토리 프로브 출력

히스토리 프로브를 생성하는 단계는 모델 설정 섹션에 설명되어 있습니다(기록 프로브 참조). 시뮬레이션에 사용된 물리 모델에 따라 각각의 History Probe에서 서로 다른 출력을 사용할 수 있습니다. 프로브를 FSI/TSE로 지정하면 유한 요소 메시 안에 들어가야 하는 위치에서 응력/스트레인 데이터만 제공한다. 유체 프로브가 솔리드 형상 구성 요소에 의해 차단된 영역 내에 위치하는 경우, 기하학적 구조와 관련된 수량(예: 벽 온도)만 계산된다. 일반적으로 프로브 좌표에 의해 정의된 위치에서 이러한 양을 계산하려면 보간이 필요하다.

플럭스 표면 출력

플럭스 표면은 이를 통과하는 수량의 흐름을 측정하는데 사용되는 특별한 물체입니다. 플럭스 표면을 만드는 단계는 모델 설정 섹션에 설명되어 있습니다(플럭스 표면 참조). 각 플럭스 표면에 대해 계산된 수량은 다음과 같습니다.

  • Volume flow rate for fluid #1
  • Volume flow rate for fluid #2 (for two-fluid problems only)
  • Combined volume flow rate (for two-fluid problems only)
  • Total mass flow rate
  • Flux surface area wetted by fluid #1
  • Flux-averaged hydraulic head when 3D Hydraulic Head is requested from additional output options
  • Hydraulic energy flow when hydraulic data output is requested
  • Total number of particles of each defined species in each particle class crossing flux surface when the particle model is active
  • Flow rate for all active and passive scalars this includes scalar quantities associated with active physical models (eg. suspended sediment, air entrainment, ect.)

 노트

  • 유속과 입자수의 기호는 유동 표면을 설명하는 함수의 기호에 의해 정의된 대로 흐름이나 입자가 플럭스 표면의 음에서 양으로 교차할 때 양의 부호가 됩니다.
  • 플럭스 표면은 각 표면의 유량과 입자 수가 정확하도록 그들 사이에 적어도 두 개의 메쉬 셀이 있어야 합니다.
  • 유압 데이터 및 총 유압 헤드 3D 옵션을 사용할 때는 유압 헤드 계산이 스트림 라인이 평행하다고 가정한다는 점을 유념해야 한다. 예를 들어 플럭스 표면이 재순환 흐름 영역에 배치되는 경우 이 문제가 발생할 수 있습니다. 이 경우, 유량 표면에서 보고된 유량 평균 유압 헤드는 헤드의 계산에서 흐름 방향이 무시되기 때문에 예상보다 클 수 있습니다.

샘플링 볼륨 출력

샘플링 볼륨은 해당 범위 내에서 볼륨을 측정하는 3 차원 데이터 수집 영역입니다. 샘플링 볼륨을 만드는 단계는 모델 설정 섹션에 설명되어 있습니다(샘플링 볼륨 참조). 각 샘플링 볼륨의 계산 수량은 다음과 같습니다.

  • 시료채취량 내에서 #1 유체 총량
  • 시료채취량 내 #1 유체질량 중심
  • 샘플링 용적 가장자리에 위치한 솔리드 표면을 포함하여 샘플링 용적 내의 모든 벽 경계에 작용하는 좌표계의 원점에 상대적인 유압력 및 모멘트.
  • 샘플링 용적 내 총 스칼라 종량: 이것은 부피 적분으로 계산되므로 스칼라 양이 질량 농도를 나타내면 샘플링 용적 내의 총 질량이 계산된다. 거주 시간과 같은 일부 종의 경우, 평균 값이 대신 계산됩니다.
  • 샘플링 볼륨 내의 입자 수: 각 샘플링 볼륨 내에 있는 각 입자 등급의 정의된 각 종별 입자 수(입자 모델이 활성화된 경우)
  • 운동 에너지, 난류 에너지, 난류 소실율 및 와류에 대한 질량 평균
  • 표본 체적의 6개 경계 각각에서 열 유속: 유체 대류, 유체 및 고체 성분의 전도 및 유체/구성 요소 열 전달이 포함됩니다. 각 플럭스의 기호는 좌표 방향에 의해 결정되는데, 예를 들어, 양방향의 열 플럭스도 양수입니다. 출력에서 확장 또는 최대 디버그 수준을 선택하지 않는 한 이러한 디버그 수준은 fsplt에 자동으로 표시되지 않습니다.

FLOW-3D 및TruVOF는 미국 및 기타 국가에서 등록 상표입니다.

FLOW-3D HYDRO Conveyance Infrastructure

FLOW-3D & computational fluid dynamics for civil engineering

Conveyance systems

  • Tunnels
  • Overflows
  • Hydraulic controls
    • Gates
    • Weirs
    • Orifice
  • Drop structures
  • Flow splitting
  • Open channel conveyance
  • Pumps
  • Flap gates (moving objects)
  • Air flow / air supply
  • Entrained air (entrainment, evolution, drift flux, buoyancy, bulking, de-aeration)

Baffle dropshaft

Tangential dropshaft

Sample GUI packaged conveyance examples

Conveyance systems: simulation outputs

해석 결과로 얻을 수 있는 Simulation outputs

  • Pressure, velocity field
  • Water elevation profiles
  • 3D transient behaviors
  • Surges & sloshing
  • Pump approach flow
  • Pump discharge & operations
  • Air phase
  • Entrained air
  • Forces & coupled motion for moving objects

Gravitational and sedimentation microfluidic technique (Huh et al. Anal Chem 2007)의 중력 회로도를 사용한 입자 분류

중력을 사용한 미세 유체 입자 분류

Microfluidics Particle Sorting Using Gravity

미세 유체 입자 분류는 진단, 화학적 및 생물학적 분석, 식품 및 화학 처리, 환경 평가에 적용됩니다. 이전 블로그에서 유체 역학을 사용한 미세 유체 입자 분류에 대해 이야기했습니다 . 같은 주제를 바탕으로 중력을 사용하여 미세 입자를 분류하는 또 다른 방법에 대해 논의하겠습니다. 아래 애니메이션에서 볼 수 있습니다.

유비쿼터스 중력(Ubiquitous gravity)은 미세 유체 장치에서 미세 입자를 분류하는 데 사용할 수 있습니다. 중력이 입자의 움직임에 수직으로 작용할 때 입자는 반경에 따른 속도로 안정됩니다. 또한 입자의 운동은 입자의 밀도, 유체의 밀도 및 유체의 점도 사이의 차이에서 비롯된 유체 역학적 효과의 영향을받습니다. 아래 이미지는 중력 분류 기술 회로도를 보여줍니다.

Gravitational and sedimentation microfluidic technique (Huh et al. Anal Chem 2007)의 중력 회로도를 사용한 입자 분류
Gravitational and sedimentation microfluidic technique (Huh et al. Anal Chem 2007)의 중력 회로도를 사용한 입자 분류

부력 대 항력

앞서 언급했듯이 중력은 서로 다른 입자가 서로 다른 속도로 침전되도록합니다. 모든 입자의 밀도가 같고 입자 밀도가 주변 유체의 밀도보다 낮 으면 부력 우세와 항력 우세라는 두 가지 유형의 분류를 사용할 수 있습니다. 반경이 더 큰 입자는 더 많은 부력을 경험하고 작은 입자 위의 경로를 따르는 경향이 있습니다. 그러나 외장 액체 (입자를 운반하는 용액)의 유입 속도가 충분히 높으면 항력 효과가 우세하기 시작하고 더 큰 입자가 더 작은 입자의 경로 아래로 이동하는 경향이 있습니다.

FLOW-3D 시뮬레이션 결과

경쟁하는 부력과 항력은 아래 FLOW-3D 에서 얻은 시뮬레이션 결과에서 명확하게 볼 수 있습니다 . 그림 1은 부력 지배적 인 입자 분류의 경우를 보여줍니다. 더 큰 (빨간색) 입자는 수평 채널의 상단을 향해 정렬됩니다. Fig. 2에 나타난 결과는 부력이 우세한 경우의 유입 초 속도를 20 배로 설정 한 후 얻은 것이다. 더 높은 입구 속도에서 더 큰 입자는 더 많은 운동량을 전달하므로 그 위치는 수직 부력의 영향을받지 않습니다. 따라서 입자는 수평 채널의 상단으로 올라가지 않습니다. 대신 그들은 계속해서 바닥으로 이동합니다.

부력

Buoyancy dominant sorting
Buoyancy dominant sorting

Drag

Figure 2. Drag dominant sorting
Figure 2. Drag dominant sorting

LOW-3D 의 입자 모델은입자 분류 또는 기타 입자 역학과 관련된 미세 유체 시뮬레이션에 성공적이고 쉽게 사용할 수 있습니다. 지금까지 우리는 FLOW-3D 의 입자 모델을사용하여 두 가지 입자 분류 기술을 보았습니다. 하나는 유체 역학을 사용하고 다른 하나는 중력을 사용합니다.

Particle sorting 2 (입자 분류)

항력/부력 및 중력 기반의 입자 분류

  • 중력이 입자 운동에 수직으로 작용할 때 분류
  • 분류 운동은 유체역학의 영향을 받음

부력 vs 항력

  • 부력에 지배되는 분류
    – 큰 입자는 더 많은 부력을 받으며 작은입자 위의 경로를 따르는 경향이 있음
  • 항력에 지배되는 분류
    – 입구 유체 속도가 높으면 항력 효과가 부력을 지배하여 큰 입자가 작은 입자의 경로 아래로 이동함

FSR_01-12_Air-Entrainment-Report [공기 혼입 모델 분석]

Overview
In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model in FLOW-3D®. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a passive scalar variable to record and transport the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
The second air-entrainment model option is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. This dynamically coupled model cannot, however, be used in conjunction with heat transport and natural (thermal) convection.
In addition, when using the variable density formulation, the model can include a relative drifting of air in water, the possible escape of air if it rises to the surface of the water and the removal or addition of air to trapped bubble regions represented as adiabatic bubbles.
The same basic entrainment process is used in both options. It is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence.
Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model. It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG model.

 

[다운로드]

FSR_01-12_Air-Entrainment-Report

Modeling Turbulent Entrainment of Air at a Free Surface

Overview
In free-surface flows the turbulence in the liquid may be sufficient to disturb the surface to the point of entraining air into the flow. This process is important, for example, in water treatment where air is needed to sustain microorganisms for water purification and in rivers and streams for sustaining a healthy fish population. Air entrainment is typically engineered into spillways downstream of hydropower plants to reduce the possibility of cavitation damage at the base of the spillway. Other situations where air entrainment is undesirable are in the sprue and runner systems used by metal casters, and in the filling of liquid containers used for consumer products.
The importance of being able to predict the amount and distribution of entrained air at a free liquid surface has led to the development of a unique model that can be easily inserted into FLOW-3D® as a user customization. The model has two options. One option, to be used when the volume fraction of entrained air is relatively low, uses a scalar variable to record the air volume fraction. This model is passive in that it does not alter the dynamics of the flow.
A second air-entrainment model, option two, is based on a variable density formulation. This model includes the “bulking” of fluid volume by the addition of air and the buoyancy effects associated with entrained air. However, this dynamically coupled model cannot be used in connection with heat transport and natural (thermal) convection.
In both model options the same basic entrainment process is used that is based on a competition between the stabilizing forces of gravity and surface tension and the destabilizing effects of surface turbulence. The model is described in the next section. Because turbulence is the main cause of entrainment, a turbulence-transport model must be used in connection with the air-entrainment model (i.e., ifvis=3 or 4). It is recommended that the RNG version of the more traditional k-epsilon turbulence model be employed. All the validation tests reported in this Technical Note were performed using the RNG turbulence model.

Aerospace Bibliography

아래는 항공 우주 분야에 대한 기술 문서 모음입니다.
이 모든 논문은 FLOW-3D  결과를 포함하고 있습니다. FLOW-3D를 사용하여 항공 우주 산업을 위한 응용 프로그램을 성공적으로 시뮬레이션  하는 방법에 대해 자세히 알아보십시오.

Aerospace Bibliography

2024년 8월 12일 Update

Below is a collection of technical papers in our Aerospace Bibliography. All of these papers feature FLOW-3D results. Learn more about how  FLOW-3D can be used to successfully simulate applications for the Aerospace Industry.

5-24 Yiming Sun, Hanwen Deng, Xinyu Liu, Xiaoming Kang, Simulation of liquid cone formation on the tip apex of indium field emission electric propulsion thrusters, Plasma Science and Technology, 2024. doi.org/10.1088/2058-6272/ad0d5b

208-23   Jason Hartwig, Narottama Esser, Shreykumar Jain, David Souders, Allen Prasad Varghese, Angelo Tafuni, CFD modeling of bidirectional PMDs inside cryogenic propellant tanks onboard parabolic flights, Journal of Spacecraft and Rockets, 2023. doi.org/10.2514/1.A35808

26-23   Jason Hartwig, Narottama Esser, Shreykumar Jain, David Souders, Allen Prasad Varghese, Angelantonio Tafuni, CFD design and analysis of a perforated plate for the control of cryogenic flow under reduced gravity, AIAA Scitech Forum, 2023. doi.org/10.2514/6.2023-0133

78-22   Timothy Aaron Blackman, Propellant optimization for a pulsed solid propellant thruster system for small satellites, Thesis, Florida Institute of Technology, 2022.

10-22   Nathan F. Andrews, Shane B. Coogan, Ellen Smith, Oliver Ouyang, Stephen Reiman, Brian Pincock, Bryan Munro, A three-dimensional, quick-running analysis method for large amplitude liquid slosh and bulk fluid motion in flight vehicles, AIAA Scitech Forum, AAIA 2022-0071, 2022. doi.org/10.2514/6.2022-0071

98-21   Pengxiang Hu, Zhihua Zhao, Shutao Yang, Yaoxiang Zeng, Feng Qi, Study on equivalent sloshing mass locations for liquid-filled cylindrical tanks, Journal of Spacecraft and Rockets, 2021. doi.org/10.2514/1.A35098

62-20   Zhang Dazhi, Meng Li, Li Yong-Qiang, Numerical simulation analysis of liquid transportation in capsule-type vane tank under microgravity, Microgravity Science and Technology, 32.3, 2020. doi.org/10.1007/s12217-020-09811-1

08-20   Li Yong-Qiang, Dong Jun-Yan and Rui Wei, Numerical simulation for capillary driven flow in capsule-type vane tank with clearances under microgravity, Microgravity Science and Technology, 2020. doi.org/10.1007/s12217-019-09773-z

107-19   Martin Konopka, Extension of a standard flow solver for simulating phase change in cryogenic tanks, Journal of Thermophysics and Heat Transfer, 33.3, 2019. doi.org/10.2514/1.T5546

79-19   Baotang Zhuang, Yong Li, Jintao Liu, and Wei Rui, Numerical simulation of fluid transport along parallel vanes for vane type propellant tanks, Microgravity Science and Technology, pp. 1-10, 2019. doi:10.1007/s12217-019-09746-2

54-19     Robert E. Manning, Ian Ballinger, Manoj Bhatia, and Mack Dowdy, Design of the Europa Clipper propellant management device, AIAA Propulsion and Energy 2019 Forum, Indianapolis, Indiana, August 19-22, 2019. doi:10.2514/6.2019-3858

48-19     Lei Wang, Tian Yan, Jiaojiao Wang, Shixuan Ye, Yanzhong Li, Rui Zhuan, and Bin Wang, CFD investigation on thermodynamic characteristics in liquid hydrogen tank during successive varied-gravity conditions, Cryogenics, Vol. 103, 2019. doi:10.1016/j.cryogenics.2019.102973

01-18   Martin Konopka, Extension of a Standard Flow Solver for Simulating Phase Change in Cryogenic Tanks, 018 AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2018-1818), https://doi.org/10.2514/6.2018-1818

69-16   Philipp Behruzi and Francesco De Rose, Coupling sloshing, GNC and rigid body motions during ballistic flight phases, Propulsion and Energy Forum, 52nd AIAA/SAE/ASEE Joint Propulsion Conference, July 25-27, 2016, Salt Lake City, UT.

55-16   Martin Konopka, Peter Noeding, Jörg Klatte, Philipp Behruzi, Jens Gerstmann, Anton Stark, Nicolas Darkow, Analysis of LN2 Filling, Draining, Stratification and Sloshing Experiments, 46th AIAA Fluid Dynamics Conference, Washington, D.C.

95-15   D Frank, Control of fluid mass center in the Gravity Probe B space mission Dewar, © 2015 IOP Publishing Ltd, Classical and Quantum Gravity, Volume 32, Number 22, November 17, 2015

58-15   Diana Gaulke and Michael E. Dreyer, CFD Simulation of Capillary Transport of Liquid Between Parallel Perforated Plates using FLOW-3D, Microgravity Science and Technology, August 2015

55-15   Sebastian Schmitt and Michael E. Dreyer, Free Surface Oscillations of Liquid Hydrogen in Microgravity Conditions, Cryogenics, doi:10.1016/j.cryogenics.2015.07.004, July 26, 2015

53-15   Jeffrey Moder and Kevin Breisacher, Preliminary Simulations of Ullage Dynamics in Microgravity during Jet Mixing Portion of the Tank Pressure Control Experiments, 51st AIAA/SAE/ASEE Joint Propulsion Conference, 2015

52-15   Philipp Behruzi, Diana Gaulke, Joerg Klatte, Nicolas Fries, Development of the MPCV ESM propellant tanks, 51st AIAA/SAE/ASEE Joint Propulsion Conference, 2015

51-15   Grant O. Musgrove and Shane B. Coogan, Validation and Rules-of-Thumb for Computational Predictions of Liquid Slosh Dynamics, 51st AIAA/SAE/ASEE Joint Propulsion Conference, 2015

23-15   Eckart Fuhrmann, Michael Dreyer, Steffen Basting, and Eberhard Bänsch, Free surface deformation and heat transfer by thermocapillary convection, Heat and Mass Transfer, June 2015, © SpringerLink

09-15   Zhicheng Zhou and Hua Huang, Constraint Surface Model for Large Amplitude Sloshing of the spacecraft with Multiple Tanks, Acta Astronautica, http://dx.doi.org/10.1016/j.actaastro.2015.02.023

43-14   C. Ludwig and M.E. Dreyer, Investigations on thermodynamic phenomena of the active-pressurization process of a cryogenic propellant tank, Cryogenics (2014), doi: http://dx.doi.org/10.1016/j.cryogenics.2014.05.005.

40-14   M. Berci, S. Mascetti; A. Incognito, P. H. Gaskell, and V. V. Toropov, Dynamic Response of Typical Section Using Variable-Fidelity Fluid Dynamics and Gust-Modeling Approaches—With Correction Methods, Journal of Aerospace Engineering, © ASCE, ISSN 0893-1321/04014026(20), May 2014.

22-14  M. Lazzarin, M. Biolo, A. Bettella, M. Manente, R. DaForno, and D. Pavarin, EUCLID satellite: Sloshing model development through computational fluid dynamics, Aerospace Science and Technology, JID:AESCTE AID:3040 /FLA, Available online 12 April 2014.

75-13   Carina Ludwig and Michael Dreyer, Analyses of Cryogenic Propellant Tank Pressurization based upon Experiments and Numerical Simulations, 5TH EUROPEAN CONFERENCE FOR AERONAUTICS AND SPACE SCIENCES (EUCASS), Munich, Germany, 1-5 July 2013

49-13 Damien Theureau, Astrium; Jean Mignot, French Space Agency (CNES); Sebastien Tanguy, Fluid Mechanics Institute of Toulouse (IMFT), Integration of low g sloshing models with spacecraft attitude control simulators, Chapter DOI: 10.2514/6.2013-4961, August 2013.

44-13  Philipp Behruzi, Jörg Klatte and Gaston Netter, Passive Phase Separation in Cryogenic Upper Stage Tanks, 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 14 – 17, 2013, San Jose, CA.

43-13  Philipp Behruzi, Jörg Klatte, Nicolas Fries, Andreas Schütte, Burkhard Schmitz and Horst Köhler, Cryogenic Propellant Management Sounding Rocket Experiments on TEXUS 48, 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, July 14 – 17, 2013, San Jose, CA.

113-12  M. Lazzarin, M. Biolo, A. Bettella, and R. Da Forno, EUCLID Mission: Theoretical Sloshing Model and CFD Comparison, 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 30 July – 01 August 2012, Atlanta, Georgia

34-12  N. Fries , P. Behruzi, T. Arndt, M. Winter, G. Netter, U. Renner, Modelling of fluid motion in spacecraft propellant tanks – Sloshing, Space Propulsion 2012 conference, 7th-10th May 2012, Bordeaux

55-11   P. Behruzi, F. de Rose, P. Netzlaf, H. Strauch, Ballistic Phase Management for Cryogenic Upper Stages, DGLR Conference, Bremen, Germany, 2011

11-11 Philipp Behruzi, Hans Strauch, and Francesco de Rose, Coasting Phase Propellant Management for Upper Stages, 38th COSPAR Scientific Assembly, 18-15 July 2010, Bremen, Germany. PowerPoint presentation.

73-10    Amber Bakkum, Kimberly Schultz, Jonathan Braun, Kevin M Crosby, Stephanie Finnvik, Isa Fritz, Bradley Frye, Cecilia Grove, Katelyn Hartstern, Samantha Kreppel and Emily Schiavone, Investigation of Propellant Sloshing and Zero Gravity Equilibrium for the Orion Service Module Propellant Tanks, Wisconsin Space Conference, Yingst, R. A., & Wisconsin Space Grant Consortium. (2010). Dawn of a new age: 20th Annual Wisconsin Space Conference, August 19-20, 2010. Green Bay, Wis: Wisconsin Space Grant Consortium; University of Wisconsin-Green Bay.

35-10   Kevin Breisacher and Jeffrey Moder, Computational Fluid Dynamics (CFD) Simulations of Jet Mixing in Tanks of Different Scales, NASA/TM—2010-216749

21-10 Berci M., Mascetti S., Incognito A., Gaskell P.H., Toropov V.V., Gust Response of a Typical Section Via CFD and Analytical Solutions, V European Conference on Computational Fluid Dynamics, ECCOMAS CFD 2010, Lisbon, Portugal, 14-17 June 2010 (A companion PowerPoint presentation in pdf format is available upon request)

49-08   Jens Gerstmann, Michael Dreyer, et al., Dependency of the apparent contact angle on nonisothermal conditions, PHYSICS OF FLUIDS 20, 042101 (2008)

35-07 N. Fries, K. Odic and M. Dreyer, Wicking of Perfectly Wetting Liquids into a Metallic Mesh, Proceedings of the 2nd International Conference on Porous Media and its Applications in Science and Engineering, ICPM2, Kauai, Hawaii, USA, June 17-21, 2007

08-07 Gary Grayson, Alfredo Lopez, Frank Chandler, Leon Hastings, Ali Hedayat, and James Brethour, CFD Modeling of Helium Pressurant Effects on Cryogenic Tank Pressure Rise Rates in Normal Gravity, 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, © 2007 by The Boeing Company. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. AIAA 2007-5524, 8 – 11 July 2007

34-06 Phillipp Behruzi, Mark Michaelis and Gaël Khimeche, Behavior of the Cryogenic Propellant Tanks during the First Flight of the Ariane 5 ESC-A Upper Stage, 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, 9-12 July 2006, Sacramento, California, © 2006 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

12-06 G. D. Grayson, A. Lopez, F. O. Chandler, L. J. Hastings, S. P. Tucker, Cryogenic Tank Modeling for the Saturn AS-203 Experiment, AIAA 2006-5258, presented at the 42nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, July 9-12, 2006, Sacramento, CA.

29-02 O. Bayle, V. L’Hullier, M. Ganet, P. Delpy, J.L. Francart and D. Paris, Influence of the ATV Propellant Sloshing on the GNC Performance, AIAA Guidance, Navigation, and Control Conference and Exhibit, Monterey, California, 5-8 August 2002, © 2002 by EADS Launch Vehicles

42-01 C. Figus and L. Ounougha, Correlations between Neutral Buoyancy Tests and CFD, Spacecraft Propulsion, Third International Conference held 10-13 October, 2000 at Cannes, France. European Space Agency ESASP-465, 2001, p.547

24-01 Hiroshi Nishino, Shujiro Sawai, & Katsumi Furukawa, Prediction of Sloshing Dynamics in Spinning Spherical Tanks, Mitsubishi Heavy Industry, The Institute of Space and Astronautical Science 9th Workshop on Astrodynamics and Flight Mechanics (1999)

5-96 D. J. Frank, Dynamics of Superfluid Helium in Low-Gravity: A Progress Report, Advanced Technology Center, Lockheed Martin Missiles & Space, Palo Alto, CA 94304, USA, To be published in Proceedings of 1996 NASA/JPL Microgravity Low Temperature Physics Workshop, April 1996

7-95 G. D. Grayson, Coupled Thermodynamic-Fluid-Dynamic Solution for a Liquid Hydrogen Tank, Journal of Spacecraft and Rockets, Vol. 32, No. 5, September-October 1995

5-94 G. Ross, Dynamics of Superfluid Helium in Low Gravity, dissertation submitted to Dept. Mech. Engrg. and Committee on Graduate Studies of Stanford University for Ph.D. degree, July 1994

9-93 N. H. Hughes, Numerical Stability Problem Encountered Modeling Large Liquid Mass in Micro Gravity, The Boeing Company, presented at the AAS/AIAA Astrodynamics Specialist Conference, Victoria, B.C., Canada, August 16-19, 1993

8-93 G. D. Grayson and J. Navickas, Interaction Between Fluid-Dynamic and Thermodynamic Phenomena in a Cryogenic Upper Stage, McDonnell Douglas, AIAA-93-2753, presented at the AIAA 28th Thermophysics Conference, Orlando, FL, July 6-9, 1993

7-93 G. Grayson and E. DiStefano, Propellant Acquisition for Single Stage Rocket Technology, McDonnell Douglas, AIAA-93-2283, presented at the AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conference and Exhibit, Monterey, CA, June 28-30, 1993

6-93 Y. Letourneur and J. Sicilian, Propellant Reorientation Effects on the Attitude of the Main Cryotechnic Stage of Ariane V, Aerospatiale, Les Mureaux and Flow Science Inc, presented at the AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conference and Exhibit, Monterey, CA, June 28-30, 1993

4-92 J. M. Sicilian, Evaluation of Space Vehicle Dynamics Including Fluid Slosh and Applied Forces, Flow Science report (FSI-92-47-01), August 1992

9-91 G. P. Sasmal, J. I. Hochstein, M. C. Wendl, Washington University and T. L. Hardy, NASA Lewis Research Center, Computational Modeling of the Pressurization Process in a NASP Vehicle Propellant Tank Experimental Simulation, (AIAA 91-2407), AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, Sacramento, CA, June 24-26, 1991

8-91 M. F. Fisher, G. R. Schmidt, and J. J. Martin,  Analysis of Cryogenic Propellant Behavior in Microgravity and Low Thrust Environments, NASA-Marshall Space Flight Center, AIAA/SAE/ASME/ASEE 27th Joint Propulsion Conference, Sacramento, CA, June 24-26, 1991

15-90 T. L. Hardy and T. M. Tomasik, Prediction of the Ullage Gas Thermal Stratification in a NASP Vehicle Propellant Tank Experimental Simulation Using FLOW-3D, NASA Technical Memorandum 103217, NASA-Lewis Research Center, Cleveland, OH, July 1990

6-90 J. Navickas, McDonnell Douglas Space Systems Co., Huntington Beach, CA and P.Y. Cheng, McDonnell Douglas Aircraft Co., St. Louis, MO, Effect of Propellant Sloshing on the Design of Space Vehicle Propellant Storage Systems, presented at the 26th AIAA/SAE/ASME/ASEE Joint Propulsion Conference, Orlando World Center, Orlando, FL, July 16-18, 1990

1-90 S. M. Dominick and J. R. Tegart, Fluid Dynamics and Thermodynamics of a Low Gravity Liquid Tank Filling Method, AIAA 28th Aerospace Sciences Meeting, AAIA-90-0509, Reno, NV, January 1990.

9-89 S. Lin and D. K. Warinner, FLOW-3D Analysis of Pressure Responses in an Enclosed Launching System, presented at the Symposium on Computational Experiments, PVP ASME Conference, Honolulu, HI, July 22-27, 1989

3-89 C. W. Hirt, Flow in a Solid-Propellant Rocket Chamber, Flow Science Technical Note #17, March 1989 (FSI-89-TN17)

1-89 J. Navickas, E. C. Cady, and J. L. Ditter, Suspension of Solid Particles in the Aerospace Plane’s Slush Hydrogen Tanks, McDonnell Douglas Astronautics Co. report, Huntington Beach, CA, 1988, presented at the Symposium on Computational Experiments, PVP ASME Conference, Honolulu, HI, July 22-27, 1989

11-88 J. Navickas, Prediction of a Liquid Tank Thermal Stratification by a Finite Difference Computing Method, presented to AIAA/ASEE/ASME/SAE 24th Joint Propulsion Conference, Boston, MA, 11-14 July 1988

10-88 J. Navickas, Space-Based System Disturbances Caused by On-Board Fluid Motion During System Maneuvers, presented to 1st National Fluid Dynamics Congress, Cincinnati, OH, July 24-28, 1988

9-88 J. Navickas, E. C. Cady, and T. L. Flaska, Modeling of Solid-Liquid Circulation in the National Aerospace Plane’s Slush Hydrogen Tanks, Advanced Propulsion, Advanced Technology Center, McDonnell Douglas Astronautics Co., Huntington Beach, CA, May 24, 1988

3-88 J. M. Sicilian and C. W. Hirt, Nozzle/Case Joint Analysis with CFD Analysis Using the FLOW-3D Program, in Redesigned Solid Rocket Motor Circumferential Flow Technical Interchange Meeting Final Report, NASA-TWR-17788, February 1988

11-87 C. W. Hirt, A Perspective on NASA-VOF3D vs. FLOW-3D, Flow Science report, December 1987 (FSI-87-00-3)

8-87 J. M. Sicilian, Fluid Slosh in a Rotating and Accelerating Tank, Flow Science report, Sept. 1987 (FSI-87-37-1)

5-87 J. J. Der and C.L. Stevens, Liquid Propellant Tank Ullage Bubble Deformation and Breakup in Low Gravity Reorientation, AIAA/SAE/ASME/ASEE 23rd Joint Propulsion Conference, San Diego, Calif., June 1987 (AIAA-87-2021)

3-87 J. Navickas and J. Ditter, Effect of the Propellant Storage Tank Geometric Configuration on the Resultant Disturbing Forces and Moments during Low-Gravity Maneuvers, McDonnell Douglas Astronautics report, MDAC H2589, April 1987, presented at 1987 ASME Winter Annual Meeting

1-87 J. J. Der and C. L. Stevens, Low-Gravity Bubble Reorientation in Liquid Propellant Tanks, AIAA 25th Aerospace Sciences Meeting, Reno, Nevada, January 12-15, 1987 (AIAA-87-0622)

7-86 J. Navickas, C. R. Cross, and D. D. Van Winkle, Propellant Tank Forces Resulting from Fluid Motion in a Low-Gravity Field, ASME Symposium in Microgravity Fluid Mechanics, Winter Annual Meeting, Anaheim, CA, December 7-12, 1986

6-86 J. Navickas and C. R. Cross, Some Typical Applications of the HYDR3D Code, FLOW-3D Experience Conference, Redondo Beach, California, November 6-7, 1986

5-86 R. E. Martin, Effects of Transient Propellant Dynamics on Deployment of Large Liquid Stages in Zero-Gravity with Application to Shuttle-Centaur, 37th Annual Astronautical Congress, Innsbruck, Austria, Oct. 3-10, 1986 (IAF-86-119), Acta Astronautical Vol. 15, No. 6/7, pp. 331-340, 1987

4-86 C. W. Hirt, FLOW-3D Test Problems for Two-Fluid Sloshing, Flow Science report, July 1986 (FSI-86-31-1)

6-85 John I. Hochstein, Computational Prediction of Propellant Motion During Separation of a Centaur G-Prime Vehicle from the Shuttle, NASA report, Washington University, St. Louis, MO, December 1985 (WU/CFDL-85/1)

4-85 T. W. Eastes, Y. M. Chang, C. W. Hirt, and J. M. Sicilian, Zero-Gravity Slosh Analysis, ASME Winter Annual Meeting, Miami, Florida, November 1985

3-84 J. M. Sicilian and C. W. Hirt, Numerical Simulation of Propellant Sloshing for Spacecraft, ASME Winter Annual Meeting, New Orleans, LA, December 9-14, 1984

Coastal & Maritime Bibliography

Coastal & Maritime Bibliography

다음은 연안 및 해양 분야의 기술 문서 모음입니다.
이 모든 논문은 FLOW-3D  결과를 포함하고 있습니다. FLOW-3D를 사용하여 연안 및 해양 시설물을 성공적으로 시뮬레이션 하는 방법에 대해 자세히 알아보십시오.

2024년 11월 20일 Update

119-24 Faris Ali Hamood Al-Towayti, Hee-Min Teh, Zhe Ma, Idris Ahmed Jae, Agusril Syamsir, Ebrahim Hamid Hussein Al-Qadami, Hydrodynamic performance assessment of emerged, alternatively submerged and submerged semicircular breakwater: An experimental and computational study, Journal of Marine Science and Engineering, 12; 1105, 2024. doi.org/10.3390/jmse12071105

117-24 Dong Zeng, Wuyang Bi, Yi Yu, Yun Yan, Weiqiu Chen, Yong Yao, Cheng Zhang, Tianyu Wu, Prediction of local scouring of offshore wind turbine foundations based on the amplification principle of local seabed shear stress, The 34th International Ocean and Polar Engineering Conference, ISOPE-I-24-125, 2024.

116-24 Chen-Shan Kung, Ya-Cing You, Pei-Yu Lee, Siu-Yu Pan, The air entrainment effect of pump blades operation under different water depths, The 34th International Ocean and Polar Engineering Conference, ISOPE-I-24-595, 2024.

114-24 Chen-Shan Kung, Siu-Yu Pan, Pei-Yu Lee, Ya-Cing You, Sediment flushing of different angle on density outflow, The 34th International Ocean and Polar Engineering Conference, ISOPE-I-24-183, 2024.

102-24 Mary Kathryn Walker, Computational fluid dynamics study of perforated monopiles, Thesis, Florida Institute of Technology, 2024.

80-24 Deniz Velioglu Sogut, Erdinc Sogut, Ali Farhadzadeh, Tian-Jian Hsu, Non-equilibrium scour evolution around an emerged structure exposed to a transient wave, Journal of Marine Science and Engineering, 12; 946, 2024. doi.org/10.3390/jmse12060946

79-24 Sujantoko, D.R. Ahidah, W. Wardhana, E.B. Djatmiko, M. Mustain, Numerical modeling of wave reflection and transmission in I-shaped floating breakwater series, IOP Conference Series: Earth and Environmental Science, 1321; 012010, 2024. doi.org/10.1088/1755-1315/1321/1/012010

75-24 Sahel Sohrabi, Mohamad Ali Lofollahi Yaghin, Alireza Mojtahedi, Mohamad Hosein Aminfar, Mehran Dadashzadeh, Experimental and numerical investigation of a hybrid floating breakwater-WEC system, Ocean Engineering, 303; 117613, 2024. doi.org/10.1016/j.oceaneng.2024.117613

73-24 Penghui Wang, Chunning Ji, Xiping Sun, Dong Xu, Chao Ying, Development and test of FDEM–FLOW-3D—A CFD–DEM model for the fluid–structure interaction of AccropodeTM blocks under wave loads, Ocean Engineering, 303; 117735, 2024. doi.org/10.1016/j.oceaneng.2024.117735

67-24 Alexander Schendel, Stefan Schimmels, Mario Welzel, Philippe April-LeQuéré, Abdolmajid Mohammadian, Clemens Krautwald, Jacob Stolle, Ioan Nistor, Nils Goseberg, Spatiotemporal scouring processes around a square column on a sloped beach induced by tsunami bores, Journal of Waterway, Port, Coastal, and Ocean Engineering, 150.3; 2024. https://doi.org/10.1061/JWPED5.WWENG-2052

65-24 Kaiqi Yu, Elda Miramontes, Matthieu J.B. Cartigny, Yuping Yang, Jingping Xu, The impacts of profile concavity on turbidite deposits: Insights from the submarine canyons on global continental margins, Geomorphology, 454; 109157, 2024. doi.org/10.1016/j.geomorph.2024.109157

61-24 M.T. Mansouri Kia, H.R. Sheibani, A. Hoback, Initial maintenance notes about the first river ship lock in Iran, Journal of Hydraulic and Water Engineering, 1.2; pp. 143-162, 2024.

47-24 Cheng Yee Ng, Nauman Riyaz Maldar, Muk Chen Ong, Numerical investigation on performance enhancement in a drag-based hydrokinetic turbine with a diffuser, Ocean Engineering, 298; 117179, 2024. doi.org/10.1016/j.oceaneng.2024.117179

26-24 Zegao Yin, Guoqing Li, Fei Wu, Zihan Ni, Feifan Li, Experimental and numerical study on hydrodynamic characteristics of a bottom-hinged pitching flap breakwater under regular waves, Ocean Engineering, 293; 116665, 2024. doi.org/10.1016/j.oceaneng.2024.116665

21-24   Young-Ki Moon, Chang-Ill Yoo, Jong-Min Lee, Sang-Hyub Lee, Han-Sam Yoon, Evaluation of pedestrian safety for wave overtopping by ship-induced waves in waterfront revetment, Journal of Coastal Research, 116; pp.314-318, 2024. doi.org/10.2112/JCR-SI116-064.1

14-24   Hongliang Wang, Xuanwen Jia, Chuan Wang, Bo Hu, Weidong Cao, Shanshan Li, Hui Wang, Study on the sand-scouring characteristics of pulsed submerged jets based on experiments and numerical models, Journal of Marine Science and Engineering, 12.1; 57, 2024. doi.org/10.3390/jmse12010057

239-23 Sara Tuozzo, Angela Di Leo, Mariano Buccino, Fabio Dentale, Eugenio Pugliese Carratelli, Mario Calabrese, The effect of wind stress on wave overtopping on vertical seawall, Coastal Engineering Proceedings, 37; 2023. doi.org/10.9753/icce.v37.papers.49

224-23   Helia Molaei Nodeh, Reza Dezvareh, Mahdi Yousefifard, Numerical analysis of the effects of rubble mound breakwater geometry under the effect of nonlinear wave force, Arabian Journal for Science and Engineering, 2023. doi.org/10.1007/s13369-023-08520-2

212-23   Feifei Cao, Mingqi Yu, Meng Han, Bing Liu, Zhiwen Wei, Juan Jiang, Huiyuan Tian, Hongda Shi, Yanni Li, WECs microarray effect on the coupled dynamic response and power performance of a floating combined wind and wave energy system, Renewable Energy, 219.2; 119476, 2023. doi.org/10.1016/j.renene.2023.119476

210-23   H. Omara, Sherif M. Elsayed, Karim Adel Nassar, Reda Diab, Ahmed Tawfik, Hydrodynamic and morphologic investigating of the discrepancy in flow performance between inclined rectangular and oblong piers, Ocean Engineering, 288.2; 116132, 2023. doi.org/10.1016/j.oceaneng.2023.116132

190-23   M.F. Ahmad, M.I. Ramli, M.A. Musa, S.E.G. Goh, C.W.M.N Che Wan Othman, E.H. Ariffin, N.A. Mokhtar, Numerical simulation for overtopping discharge on tetrapod breakwater, AIP Conference Proceedings, 2746.1; 2023. doi.org/10.1063/5.0153371

183-23   Youkou Dong, Enjin Zhao, Lan Cui, Yizhe Li, Yang Wang, Dynamic performance of suspended pipelines with permeable wrappers under solitary waves, Journal of Marine Science and Engineering, 11.10; 1872, 2023. doi.org/10.3390/jmse11101872

176-23   Guoxu Niu, Yaoyong Chen, Jiao Lu, Jing Zhang, Ning Fan, Determination of formulae for the hydrodynamic performance of a fixed box-type free surface breakwater in the intermediate water, Journal of Marine Science and Engineering, 11.9; 1812, 2023. doi.org/10.3390/jmse11091812

168-23   Yupeng Ren, Huiguang Zhou, Houjie Wang, Xiao Wu, Guohui Xu, Qingsheng Meng, Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition, Marine Geology, 464; 107142, 2023. doi.org/10.1016/j.margeo.2023.107142

163-23   Ahmad Fitriadhy, Sheikh Fakruradzi, Alamsyah Kurniawan, Nita Yuanita, Anuar Abu Bakar, 3D computational fluid dynamic investigation on wave transmission behind low-crested submerged geo-bag breakwater, CFD Letters, 15.10; 2023. doi.org/10.37934/cfdl.15.10.1222

162-23   Ramtin Sabeti, Landslide-generated tsunami waves-physical and numerical modelling, International Seminar on Tsunami Research, University of Bath, 2023.

161-23   Duy Linh Du, Study on the optimal location for pile-rock breakwater in reducing wave height in Dong Hai District, Bac Lieu Province, Vietnam, Thesis, Can Tho University, 2023.

160-23   Duy Linh Du, Dai Bang Pham, Van Duy Dinh, Tan Ngoc Cao, Van Ty Tran, Gia Bao Tran, Hieu Duc Tran, Modelling the wave reduction effectiveness of pile-rock breakwater using FLOW-3D, (in Vietnamese) Journal of Materials and Construction, 13.04; 2023. doi.org/10.54772/jomc.04.2023.537

151-23 Zhiguo Zhang, Jinpeng Chen, Tong Ye, Zhengguo Zhu, Mengxi Zhang, Yutao Pan, Wave-induced response of seepage pressure around shield tunnel in sand seabed slope, International Journal of Geomechanics, 23.10; 2023. doi.org/10.1061/IJGNAI.GMENG-8072

147-23 Jiale Li, Jijian Lian, Haijun Wang, Yaohua Guo, Sha Liu, Yutong Zhang, FengWu Zhang, Numerical study of the local scour characteristics of bottom-supported installation platforms during the installation of a monopile, Ships and Offshore Structures, 2023. doi.org/10.1080/17445302.2023.2243700

144-23 Weixang Liang, Min Lou, Changhong Fan, Deguang Zhao, Xiang Li, Coupling effect of vortex-induced vibration and local scour of double tandem pipelines in steady current, Ocean Engineering, 286.1; 115495, 2023. doi.org/10.1016/j.oceaneng.2023.11549

136-23 Zegao Yin, Jiahao Li, Yanxu Wang, Haojian Wang, Tianxu Yin, Solitary wave attenuation characteristics of mangroves and multi-parameter prediction model, Ocean Engineering, 285.2; 115372, 2023. doi.org/10.1016/j.oceaneng.2023.115372

130-23 Sheng Wang, Chaozhe Yuan, Yuchi Hao, Xiaowei Yan, Feasibility analysis of laying and construction of deep-water dredging sinking pipeline, The 33rd International Ocean and Polar Engineering Conference, ISOPE-1-23-030, 2023.

127-23 Chen-Shan Kung, Ya-Cing You, Pei-Yu Lee, Siu-Yu Pan, Yu-Chun Chen, The air entrainment effect stability on the marine pipeline, The 33rd International Ocean and Polar Engineering Conference, ISOPE-I-23-242, 2023.

126-23 Yuting Wang, Zhaode Zhang, Yuan Zhang, Numerical simulationa and measurement of artificial flow creation in reclamation projects, The 33rd International Ocean and Polar Engineering Conference, ISOPE-1-23-168, 2023.

125-23 Chen-Shan Kung, Siu-Yu Pan, Pei-Yu Lee, Ya-Cing You, Yu-Chun Chen, Numerical simulation of wave motion on the submarine HDPE pipe system, The 33rd International Ocean and Polar Engineering Conference, ISOPE-I-23-327, 2023.

115-23 Qishun Li, Yanpeng Hao, Peng Zhang, Haotian Tan, Wanxing Tian, Linhao Chen, Lin Yang, Numerical study of the local scouring process and influencing factors of semi-exposed submarine cables, Journal of Marine Science and Engineering, 11.7; 1349, 2023. doi.org/10.3390/jmse11071349

113-23 Minxi Zhang, Hanyan Zhao, Dongliang Zhao, Shaolin Yue, Huan Zhou, Xudong Zhao, Carlo Gualtieri, Guoliang Yu, Numerical study of the flow at a vertical pile with net-like scour protection mat, Journal of Ocean Engineering and Science, 2023. doi.org/10.1016/j.joes.2023.06.002

108-23 Seyed A. Ghaherinezhad, M. Behdarvandi Askar, Investigating effect of changing vegetation height with irregular layout on reduction of waves using FLOW-3D numerical model, Journal of Hydraulic and Water Engineering, 1.1; pp.55-64, 2023. doi.org/10.22044/JHWE.2023.12844.1004

92-23 Tongshun Yu, Xingyu Chen, Yuying Tang, Junrong Wang, Yuqiao Wang, Shuting Huang, Numerical modelling of wave run-up heights and loads on multi-degree-of-freedom buoy wave energy converters, Applied Energy, 344; 121255, 2023. doi.org/10.1016/j.apenergy.2023.121255

85-23   Emilee A. Wissmach, Biomimicry of natural reef hydrodynamics in an artificial spur and groove reef formation, Thesis, Florida Institute of Technology, 2023.

81-23   Zhi Fan, Feifei Cao, Hongda Shi, Numerical simulation on the energy capture spectrum of heaving buoy wave energy converter, Ocean Engineering, 280; 114475, 2023. doi.org/10.1016/j.oceaneng.2023.114475

72-23   Zegao Yin, Fei Wu, Yingni Luan, Xuecong Zhang, Xiutao Jiang, Jie Xiong, Hydrodynamic and aeration characteristics of an aerator of a surging water tank with a vertical baffle under a horizontal sinusoidal motion, Ocean Engineering, 287; 114396, 2023. doi.org/10.1016/j.oceaneng.2023.114396

71-23   Erfan Amini, Mahdieh Nasiri, Navid Salami Pargoo, Zahra Mozhgani, Danial Golbaz, Mehrdad Baniesmaeil, Meysam Majidi Nezhad, Mehdi Neshat, Davide Astiaso Garcia, Georgios Sylaios, Design optimization of ocean renewable energy converter using a combined Bi-level metaheuristic approach, Energy Conversion and Management: X, 19; 100371, 2023. doi.org/10.1016/j.ecmx.2023.100371

70-23   Ali Ghasemi, Rouholla Amirabadi, Ulrich Reza Kamalian, Numerical investigation of hydrodynamic responses and statistical analysis of imposed forces for various geometries of the crown structure of caisson breakwater, Ocean Engineering, 278; 114358, 2023. doi.org/10.1016/j.oceaneng.2023.114358

67-23   Aisyah Dwi Puspasari, Jyh-Haw Tang, Numerical simulation of scouring around groups of six cylinders with different flow directions, Journal of the Chinese Institute of Engineers, 46.4; 2023. doi.org/10.1080/02533839.2023.2194919

62-23   Rob Nairn, Qimiao Lu, Rebecca Quan, Matthew Hoy, Dain Gillen, Data collection and modeling in support of the Mid-Breton Sediment Diversion Project, Coastal Sediments, 2023. doi.org/10.1142/9789811275135_0246

55-23   Yupeng Ren, Hao Tian, Zhiyuan Chen, Guohui Xu, Lejun Liu, Yibing Li, Two kinds of waves causing the resuspension of deep-sea sediments: excitation and internal solitary waves, Journal of Ocean University of China, 22; pp. 429-440, 2023. doi.org/10.1007/s11802-023-5293-2

42-23   Antonija Harasti, Gordon Gilja, Simulation of equilibrium scour hole development around riprap sloping structure using the numerical model, EGU General Assembly, 2023. doi.org/10.5194/egusphere-egu23-6811

25-23   Ke Hu, Xinglan Bai, Murilo A. Vaz, Numerical simulation on the local scour processing and influencing factors of submarine pipeline, Journal of Marine Science and Engineering, 11.1; 234, 2023. doi.org/10.3390/jmse11010234

12-23   Fan Zhang, Zhipeng Zang, Ming Zhao, Jinfeng Zhang, Numerical investigations on scour and flow around two crossing pipelines on a sandy seabed, Journal of Marine Science and Engineering, 10.12; 2019, 2023. doi.org/10.3390/jmse10122019

10-23 Wenshe Zhou, Yongzhou Cheng, Zhiyuan Lin, Numerical simulation of long-wave wave dissipation in near-water flat-plate array breakwaters, Ocean Engineering, 268; 113377, 2023. doi.org/10.1016/j.oceaneng.2022.113377

181-22   Ramtin Sabeti, Mohammad Heidarzadeh, Numerical simulations of water waves generated by subaerial granular and solid-block landslides: Validation, comparison, and predictive equations, Ocean Engineering, 266.3; 112853, 2022. doi.org/10.1016/j.oceaneng.2022.112853 

167-22 Zhiyong Zhang, Cunhong Pan, Jian Zeng, Fuyuan Chen, Hao Qin, Kun He, Kui Zhu, Enjin Zhao, Hydrodynamics of tidal bore overflow on the spur dike and its infuence on the local scour, Ocean Engineering, 266.4; 113140, 2022. doi.org/10.1016/j.oceaneng.2022.113140

166-22 Nguyet-Minh Nguyen, Duong Do Van, Duy Tu Le, Quyen Nguyen, Bang Tran, Thanh Cong Nguyen, David Wright, Ahad Hasan Tanim, Phong Nguyen Thanh, Duong Tran Anh, Physical and numerical modeling of four different shapes of breakwaters to test the suspended sediment trapping capacity in the Mekong Delta, Estuarine, Coastal and Shelf Science, 279; 108141, 2022. doi.org/10.1016/j.ecss.2022.108141

163-22 Sahameddin Mahmoudi Kurdistani, Giuseppe Roberto Tomasicchio, Felice D’Alessandro, Antonio Francone, Formula for wave transmission at submerged homogeneous porous breakwaters, Ocean Engineering, 266.4; 113053, 2022. doi.org/10.1016/j.oceaneng.2022.113053

162-22 Kai Wei, Xueshuang Yin, Numerical study into configuration of horizontal flanges on hydrodynamic performance of moored box-type floating breakwater, Ocean Engineering, 266.4; 112991, 2022. doi.org/10.1016/j.oceaneng.2022.112991

161-22 Sung-Chul Jang, Jin-Yong Jeong, Seung-Woo Lee, Dongha Kim, Identifying hydraulic characteristics related to fishery activities using numerical analysis and an automatic identification system of a fishing vessel, Journal of Marine Science and Engineering, 10; 1619, 2022. doi.org/10.3390/jmse10111619

156-22 Keith Adams, Mohammad Heidarzadeh, Extratropical cyclone damage to the seawall in Dawlish, UK: Eyewitness accounts, sea level analysis and numerical modelling, Natural Hazards, 2022. doi.org/10.1007/s11069-022-05692-2

155-22 Youxiang Lu, Zhenlu Wang, Zegao Yin, Guoxiang Wu, Bingchen Liang, Experimental and numerical studies on local scour around closely spaced circular piles under the action of steady current, Journal of Marine Science and Engineering, 10; 1569, 2022. doi.org/10.3390/jmse10111569

152-22 Nauman Riyaz Maldar, Ng Cheng Yee, Elif Oguz, Shwetank Krishna, Performance investigation of a drag-based hydrokinetic turbine considering the effect of deflector, flow velocity, and blade shape, Ocean Engineering, 266.2; 112765, 2022. doi.org/10.1016/j.oceaneng.2022.112765

148-22   Ramtin Sabeti, Mohammad Heidarzadeh, Numerical simulations of water waves generated by subaerial granular and solid-block landslides: Validation, comparison, and predictive equations, Ocean Engineering, 266.3; 112853, 2022. doi.org/10.1016/j.oceaneng.2022.112853

145-22   I-Fan Tseng, Chih-Hung Hsu, Po-Hung Yeh, Ting-Chieh Lin, Physical mechanism for seabed scouring around a breakwater—a case study in Mailiao Port, Journal of Marine Science and Engineering, 10; 1386, 2022. doi.org/10.3390/jmse10101386

144-22   Jiarui Yu, Baozeng Yue, Bole Ma, Isogeometric analysis with level set method for large-amplitude liquid sloshing, Ocean Engineering, 265; 112613, 2022. doi.org/10.1016/j.oceaneng.2022.112613

141-22   Qi Yang, Peng Yu, Hongjun Liu, Computational investigation of scour characteristics of USAF in multi-specie sand under steady current, Ocean Engineering, 262; 112141, 2022. doi.org/10.1016/j.oceaneng.2022.112141

128-22   Atish Deoraj, Calvin Wells, Justin Pringle, Derek Stretch, On the reef scale hydrodynamics at Sodwana Bay, South Africa, Environmental Fluid Mechanics, 2022. doi.org/10.1007/s10652-022-09896-9

108-22   Angela Di Leo, Mariano Buccino, Fabio Dentale, Eugenio Pugliese Carratelli, CFD analysis of wind effect on wave overtopping, 32nd International Ocean and Polar Engineering Conference,  ISOPE-I-22-428, 2022.

105-22   Pin-Tzu Su, Chen-shan Kung, Effects of currents and sediment flushing on marine pipes, 32nd International Ocean and Polar Engineering Conference, ISOPE-I-22-153, 2022.

89-22   Kai Wei, Cong Zhou, Bo Xu, Spatial distribution models of horizontal and vertical wave impact pressure on the elevated box structure, Applied Ocean Research, 125; 103245, 2022. doi.org/10.1016/j.apor.2022.103245

87-22   Tran Thuy Linh, Numerical modelling (3D) of wave interaction with porous structures in the Mekong Delta coastal zone, Thesis, Ho Chi Minh City University of Technology, 2022.

82-22   Seyyed-Mahmood Ghassemizadeh, Mohammad Javad Ketabdari, Modeling of solitary wave interaction with curved-facing seawalls using numerical method, Advances in Civil Engineering, 5649637, 2022. doi.org/10.1155/2022/5649637

81-22   Raphael Alwan, Boyin Ding, David M. Skene, Zhaobin Li, Luke G. Bennetts, On the structure of waves radiated by a submerged cylinder undergoing large-amplitude heave motions, 32nd International Ocean and Polar Engineering Conference, Shanghai, China, June 5-10, 2022. doi.org/10.1111/jfr3.12828

77-22   Weiyun Chen, Linchong Huang, Dan Wang, Chao Liu, Lingyu Xu, Zhi Ding, Effects of siltation and desiltation on the wave-induced stability of foundation trench of immersed tunnel, Soil Dynamics and Earthquake Engineering, 160; 107360, 2022. doi.org/10.1016/j.soildyn.2022.107360

63-22   Yongzhou Cheng, Zhiyuan Lin, Gan Hu, Xing Lyu, Numerical simulation of the hydrodynamic characteristics of the porous I-type composite breakwater, Journal of Marine Science and Application, 21; pp. 140-150, 2022. doi.org/10.1007/s11804-022-00251-4

37-22   Ray-Yeng Yang, Chuan-Wen Wang, Chin-Cheng Huang, Cheng-Hsien Chung, Chung-Pang, Chen, Chih-Jung Huang, The 1:20 scaled hydraulic model test and field experiment of barge-type floating offshore wind turbine system, Ocean Engineering, 247.1; 110486, 2022. doi.org/10.1016/j.oceaneng.2021.110486

35-22   Mingchao Cui, Zhisong Li, Chenglin Zhang, Xiaoyu Guo, Statistical investigation into the flow field of closed aquaculture tanks aboard a platform under periodic oscillation, Ocean Engineering, 248; 110677, 2022. doi.org/10.1016/j.oceaneng.2022.110677

30-22   Jijian Lian, Jiale Li, Yaohua Guo, Haijun Wang, Xu Yang, Numerical study on local scour characteristics of multi-bucket jacket foundation considering exposed height, Applied Ocean Research, 121; 103092. doi.org/10.1016/j.apor.2022.103092

19-22   J.J. Wiegerink, T.E. Baldock, D.P. Callaghan, C.M. Wang, Slosh suppression blocks – A concept for mitigating fluid motions in floating closed containment fish pen in high energy environments, Applied Ocean Research, 120; 103068, 2022. doi.org/10.1016/j.apor.2022.103068

9-22   Amir Bordbar, Soroosh Sharifi, Hassan Hemida, Investigation of scour around two side-by-side piles with different spacing ratios in live-bed, Lecture Notes in Civil Engineering, 208; pp. 302-309, 2022. doi.org/10.1007/978-981-16-7735-9_33

7-22   Jinzhao Li, Xuan Kong, Yilin Yang, Lu Deng, Wen Xiong, CFD investigations of tsunami-induced scour around bridge piers, Ocean Engineering, 244; 110373, 2022. doi.org/10.1016/j.oceaneng.2021.110373

3-22   Ana Gomes, José Pinho, Wave loads assessment on coastal structures at inundation risk using CFD modelling, Climate Change and Water Security, 178; pp. 207-218, 2022. doi.org/10.1007/978-981-16-5501-2_17

2-22   Ramtin Sabeti, Mohammad Heidarzadeh, Numerical simulations of tsunami wave generation by submarine landslides: Validation and sensitivity analysis to landslide parameters, Journal of Waterway, Port, Coastal, and Ocean Engineering, 148.2; 05021016, 2022. doi.org/10.1061/(ASCE)WW.1943-5460.0000694

146-21   Ming-ming Liu, Hao-cheng Wang, Guo-qiang Tang, Fei-fei Shao, Xin Jin, Investigation of local scour around two vertical piles by using numerical method, Ocean Engineering, 244; 110405, 2021. doi.org/10.1016/j.oceaneng.2021.110405

135-21   Jian Guo, Jiyi Wu, Tao Wang, Prediction of local scour depth of sea-crossing bridges based on the energy balance theory, Ships and Offshore Structures, 16.10, 2021. doi.org/10.1080/17445302.2021.2005362

133-21   Sahel Sohrabi, Mohamad Ali Lofollahi Yaghin, Mohamad Hosein Aminfar, Alireza Mojtahedi, Experimental and numerical investigation of hydrodynamic performance of a sloping floating breakwater with and without chain-net, Iranian Journal of Science and Technology: Transactions of Civil Engineering, , 2021. doi.org/10.1007/s40996-021-00780-y

131-21   Seyed Morteza Marashian, Mehdi Adjami, Ahmad Rezaee Mazyak, Numerical modelling investigation of wave interaction on composite berm breakwater, China Ocean Engineering, 35; pp. 631-645, 2021. doi.org/10.1007/s13344-021-0060-x

124-21   Ramin Safari Ghaleh, Omid Aminoroayaie Yamini, S. Hooman Mousavi, Mohammad Reza Kavianpour, Numerical modeling of failure mechanisms in articulated concrete block mattress as a sustainable coastal protection structure, Sustainability, 13.22; pp. 1-19, 2021.

118-21   A. Keshavarz, M. Vaghefi, G. Ahmadi, Investigation of flow patterns around rectangular and oblong peirs with collar located in a 180-degree sharp bend, Scientia Iranica A, 28.5; pp. 2479-2492, 2021.

109-21   Jacek Jachowski, Edyta Książkiewicz, Izabela Szwoch, Determination of the aerodynamic drag of pneumatic life rafts as a factor for increasing the reliability of rescue operations, Polish Maritime Research, 28.3; p. 128-136, 2021. doi.org/10.2478/pomr-2021-0040

107-21   Jiay Han, Bing Zhu, Baojie Lu, Hao Ding, Ke Li, Liang Cheng, Bo Huang, The influence of incident angles and length-diameter ratios on the round-ended cylinder under regular wave action, Ocean Engineering, 240; 109980, 2021. doi.org/10.1016/j.oceaneng.2021.109980

96-21   Andrea Franco, Jasper Moernaut, Barbara Schneider-Muntau, Michael Strasser, Bernhard Gems, Triggers and consequences of landslide-induced impulse waves – 3D dynamic reconstruction of the Taan Fiord 2015 tsunami event, Engineering Geology, 294; 106384, 2021. doi.org/10.1016/j.enggeo.2021.106384

95-21   Ahmed A. Romya, Hossam M. Moghazy, M.M. Iskander, Ahmed M. Abdelrazek, Performance assessment of corrugated semi-circular breakwaters for coastal protection, Alexandria Engineering Journal, in press, 2021. doi.org/10.1016/j.aej.2021.08.086

87-21   Ruigeng Hu, Hongjun Liu, Hao Leng, Peng Yu, Xiuhai Wang, Scour characteristics and equilibrium scour depth prediction around umbrella suction anchor foundation under random waves, Journal of Marine Science and Engineering, 9; 886, 2021. doi.org/10.3390/jmse9080886

78-21   Sahir Asrari, Habib Hakimzadeh, Nazila Kardan, Investigation on the local scour beneath piggyback pipelines under clear-water conditions, China Ocean Engineering, 35; pp. 422-431, 2021. doi.org/10.1007/s13344-021-0039-7

64-21   Pin-Tzu Su, Chen-shan Kung, Effects of diffusers on discharging jet, 31st International Ocean and Polar Engineering Conference (ISOPE), Rhodes, Greece, June 20-25, 2021.

62-21   Fei Wu, Wei Li, Shuzhao Li, Xiaopeng Shen, Delong Dong, Numerical simulation of scour of backfill soil by jetting flows on the top of buried caisson, 31st International Ocean and Polar Engineering Conference (ISOPE), Rhodes, Greece, June 20-25, 2021.

56-21   Murat Aksel, Oral Yagci, V.S. Ozgur Kirca, Eryilmaz Erdog, Naghmeh Heidari, A comparitive analysis of coherent structures around a pile over rigid-bed and scoured-bottom, Ocean Engineering, 226; 108759, 2021. doi.org/10.1016/j.oceaneng.2021.108759

52-21   Byeong Wook Lee, Changhoon Lee, Equation for ship wave crests in a uniform current in the entire range of water depths, Coastal Engineering, 167; 103900, 2021. doi.org/10.1016/j.coastaleng.2021.103900

43-21   Agnieszka Faulkner, Claire E. Bulgin, Christopher J. Merchant, Characterising industrial thermal plumes in coastal regions using 3-D numerical simulations, Environmental Research Communications, 3; 045003, 2021. doi.org/10.1088/2515-7620/abf62e

39-21   Fan Yang, Yiqi Zhang, Chao Liu, Tieli Wang, Dongin Jiang, Yan Jin, Numerical and experimental investigations of flow pattern and anti-vortex measures of forebay in a multi-unit pumping station, Water, 13.7; 935, 2021. doi.org/10.3390/w13070935

30-21   Norfadhlina Khalid, Aqil Azraie Che Shamshudin, Megat Khalid Puteri Zarina, Analysis on wave generation and hull: Modification for fishing vessels, Advanced Engineering for Processes and Technologies II: Advanced Structured Materials, 147; pp. 77-89, 2021. doi.org/10.1007/978-3-030-67307-9_9

28-21   Jae-Sang Jung, Jae-Seon Yoon, Seokkoo Kang, Seokil Jeong, Seung Oh Lee, Yong-Sung Park, Discharge characteristics of drainage gates on Saemangeum tidal dyke, South Korea, KSCE Journal of Engineering, 25; pp. 1308-1325, 2021. doi.org/10.1007/s12205-021-0590-z

24-21   Ali Temel, Mustafa Dogan, Time dependent investigation of the wave induced scour at the trunk section of a rubble mound breakwater, Ocean Engineering, 221; 108564, 2021. doi.org/10.1016/j.oceaneng.2020.108564

13-21   P.X. Zou, L.Z. Chen, The coupled tube-mooring system SFT hydrodynamic characteristics under wave excitations, Proceedings, 14th International Conference on Vibration Problems, Crete, Greece, September 1 – 4, 2019, pp. 907-923, 2021. doi.org/10.1007/978-981-15-8049-9_55

122-20  M.A. Musa, M.F. Roslan, M.F. Ahmad, A.M. Muzathik, M.A. Mustapa, A. Fitriadhy, M.H. Mohd, M.A.A. Rahman, The influence of ramp shape parameters on performance of overtopping breakwater for energy conversion, Journal of Marine Science and Engineering, 8.11; 875, 2020. doi.org/10.3390/jmse8110875

120-20  Lee Hooi Chie, Ahmad Khairi Abd Wahab, Derivation of engineering design criteria for flow field around intake structure: A numerical simulation study, Journal of Marine Science and Engineering, 8.10; 827, 2020.  doi.org/10.3390/jmse8100827

109-20  Mario Maiolo, Riccardo Alvise Mel, Salvatore Sinopoli, A stepwise approach to beach restoration at Calabaia Beach, Water, 12.10; 2677, 2020. doi.org/10.3390/w12102677

107-20  S. Deshpande, P. Sundsbø, S. Das, Ship resistance analysis using CFD simulations in Flow-3D, International Journal of Multiphysics, 14.3; pp. 227-236, 2020. doi.org/10.21152/1750-9548.14.3.227

103-20   Mahmood Nematollahi, Mohammad Navim Moghid, Numerical simulation of spatial distribution of wave overtopping on non-reshaping berm breakwaters, Journal of Marine Science and Application, 19; pp. 301-316, 2020. doi.org/10.1007/s11804-020-00147-1

98-20   Lin Zhao, Ning Wang, Qian Li, Analysis of flow characteristics and wave dissipation performances of a new structure, Proceedings, 30th International Ocean and Polar Engineering Conference (ISOPE), Online, October 11-16, ISOPE-I-20-3289, 2020.

96-20   Xiaoyu Guo, Zhisong Li, Mingchao Cui, Benlong Wang, Numerical investigation on flow characteristics of water in the fish tank on a force-rolling aquaculture platform, Ocean Engineering, 217; 107936, 2020. doi.org/10.1016/j.oceaneng.2020.107936

92-20   Yong-Jun Cho, Scour controlling effect of hybrid mono-pile as a substructure of offshore wind turbine: A numerical study, Journal of Marine Science and Engineering, 8.9; 637, 2020. doi.org/10.3390/jmse8090637

89-20   Andrea Franco, Jasper Moernaut, Barbara Schneider-Muntau, Michael Strasser, Bernhard Gems, The
1958 Lituya Bay tsunami – pre-event bathymetry reconstruction and 3D numerical modelling utilising the computational fluid dynamics software
Flow-3D, Natural Hazards and Earth Systems Sciences, 20; pp. 2255–2279, 2020. doi.org/10.5194/nhess-20-2255-2020

81-20   Eliseo Marchesi, Marco Negri, Stefano Malavasi, Development and analysis of a numerical model for a two-oscillating-body wave energy converter in shallow water, Ocean Engineering, 214; 107765, 2020. doi.org/10.1016/j.oceaneng.2020.107765

79-20   Zegao Yin, Yanxu Wang, Yong Liu, Wei Zou, Wave attenuation by rigid emergent vegetation under combined wave and current flows, Ocean Engineering, 213; 107632, 2020. doi.org/10.1016/j.oceaneng.2020.107632

71-20   B. Pan, N. Belyaev, FLOW-3D software for substantiation the layout of the port water area, IOP Conference Series: Materials Science and Engineering, Construction Mechanics, Hydraulics and Water Resources Engineering (CONMECHYDRO), Tashkent, Uzbekistan, 23-25 April, 883; 012020, 2020. doi.org/10.1088/1757-899X/883/1/012020

51-20       Yupeng Ren, Xingbei Xu, Guohui Xu, Zhiqin Liu, Measurement and calculation of particle trajectory of liquefied soil under wave action, Applied Ocean Research, 101; 102202, 2020. doi.org/10.1016/j.apor.2020.102202

50-20       C.C. Battiston, F.A. Bombardelli, E.B.C. Schettini, M.G. Marques, Mean flow and turbulence statistics through a sluice gate in a navigation lock system: A numerical study, European Journal of Mechanics – B/Fluids, 84; pp.155-163, 2020. doi.org/10.1016/j.euromechflu.2020.06.003

49-20     Ahmad Fitriadhy, Nur Amira Adam, Nurul Aqilah Mansor, Mohammad Fadhli Ahmad, Ahmad Jusoh, Noraieni Hj. Mokhtar, Mohd Sofiyan Sulaiman, CFD investigation into the effect of heave plate on vertical motion responses of a floating jetty, CFD Letters, 12.5; pp. 24-35, 2020. doi.org/10.37934/cfdl.12.5.2435

40-20       P. April Le Quéré, I. Nistor, A. Mohammadian, Numerical modeling of tsunami-induced scouring around a square column: Performance assessment of FLOW-3D and Delft3D, Journal of Coastal Research (preprint), 2020. doi.org/10.2112/JCOASTRES-D-19-00181

38-20       Sahameddin Mahmoudi Kurdistani, Giuseppe Roberto Tomasicchio, Daniele Conte, Stefano Mascetti, Sensitivity analysis of existing exponential empirical formulas for pore pressure distribution inside breakwater core using numerical modeling, Italian Journal of Engineering Geology and Environment, 1; pp. 65-71, 2020. doi.org/10.4408/IJEGE.2020-01.S-08

36-20       Mohammadamin Torabi, Bruce Savage, Efficiency improvement of a novel submerged oscillating water column (SOWC) energy harvester, Proceedings, World Environmental and Water Resources Congress (Cancelled), Henderson, Nevada, May 17–21, 2020. doi.org/10.1061/9780784482940.003

32-20       Adriano Henrique Tognato, Modelagem CFD da interação entre hidrodinâmica costeira e quebra-mar submerso: estudo de caso da Ponta da Praia em Santos, SP (CFD modeling of interaction between sea waves and submerged breakwater at Ponta de Praia – Santos, SP: a case study, Thesis, Universidad Estadual de Campinas, Campinas, Brazil, 2020.

29-20   Ana Gomes, José L. S. Pinho, Tiago Valente, José S. Antunes do Carmo and Arkal V. Hegde, Performance assessment of a semi-circular breakwater through CFD modelling, Journal of Marine Science and Engineering, 8.3, art. no. 226, 2020. doi.org/10.3390/jmse8030226

23-20  Qi Yang, Peng Yu, Yifan Liu, Hongjun Liu, Peng Zhang and Quandi Wang, Scour characteristics of an offshore umbrella suction anchor foundation under the combined actions of waves and currents, Ocean Engineering, 202, art. no. 106701, 2020. doi.org/10.1016/j.oceaneng.2019.106701

04-20  Bingchen Liang, Shengtao Du, Xinying Pan and Libang Zhang, Local scour for vertical piles in steady currents: review of mechanisms, influencing factors and empirical equations, Journal of Marine Science and Engineering, 8.1, art. no. 4, 2020. doi.org/10.3390/jmse8010004

104-19   A. Fitriadhy, S.F. Abdullah, M. Hairil, M.F. Ahmad and A. Jusoh, Optimized modelling on lateral separation of twin pontoon-net floating breakwater, Journal of Mechanical Engineering and Sciences, 13.4, pp. 5764-5779, 2019. doi.org/10.15282/jmes.13.4.2019.04.0460

103-19  Ahmad Fitriadhy, Nurul Aqilah Mansor, Nur Adlina Aldin and Adi Maimun, CFD analysis on course stability of an asymmetrical bridle towline model of a towed ship, CFD Letters, 11.12, pp. 43-52, 2019.

90-19   Eric P. Lemont and Karthik Ramaswamy, Computational fluid dynamics in coastal engineering: Verification of a breakwater design in the Torres Strait, Proceedings, pp. 762-768, Australian Coasts and Ports 2019 Conference, Hobart, Australia, September 10-13, 2019.

86-19   Mohammed Arab Fatiha, Benoît Augier, François Deniset, Pascal Casari, and Jacques André Astolfi, Morphing hydrofoil model driven by compliant composite structure and internal pressure, Journal of Marine Science and Engineering, 7:423, 2019. doi.org/10.3390/jmse7120423

83-19   Cong-Uy Nguyen, So-Young Lee, Thanh-Canh Huynh, Heon-Tae Kim, and Jeong-Tae Kim, Vibration characteristics of offshore wind turbine tower with gravity-based foundation under wave excitation, Smart Structures and Systems, 23:5, pp. 405-420, 2019. doi.org/10.12989/sss.2019.23.5.405

68-19   B.W. Lee and C. Lee, Development of an equation for ship wave crests in a current in whole water depths, Proceedings, 10th International Conference on Asian and Pacific Coasts (APAC 2019), Hanoi, Vietnam, September 25-28, 2019; pp. 207-212, 2019. doi.org/10.1007/978-981-15-0291-0_29

62-19   Byeong Wook Lee and Changhoon Lee, Equation for ship wave crests in the entire range of water depths, Coastal Engineering, 153:103542, 2019. doi.org/10.1016/j.coastaleng.2019.103542

23-19     Mariano Buccino, Mohammad Daliri, Fabio Dentale, Angela Di Leo, and Mario Calabrese, CFD experiments on a low crested sloping top caisson breakwater, Part 1: Nature of loadings and global stability, Ocean Engineering, Vol. 182, pp. 259-282, 2019. doi.org/10.1016/j.oceaneng.2019.04.017

21-19     Mahsa Ghazian Arabi, Deniz Velioglu Sogut, Ali Khosronejad, Ahmet C. Yalciner, and Ali Farhadzadeh, A numerical and experimental study of local hydrodynamics due to interactions between a solitary wave and an impervious structure, Coastal Engineering, Vol. 147, pp. 43-62, 2019. doi.org/10.1016/j.coastaleng.2019.02.004

15-19     Chencong Liao, Jinjian Chen, and Yizhou Zhang, Accumulation of pore water pressure in a homogeneous sandy seabed around a rocking mono-pile subjected to wave loads, Vol. 173, pp. 810-822, 2019. doi.org/10.1016/j.oceaneng.2018.12.072

09-19     Yaoyong Chen, Guoxu Niu, and Yuliang Ma, Study on hydrodynamics of a new comb-type floating breakwater fixed on the water surface, 2018 International Symposium on Architecture Research Frontiers and Ecological Environment (ARFEE 2018), Wuhan, China, December 14-16, 2018, E3S Web of Conferences Vol. 79, Art. No. 02003, 2019. doi.org/10.1051/e3sconf/20197902003

08-19     Hongda Shi, Zhi Han, and Chenyu Zhao, Numerical study on the optimization design of the conical bottom heaving buoy convertor, Ocean Engineering, Vol. 173, pp. 235-243, 2019. doi.org/10.1016/j.oceaneng.2018.12.061

06-19   S. Hemavathi, R. Manjula and N. Ponmani, Numerical modelling and experimental investigation on the effect of wave attenuation due to coastal vegetation, Proceedings of the Fourth International Conference in Ocean Engineering (ICOE2018), Vo