Effects of pile-cap elevation on scour and turbulence around a complex bridge pier

복잡한 교각 주변의 세굴 및 난기류에 대한 말뚝 뚜껑 높이의 영향

ABSTRACT

이 연구에서는 세 가지 다른 말뚝 뚜껑 높이에서 직사각형 말뚝 캡이 있는 복잡한 부두 주변의 지역 세굴 및 관련 흐름 유체 역학을 조사합니다. 말뚝 캡 높이가 초기 모래층에 대해 선택되었으며, 말뚝 캡이 흐름에 노출되지 않고(사례 I), 부분적으로 노출되고(사례 II) 완전히 노출(사례 III)되도록 했습니다. 실험은 맑은 물 세굴 조건 하에서 재순환 수로에서 수행되었으며, 입자 이미지 유속계 (PIV) 기술을 사용하여 다른 수직면에서 순간 유속을 얻었습니다. 부분적으로 노출된 파일 캡 케이스는 최대 수세미 깊이(MSD)를 보여주었습니다. 사례 II에서 MSD가 발생한 이유는 난류 유동장 분석을 통해 밝혀졌는데, 이는 말뚝 캡이 흐름에 노출됨에 따라 더 높은 세굴 깊이를 담당하는 말뚝 가장자리에서 와류 생성에 지배적으로 영향을 미친다는 것을 보여주었습니다. 유동장에 대한 파일 캡의 영향은 평균 속도, 소용돌이, 레이놀즈 전단 응력 및 난류 운동 에너지 윤곽을 통해 사례 III에서 두드러지게 나타났지만 파일 캡이 베드에서 떨어져 있었기 때문에 파일 캡 모서리는 수세미에 직접적인 영향을 미치지 않았습니다.

In this study, the local scour and the associated flow hydrodynamics around a complex pier with rectangular pile-cap at three different pile-cap elevations are investigated. The pile-cap elevations were selected with respect to the initial sand bed, such that the pile-cap was unexposed (case I), partially exposed (case II), and fully exposed (case III) to the flow. The experiments were performed in a recirculating flume under clear-water scour conditions, and the instantaneous flow velocity was obtained at different vertical planes using the particle image velocimetry (PIV) technique. The partially exposed pile-cap case showed the maximum obtained scour-depth (MSD). The reason behind the MSD occurrence in case II was enunciated through the analysis of turbulent flow field which showed that as the pile-cap got exposed to the flow, it dominantly affected the generation of vortices from the pile-cap corners responsible for the higher scour depth. The effect of the pile-cap on the flow field was prominently seen in case III through the mean velocities, vorticity, Reynolds shear stresses and turbulent kinetic energy contours, but since the pile-cap was away from the bed, the pile-cap corners did not show any direct effect on the scour.

KEYWORDS: 

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

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

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

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

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

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

*Author to whom correspondence should be addressed.

J. Mar. Sci. Eng. 20219(8), 886; https://doi.org/10.3390/jmse9080886

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

(This article belongs to the Section Ocean Engineering)

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Abstract

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

Keywords: 

scournumerical investigationrandom wavesequilibrium scour depthKC 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 θKC 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; uv, and w are the velocity components in xyz 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 = xyz).

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 VFAiCDIS1CDIS2 and CDIS3 are dimensionless parameters, and CDIS1CDIS3 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 iDf 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.

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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.

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Figure 3. The sketch of mesh grid.

3.2. Boundary Conditions

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

3.3. Wave Parameters

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

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

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

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

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

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

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

ε=2πgHsT2a�=2���s�a2(28)

Ur=Hsk2h3w�r=�s�2ℎw3(29)

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

Table 2. Numerical simulating cases.

Table

3.4. Mesh Sensitivity

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

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

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

3.5. Model Validation

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

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

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

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

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

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

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

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

4. Numerical Results and Discussions

4.1. Scour Evolution

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

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

where Tc is time scale of scour process.

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

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

4.2. Scour Mechanism under Random Waves

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

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

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

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

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

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

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

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

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

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Figure 13. Pressure distribution around USAF.

4.3. Equilibrium Scour Depth

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

Table 3. Uwm,rms and KC for case 1~9.

Table

Table 4. Uwm,s and KC for case 1~9.

Table

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

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

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Figure 15. Comparison of the equilibrium scour depth between the present model and the model of Raaijmakers and Rudolph [34]: (aKCrms,sKCrms,a; (bKCrms,pKCrms,m; (cKCrms,n = 1/10KCrms,n = 1/5; (dKCs,sKCs,a; (eKCs,pKCs,m; (fKCs,n = 1/10KCs,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 AB 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.

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Hu, R.; Liu, H.; Leng, H.; Yu, P.; Wang, X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. J. Mar. Sci. Eng. 20219, 886. https://doi.org/10.3390/jmse9080886

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Hu R, Liu H, Leng H, Yu P, Wang X. Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves. Journal of Marine Science and Engineering. 2021; 9(8):886. https://doi.org/10.3390/jmse9080886Chicago/Turabian Style

Hu, Ruigeng, Hongjun Liu, Hao Leng, Peng Yu, and Xiuhai Wang. 2021. “Scour Characteristics and Equilibrium Scour Depth Prediction around Umbrella Suction Anchor Foundation under Random Waves” Journal of Marine Science and Engineering 9, no. 8: 886. https://doi.org/10.3390/jmse9080886

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Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Influence of crest geometric on discharge coefficient efficiency of labyrinth weirs

Erick Mattos-Villarroel a, Jorge Flores-Velázquez b, Waldo Ojeda-Bustamante c, Carlos Díaz-Delgado d, Humberto Salinas-Tapia dShow moreAdd to MendeleyShareCite

aMexican Institute of Water Technology, Mexico
bPostgraduate College, Hydrosciences, Carr. Mex-Tex Km 36.5, Texcoco, Mexico State, 56230, Mexico
cAgricultural Engineering Graduate Program, University of Chapingo, Mexicod
Inter-American Institute of Water Science and Technology, Mexico

https://doi.org/10.1016/j.flowmeasinst.2021.102031Get rights and content

Highlights

  • •Optimizing the geometric design of weirs can improve hydraulic performance.
  • •Labyrinth type weirs allow the discharge capacity to be increased compared to linear weirs.
  • •Hydraulic heads with ratio HT/P > 0.5 generated sub-atmospheric pressures on the side walls of the weir.
  • •Numerical simulation it is a strong tool to analyze and get optimized the weir function.

Abstract

Labyrinth type weirs are structures that, due to their geometry, allow the discharge capacity to be increased compared to linear weirs. They are a favorable option for dam rehabilitation and upstream level control. There are various geometries of labyrinth type weirs such as trapezoidal, triangular or piano key as well as different types of crest profiles. Geometric changes are directly related to hydraulic efficiency. The objective of this work was to analyze the hydraulic performance of a labyrinth type weir, by simulating several geometries of the apex and of the crest using Computational Fluid Dynamics (CFD). For model validation, experimental studies reported in the literature were used. Tests were carried out with trapezoidal and circular apexes and four types of crest profiles: sharp-crest, half-round, quarter-round and Waterways Experiment Station (WES). The results revealed a determination coefficient of R2 = 0.984 between experimental and simulated data with CFD, which provides statistical agreement. Simulations showed that circular-apex weirs are more efficient than those with trapezoidal apex, because they have a higher discharge coefficient (4.7% higher). Of the four types of crest profiles analyzed, the half-round and the WES crest profiles had similar discharge coefficients and were generally greater than those of the sharp-crest and the quarter-round (5.26% y 8.5% higher) profiles. Nevertheless, to facilitate a practical construction process, it is recommended to use a half-round profile. For hydraulic heads with HT/P > 0.5 ratio, all profiles generated sub-atmospheric pressures on the side walls of the weir. However, when HT/P ≈ 0.8 ratio the half-round crest generated a higher negative pressure (−1500 Pa), while the sharp-crest profile managed to increase the pressure by 76% (−350 Pa), but with a greater area of negative pressure. On the other hand, the WES profile reduced the negative-pressure area by 50%.

Keywords

Labyrinth weir

Computational fluids dynamics (CFD)

Discharge coefficient

Apex shape

Crest profile

Figures (12)

  1. Fig. 1. Geometric parameters of a labyrinth weir
  2. Fig. 2. Crest profiles: (A) sharp-crest, (B) half-round, (C) quarter-round, (D) WES
  3. Fig. 3. Apex shapes
  4. Fig. 4. Weir and boundary conditions
  5. Fig. 5. Hydraulic head approach an asymptotic zero-grid spacing value
  6. Fig. 6. Percentage relative error of the discharge coefficient as a function of HT/P
  7. Fig. 7. Comparison of the discharge coefficients obtained numerically against the…
  8. Fig. 8. Pressure distribution in the downstream side walls of the labyrinth weir
  9. Fig. 9. Comparison of the discharge coefficient in trapezoidal apex labyrinth weirs
  10. Fig. 10. Comparison of the discharge coefficient in circular apex labyrinth weirs
  11. Fig. 11. Local drowning at the upstream apex
  12. Fig. 12. Ratio of the discharge coefficient of the circular apex weir with the…
Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

Optimized Vegetation Density to Dissipate Energy of Flood Flow in Open Canals

열린 운하에서 홍수 흐름의 에너지를 분산시키기 위해 최적화된 식생 밀도

Mahdi Feizbahr,1Navid Tonekaboni,2Guang-Jun Jiang,3,4and Hong-Xia Chen3,4
Academic Editor: Mohammad Yazdi

Abstract

강을 따라 식생은 조도를 증가시키고 평균 유속을 감소시키며, 유동 에너지를 감소시키고 강 횡단면의 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받기 때문에 홍수시 유동저항에 큰 영향을 미친다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건과 식물에 따라 달라지므로 모델은 유속, 유속 깊이 및 수로를 따라 식생 유형의 영향을 고려하여 유속을 시뮬레이션해야 합니다. 총 48개의 모델을 시뮬레이션하여 근관의 거칠기 효과를 조사했습니다. 결과는 속도를 높임으로써 베드 속도를 감소시키는 식생의 영향이 무시할만하다는 것을 나타냅니다.

Abstract

Vegetation along the river increases the roughness and reduces the average flow velocity, reduces flow energy, and changes the flow velocity profile in the cross section of the river. Many canals and rivers in nature are covered with vegetation during the floods. Canal’s roughness is strongly affected by plants and therefore it has a great effect on flow resistance during flood. Roughness resistance against the flow due to the plants depends on the flow conditions and plant, so the model should simulate the current velocity by considering the effects of velocity, depth of flow, and type of vegetation along the canal. Total of 48 models have been simulated to investigate the effect of roughness in the canal. The results indicated that, by enhancing the velocity, the effect of vegetation in decreasing the bed velocity is negligible, while when the current has lower speed, the effect of vegetation on decreasing the bed velocity is obviously considerable.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [114]. This can help research for better modeling considering the relation of variables or interaction of them toward reaching a better condition for the objective function in control and engineering [1527]. Consequently, it is necessary to study the effects of the passive factors on the active domain [2836]. Because of the effect of vegetation on reducing the discharge capacity of rivers [37], pruning plants was necessary to improve the condition of rivers. One of the important effects of vegetation in river protection is the action of roots, which cause soil consolidation and soil structure improvement and, by enhancing the shear strength of soil, increase the resistance of canal walls against the erosive force of water. The outer limbs of the plant increase the roughness of the canal walls and reduce the flow velocity and deplete the flow energy in vicinity of the walls. Vegetation by reducing the shear stress of the canal bed reduces flood discharge and sedimentation in the intervals between vegetation and increases the stability of the walls [3841].

One of the main factors influencing the speed, depth, and extent of flood in this method is Manning’s roughness coefficient. On the other hand, soil cover [42], especially vegetation, is one of the most determining factors in Manning’s roughness coefficient. Therefore, it is expected that those seasonal changes in the vegetation of the region will play an important role in the calculated value of Manning’s roughness coefficient and ultimately in predicting the flood wave behavior [4345]. The roughness caused by plants’ resistance to flood current depends on the flow and plant conditions. Flow conditions include depth and velocity of the plant, and plant conditions include plant type, hardness or flexibility, dimensions, density, and shape of the plant [46]. In general, the issue discussed in this research is the optimization of flood-induced flow in canals by considering the effect of vegetation-induced roughness. Therefore, the effect of plants on the roughness coefficient and canal transmission coefficient and in consequence the flow depth should be evaluated [4748].

Current resistance is generally known by its roughness coefficient. The equation that is mainly used in this field is Manning equation. The ratio of shear velocity to average current velocity  is another form of current resistance. The reason for using the  ratio is that it is dimensionless and has a strong theoretical basis. The reason for using Manning roughness coefficient is its pervasiveness. According to Freeman et al. [49], the Manning roughness coefficient for plants was calculated according to the Kouwen and Unny [50] method for incremental resistance. This method involves increasing the roughness for various surface and plant irregularities. Manning’s roughness coefficient has all the factors affecting the resistance of the canal. Therefore, the appropriate way to more accurately estimate this coefficient is to know the factors affecting this coefficient [51].

To calculate the flow rate, velocity, and depth of flow in canals as well as flood and sediment estimation, it is important to evaluate the flow resistance. To determine the flow resistance in open ducts, Manning, Chézy, and Darcy–Weisbach relations are used [52]. In these relations, there are parameters such as Manning’s roughness coefficient (n), Chézy roughness coefficient (C), and Darcy–Weisbach coefficient (f). All three of these coefficients are a kind of flow resistance coefficient that is widely used in the equations governing flow in rivers [53].

The three relations that express the relationship between the average flow velocity (V) and the resistance and geometric and hydraulic coefficients of the canal are as follows:where nf, and c are Manning, Darcy–Weisbach, and Chézy coefficients, respectively. V = average flow velocity, R = hydraulic radius, Sf = slope of energy line, which in uniform flow is equal to the slope of the canal bed,  = gravitational acceleration, and Kn is a coefficient whose value is equal to 1 in the SI system and 1.486 in the English system. The coefficients of resistance in equations (1) to (3) are related as follows:

Based on the boundary layer theory, the flow resistance for rough substrates is determined from the following general relation:where f = Darcy–Weisbach coefficient of friction, y = flow depth, Ks = bed roughness size, and A = constant coefficient.

On the other hand, the relationship between the Darcy–Weisbach coefficient of friction and the shear velocity of the flow is as follows:

By using equation (6), equation (5) is converted as follows:

Investigation on the effect of vegetation arrangement on shear velocity of flow in laboratory conditions showed that, with increasing the shear Reynolds number (), the numerical value of the  ratio also increases; in other words the amount of roughness coefficient increases with a slight difference in the cases without vegetation, checkered arrangement, and cross arrangement, respectively [54].

Roughness in river vegetation is simulated in mathematical models with a variable floor slope flume by different densities and discharges. The vegetation considered submerged in the bed of the flume. Results showed that, with increasing vegetation density, canal roughness and flow shear speed increase and with increasing flow rate and depth, Manning’s roughness coefficient decreases. Factors affecting the roughness caused by vegetation include the effect of plant density and arrangement on flow resistance, the effect of flow velocity on flow resistance, and the effect of depth [4555].

One of the works that has been done on the effect of vegetation on the roughness coefficient is Darby [56] study, which investigates a flood wave model that considers all the effects of vegetation on the roughness coefficient. There are currently two methods for estimating vegetation roughness. One method is to add the thrust force effect to Manning’s equation [475758] and the other method is to increase the canal bed roughness (Manning-Strickler coefficient) [455961]. These two methods provide acceptable results in models designed to simulate floodplain flow. Wang et al. [62] simulate the floodplain with submerged vegetation using these two methods and to increase the accuracy of the results, they suggested using the effective height of the plant under running water instead of using the actual height of the plant. Freeman et al. [49] provided equations for determining the coefficient of vegetation roughness under different conditions. Lee et al. [63] proposed a method for calculating the Manning coefficient using the flow velocity ratio at different depths. Much research has been done on the Manning roughness coefficient in rivers, and researchers [496366] sought to obtain a specific number for n to use in river engineering. However, since the depth and geometric conditions of rivers are completely variable in different places, the values of Manning roughness coefficient have changed subsequently, and it has not been possible to choose a fixed number. In river engineering software, the Manning roughness coefficient is determined only for specific and constant conditions or normal flow. Lee et al. [63] stated that seasonal conditions, density, and type of vegetation should also be considered. Hydraulic roughness and Manning roughness coefficient n of the plant were obtained by estimating the total Manning roughness coefficient from the matching of the measured water surface curve and water surface height. The following equation is used for the flow surface curve:where  is the depth of water change, S0 is the slope of the canal floor, Sf is the slope of the energy line, and Fr is the Froude number which is obtained from the following equation:where D is the characteristic length of the canal. Flood flow velocity is one of the important parameters of flood waves, which is very important in calculating the water level profile and energy consumption. In the cases where there are many limitations for researchers due to the wide range of experimental dimensions and the variety of design parameters, the use of numerical methods that are able to estimate the rest of the unknown results with acceptable accuracy is economically justified.

FLOW-3D software uses Finite Difference Method (FDM) for numerical solution of two-dimensional and three-dimensional flow. This software is dedicated to computational fluid dynamics (CFD) and is provided by Flow Science [67]. The flow is divided into networks with tubular cells. For each cell there are values of dependent variables and all variables are calculated in the center of the cell, except for the velocity, which is calculated at the center of the cell. In this software, two numerical techniques have been used for geometric simulation, FAVOR™ (Fractional-Area-Volume-Obstacle-Representation) and the VOF (Volume-of-Fluid) method. The equations used at this model for this research include the principle of mass survival and the magnitude of motion as follows. The fluid motion equations in three dimensions, including the Navier–Stokes equations with some additional terms, are as follows:where  are mass accelerations in the directions xyz and  are viscosity accelerations in the directions xyz and are obtained from the following equations:

Shear stresses  in equation (11) are obtained from the following equations:

The standard model is used for high Reynolds currents, but in this model, RNG theory allows the analytical differential formula to be used for the effective viscosity that occurs at low Reynolds numbers. Therefore, the RNG model can be used for low and high Reynolds currents.

Weather changes are high and this affects many factors continuously. The presence of vegetation in any area reduces the velocity of surface flows and prevents soil erosion, so vegetation will have a significant impact on reducing destructive floods. One of the methods of erosion protection in floodplain watersheds is the use of biological methods. The presence of vegetation in watersheds reduces the flow rate during floods and prevents soil erosion. The external organs of plants increase the roughness and decrease the velocity of water flow and thus reduce its shear stress energy. One of the important factors with which the hydraulic resistance of plants is expressed is the roughness coefficient. Measuring the roughness coefficient of plants and investigating their effect on reducing velocity and shear stress of flow is of special importance.

Roughness coefficients in canals are affected by two main factors, namely, flow conditions and vegetation characteristics [68]. So far, much research has been done on the effect of the roughness factor created by vegetation, but the issue of plant density has received less attention. For this purpose, this study was conducted to investigate the effect of vegetation density on flow velocity changes.

In a study conducted using a software model on three density modes in the submerged state effect on flow velocity changes in 48 different modes was investigated (Table 1).

Table 1 

The studied models.

The number of cells used in this simulation is equal to 1955888 cells. The boundary conditions were introduced to the model as a constant speed and depth (Figure 1). At the output boundary, due to the presence of supercritical current, no parameter for the current is considered. Absolute roughness for floors and walls was introduced to the model (Figure 1). In this case, the flow was assumed to be nonviscous and air entry into the flow was not considered. After  seconds, this model reached a convergence accuracy of .

Figure 1 

The simulated model and its boundary conditions.

Due to the fact that it is not possible to model the vegetation in FLOW-3D software, in this research, the vegetation of small soft plants was studied so that Manning’s coefficients can be entered into the canal bed in the form of roughness coefficients obtained from the studies of Chow [69] in similar conditions. In practice, in such modeling, the effect of plant height is eliminated due to the small height of herbaceous plants, and modeling can provide relatively acceptable results in these conditions.

48 models with input velocities proportional to the height of the regular semihexagonal canal were considered to create supercritical conditions. Manning coefficients were applied based on Chow [69] studies in order to control the canal bed. Speed profiles were drawn and discussed.

Any control and simulation system has some inputs that we should determine to test any technology [7077]. Determination and true implementation of such parameters is one of the key steps of any simulation [237881] and computing procedure [8286]. The input current is created by applying the flow rate through the VFR (Volume Flow Rate) option and the output flow is considered Output and for other borders the Symmetry option is considered.

Simulation of the models and checking their action and responses and observing how a process behaves is one of the accepted methods in engineering and science [8788]. For verification of FLOW-3D software, the results of computer simulations are compared with laboratory measurements and according to the values of computational error, convergence error, and the time required for convergence, the most appropriate option for real-time simulation is selected (Figures 2 and 3 ).

Figure 2 

Modeling the plant with cylindrical tubes at the bottom of the canal.

Figure 3 

Velocity profiles in positions 2 and 5.

The canal is 7 meters long, 0.5 meters wide, and 0.8 meters deep. This test was used to validate the application of the software to predict the flow rate parameters. In this experiment, instead of using the plant, cylindrical pipes were used in the bottom of the canal.

The conditions of this modeling are similar to the laboratory conditions and the boundary conditions used in the laboratory were used for numerical modeling. The critical flow enters the simulation model from the upstream boundary, so in the upstream boundary conditions, critical velocity and depth are considered. The flow at the downstream boundary is supercritical, so no parameters are applied to the downstream boundary.

The software well predicts the process of changing the speed profile in the open canal along with the considered obstacles. The error in the calculated speed values can be due to the complexity of the flow and the interaction of the turbulence caused by the roughness of the floor with the turbulence caused by the three-dimensional cycles in the hydraulic jump. As a result, the software is able to predict the speed distribution in open canals.

2. Modeling Results

After analyzing the models, the results were shown in graphs (Figures 414 ). The total number of experiments in this study was 48 due to the limitations of modeling.


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Figure 4 

Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5 

Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6 

Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7 

Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8 

Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.


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Figure 9 

Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10 

Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11 

Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12 

Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13 

Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.


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Figure 14 

Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

To investigate the effects of roughness with flow velocity, the trend of flow velocity changes at different depths and with supercritical flow to a Froude number proportional to the depth of the section has been obtained.

According to the velocity profiles of Figure 5, it can be seen that, with the increasing of Manning’s coefficient, the canal bed speed decreases.

According to Figures 5 to 8, it can be found that, with increasing the Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the models 1 to 12, which can be justified by increasing the speed and of course increasing the Froude number.

According to Figure 10, we see that, with increasing Manning’s coefficient, the canal bed speed decreases.

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 510, which can be justified by increasing the speed and, of course, increasing the Froude number.

With increasing Manning’s coefficient, the canal bed speed decreases (Figure 12). But this deceleration is more noticeable than the deceleration of the higher models (Figures 58 and 1011), which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 13, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 5 to 12, which can be justified by increasing the speed and, of course, increasing the Froude number.

According to Figure 15, with increasing Manning’s coefficient, the canal bed speed decreases.

Figure 15 

Canal diagram with a depth of 3 meters and a flow rate of 5 meters per second.

According to Figure 16, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher model, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 16 

Canal diagram with a depth of 3 meters and a flow rate of 5.1 meters per second.

According to Figure 17, it is clear that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 17 

Canal diagram with a depth of 3 meters and a flow rate of 5.2 meters per second.

According to Figure 18, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of the higher models, which can be justified by increasing the speed and, of course, increasing the Froude number.

Figure 18 

Canal diagram with a depth of 3 meters and a flow rate of 5.3 meters per second.

According to Figure 19, it can be seen that the vegetation placed in front of the flow input velocity has negligible effect on the reduction of velocity, which of course can be justified due to the flexibility of the vegetation. The only unusual thing is the unexpected decrease in floor speed of 3 m/s compared to higher speeds.


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Figure 19 

Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.


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Figure 20 

Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].


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Figure 21 

Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

The effects of vegetation on the flood canal were investigated by numerical modeling with FLOW-3D software. After analyzing the results, the following conclusions were reached:(i)Increasing the density of vegetation reduces the velocity of the canal floor but has no effect on the velocity of the canal surface.(ii)Increasing the Froude number is directly related to increasing the speed of the canal floor.(iii)In the canal with a depth of one meter, a sudden increase in speed can be observed from the lowest speed and higher speed, which is justified by the sudden increase in Froude number.(iv)As the inlet flow rate increases, the slope of the profiles from the bed to the water surface increases.(v)By reducing the Froude number, the effect of vegetation on reducing the flow bed rate becomes more noticeable. And the input velocity in reducing the velocity of the canal floor does not have much effect.(vi)At a flow rate between 3 and 3.3 meters per second due to the shallow depth of the canal and the higher landing number a more critical area is observed in which the flow bed velocity in this area is between 2.86 and 3.1 m/s.(vii)Due to the critical flow velocity and the slight effect of the roughness of the horseshoe vortex floor, it is not visible and is only partially observed in models 1-2-3 and 21.(viii)As the flow rate increases, the effect of vegetation on the rate of bed reduction decreases.(ix)In conditions where less current intensity is passing, vegetation has a greater effect on reducing current intensity and energy consumption increases.(x)In the case of using the flow rate of 0.8 cubic meters per second, the velocity distribution and flow regime show about 20% more energy consumption than in the case of using the flow rate of 1.3 cubic meters per second.

Nomenclature

n:Manning’s roughness coefficient
C:Chézy roughness coefficient
f:Darcy–Weisbach coefficient
V:Flow velocity
R:Hydraulic radius
g:Gravitational acceleration
y:Flow depth
Ks:Bed roughness
A:Constant coefficient
:Reynolds number
y/∂x:Depth of water change
S0:Slope of the canal floor
Sf:Slope of energy line
Fr:Froude number
D:Characteristic length of the canal
G:Mass acceleration
:Shear stresses.

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

This work was partially supported by the National Natural Science Foundation of China under Contract no. 71761030 and Natural Science Foundation of Inner Mongolia under Contract no. 2019LH07003.

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Numerical simulation on molten pool behavior of narrow gap gas tungsten arc welding

좁은 간격 가스 텅스텐 아크 용접의 용융 풀 거동에 대한 수치 시뮬레이션

Numerical simulation on molten pool behavior of narrow gap gas tungsten arc welding

The International Journal of Advanced Manufacturing Technology (2023)Cite this article

Abstract

As a highly efficient thick plate welding resolution, narrow gap gas tungsten arc welding (NG-GTAW) is in the face of a series of problems like inter-layer defects like pores, lack of fusion, inclusion of impurity, and the sensitivity to poor sidewall fusion, which is hard to be repaired after the welding process. This study employs numerical simulation to investigate the molten pool behavior in NG-GTAW root welding. A 3D numerical model was established, where a body-fitted coordinate system was applied to simulate the electromagnetic force, and a bridge transition model was developed to investigate the wire–feed root welding. The simulated results were validated experimentally. Results show that the molten pool behavior is dominated by electromagnetic force when the welding current is relatively high, and the dynamic change of the vortex actually determines the molten pool morphology. For self-fusion welding, there are two symmetric inward vortices in the cross-section and one clockwise vortex in the longitudinal section. With the increasing welding current, the vortices in the cross-section gradually move to the arc center with a decreasing range, while the vortex in the longitudinal section moves backward. With the increasing traveling speed, the vortices in the cross-section move toward the surface of the molten pool with a decreasing range, and the horizontal component of liquid metal velocity changes in the longitudinal section. For wire–feed welding, the filling metal strengthens the downward velocity component; as a result, the vortex formation is blocked in the cross-section and is strengthened in the longitudinal section.

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Data availability

The raw/processed data required cannot be shared at this time as the data also forms part of an ongoing study.

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Strain rate magnitude at the free surface, illustrating Kelvin-Helmoltz (KH) shear instabilities.

On the reef scale hydrodynamics at Sodwana Bay, South Africa

Environmental Fluid Mechanics (2022)Cite this article

Abstract

The hydrodynamics of coral reefs strongly influences their biological functioning, impacting processes such as nutrient availability and uptake, recruitment success and bleaching. For example, coral reefs located in oligotrophic regions depend on upwelling for nutrient supply. Coral reefs at Sodwana Bay, located on the east coast of South Africa, are an example of high latitude marginal reefs. These reefs are subjected to complex hydrodynamic forcings due to the interaction between the strong Agulhas current and the highly variable topography of the region. In this study, we explore the reef scale hydrodynamics resulting from the bathymetry for two steady current scenarios at Two-Mile Reef (TMR) using a combination of field data and numerical simulations. The influence of tides or waves was not considered for this study as well as reef-scale roughness. Tilt current meters with onboard temperature sensors were deployed at selected locations within TMR. We used field observations to identify the dominant flow conditions on the reef for numerical simulations that focused on the hydrodynamics driven by mean currents. During the field campaign, southerly currents were the predominant flow feature with occasional flow reversals to the north. Northerly currents were associated with greater variability towards the southern end of TMR. Numerical simulations showed that Jesser Point was central to the development of flow features for both the northerly and southerly current scenarios. High current variability in the south of TMR during reverse currents is related to the formation of Kelvin-Helmholtz type shear instabilities along the outer edge of an eddy formed north of Jesser Point. Furthermore, downward vertical velocities were computed along the offshore shelf at TMR during southerly currents. Current reversals caused a change in vertical velocities to an upward direction due to the orientation of the bathymetry relative to flow directions.

Highlights

  • A predominant southerly current was measured at Two-Mile Reef with occasional reversals towards the north.
  • Field observations indicated that northerly currents are spatially varied along Two-Mile Reef.
  • Simulation of reverse currents show the formation of a separated flow due to interaction with Jesser Point with Kelvin–Helmholtz type shear instabilities along the seaward edge.

지금까지 Sodwana Bay에서 자세한 암초 규모 유체 역학을 모델링하려는 시도는 없었습니다. 이러한 모델의 결과는 규모가 있는 산호초 사이의 흐름이 산호초 건강에 어떤 영향을 미치는지 탐색하는 데 사용할 수 있습니다. 이 연구에서는 Sodwana Bay의 유체역학을 탐색하는 데 사용할 수 있는 LES 모델을 개발하기 위한 단계별 접근 방식을 구현합니다. 여기서 우리는 이 초기 단계에서 파도와 조수의 영향을 배제하면서 Agulhas 해류의 유체역학에 초점을 맞춥니다. 이 접근법은 흐름의 첫 번째 LES를 제시하고 Sodwana Bay의 산호초에서 혼합함으로써 향후 연구의 기초를 제공합니다.

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Text and image taken from Deoraj, et al. (2022), On the reef scale hydrodynamics at Sodwana Bay, South Africa. Preprint courtesy the authors.

Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)

Three-dimensional Numerical Evaluation of Hydraulic Efficiency and Discharge Coefficient in Grate Inlets

쇠창살 격자 유입구의 수리효율 및 배출계수에 대한 3차원 수치적 평가

Melquisedec Cortés Zambrano*, Helmer Edgardo Monroy González,
Wilson Enrique Amaya Tequia
Faculty of Civil Engineering, Santo Tomas Tunja University. Address Av. Universitaria No. 45-202.
Tunja – Boyacá – Colombia

Abstract

홍수는 지반이동 및 이동의 원인 중 하나이며, 급속한 도시화 및 도시화로 인해 이전보다 빈번하게 발생할 수 있다. 도시 배수 시스템의 특성은 집수 요소가 결정적인 역할을 하는 범람의 발생 및 범위를 정의할 수 있습니다. 이 문서는 7가지 유형의 화격자 유입구의 수력 유입 효율 및 배출 계수에 대한 수치 조사를 제시합니다. FLOW-3D® 시뮬레이터는 Q = 24, 34.1, 44, 100, 200 및 300 L/s의 유속에서 풀 스케일로 격자를 테스트하는 데 사용되며 종방향 기울기가 1.0인 실험 프로토타입의 구성을 유지합니다. %, 1.5% 및 2.0% 및 고정 횡단 경사, 총 126개 모델. 그 결과를 바탕으로 종류별 및 종단경사 조건에 따른 수력유입구 효율곡선과 토출계수를 구성하였다. 결과는 다른 조사에서 제안된 경험적 공식으로 조정되어 프로토타입의 물리적 테스트 결과를 검증하는 역할을 합니다.

Floods are one of the causes of ground movement and displacement, and due to rapid urbanization and urban growth may occur more frequently than before. The characteristics of an urban drainage system can define the occurrence and extent of flooding, where catchment elements have a determining role. This document presents the numerical investigation of the hydraulic inlet efficiency and the discharge coefficient of seven types of grate inlets. The FLOW-3D® simulator is used to test the gratings at a full scale, under flow rates of Q = 24, 34.1, 44, 100, 200 and 300 L/s, preserving the configuration of the experimental prototype with longitudinal slopes of 1.0%, 1.5% and 2.0% and a fixed cross slope, for a total of 126 models. Based on the results, hydraulic inlet efficiency curves and discharge coefficients are constructed for each type and a longitudinal slope condition. The results are adjusted with empirical formulations proposed in other investigations, serving to verify the results of physical testing of prototypes.

Keywords

grate inlet, inlet efficiency, discharge coefficient, computational fluid dynamic, 3D modelling.

Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 1. Physical model of the experimental campaign (source: Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade
and Abaunza Tabares, 2021)
Fig. 2. Design of the grate inlet types studied: (a) R1, (b) R2, (c) R3, (d) R4, (e) R5, (f) R6, (g) R7 (source: based on geometries of Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source:
made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 4. Comparison between the results obtained during physical experimentation in prototype 7 and simulation results with FLOW-3D® (source: made with FlowSight® and photographic record by Chaparro Andrade and Abaunza Tabares, 2021)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface
configuration and flow regime, of some grating types (source: produced with FlowSight®)
Fig. 6. Example of the results of flow depth and velocity vectors in the xy plane, for a stable flow condition in a grate inlet type and free surface configuration and flow regime, of some grating types (source: produced with FlowSight®)

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Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system

데이터 기반 방법을 활용한 재생 가능 에너지 변환기의 전력 및 수소 생성 예측 지속 가능한 스마트 그리드 사례 연구

Fatemehsadat Mirshafiee1, Emad Shahbazi 2, Mohadeseh Safi 3, Rituraj Rituraj 4,*
1Department of Electrical and Computer Engineering, K.N. Toosi University of Technology, Tehran 1999143344 , Iran
2Department of Mechatronic, Amirkabir University of Technology, Tehran 158754413, Iran
3Department of Mechatronic, Electrical and Computer Engineering, University of Tehran, Tehran 1416634793, Iran
4 Faculty of Informatics, Obuda University, 1023, Budapest, Hungary

  • Correspondence: rituraj88@stud.uni-obuda.hu

ABSTRACT

본 연구는 지속가능한 에너지 변환기의 전력 및 수소 발생 모델링을 위한 데이터 기반 방법론을 제안합니다. 파고와 풍속을 달리하여 파고와 수소생산을 예측합니다.

또한 이 연구는 파도에서 수소를 추출할 수 있는 가능성을 강조하고 장려합니다. FLOW-3D 소프트웨어 시뮬레이션에서 추출한 데이터와 해양 특수 테스트의 실험 데이터를 사용하여 두 가지 데이터 기반 학습 방법의 비교 분석을 수행합니다.

결과는 수소 생산의 양은 생성된 전력의 양에 비례한다는 것을 보여줍니다. 제안된 재생 에너지 변환기의 신뢰성은 지속 가능한 스마트 그리드 애플리케이션으로 추가로 논의됩니다.

This study proposes a data-driven methodology for modeling power and hydrogen generation of a sustainable energy converter. The wave and hydrogen production at different wave heights and wind speeds are predicted. Furthermore, this research emphasizes and encourages the possibility of extracting hydrogen from ocean waves. By using the extracted data from FLOW-3D software simulation and the experimental data from the special test in the ocean, the comparison analysis of two data-driven learning methods is conducted. The results show that the amount of hydrogen production is proportional to the amount of generated electrical power. The reliability of the proposed renewable energy converter is further discussed as a sustainable smart grid application.

Key words

Cavity, Combustion efficiency, hydrogen fuel, Computational Fluent and Gambit.

Figure 1. The process of power and hydrogen production with Searaser.
Figure 1. The process of power and hydrogen production with Searaser.
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 2. The cross-section A-A of the two essential parts of a Searaser
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 3. Different parts of a Searaser; 1) Buoy 2) Chamber 3) Valves 4) Generator 5) Anchor system
Figure 4. The boundary conditions of the control volume
Figure 4. The boundary conditions of the control volume
Figure 5. The wind velocity during the period of the experimental test
Figure 5. The wind velocity during the period of the experimental test

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Experiments and analysis of dynamic characteristics of liquid sloshing in horizontal Cassini tank

수평 Cassini 탱크에서 액체 슬로싱의 동적 특성에 대한 실험 및 분석

Experiments and analysis of dynamic characteristics of liquid sloshing in horizontal Cassini tank

Houlin Luo1, Wenjun Wu2, Bingchao Jiang3, Shouyi Guo3, Libing Huang3 and Baozeng Yue4

Accepted Manuscript online 23 May 2023 • © 2023 IOP Publishing Ltd

What is an Accepted Manuscript?DOI 10.1088/1402-4896/acd81a

Abstract

In this study, the sloshing behaviors and dynamic characteristics of liquid sloshing in a horizontal Cassini tank were studied. The forces and torques generated by the liquid sloshing in non-equilibrium states were experimentally measured with force transducers which have been mounted on the experiment platform. In small-amplitude rotational and translational nonlinear sloshing cases, the CFD simulations were in good agreement with the experimental data. However, as the dynamic ratio of longitudinal and transversal sloshing force became large, errors occurred and became obvious in CFD simulations. Further experiments on the sloshing forces and torques in the rotating sloshing state were performed.The effects of the magnitude and frequency of the external excitations and the tank-filling ratio son the sloshing characteristics were also studied. The experiments results show that the liquid sloshing in the Cassini tank is highly correlated with the excitation frequency where small variation in the frequency leads to complex changes in the liquid sloshing characteristics. In the cases with low liquid-filling ratio, in resonance state, the rotational sloshing is easier to be excited, however, in the stable-state the amplitudes of longitudinal sloshing force and torque are more significant than those of other sloshing conditions. The transversal sloshing force and torque are very small in both, rotational and translational nonlinear sloshing of small amplitude.

본 연구에서는 수평 카시니 수조에서 액체 슬로싱의 슬로싱 거동과 동적 특성을 연구하였다. 비평형 상태에서 액체 슬로싱에 의해 생성된 힘과 토크는 실험 플랫폼에 장착된 힘 변환기로 실험적으로 측정 되었습니다.

진폭이 작은 회전 및 병진 비선형 슬로싱 사례에서 CFD 시뮬레이션은 실험 데이터와 잘 일치했습니다. 그러나 종방향 슬로싱력과 횡방향 슬로싱력의 동적 비율이 커짐에 따라 오류가 발생하고 CFD 시뮬레이션에서 명백해졌습니다.

회전 슬로싱 상태에서 슬로싱 힘과 토크에 대한 추가 실험이 수행되었습니다. 외부 가진의 크기와 빈도 및 슬로싱 특성에 따른 탱크 충전 비율의 영향도 연구되었습니다.

실험 결과는 카시니 탱크의 액체 슬로싱이 여기 주파수와 높은 상관 관계가 있음을 보여줍니다. 여기 주파수의 작은 변화가 액체 슬로싱 특성의 복잡한 변화로 이어집니다. 액체 충전율이 낮은 경우에는 공진 상태에서 회전 슬로싱이 들기 쉽지만 안정 상태에서는 종방향 슬로싱 힘과 토크의 진폭이 다른 슬로싱 조건보다 더 중요합니다.

횡방향 슬로싱 힘과 토크는 작은 진폭의 회전 및 병진 비선형 슬로싱 모두에서 매우 작습니다.

Figure 1 | Laboratory channel dimensions.

강화된 조도 계수 및 인버트 레벨 변화가 있는 90도 측면 턴아웃에서의 유동에 대한 실험적 및 수치적 연구

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes

Maryam Bagheria, Seyed M. Ali Zomorodianb, Masih Zolghadrc, H. Md. Azamathulla d,*
and C. Venkata Siva Rama Prasade
a Hydraulic Structures, Department of Water Engineering, Shiraz University, Shiraz, Iran
b Department of Water Engineering, College of Agriculture, Shiraz University, Shiraz, Iran
c Department of Water Sciences Engineering, College of Agriculture, Jahrom University, Jahrom, Iran
d Civil & Environmental Engineering, The University of the West Indies, St. Augustine Campus, Port of Spain, Trinidad
e Department of Civil Engineering, St. Peters Engineering College, Hyderabad, India
*Corresponding author. E-mail: azmatheditor@gmail.com

ABSTRACT

측면 분기기(흡입구)의 상류측에서 유동 분리는 분기기 입구에서 맴돌이 전류를 일으키는 중요한 문제입니다. 이는 흐름의 유효 폭, 분기 용량 및 효율성을 감소시킵니다. 따라서 분리구역의 크기를 파악하고 그 크기를 줄이기 위한 방안을 제시하는 것이 필수적이다.

본 연구에서는 분리 구역의 크기를 줄이기 위한 방법으로 분출구 입구에 7가지 유형의 조면화 요소와 4가지 다른 방류가 있는 3가지 다른 베드 인버트 레벨의 설치(총 84회 실험)를 조사했습니다. 또한 3D 전산 유체 역학(CFD) 모델을 사용하여 분리 구역의 흐름 패턴과 치수를 평가했습니다.

결과는 조도 계수를 향상시키면 분리 영역 치수를 최대 38%까지 줄일 수 있는 반면 드롭 구현 효과는 사용된 조도 계수에 따라 이 영역을 다르게 축소할 수 있음을 보여주었습니다. 두 방법을 결합하면 분리 구역 치수를 최대 63%까지 줄일 수 있습니다.

Flow separation at the upstream side of lateral turnouts (intakes) is a critical issue causing eddy currents at the turnout entrance. It reduces the effective width of flow, turnout capacity and efficiency. Therefore, it is essential to identify the dimensions of the separation zone and propose remedies to reduce its dimensions.

Installation of 7 types of roughening elements at the turnout entrance and 3 different bed invert levels, with 4 different discharges (making a total of 84 experiments) were examined in this study as a method to reduce the dimensions of the separation zone. Additionally, a 3-D Computational Fluid Dynamic (CFD) model was utilized to evaluate the flow pattern and dimensions of the separation zone.

Results showed that enhancing the roughness coefficient can reduce the separation zone dimensions up to 38% while the drop implementation effect can scale down this area differently based on the roughness coefficient used. Combining both methods can reduce the separation zone dimensions up to 63%.

Key words

discharge ratio, flow separation zone, intake, three dimensional simulation

Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced
roughness coefficient and invert level changes
Experimental and numerical study of flow at a 90 degree lateral turnout with enhanced roughness coefficient and invert level changes
Figure 1 | Laboratory channel dimensions.
Figure 1 | Laboratory channel dimensions.
Figure 2 | Roughness plates.
Figure 2 | Roughness plates.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 4 | Effect of roughness on separation zone dimensions.
Figure 10 | Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).
Figure 10 | Comparision of the vortex area (software output) for three roughnesses (0.009, 0.023 and 0.032).
Figure 11 | Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.
Figure 11 | Comparison of vortex area in 3D mode (tecplot output) with two roughnesses (a) 0.009 and (b) 0.032.
Figure 12 | Velocity vector for flow condition Q¼22 l/s, near surface.
Figure 12 | Velocity vector for flow condition Q¼22 l/s, near surface.

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Figure 5. Schematic view of flap and support structure [32]

Design Optimization of Ocean Renewable Energy Converter Using a Combined Bi-level Metaheuristic Approach

결합된 Bi-level 메타휴리스틱 접근법을 사용한 해양 재생 에너지 변환기의 설계 최적화

Erfan Amini a1, Mahdieh Nasiri b1, Navid Salami Pargoo a, Zahra Mozhgani c, Danial Golbaz d, Mehrdad Baniesmaeil e, Meysam Majidi Nezhad f, Mehdi Neshat gj, Davide Astiaso Garcia h, Georgios Sylaios i

Abstract

In recent years, there has been an increasing interest in renewable energies in view of the fact that fossil fuels are the leading cause of catastrophic environmental consequences. Ocean wave energy is a renewable energy source that is particularly prevalent in coastal areas. Since many countries have tremendous potential to extract this type of energy, a number of researchers have sought to determine certain effective factors on wave converters’ performance, with a primary emphasis on ambient factors. In this study, we used metaheuristic optimization methods to investigate the effects of geometric factors on the performance of an Oscillating Surge Wave Energy Converter (OSWEC), in addition to the effects of hydrodynamic parameters. To do so, we used CATIA software to model different geometries which were then inserted into a numerical model developed in Flow3D software. A Ribed-surface design of the converter’s flap is also introduced in this study to maximize wave-converter interaction. Besides, a Bi-level Hill Climbing Multi-Verse Optimization (HCMVO) method was also developed for this application. The results showed that the converter performs better with greater wave heights, flap freeboard heights, and shorter wave periods. Additionally, the added ribs led to more wave-converter interaction and better performance, while the distance between the flap and flume bed negatively impacted the performance. Finally, tracking the changes in the five-dimensional objective function revealed the optimum value for each parameter in all scenarios. This is achieved by the newly developed optimization algorithm, which is much faster than other existing cutting-edge metaheuristic approaches.

Keywords

Wave Energy Converter

OSWEC

Hydrodynamic Effects

Geometric Design

Metaheuristic Optimization

Multi-Verse Optimizer

1Introduction

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.

2.1Model 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.

2.2Verification

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.

3Sensitivity 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.

4Design 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

Figure 1: Drawing of the experimental set-up, Figure 2: Experimental tank with locations of temperature sensors

실험 및 수치 시뮬레이션에 기반한 극저온 추진제 탱크 가압 분석

Analyses of Cryogenic Propellant Tank Pressurization based upon Experiments and Numerical Simulations
Carina Ludwig? and Michael Dreyer**
*DLR – German Aerospace Center, Space Launcher Systems Analysis (SART),
Institute of Space Systems, 28359 Bremen, Germany, Carina.Ludwig@dlr.de
**ZARM – Center for Applied Space Technology and Microgravity,
University of Bremen, 28359 Bremen, Germany

Abstract

본 연구에서는 발사대 적용을 위한 극저온 추진제 탱크의 능동 가압을 분석하였다. 따라서 지상 실험, 수치 시뮬레이션 및 분석 연구를 수행하여 다음과 같은 중요한 결과를 얻었습니다.

필요한 가압 기체 질량을 최소화하기 위해 더 높은 가압 기체 온도가 유리하거나 헬륨을 가압 기체로 적용하는 것이 좋습니다.

Flow-3D를 사용한 가압 가스 질량의 수치 시뮬레이션은 실험 결과와 잘 일치함을 보여줍니다. 가압 중 지배적인 열 전달은 주입된 가압 가스에서 축방향 탱크 벽으로 나타나고 능동 가압 단계 동안 상 변화의 주된 방식은 가압 가스의 유형에 따라 다릅니다.

가압 단계가 끝나면 상당한 압력 강하가 발생합니다. 이 압력 강하의 분석적 결정을 위해 이론적 모델이 제공됩니다.

The active-pressurization of cryogenic propellant tanks for the launcher application was analyzed in this study. Therefore, ground experiments, numerical simulations and analytical studies were performed with the following important results: In order to minimize the required pressurant gas mass, a higher pressurant gas temperature is advantageous or the application of helium as pressurant gas. Numerical simulations of the pressurant gas mass using Flow-3D show good agreement to the experimental results. The dominating heat transfer during pressurization appears from the injected pressurant gas to the axial tank walls and the predominant way of phase change during the active-pressurization phase depends on the type of the pressurant gas. After the end of the pressurization phase, a significant pressure drop occurs. A theoretical model is presented for the analytical determination of this pressure drop.

Figure 1: Drawing of the experimental set-up, Figure 2: Experimental tank with locations of temperature sensors
Figure 1: Drawing of the experimental set-up, Figure 2: Experimental tank with locations of temperature sensors
Figure 3: Non-dimensional (a) tank pressure, (b) liquid temperatures, (c) vapor temperatures, (d) wall and lid temperatures during pressurization and relaxation of the N300h experiment (for details see Table 2). T14 is the pressurant
gas temperature at the diffuser. Pressurization starts at tp,0 (t
∗ = 0.06·10−4
) and ends at tp, f (t
∗ = 0.84·10−4
). Relaxation
takes place until tp,T (t
∗ = 2.79·10−4
) and ∆p is the characteristic pressure drop
Figure 3: Non-dimensional (a) tank pressure, (b) liquid temperatures, (c) vapor temperatures, (d) wall and lid temperatures during pressurization and relaxation of the N300h experiment (for details see Table 2). T14 is the pressurant gas temperature at the diffuser. Pressurization starts at tp,0 (t ∗ = 0.06·10−4 ) and ends at tp, f (t ∗ = 0.84·10−4 ). Relaxation takes place until tp,T (t ∗ = 2.79·10−4 ) and ∆p is the characteristic pressure drop
Figure 5: Nondimensional vapor mass at pressurization start (m
∗
v,0
), pressurant gas mass (m
∗
pg), condensed vapor mass
from pressurization start to pressurization end (m
∗
cond,0,f
) and condensed vapor mass from pressurization end to relaxation end (m
∗
cond, f,T
) for all GN2 (a) and the GHe (b) pressurized experiments with the relating errors.
Figure 5: Nondimensional vapor mass at pressurization start (m ∗ v,0 ), pressurant gas mass (m ∗ pg), condensed vapor mass from pressurization start to pressurization end (m ∗ cond,0,f ) and condensed vapor mass from pressurization end to relaxation end (m ∗ cond, f,T ) for all GN2 (a) and the GHe (b) pressurized experiments with the relating errors.
Figure 6: Schematical propellant tank with vapor and liquid phase, pressurant gas and condensation mass flow as well as the applied control volumes. ., Figure 7: N300h experiment: wall to fluid heat flux at pressurization end (tp, f) over the tank height.
Figure 6: Schematical propellant tank with vapor and liquid phase, pressurant gas and condensation mass flow as well as the applied control volumes. ., Figure 7: N300h experiment: wall to fluid heat flux at pressurization end (tp, f) over the tank height.

References

[1] M.E. Nein and R.R. Head. Experiences with pressurized discharge of liquid oxygen from large flight vehicle
propellant tanks. In Advances in Cryogenig Engineering, vol. 7, New York, Plenum Press, 244–250.
[2] M.E. Nein and J.F. Thompson. Experimental and analytical studies of cryogenic propellant tank pressurant
requirements: NASA TN D-3177, 1966.
[3] R.J. Stochl, J.E. Maloy, P.A. Masters and R.L. DeWitt. Gaseous-helium requirements for the discharge of liquid
hydrogen from a 1.52-meter- (5-ft-) diameter spherical tank: NASA TN D-5621, 1970.
[4] R.J. Stochl, J.E. Maloy, P.A. Masters and R.L. DeWitt. Gaseous-helium requirements for the discharge of liquid
hydrogen from a 3.96-meter- (13-ft-) diameter spherical tank: NASA TN D-7019, 1970.
[5] R.J. Stochl, P.A. Masters, R.L. DeWitt and J.E. Maloy. Gaseous-hydrogen requirements for the discharge of
liquid hydrogen from a 1.52-meter- (5-ft-) diameter spherical tank: NASA TN D-5336, 1969.
[6] R.J. Stochl, P.A. Masters, R.L. DeWitt and J.E. Maloy. Gaseous-hydrogen requirements for the discharge of
liquid hydrogen from a 3.96-meter- (13-ft-) diameter spherical tank: NASA TN D-5387, 1969.
[7] R.F. Lacovic. Comparison of experimental and calculated helium requirements for pressurization of a Centaur
liquid oxygen tank: NASA TM X-2013, 1970.
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1966, 1993.
[9] T.L. Hardy and T.M. Tomsik. Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank
experimental simulation using Flow-3D: Nasa technical memorandum 103217, 1990.
[10] G.P. Samsal, J.I. Hochstein, M.C. Wendl and T.L. Hardy. Computational modeling of the pressurization process
in a NASP vehicle propellant tank experimental simulation: AIAA 91-2407. AIAA Joint Propulsion Conference
and Exhibit, 1991.
[11] P. Adnani and R.W. Jennings. Pressurization analysis of cryogenic propulsion systems: AIAA 2000-3788. In
36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Huntsville, Alabama, USA, 2000.
[12] C. Ludwig and M. Dreyer. Analyses of cryogenic propellant tank pressurization based upon ground experiments:
AIAA 2012-5199. In AIAA Space 2012 Conference & Exhibit, Pasadena, California, USA, 2012.
[13] Flow Science Inc. Flow-3D User Manual – Version 10.0, 2011.
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Standard Reference Data Program, Gaithersburg, 2010.
[16] E.J. Hopfinger and S.P. Das. Mass transfer enhancement by capillary waves at a liquid–vapour interface. Experiments in Fluids, Vol. 46, No.4: 597-605, 2009.
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Image (1) the view of vortex breaker morning glory spillway in operation

흐름의 수리학에 대한 와류 차단기의 영향 조사

Investigating the impact of the vortex breaker on the hydraulics of the flow
(empirical hydraulic coefficient) passing over the morning glory spillway
Roozbeh Aghamajidi1 1– Assistant Professor, Faculty of Engineering, Islamic Azad University, Sepidan Unit, Fars, Iran
Received: 05 November 2022; Revised: 11 December 2022; Accepted: 10 January 2023; Published: 11 January
2023

Abstract

In recent decades, many dams have been built. Due to the high need for water and the increasing soil
erosion in different areas, the need and sensation to build a dam is quite obvious. In 1900, the number
of large dams did not exceed 50. However, between 1950 and 1986, the number of large dams (more
than 15 meters high) was more than 39,000. Since the 70s, the construction of dams has been
developing more and more. This expansion has been more visible in the Asian, Central and South
American regions. According to the construction purpose, each dam structure must be able to pass the
volume of excess water caused by the flood, and for this purpose, various structures such as spillways
are used. The spillways are different according to the type of exploitation and the type of project. In
other words, there are different types of leaks. Which are one of these types of shaft spillway. The
spillway of a morning glory consists of a circular crest that directs the flow to an inclined or vertical
axis. The mentioned axis is connected to a conduct way with a low gradient. In this research, in order
to investigate the performance of both vortex breakers on the hydraulic spillway of morning glory,
several tests have been conducted with various types of vortex breakers. The results show that the best
vorticity channel with a low height and length is an arrangement of 6, which increases the flow rate by
23%. It should be noted that increasing the thickness of the vortex breaker by more than 7% of the
spillway radius does not have much effect on the increase of the hydraulic coefficient.

Image (1) the view of old stepped morning glory spillway in operation
Image (1) the view of old stepped morning glory spillway in operation

최근 수십 년 동안 많은 댐이 건설되었습니다. 물에 대한 높은 수요와 여러 지역에서 증가하는 토양 침식으로 인해 댐 건설의 필요성과 감각은 매우 분명합니다. 1900년에는 대형 댐의 수가 50개를 넘지 않았지만 1950년에서 1986년 사이에 대형 댐(높이 15미터 이상)의 수는 39,000개가 넘었습니다. 70년대 이후 댐 건설은 점점 더 발전해 왔습니다.

이러한 확장은 아시아, 중남미 지역에서 더 두드러졌습니다. 각 댐 구조물은 시공목적에 따라 홍수로 인한 과잉수량을 통과할 수 있어야 하며 이를 위해 여수로 등 다양한 구조물이 사용된다. 여수로는 개발 유형과 프로젝트 유형에 따라 다릅니다. 즉, 다양한 유형의 누출이 있습니다.

샤프트 여수로의 이러한 유형 중 하나입니다. 나팔꽃의 여수로는 흐름을 경사 또는 수직 축으로 향하게 하는 원형 마루로 구성됩니다. 언급된 축은 기울기가 낮은 전도 방식에 연결됩니다. 본 연구에서는 나팔꽃 수로에서 두 가지 와류 차단기의 성능을 조사하기 위해 다양한 유형의 와류 차단기로 여러 테스트를 수행했습니다.

그 결과 높이와 길이가 낮은 최적의 vorticity 채널은 6개 배열로 유량이 23% 증가하는 것으로 나타났다. 와류 차단기의 두께를 여수로 반경의 7% 이상 증가시키는 것은 수리 계수의 증가에 큰 영향을 미치지 않는다는 점에 유의해야 합니다.

Keywords:

Morning Glory Spillway, Vortex Breaker, Arrangement, Hydraulic Behavior

Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low overlapping rate defects(Scheme NO.5).

Molten pool structure, temperature and velocity
flow in selective laser melting AlCu5MnCdVA alloy

용융 풀 구조, 선택적 온도 및 속도 흐름 레이저 용융 AlCu5MnCdVA 합금

Pan Lu1 , Zhang Cheng-Lin2,6,Wang Liang3, Liu Tong4 and Liu Jiang-lin5
1 Aviation and Materials College, Anhui Technical College of Mechanical and Electrical Engineering, Wuhu Anhui 241000, People’s
Republic of China 2 School of Engineering Science, University of Science and Technology of China, Hefei Anhui 230026, People’s Republic of China 3 Anhui Top Additive Manufacturing Technology Co., Ltd., Wuhu Anhui 241300, People’s Republic of China 4 Anhui Chungu 3D Printing Institute of Intelligent Equipment and Industrial Technology, Anhui 241300, People’s Republic of China 5 School of Mechanical and Transportation Engineering, Taiyuan University of Technology, Taiyuan Shanxi 030024, People’s Republic of
China 6 Author to whom any correspondence should be addressed.
E-mail: ahjdpanlu@126.com, jiao__zg@126.com, ahjdjxx001@126.com,tongliu1988@126.com and liujianglin@tyut.edu.cn

Keywords

SLM, molten pool, AlCu5MnCdVA alloy, heat flow, velocity flow, numerical simulation

Abstract

선택적 레이저 용융(SLM)은 열 전달, 용융, 상전이, 기화 및 물질 전달을 포함하는 복잡한 동적 비평형 프로세스인 금속 적층 제조(MAM)에서 가장 유망한 기술 중 하나가 되었습니다. 용융 풀의 특성(구조, 온도 흐름 및 속도 흐름)은 SLM의 최종 성형 품질에 결정적인 영향을 미칩니다. 이 연구에서는 선택적 레이저 용융 AlCu5MnCdVA 합금의 용융 풀 구조, 온도 흐름 및 속도장을 연구하기 위해 수치 시뮬레이션과 실험을 모두 사용했습니다.

그 결과 용융풀의 구조는 다양한 형태(깊은 오목 구조, 이중 오목 구조, 평면 구조, 돌출 구조 및 이상적인 평면 구조)를 나타냈으며, 용융 풀의 크기는 약 132 μm × 107 μm × 50 μm였습니다. : 용융풀은 초기에는 여러 구동력에 의해 깊이 15μm의 깊은 오목형상이었으나, 성형 후기에는 장력구배에 의해 높이 10μm의 돌출형상이 되었다. 용융 풀 내부의 금속 흐름은 주로 레이저 충격력, 금속 액체 중력, 표면 장력 및 반동 압력에 의해 구동되었습니다.

AlCu5MnCdVA 합금의 경우, 금속 액체 응고 속도가 매우 빠르며(3.5 × 10-4 S), 가열 속도 및 냉각 속도는 각각 6.5 × 107 K S-1 및 1.6 × 106 K S-1 에 도달했습니다. 시각적 표준으로 표면 거칠기를 선택하고, 낮은 레이저 에너지 AlCu5MnCdVA 합금 최적 공정 매개변수 창을 수치 시뮬레이션으로 얻었습니다: 레이저 출력 250W, 부화 공간 0.11mm, 층 두께 0.03mm, 레이저 스캔 속도 1.5m s-1 .

또한, 실험 프린팅과 수치 시뮬레이션과 비교할 때, 용융 풀의 폭은 각각 약 205um 및 약 210um이었고, 인접한 두 용융 트랙 사이의 중첩은 모두 약 65um이었다. 결과는 수치 시뮬레이션 결과가 실험 인쇄 결과와 기본적으로 일치함을 보여 수치 시뮬레이션 모델의 정확성을 입증했습니다.

Selective Laser Melting (SLM) has become one of the most promising technologies in Metal Additive Manufacturing (MAM), which is a complex dynamic non-equilibrium process involving heat transfer, melting, phase transition, vaporization and mass transfer. The characteristics of the molten pool (structure, temperature flow and velocity flow) have a decisive influence on the final forming quality of SLM. In this study, both numerical simulation and experiments were employed to study molten pool structure, temperature flow and velocity field in Selective Laser Melting AlCu5MnCdVA alloy. The results showed the structure of molten pool showed different forms(deep-concave structure, double-concave structure, plane structure, protruding structure and ideal planar structure), and the size of the molten pool was approximately 132 μm × 107 μm × 50 μm: in the early stage, molten pool was in a state of deep-concave shape with a depth of 15 μm due to multiple driving forces, while a protruding shape with a height of 10 μm duo to tension gradient in the later stages of forming. The metal flow inside the molten pool was mainly driven by laser impact force, metal liquid gravity, surface tension and recoil pressure. For AlCu5MnCdVA alloy, metal liquid solidification speed was extremely fast(3.5 × 10−4 S), the heating rate and cooling rate reached 6.5 × 107 K S−1 and 1.6 × 106 K S−1 , respectively. Choosing surface roughness as a visual standard, low-laser energy AlCu5MnCdVA alloy optimum process parameters window was obtained by numerical simulation: laser power 250 W, hatching space 0.11 mm, layer thickness 0.03 mm, laser scanning velocity 1.5 m s−1 . In addition, compared with experimental printing and numerical simulation, the width of the molten pool was about 205 um and about 210 um, respectively, and overlapping between two adjacent molten tracks was all about 65 um. The results showed that the numerical simulation results were basically consistent with the experimental print results, which proved the correctness of the numerical simulation model.

Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 1. AlCu5MnCdVA powder particle size distribution.
Figure 2. AlCu5MnCdVA powder
Figure 2. AlCu5MnCdVA powder
Figure 3. Finite element model and calculation domains of SLM.
Figure 3. Finite element model and calculation domains of SLM.
Figure 4. SLM heat transfer process.
Figure 4. SLM heat transfer process.
Figure 14. Defects: (a) Unmelt defects(Scheme NO.4);(b) Pores defects(Scheme NO.1); (c); Spattering defect (Scheme NO.3); (d) Low
overlapping rate defects(Scheme NO.5).
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.
Figure 17. Two-pass molten tracks overlapping for Scheme NO.2.

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Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment

by Hongbo Mi 1,2, Chuan Wang 1,3, Xuanwen Jia 3,*, Bo Hu 2, Hongliang Wang 4, Hui Wang 3 and Yong Zhu 5

1College of Mechatronics Engineering, Hainan Vocational University of Science and Technology, Haikou 571126, China

2Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China

3College of Hydraulic Science and Engineering, Yangzhou University, Yangzhou 225009, China

4School of Aerospace and Mechanical Engineering/Flight College, Changzhou Institute of Technology, Changzhou 213032, China

5National Research Center of Pumps, Jiangsu University, Zhenjiang 212013, China

*Author to whom correspondence should be addressed.Sustainability202315(6), 5159; https://doi.org/10.3390/su15065159

Received: 30 January 2023 / Revised: 4 March 2023 / Accepted: 10 March 2023 / Published: 14 March 2023(This article belongs to the Special Issue Advanced Technologies of Renewable Energy and Water Management for Sustainable Environment

Abstract

Due to their high efficiency, low heat loss and associated sustainability advantages, impinging jets have been used extensively in marine engineering, geotechnical engineering and other engineering practices. In this paper, the flow structure and impact characteristics of impinging jets with different Reynolds numbers and impact distances are systematically studied by Flow-3D based on PIV experiments. In the study, the relevant state parameters of the jets are dimensionlessly treated, obtaining not only the linear relationship between the length of the potential nucleation zone and the impinging distance, but also the linear relationship between the axial velocity and the axial distance in the impinging zone. In addition, after the jet impinges on the flat plate, the vortex action range caused by the wall-attached flow of the jet gradually decreases inward with the increase of the impinging distance. By examining the effect of Reynolds number Re on the hydraulic characteristics of the submerged impact jet, it can be found that the structure of the continuous submerged impact jet is relatively independent of the Reynolds number. At the same time, the final simulation results demonstrate the applicability of the linear relationship between the length of the potential core region and the impact distance. This study provides methodological guidance and theoretical support for relevant engineering practice and subsequent research on impinging jets, which has strong theoretical and practical significance.

Keywords: 

PIVFlow-3Dimpinging jethydraulic characteristicsimpinging distance

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Figure 1. Geometric model.

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Figure 2. Model grid schematic.

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Figure 3. (a) Schematic diagram of the experimental setup; (b) PIV images of vertical impinging jets with velocity fields.

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Figure 4. (a) Velocity distribution verification at the outlet of the jet pipe; (b) Distribution of flow angle in the mid-axis of the jet [39].

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Figure 5. Along-range distribution of the dimensionless axial velocity of the jet at different impact distances.Figure 6 shows the variation of H

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Figure 6. Relationship between the distribution of potential core region and the impact height H/D.

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Figure 7. The relationship between the potential core length 

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Figure 8. Along-range distribution of the flow angle φ of the jet at different impact distances.

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Figure 9. Velocity distribution along the axis of the jet at different impinging regions.

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Figure 10. The absolute value distribution of slope under different impact distances.

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Figure 11. Velocity distribution of impinging jet on wall under different impinging distances.

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Figure 12. Along-range distribution of the dimensionless axial velocity of the jet at different Reynolds numbers.

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Figure 13. Along-range distribution of the flow angle φ of the jet at different Reynolds numbers.

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Figure 14. Velocity distribution along the jet axis at different Reynolds numbers.

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Figure 15. Velocity distribution of impinging jet on a wall under different Reynolds numbers.

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Mi, H.; Wang, C.; Jia, X.; Hu, B.; Wang, H.; Wang, H.; Zhu, Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability 202315, 5159. https://doi.org/10.3390/su15065159

AMA Style

Mi H, Wang C, Jia X, Hu B, Wang H, Wang H, Zhu Y. Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment. Sustainability. 2023; 15(6):5159. https://doi.org/10.3390/su15065159Chicago/Turabian Style

Mi, Hongbo, Chuan Wang, Xuanwen Jia, Bo Hu, Hongliang Wang, Hui Wang, and Yong Zhu. 2023. “Hydraulic Characteristics of Continuous Submerged Jet Impinging on a Wall by Using Numerical Simulation and PIV Experiment” Sustainability 15, no. 6: 5159. https://doi.org/10.3390/su15065159

Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

Abstract

Flow hydrodynamics in the main channel due to floodplain sand mining is important for a better understanding of maintaining the natural habitat or the reliance between the flood plain and the main channel for the river’s long-term survival and also facilitates more effective river restoration engineering. Day by day anthropogenic stresses are increasing in the river corridor system, indiscriminate sand mining is one of them. In this study, a computational fluid dynamics (CFD)-based software Flow-3D hydro (renormalized group K-ε turbulence model used) is used to study the flow hydrodynamics of sinuous (sinuosity index = 1.25) channel 18 m long, 1 m width, and 0.3 m height with floodplain sand mining pit. Sand mining additionally increases the secondary current near the outer bank of the channel, therefore leading to scouring or erosion at the outer bank, as a result, rivers migrate laterally. The turbulence kinetic energy (TKE) is concentrated in the mining pit and near the inner bank. This study result can be used to understand the flow hydrodynamic of the river system due to the series of sand mining.

Keywords

  • Flow hydrodynamics
  • Turbulence modeling
  • Flow-3D
  • Sinuosity
  • Sand mining

References

  1. Best, J.: Anthropogenic stresses on the world’s big rivers. Nat. Geosci. 12(1), 7–21 (2019)CrossRef CAS Google Scholar 
  2. Bagnold, R.A.: Some Aspects of the Shape of River Meanders. US Government Printing Office (1960)Google Scholar 
  3. Kondolf, G.M.: Freshwater Gravel Mining and Dredging Issues: White Paper. Washington Department of Fish and Wildlife (2002)Google Scholar 
  4. Molnár, P., Ramírez, J.A.: Energy dissipation theories and optimal channel characteristics of river networks. Water Resour. Res. 34(7), 1809–1818 (1998)CrossRef Google Scholar 
  5. Padmalal, D., Maya, K.: Sand Mining: Environmental Impacts and Selected Case Studies. Springer (2014)Google Scholar 
  6. Hübler, M., Pothen, F.: Can smart policies solve the sand mining problem? PLoS ONE 16(4), e0248882 (2021)CrossRef Google Scholar 
  7. Khan, S., Sugie, A.: Sand mining and its social impacts on local society in rural Bangladesh: a case study of a village in Tangail district. J. Urban Reg. Stud. Contemp. India 2(1), 1–11 (2015)Google Scholar 
  8. Daneshfaraz, R. et al.: The experimental study of the effects of river mining holes on the bridge piers. Iranian J. Soil Water Res. 50(7), 1619–1633 (2019)Google Scholar 
  9. Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Best, J. L., Aalto, R., … & Houseago, R. C.: River bank instability from unsustainable sand mining in the lower Mekong River. Nat. Sustain. 3(3), 217–225 (2020)Google Scholar 
  10. Callander, R.A.: River meandering. Annu. Rev. Fluid Mech. 10(1), 129–158 (1978)CrossRef Google Scholar 
  11. Koehnken, L., Rintoul, M.: Impacts of sand mining on ecosystem structure, process and biodiversity in rivers. World Wildlife Fund International (2018)Google Scholar 
  12. Gavriletea, M.D.: Environmental impacts of sand exploitation. Analysis of sand market. Sustainability 9(7), 1118 (2017)Google Scholar 
  13. Koehnken, L., et al.: Impacts of riverine sand mining on freshwater ecosystems: a review of the scientific evidence and guidance for future research. River Res. Appl. 36(3), 362–370 (2020)Google Scholar 
  14. Myers, W.R.C.: Momentum transfer in a compound channel. J. Hydraul. Res. 16(2), 139–150 (1978)CrossRef Google Scholar 
  15. Rajaratnam, N., Ahmadi, R.M.: Interaction between main channel and flood-plain flows. J. Hydraul. Div. 105(5), 573–588 (1979)CrossRef Google Scholar 
  16. Sellin, R.H.J.: A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche 7, 793–802 (1964)CrossRef Google Scholar 
  17. Karami, H., et al.: Verification of numerical study of scour around spur dikes using experimental data. Water Environ. J. 28(1), 124–134 (2014)Google Scholar 
  18. Bathurst, J.C., et al.: Overbank sediment deposition patterns for straight and meandering flume channels. Earth Surf. Proc. Land. 27(6), 659–665 (2002)CrossRef Google Scholar 
  19. Xu, D., Bai, Y.: Experimental study on the bed topography evolution in alluvial meandering rivers with various sinuousnesses. J. Hydro-Environ. Res. 7(2), 92–102 (2013)CrossRef Google Scholar 
  20. Priego-Hernández, G.A., Rivera-Trejo, F.: Secondary currents: measurement and analysis. Atmósfera 29(1), 23–34 (2016)Google Scholar 
  21. Alshamani, K.M.M.: Correlations among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity. AIAA J. 16(8), 859–861 (1978)CrossRef Google Scholar 
  22. Biron, P.M., et al.: Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surface Process. Landforms: J. British Geomorphol. Res. Group 29(11), 1403–1415 (2004)Google Scholar 
  23. Clark, L.A., Theresa, M.W.: Boundary Shear Stress Along Vegetated Streambanks (2007)Google Scholar 
  24. Kim, S.-C., et al.: Estimating bottom stress in tidal boundary layer from acoustic Doppler velocimeter data. J. Hydraul. Eng. 126(6), 399–406 (2000)CrossRef Google Scholar 

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Flow Hydrodynamics Influences Due to Flood Plain Sand Mining in a Meandering Channel

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Abstract

Flow hydrodynamics in the main channel due to floodplain sand mining is important for a better understanding of maintaining the natural habitat or the reliance between the flood plain and the main channel for the river’s long-term survival and also facilitates more effective river restoration engineering. Day by day anthropogenic stresses are increasing in the river corridor system, indiscriminate sand mining is one of them. In this study, a computational fluid dynamics (CFD)-based software Flow-3D hydro (renormalized group K-ε turbulence model used) is used to study the flow hydrodynamics of sinuous (sinuosity index = 1.25) channel 18 m long, 1 m width, and 0.3 m height with floodplain sand mining pit. Sand mining additionally increases the secondary current near the outer bank of the channel, therefore leading to scouring or erosion at the outer bank, as a result, rivers migrate laterally. The turbulence kinetic energy (TKE) is concentrated in the mining pit and near the inner bank. This study result can be used to understand the flow hydrodynamic of the river system due to the series of sand mining.

Keywords

  • Flow hydrodynamics
  • Turbulence modeling
  • Flow-3D
  • Sinuosity
  • Sand mining

This is a preview of subscription content, access via your institution.

References

  1. Best, J.: Anthropogenic stresses on the world’s big rivers. Nat. Geosci. 12(1), 7–21 (2019)CrossRef CAS Google Scholar 
  2. Bagnold, R.A.: Some Aspects of the Shape of River Meanders. US Government Printing Office (1960)Google Scholar 
  3. Kondolf, G.M.: Freshwater Gravel Mining and Dredging Issues: White Paper. Washington Department of Fish and Wildlife (2002)Google Scholar 
  4. Molnár, P., Ramírez, J.A.: Energy dissipation theories and optimal channel characteristics of river networks. Water Resour. Res. 34(7), 1809–1818 (1998)CrossRef Google Scholar 
  5. Padmalal, D., Maya, K.: Sand Mining: Environmental Impacts and Selected Case Studies. Springer (2014)Google Scholar 
  6. Hübler, M., Pothen, F.: Can smart policies solve the sand mining problem? PLoS ONE 16(4), e0248882 (2021)CrossRef Google Scholar 
  7. Khan, S., Sugie, A.: Sand mining and its social impacts on local society in rural Bangladesh: a case study of a village in Tangail district. J. Urban Reg. Stud. Contemp. India 2(1), 1–11 (2015)Google Scholar 
  8. Daneshfaraz, R. et al.: The experimental study of the effects of river mining holes on the bridge piers. Iranian J. Soil Water Res. 50(7), 1619–1633 (2019)Google Scholar 
  9. Hackney, C. R., Darby, S. E., Parsons, D. R., Leyland, J., Best, J. L., Aalto, R., … & Houseago, R. C.: River bank instability from unsustainable sand mining in the lower Mekong River. Nat. Sustain. 3(3), 217–225 (2020)Google Scholar 
  10. Callander, R.A.: River meandering. Annu. Rev. Fluid Mech. 10(1), 129–158 (1978)CrossRef Google Scholar 
  11. Koehnken, L., Rintoul, M.: Impacts of sand mining on ecosystem structure, process and biodiversity in rivers. World Wildlife Fund International (2018)Google Scholar 
  12. Gavriletea, M.D.: Environmental impacts of sand exploitation. Analysis of sand market. Sustainability 9(7), 1118 (2017)Google Scholar 
  13. Koehnken, L., et al.: Impacts of riverine sand mining on freshwater ecosystems: a review of the scientific evidence and guidance for future research. River Res. Appl. 36(3), 362–370 (2020)Google Scholar 
  14. Myers, W.R.C.: Momentum transfer in a compound channel. J. Hydraul. Res. 16(2), 139–150 (1978)CrossRef Google Scholar 
  15. Rajaratnam, N., Ahmadi, R.M.: Interaction between main channel and flood-plain flows. J. Hydraul. Div. 105(5), 573–588 (1979)CrossRef Google Scholar 
  16. Sellin, R.H.J.: A laboratory investigation into the interaction between the flow in the channel of a river and that over its flood plain. La Houille Blanche 7, 793–802 (1964)CrossRef Google Scholar 
  17. Karami, H., et al.: Verification of numerical study of scour around spur dikes using experimental data. Water Environ. J. 28(1), 124–134 (2014)Google Scholar 
  18. Bathurst, J.C., et al.: Overbank sediment deposition patterns for straight and meandering flume channels. Earth Surf. Proc. Land. 27(6), 659–665 (2002)CrossRef Google Scholar 
  19. Xu, D., Bai, Y.: Experimental study on the bed topography evolution in alluvial meandering rivers with various sinuousnesses. J. Hydro-Environ. Res. 7(2), 92–102 (2013)CrossRef Google Scholar 
  20. Priego-Hernández, G.A., Rivera-Trejo, F.: Secondary currents: measurement and analysis. Atmósfera 29(1), 23–34 (2016)Google Scholar 
  21. Alshamani, K.M.M.: Correlations among turbulent shear stress, turbulent kinetic energy, and axial turbulence intensity. AIAA J. 16(8), 859–861 (1978)CrossRef Google Scholar 
  22. Biron, P.M., et al.: Comparing different methods of bed shear stress estimates in simple and complex flow fields. Earth Surface Process. Landforms: J. British Geomorphol. Res. Group 29(11), 1403–1415 (2004)Google Scholar 
  23. Clark, L.A., Theresa, M.W.: Boundary Shear Stress Along Vegetated Streambanks (2007)Google Scholar 
  24. Kim, S.-C., et al.: Estimating bottom stress in tidal boundary layer from acoustic Doppler velocimeter data. J. Hydraul. Eng. 126(6), 399–406 (2000)CrossRef Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, IndiaO. P. Maurya, K. K. Nandi, S. Modalavalasa & S. Dutta

Corresponding author

Correspondence to O. P. Maurya .

Editor information

Editors and Affiliations

  1. Centre for the Environment, Indian Institute of Technology Guwahati, Guwahati, IndiaDeepmoni Deka
  2. Department of Chemical engineering, Indian Institute of Technology Guwahati, Guwahati, IndiaSubrata Kumar Majumder
  3. Department of Chemical engineering, Indian Institute of Technology Guwahati, Guwahati, IndiaMihir Kumar Purkait
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

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Data Availability Statement

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Abstract

This paper presents the results of tests on the suitability of designed heads (impellers) for aluminum refining. The research was carried out on a physical model of the URO-200, followed by numerical simulations in the FLOW 3D program. Four design variants of impellers were used in the study. The degree of dispersion of the gas phase in the model liquid was used as a criterion for evaluating the performance of each solution using different process parameters, i.e., gas flow rate and impeller speed. Afterward, numerical simulations in Flow 3D software were conducted for the best solution. These simulations confirmed the results obtained with the water model and verified them.

Keywords: aluminum, impeller construction, degassing process, numerical modeling, physical modeling

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1. Introduction

Constantly increasing requirements concerning metallurgical purity in terms of hydrogen content and nonmetallic inclusions make casting manufacturers use effective refining techniques. The answer to this demand is the implementation of the aluminum refining technique making use of a rotor with an original design guaranteeing efficient refining [1,2,3,4]. The main task of the impeller (rotor) is to reduce the contamination of liquid metal (primary and recycled aluminum) with hydrogen and nonmetallic inclusions. An inert gas, mainly argon or a mixture of gases, is introduced through the rotor into the liquid metal to bring both hydrogen and nonmetallic inclusions to the metal surface through the flotation process. Appropriately and uniformly distributed gas bubbles in the liquid metal guarantee achieving the assumed level of contaminant removal economically. A very important factor in deciding about the obtained degassing effect is the optimal rotor design [5,6,7,8]. Thanks to the appropriate geometry of the rotor, gas bubbles introduced into the liquid metal are split into smaller ones, and the spinning movement of the rotor distributes them throughout the volume of the liquid metal bath. In this solution impurities in the liquid metal are removed both in the volume and from the upper surface of the metal. With a well-designed impeller, the costs of refining aluminum and its alloys can be lowered thanks to the reduced inert gas and energy consumption (optimal selection of rotor rotational speed). Shorter processing time and a high degree of dehydrogenation decrease the formation of dross on the metal surface (waste). A bigger produced dross leads to bigger process losses. Consequently, this means that the choice of rotor geometry has an indirect impact on the degree to which the generated waste is reduced [9,10].

Another equally important factor is the selection of process parameters such as gas flow rate and rotor speed [11,12]. A well-designed gas injection system for liquid metal meets two key requirements; it causes rapid mixing of the liquid metal to maintain a uniform temperature throughout the volume and during the entire process, to produce a chemically homogeneous metal composition. This solution ensures effective degassing of the metal bath. Therefore, the shape of the rotor, the arrangement of the nozzles, and their number are significant design parameters that guarantee the optimum course of the refining process. It is equally important to complete the mixing of the metal bath in a relatively short time, as this considerably shortens the refining process and, consequently, reduces the process costs. Another important criterion conditioning the implementation of the developed rotor is the generation of fine diffused gas bubbles which are distributed throughout the metal volume, and whose residence time will be sufficient for the bubbles to collide and adsorb the contaminants. The process of bubble formation by the spinning rotors differs from that in the nozzles or porous molders. In the case of a spinning rotor, the shear force generated by the rotor motion splits the bubbles into smaller ones. Here, the rotational speed, mixing force, surface tension, and fluid density have a key effect on the bubble size. The velocity of the bubbles, which depends mainly on their size and shape, determines their residence time in the reactor and is, therefore, very important for the refining process, especially since gas bubbles in liquid aluminum may remain steady only below a certain size [13,14,15].

The impeller designs presented in the article were developed to improve the efficiency of the process and reduce its costs. The impellers used so far have a complicated structure and are very pricey. The success of the conducted research will allow small companies to become independent of external supplies through the possibility of making simple and effective impellers on their own. The developed structures were tested on the water model. The results of this study can be considered as pilot.

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2. Materials and Methods

Rotors were realized with the SolidWorks computer design technique and a 3D printer. The developed designs were tested on a water model. Afterward, the solution with the most advantageous refining parameters was selected and subjected to calculations with the Flow3D package. As a result, an impeller was designed for aluminum refining. Its principal lies in an even distribution of gas bubbles in the entire volume of liquid metal, with the largest possible participation of the bubble surface, without disturbing the metal surface. This procedure guarantees the removal of gaseous, as well as metallic and nonmetallic, impurities.

2.1. Rotor Designs

The developed impeller constructions, shown in Figure 1Figure 2Figure 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 1Figure 2 and Figure 3 show the same impeller model but with a different number of gas outlets. The arrangement of four, eight, and 12 outlet holes was adopted in the developed design. A triangle-shaped structure equipped with three gas outlet holes is presented in Figure 4.

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Figure 1

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

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Figure 2

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

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Figure 3

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

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Figure 4

A 3D model—‘red triangle’ impeller with three holes—variant RT3.

2.2. Physical Models

Investigations were carried out on a water model of the URO 200 reactor of the barbotage refining process (see Figure 5).

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Figure 5

A schematic of the water model of reactor URO 200.

The URO 200 reactor can be classified as a cyclic reactor. The main element of the device is a rotor, which ends the impeller. The whole system is attached to a shaft via which the refining gas is supplied. Then, the shaft with the rotor is immersed in the liquid metal in the melting pot or the furnace chamber. In URO 200 reactors, the refining process lasts 600 s (10 min), the gas flow rate that can be obtained ranges from 5 to 20 dm3·min−1, and the speed at which the rotor can move is 0 to 400 rpm. The permissible quantity of liquid metal for barbotage refining is 300 kg or 700 kg [8,16,17]. The URO 200 has several design solutions which improve operation and can be adapted to the existing equipment in the foundry. These solutions include the following [8,16]:

  • URO-200XR—used for small crucible furnaces, the capacity of which does not exceed 250 kg, with no control system and no control of the refining process.
  • URO-200SA—used to service several crucible furnaces of capacity from 250 kg to 700 kg, fully automated and equipped with a mechanical rotor lift.
  • URO-200KA—used for refining processes in crucible furnaces and allows refining in a ladle. The process is fully automated, with a hydraulic rotor lift.
  • URO-200KX—a combination of the XR and KA models, designed for the ladle refining process. Additionally, refining in heated crucibles is possible. The unit is equipped with a manual hydraulic rotor lift.
  • URO-200PA—designed to cooperate with induction or crucible furnaces or intermediate chambers, the capacity of which does not exceed one ton. This unit is an integral part of the furnace. The rotor lift is equipped with a screw drive.

Studies making use of a physical model can be associated with the observation of the flow and circulation of gas bubbles. They require meeting several criteria regarding the similarity of the process and the object characteristics. The similarity conditions mainly include geometric, mechanical, chemical, thermal, and kinetic parameters. During simulation of aluminum refining with inert gas, it is necessary to maintain the geometric similarity between the model and the real object, as well as the similarity related to the flow of liquid metal and gas (hydrodynamic similarity). These quantities are characterized by the Reynolds, Weber, and Froude numbers. The Froude number is the most important parameter characterizing the process, its magnitude is the same for the physical model and the real object. Water was used as the medium in the physical modeling. The factors influencing the choice of water are its availability, relatively low cost, and kinematic viscosity at room temperature, which is very close to that of liquid aluminum.

The physical model studies focused on the flow of inert gas in the form of gas bubbles with varying degrees of dispersion, particularly with respect to some flow patterns such as flow in columns and geysers, as well as disturbance of the metal surface. The most important refining parameters are gas flow rate and rotor speed. The barbotage refining studies for the developed impeller (variants B4, B8, B12, and RT3) designs were conducted for the following process parameters:

  • Rotor speed: 200, 300, 400, and 500 rpm,
  • Ideal gas flow: 10, 20, and 30 dm3·min−1,
  • Temperature: 293 K (20 °C).

These studies were aimed at determining the most favorable variants of impellers, which were then verified using the numerical modeling methods in the Flow-3D program.

2.3. Numerical Simulations with Flow-3D Program

Testing different rotor impellers using a physical model allows for observing the phenomena taking place while refining. This is a very important step when testing new design solutions without using expensive industrial trials. Another solution is modeling by means of commercial simulation programs such as ANSYS Fluent or Flow-3D [18,19]. Unlike studies on a physical model, in a computer program, the parameters of the refining process and the object itself, including the impeller design, can be easily modified. The simulations were performed with the Flow-3D program version 12.03.02. A three-dimensional system with the same dimensions as in the physical modeling was used in the calculations. The isothermal flow of liquid–gas bubbles was analyzed. As in the physical model, three speeds were adopted in the numerical tests: 200, 300, and 500 rpm. During the initial phase of the simulations, the velocity field around the rotor generated an appropriate direction of motion for the newly produced bubbles. When the required speed was reached, the generation of randomly distributed bubbles around the rotor was started at a rate of 2000 per second. Table 1 lists the most important simulation parameters.

Table 1

Values of parameters used in the calculations.

ParameterValueUnit
Maximum number of gas particles1,000,000
Rate of particle generation20001·s−1
Specific gas constant287.058J·kg−1·K−1
Atmospheric pressure1.013 × 105Pa
Water density1000kg·m−3
Water viscosity0.001kg·m−1·s−1
Boundary condition on the wallsNo-slip
Size of computational cell0.0034m

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In the case of the CFD analysis, the numerical solutions require great care when generating the computational mesh. Therefore, computational mesh tests were performed prior to the CFD calculations. The effect of mesh density was evaluated by taking into account the velocity of water in the tested object on the measurement line A (height of 0.065 m from the bottom) in a characteristic cross-section passing through the object axis (see Figure 6). The mesh contained 3,207,600, 6,311,981, 7,889,512, 11,569,230, and 14,115,049 cells.

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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 βmaxβmin 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).

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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 XYZ).

In the simulations, the fluid flow was assumed to be incompressible, in which case the following equation is applicable:

∂u∂t+(u⋅∇)u=−1ρ∇p+ν∇2u+F.

(3)

Due to the large range of liquid velocities during flows, the turbulence formation process was included in the modeling. For this purpose, the k–ε model turbulence kinetic energy k and turbulence dissipation ε were the target parameters, as expressed by the following equations [21]:

∂(ρk)∂t+∂(ρkvi)∂xi=∂∂xj[(μ+μtσk)⋅∂k∂xi]+Gk+Gb−ρε−Ym+Sk,

(4)

∂(ρε)∂t+∂(ρεui)∂xi=∂∂xj[(μ+μtσε)⋅∂k∂xi]+C1εεk(Gk+G3εGb)+C2ερε2k+Sε,

(5)

where ρ is the gas density, σκ and σε are the Prandtl turbulence numbers, k and ε are constants of 1.0 and 1.3, and Gk and Gb are the kinetic energy of turbulence generated by the average velocity and buoyancy, respectively.

As mentioned earlier, there are two gas phases in the considered problem. In addition to the gas bubbles, which are treated here as particles, there is also air, which surrounds the system. The boundary of phase separation is in this case the free surface of the water. The shape of the free surface can change as a result of the forming velocity field in the liquid. Therefore, it is necessary to use an appropriate approach to free surface tracking. The most commonly used concept in liquid–gas flow modeling is the volume of fluid (VOF) method [22,23], and Flow-3D uses a modified version of this method called TrueVOF. It introduces the concept of the volume fraction of the liquid phase fl. This parameter can be used for classifying the cells of a discrete grid into areas filled with liquid phase (fl = 1), gaseous phase, or empty cells (fl = 0) and those through which the phase separation boundary (fl ∈ (0, 1)) passes (free surface). To determine the local variations of the liquid phase fraction, it is necessary to solve the following continuity equation:

dfldt=0.

(6)

Then, the fluid parameters in the region of coexistence of the two phases (the so-called interface) depend on the volume fraction of each phase.

ρ=flρl+(1−fl)ρg,

(7)

ν=flνl+(1−fl)νg,

(8)

where indices l and g refer to the liquid and gaseous phases, respectively.

The parameter of fluid velocity in cells containing both phases is also determined in the same way.

u=flul+(1−fl)ug.

(9)

Since the processes taking place in the surrounding air can be omitted, to speed up the calculations, a single-phase, free-surface model was used. This means that no calculations were performed in the gas cells (they were treated as empty cells). The liquid could fill them freely, and the air surrounding the system was considered by the atmospheric pressure exerted on the free surface. This approach is often used in modeling foundry and metallurgical processes [24].

2.3.2. Modeling of Gas Bubble Flow 

As stated, a particle model was used to model bubble flow. Spherical particles (gas bubbles) of a given size were randomly generated in the area marked with green in Figure 7b. In the simulations, the gas bubbles were assumed to have diameters of 0.016 and 0.02 m corresponding to the gas flow rates of 10 and 30 dm3·min−1, respectively.

Experimental studies have shown that, as a result of turbulent fluid motion, some of the bubbles may burst, leading to the formation of smaller bubbles, although merging of bubbles into larger groupings may also occur. Therefore, to be able to observe the behavior of bubbles of different sizes (diameter), the calculations generated two additional particle types with diameters twice smaller and twice larger, respectively. The proportion of each species in the system was set to 33.33% (Table 2).

Table 2

Data assumed for calculations.

NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
NoRotor Speed (Rotational Speed)
rpm
Bubbles Diameter
m
Corresponding Gas Flow Rate
dm3·min−1
A2000.01610D2000.0230
0.0080.01
0.0320.04
B3000.01610E3000.0230
0.0080.01
0.0320.04
C5000.01610F5000.0230
0.0080.01
0.0320.04

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The velocity of the particle results from the generated velocity field (calculated from Equation (3) in the liquid ul around it and its velocity resulting from the buoyancy force ub. The effect of particle radius r on the terminal velocity associated with buoyancy force can be determined according to Stokes’ law.

ub=29 (ρg−ρl)μlgr2,

(10)

where g is the acceleration (9.81).

The DPM model was used for modeling the two-phase (water–air) flow. In this model, the fluid (water) is treated as a continuous phase and described by the Navier–Stokes equation, while gas bubbles are particles flowing in the model fluid (discrete phase). The trajectories of each bubble in the DPM system are calculated at each timestep taking into account the mass forces acting on it. Table 3 characterizes the DPM model used in our own research [18].

Table 3

Characteristic of the DPM model.

MethodEquations
Euler–LagrangeBalance equation:
dugdt=FD(u−ug)+g(ϱg−ϱ)ϱg+F.
FD (u − up) denotes the drag forces per mass unit of a bubble, and the expression for the drag coefficient FD is of the form
FD=18μCDReϱ⋅gd2g24.
The relative Reynolds number has the form
Re≡ρdg|ug−u|μ.
On the other hand, the force resulting from the additional acceleration of the model fluid has the form
F=12dρdtρg(u−ug),
where ug is the gas bubble velocity, u is the liquid velocity, dg is the bubble diameter, and CD is the drag coefficient.

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3. Results and Discussion

3.1. Calculations of Power and Mixing Time by the Flowing Gas Bubbles

One of the most important parameters of refining with a rotor is the mixing power induced by the spinning rotor and the outflowing gas bubbles (via impeller). The mixing power of liquid metal in a ladle of height (h) by gas injection can be determined from the following relation [15]:

pgVm=ρ⋅g⋅uB,

(11)

where pg is the mixing power, Vm is the volume of liquid metal in the reactor, ρ is the density of liquid aluminum, and uB is the average speed of bubbles, given below.

uB=n⋅R⋅TAc⋅Pm⋅t,

(12)

where n is the number of gas moles, R is the gas constant (8.314), Ac is the cross-sectional area of the reactor vessel, T is the temperature of liquid aluminum in the reactor, and Pm is the pressure at the middle tank level. The pressure at the middle level of the tank is calculated by a function of the mean logarithmic difference.

Pm=(Pa+ρ⋅g⋅h)−Paln(Pa+ρ⋅g⋅h)Pa,

(13)

where Pa is the atmospheric pressure, and h is the the height of metal in the reactor.

Themelis and Goyal [25] developed a model for calculating mixing power delivered by gas injection.

pg=2Q⋅R⋅T⋅ln(1+m⋅ρ⋅g⋅hP),

(14)

where Q is the gas flow, and m is the mass of liquid metal.

Zhang [26] proposed a model taking into account the temperature difference between gas and alloy (metal).

pg=QRTgVm[ln(1+ρ⋅g⋅hPa)+(1−TTg)],

(15)

where Tg is the gas temperature at the entry point.

Data for calculating the mixing power resulting from inert gas injection into liquid aluminum are given below in Table 4. The design parameters were adopted for the model, the parameters of which are shown in Figure 5.

Table 4

Data for calculating mixing power introduced by an inert gas.

ParameterValueUnit
Height of metal column0.7m
Density of aluminum2375kg·m−3
Process duration20s
Gas temperature at the injection site940K
Cross-sectional area of ladle0.448m2
Mass of liquid aluminum546.25kg
Volume of ladle0.23M3
Temperature of liquid aluminum941.15K

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Table 5 presents the results of mixing power calculations according to the models of Themelis and Goyal and of Zhang for inert gas flows of 10, 20, and 30 dm3·min−1. The obtained calculation results significantly differed from each other. The difference was an order of magnitude, which indicates that the model is highly inaccurate without considering the temperature of the injected gas. Moreover, the calculations apply to the case when the mixing was performed only by the flowing gas bubbles, without using a rotor, which is a great simplification of the phenomenon.

Table 5

Mixing power calculated from mathematical models.

Mathematical ModelMixing Power (W·t−1)
for a Given Inert Gas Flow (dm3·min−1)
102030
Themelis and Goyal11.4923.3335.03
Zhang0.821.662.49

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The mixing time is defined as the time required to achieve 95% complete mixing of liquid metal in the ladle [27,28,29,30]. Table 6 groups together equations for the mixing time according to the models.

Table 6

Models for calculating mixing time.

AuthorsModelRemarks
Szekely [31]τ=800ε−0.4ε—W·t−1
Chiti and Paglianti [27]τ=CVQlV—volume of reactor, m3
Ql—flow intensity, m3·s−1
Iguchi and Nakamura [32]τ=1200⋅Q−0.4D1.97h−1.0υ0.47υ—kinematic viscosity, m2·s−1
D—diameter of ladle, m
h—height of metal column, m
Q—liquid flow intensity, m3·s−1

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Figure 8 and Figure 9 show the mixing time as a function of gas flow rate for various heights of the liquid column in the ladle and mixing power values.

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Figure 8

Mixing time as a function of gas flow rate for various heights of the metal column (Iguchi and Nakamura model).

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Figure 9

Mixing time as a function of mixing power (Szekly model).

3.2. Determining the Bubble Size

The mechanisms controlling bubble size and mass transfer in an alloy undergoing refining are complex. Strong mixing conditions in the reactor promote impurity mass transfer. In the case of a spinning rotor, the shear force generated by the rotor motion separates the bubbles into smaller bubbles. Rotational speed, mixing force, surface tension, and liquid density have a strong influence on the bubble size. To characterize the kinetic state of the refining process, parameters k and A were introduced. Parameters kA, 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).

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Figure 10

Effect of rotational speed on the bubble diameter.

In a flow of given turbulence intensity, the diameter of the bubble does not exceed the maximum size dmax, which is inversely proportional to the rate of kinetic energy dissipation in a viscous flow ε. The size of the gas bubble diameter as a function of the mixing energy, also considering the Weber number and the mixing energy in the negative power, can be determined from the following equations [31,34]:

  • —Sevik and Park:

dBmax=We0.6kr⋅(σ⋅103ρ⋅10−3)0.6⋅(10⋅ε)−0.4⋅10−2.

(20)

  • —Evans:

dBmax=⎡⎣Wekr⋅σ⋅1032⋅(ρ⋅10−3)13⎤⎦35 ⋅(10⋅ε)−25⋅10−2.

(21)

The results of calculating the maximum diameter of the bubble dBmax determined from Equation (21) are given in Table 7.

Table 7

The results of calculating the maximum diameter of the bubble using Equation (21).

ModelMixing Energy
ĺ (m2·s−3)
Weber Number (Wekr)
0.591.01.2
Zhang and Taniguchi
dmax
0.10.01670.02300.026
0.50.00880.01210.013
1.00.00670.00910.010
1.50.00570.00780.009
Sevik and Park
dBmax
0.10.2650.360.41
0.50.1390.190.21
1.00.1060.140.16
1.50.0900.120.14
Evans
dBmax
0.10.2470.3400.38
0.50.1300.1780.20
1.00.0980.1350.15
1.50.0840.1150.13

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3.3. Physical Modeling

The first stage of experiments (using the URO-200 water model) included conducting experiments with impellers equipped with four, eight, and 12 gas outlets (variants B4, B8, B12). The tests were carried out for different process parameters. Selected results for these experiments are presented in Figure 11Figure 12Figure 13 and Figure 14.

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Figure 11

Impeller variant B4—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 12

Impeller variant B8—gas bubbles dispersion registered for a gas flow rate of 10 dm3·min−1 and rotor speed of (a) 200, (b) 300, (c) 400, and (d) 500 rpm.

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Figure 13

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

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Figure 14

Gas bubble dispersion registered for different processing parameters (impeller variant RT3).

The analysis of the refining variants presented in Figure 11Figure 12Figure 13 and Figure 14 reveals that the proposed impellers design model is not useful for the aluminum refining process. The number of gas outlet orifices, rotational speed, and flow did not affect the refining efficiency. In all the variants shown in the figures, very poor dispersion of gas bubbles was observed in the object. The gas bubble flow had a columnar character, and so-called dead zones, i.e., areas where no inert gas bubbles are present, were visible in the analyzed object. Such dead zones were located in the bottom and side zones of the ladle, while the flow of bubbles occurred near the turning rotor. Another negative phenomenon observed was a significant agitation of the water surface due to excessive (rotational) rotor speed and gas flow (see Figure 13, cases 20; 400, 30; 300, 30; 400, and 30; 500).

Research results for a ‘red triangle’ impeller equipped with three gas supply orifices (variant RT3) are presented in Figure 14.

In this impeller design, a uniform degree of bubble dispersion in the entire volume of the modeling fluid was achieved for most cases presented (see Figure 14). In all tested variants, single bubbles were observed in the area of the water surface in the vessel. For variants 20; 200, 30; 200, and 20; 300 shown in Figure 14, the bubble dispersion results were the worst as the so-called dead zones were identified in the area near the bottom and sidewalls of the vessel, which disqualifies these work parameters for further applications. Interestingly, areas where swirls and gas bubble chains formed were identified only for the inert gas flows of 20 and 30 dm3·min−1 and 200 rpm in the analyzed model. This means that the presented model had the best performance in terms of dispersion of gas bubbles in the model liquid. Its design with sharp edges also differed from previously analyzed models, which is beneficial for gas bubble dispersion, but may interfere with its suitability in industrial conditions due to possible premature wear.

3.4. Qualitative Comparison of Research Results (CFD and Physical Model)

The analysis (physical modeling) revealed that the best mixing efficiency results were obtained with the RT3 impeller variant. Therefore, numerical calculations were carried out for the impeller model with three outlet orifices (variant RT3). The CFD results are presented in Figure 15 and Figure 16.

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Figure 15

Simulation results of the impeller RT3, for given flows and rotational speeds after a time of 1 s: simulation variants (a) A, (b) B, (c) C, (d) D, (e) E, and (f) F.

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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.

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Figure 17

Compilations of model research results (CFD and physical): A—single gas bubbles formed on the surface of the modeling liquid, B—excessive formation of gas chains and swirls, C—uniform distribution of gas bubbles in the entire volume of the tank, and D—dead zones without gas bubbles, no dispersion. (a) Variant B; (b) variant F.

It should be mentioned here that, in numerical simulations, it is necessary to make certain assumptions and simplifications. The calculations assumed three particle size classes (Table 2), which represent the different gas bubbles that form due to different gas flow rates. The maximum number of particles/bubbles (Table 1) generated was assumed in advance and related to the computational capabilities of the computer. Too many particles can also make it difficult to visualize and analyze the results. The size of the particles, of course, affects their behavior during simulation, while, in the figures provided in the article, the bubbles are represented by spheres (visualization of the results) of the same size. Please note that, due to the adopted Lagrangian–Eulerian approach, the simulation did not take into account phenomena such as bubble collapse or fusion. However, the obtained results allow a comprehensive analysis of the behavior of gas bubbles in the system under consideration.

The comparative analysis of the visualization (quantitative) results obtained with the water model and CFD simulations (see Figure 17) generated a sufficient agreement from the point of view of the trends. A precise quantitative evaluation is difficult to perform because of the lack of a refraction compensating system in the water model. Furthermore, in numerical simulations, it is not possible to determine the geometry of the forming gas bubbles and their interaction with each other as opposed to the visualization in the water model. The use of both research methods is complementary. Thus, a direct comparison of images obtained by the two methods requires appropriate interpretation. However, such an assessment gives the possibility to qualitatively determine the types of the present gas bubble dispersion, thus ultimately validating the CFD results with the water model.

A summary of the visualization results for impellers RT3, i.e., analysis of the occurring gas bubble dispersion types, is presented in Table 8.

Table 8

Summary of visualization results (impeller RT3)—different types of gas bubble dispersion.

No Exp.ABCDEF
Gas flow rate, dm3·min−11030
Impeller speed, rpm200300500200300500
Type of dispersionAccurateUniformUniform/excessiveMinimalExcessiveExcessive

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Tests carried out for impeller RT3 confirmed the high efficiency of gas bubble distribution in the volume of the tested object at a low inert gas flow rate of 10 dm3·min−1. The most optimal variant was variant B (300 rpm, 10 dm3·min−1). However, the other variants A and C (gas flow rate 10 dm3·min−1) seemed to be favorable for this type of impeller and are recommended for further testing. The above process parameters will be analyzed in detail in a quantitative analysis to be performed on the basis of the obtained efficiency curves of the degassing process (oxygen removal). This analysis will give an unambiguous answer as to which process parameters are the most optimal for this type of impeller; the results are planned for publication in the next article.

It should also be noted here that the high agreement between the results of numerical calculations and physical modelling prompts a conclusion that the proposed approach to the simulation of a degassing process which consists of a single-phase flow model with a free surface and a particle flow model is appropriate. The simulation results enable us to understand how the velocity field in the fluid is formed and to analyze the distribution of gas bubbles in the system. The simulations in Flow-3D software can, therefore, be useful for both the design of the impeller geometry and the selection of process parameters.

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4. Conclusions

The results of experiments carried out on the physical model of the device for the simulation of barbotage refining of aluminum revealed that the worst results in terms of distribution and dispersion of gas bubbles in the studied object were obtained for the black impellers variants B4, B8, and B12 (multi-orifice impellers—four, eight, and 12 outlet holes, respectively).

In this case, the control of flow, speed, and number of gas exit orifices did not improve the process efficiency, and the developed design did not meet the criteria for industrial tests. In the case of the ‘red triangle’ impeller (variant RT3), uniform gas bubble dispersion was achieved throughout the volume of the modeling fluid for most of the tested variants. The worst bubble dispersion results due to the occurrence of the so-called dead zones in the area near the bottom and sidewalls of the vessel were obtained for the flow variants of 20 dm3·min−1 and 200 rpm and 30 dm3·min−1 and 200 rpm. For the analyzed model, areas where swirls and gas bubble chains were formed were found only for the inert gas flow of 20 and 30 dm3·min−1 and 200 rpm. The model impeller (variant RT3) had the best performance compared to the previously presented impellers in terms of dispersion of gas bubbles in the model liquid. Moreover, its design differed from previously presented models because of its sharp edges. This can be advantageous for gas bubble dispersion, but may negatively affect its suitability in industrial conditions due to premature wearing.

The CFD simulation results confirmed the results obtained from the experiments performed on the physical model. The numerical simulation of the operation of the ‘red triangle’ impeller model (using Flow-3D software) gave good agreement with the experiments performed on the physical model. This means that the presented model impeller, as compared to other (analyzed) designs, had the best performance in terms of gas bubble dispersion in the model liquid.

In further work, the developed numerical model is planned to be used for CFD simulations of the gas bubble distribution process taking into account physicochemical parameters of liquid aluminum based on industrial tests. Consequently, the obtained results may be implemented in production practice.

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Funding Statement

This paper was created with the financial support grants from the AGH-UST, Faculty of Foundry Engineering, Poland (16.16.170.654 and 11/990/BK_22/0083) for the Faculty of Materials Engineering, Silesian University of Technology, Poland.

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Author Contributions

Conceptualization, K.K. and D.K.; methodology, J.P. and T.M.; validation, M.S. and S.G.; formal analysis, D.K. and T.M.; investigation, J.P., K.K. and S.G.; resources, M.S., J.P. and K.K.; writing—original draft preparation, D.K. and T.M.; writing—review and editing, D.K. and T.M.; visualization, J.P., K.K. and S.G.; supervision, D.K.; funding acquisition, D.K. and T.M. All authors have read and agreed to the published version of the manuscript.

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Institutional Review Board Statement

Not applicable.

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Informed Consent Statement

Not applicable.

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Data Availability Statement

Data are contained within the article.

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Conflicts of Interest

The authors declare no conflict of interest.

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Footnotes

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

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CFD Modelling of Local Scour and Flow Field around Isolated and In-Line Bridge Piers using FLOW-3D

CFD Modelling of Local Scour and Flow Field around Isolated and In-Line Bridge Piers using FLOW-3D

Abstract

CFD Modelling of Local Scour and Flow Field around Isolated and In-Line Bridge Piers using FLOW-3D
CFD Modelling of Local Scour and Flow Field around Isolated and In-Line Bridge Piers using FLOW-3D

Harshvardhan Harshvardhan1and Deo Raj Kaushal2

  • 1Research Scholar, Civil Engineering, Indian Institute of Technology Delhi, New Delhi, India (cez198227@iitd.ac.in)
  • 2Professor, Civil Engineering, Indian Institute of Technology Delhi, New Delhi, India (Deo.Raj.Kaushal@civil.iitd.ac.in)

Scouring at bridge piers is troublesome and inevitable at the same time. Numerous empirical studies have been conducted in the last century to predict scour depth, but they completely ignore the physics of the problem. The physics behind scouring at bridge piers can be best understood in terms of the effect of the flow field around the pier at different stages of scour. This study comprises experimental and numerical parts. Experiments are conducted in the laboratory in which the flow field data at equilibrium is collected using Acoustic Doppler Velocimeter (ADV) and the equilibrium scoured bed is measured around isolated and In-Line Piers. Additionally, the commercial CFD code “FLOW-3D HYDRO 2022 R1” is utilized to simulate the flow field and scour around bridge piers. The FLOW-3D model solves the three–dimensional momentum and continuity equations coupled with the sediment transport equations to calculate and predict the flow field and the equilibrium scoured bed. While the maximum scour depth at equilibrium has been used to validate various CFD codes in the past, point-wise comparison of scour depth is scanty in previous research works. Moreover, the flow field at the equilibrium scour stage obtained using FLOW-3D has also been compared with experimental data available in the literature and experiment conducted in the laboratory. The performance of the CFD model is evaluated, the flow field and scoured bed geometry at equilibrium are analyzed and results are presented.

How to cite: Harshvardhan, H. and Kaushal, D. R.: CFD Modelling of Local Scour and Flow Field around Isolated and In-Line Bridge Piers using FLOW-3D , EGU General Assembly 2023, Vienna, Austria, 24–28 Apr 2023, EGU23-3820,

https://doi.org/10.5194/egusphere-egu23-3820, 2023.

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling

Optimization of filling systems for low pressure by Flow-3D

Dissertação de Mestrado
Ciclo de Estudos Integrados Conducentes ao
Grau de Mestre em Engenharia Mecânica
Trabalho efectuado sob a orientação do
Doutor Hélder de Jesus Fernades Puga
Professor Doutor José Joaquim Carneiro Barbosa

ABSTRACT

논문의 일부로 튜터 선택 가능성과 해결해야 할 주제가 설정되는 매개변수를 염두에 두고 개발 주제 ‘Flow- 3D ®에 의한 저압 충전 시스템 최적화’가 선택되었습니다. 이를 위해서는 달성해야 할 목표와 이를 달성하기 위한 방법을 정의하는 것이 필요했습니다.

충전 시스템을 시뮬레이션하고 검증할 수 있는 광범위한 소프트웨어에도 불구하고 Flow-3D®는 시장에서 최고의 도구 중 하나로 표시되어 전체 충전 프로세스 및 행동 표현과 관련하여 탁월한 정확도로 시뮬레이션하는 능력을 입증했습니다.

이를 위해 관련 프로세스를 더 잘 이해하고 충진 시스템 시뮬레이션을 위한 탐색적 기반 역할을 하기 위해 이 도구를 탐색하는 것이 중요합니다. 지연 및 재료 낭비에 반영되는 실제적인 측면에서 충전 장치의 치수를 완벽하게 만드는 비용 및 시간 낭비. 이러한 방식으로 저압 주조 공정에서 충진 시스템을 설계하고 물리적 모델을 탐색하여 특성화하는 방법론을 검증하기 위한 것입니다.

이를 위해 다음 주요 단계를 고려하십시오.

시뮬레이션 소프트웨어 Flow 3D® 탐색;
충전 시스템 모델링;
모델의 매개변수를 탐색하여 모델링된 시스템의 시뮬레이션, 검증 및 최적화.

따라서 연구 중인 압력 곡선과 주조 분석에서 가장 관련성이 높은 정보의 최종 마이닝을 검증하기 위한 것입니다.

사용된 압력 곡선은 수집된 문헌과 이전에 수행된 실제 작업을 통해 얻었습니다. 결과를 통해 3단계 압력 곡선이 층류 충진 체계의 의도된 목적과 관련 속도가 0.5 𝑚/𝑠를 초과하지 않는다는 결론을 내릴 수 있었습니다.

충전 수준이 2인 압력 곡선은 0.5 𝑚/𝑠 이상의 속도로 영역을 채우는 더 난류 시스템을 갖습니다. 열전달 매개변수는 이전에 얻은 값이 주물에 대한 소산 거동을 확증하지 않았기 때문에 연구되었습니다.

이러한 방식으로 주조 공정에 더 부합하는 새로운 가치를 얻었습니다. 달성된 결과는 유사한 것으로 나타난 NovaFlow & Solid®에 의해 생성된 결과와 비교되어 시뮬레이션에서 설정된 매개변수를 검증했습니다. Flow 3D®는 주조 부품 시뮬레이션을 위한 강력한 도구로 입증되었습니다.

As part of the dissertation and bearing in mind the parameters in which the possibility of a choice of tutor and the subject to be addressed is established, the subject for development ’Optimization of filling systems for low pressure by Flow 3D ®’ was chosen. For this it was necessary to define the objectives to achieve and the methods to attain them. Despite the wide range of software able to simulate and validate filling systems, Flow 3D® has been shown as one of the best tools in the market, demonstrating its ability to simulate with distinctive accuracy with respect to the entire process of filling and the behavioral representation of the fluid obtained. To this end, it is important to explore this tool for a better understanding of the processes involved and to serve as an exploratory basis for the simulation of filling systems, simulation being one of the great strengths of the current industry due to the need to reduce costs and time waste, in practical terms, that lead to the perfecting of the dimensioning of filling devices, which are reflected in delays and wasted material. In this way it is intended to validate the methodology to design a filling system in lowpressure casting process, exploring their physical models and thus allowing for its characterization. For this, consider the following main phases: The exploration of the simulation software Flow 3D®; modeling of filling systems; simulation, validation and optimization of systems modeled by exploring the parameters of the models. Therefore, it is intended to validate the pressure curves under study and the eventual mining of the most relevant information in a casting analysis. The pressure curves that were used were obtained through the gathered literature and the practical work previously performed. Through the results it was possible to conclude that the pressure curve with 3 levels meets the intended purpose of a laminar filling regime and associated speeds never exceeding 0.5 𝑚/𝑠. The pressure curve with 2 filling levels has a more turbulent system, having filling areas with velocities above 0.5 𝑚/𝑠. The heat transfer parameter was studied due to the values previously obtained didn’t corroborate the behavior of dissipation regarding to the casting. In this way, new values, more in tune with the casting process, were obtained. The achieved results were compared with those generated by NovaFlow & Solid®, which were shown to be similar, validating the parameters established in the simulations. Flow 3D® was proven a powerful tool for the simulation of casting parts.

키워드

저압, Flow 3D®, 시뮬레이션, 파운드리, 압력-시간 관계,Low Pressure, Flow 3D®, Simulation, Foundry, Pressure-time relation

Figure 4.24 - Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.24 – Model with virtual valves in the extremities of the geometries to simulate the permeability of the mold promoting a more uniformed filling
Figure 4.39 - Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.39 – Values of temperature contours using full energy heat transfer parameter for simula
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation,
(b) NovaFlow & Solid® simulation
Figure 4.40 – Comparison between software simulations (a) Flow 3D® simulation, (b) NovaFlow & Solid® simulation

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Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.

Numerical modelling of air-water flows in sewer drops

하수구 방울의 공기-물 흐름 수치 모델링

Paula Beceiro (corresponding author)
Maria do Céu Almeida
Hydraulic and Environment Department (DHA), National Laboratory for Civil Engineering, Avenida do Brasil 101, 1700-066 Lisbon, Portugal
E-mail: pbeceiro@lnec.pt
Jorge Matos
Department of Civil Engineering, Arquitecture and Geosources,
Technical University of Lisbon (IST), Avenida Rovisco Pais 1, 1049-001 Lisbon, Portugal

ABSTRACT

물 흐름에 용존 산소(DO)의 존재는 해로운 영향의 발생을 방지하는 데 유익한 것으로 인식되는 호기성 조건을 보장하는 중요한 요소입니다.

하수도 시스템에서 흐르는 폐수에 DO를 통합하는 것은 공기-액체 경계면 또는 방울이나 접합부와 같은 특이점의 존재로 인해 혼입된 공기를 통한 연속 재방출의 영향을 정량화하기 위해 광범위하게 조사된 프로세스입니다. 공기 혼입 및 후속 환기를 향상시키기 위한 하수구 드롭의 위치는 하수구의 호기성 조건을 촉진하는 효과적인 방법입니다.

본 논문에서는 수직 낙하, 배경 및 계단식 낙하를 CFD(전산유체역학) 코드 FLOW-3D®를 사용하여 모델링하여 이러한 유형의 구조물의 존재로 인해 발생하는 난류로 인한 공기-물 흐름을 평가했습니다. 이용 가능한 실험적 연구에 기초한 수력학적 변수의 평가와 공기 혼입의 분석이 수행되었습니다.

이러한 구조물에 대한 CFD 모델의 결과는 Soares(2003), Afonso(2004) 및 Azevedo(2006)가 개발한 해당 물리적 모델에서 얻은 방류, 압력 헤드 및 수심의 측정을 사용하여 검증되었습니다.

유압 거동에 대해 매우 잘 맞았습니다. 수치 모델을 검증한 후 공기 연행 분석을 수행했습니다.

The presence of dissolved oxygen (DO) in water flows is an important factor to ensure the aerobic conditions recognised as beneficial to prevent the occurrence of detrimental effects. The incorporation of DO in wastewater flowing in sewer systems is a process widely investigated in order to quantify the effect of continuous reaeration through the air-liquid interface or air entrained due the presence of singularities such as drops or junctions. The location of sewer drops to enhance air entrainment and subsequently reaeration is an effective practice to promote aerobic conditions in sewers. In the present paper, vertical drops, backdrops and stepped drop was modelled using the computational fluid dynamics (CFD) code FLOW-3D® to evaluate the air-water flows due to the turbulence induced by the presence of this type of structures. The assessment of the hydraulic variables and an analysis of the air entrainment based in the available experimental studies were carried out. The results of the CFD models for these structures were validated using measurements of discharge, pressure head and water depth obtained in the corresponding physical models developed by Soares (2003), Afonso (2004) and Azevedo (2006). A very good fit was obtained for the hydraulic behaviour. After validation of numerical models, analysis of the air entrainment was carried out.

Key words | air entrainment, computational fluid dynamics (CFD), sewer drops

Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 1.| Physical models of the vertical drop, backdrop and stepped drop developed in the Technical University of Lisbon.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 3. Comparison between the experimental and numerical pressure head along of the invert of the outlet pipe.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.
Figure 4. Average void fraction along the longitudinal axis of the outlet pipe for the lower discharges in the vertical drop and backdrop.

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Fig. 1 Geometrical 3D model of Caisson

환기실에서 의도된 삼중수소 방출 후 삼중수소 거동 시뮬레이션

Simulation of Tritium Behavior after Intended Tritium Release in Ventilated Room


Yasunori IWAI
, Takumi HAYASHI, Toshihiko YAMANISHI, Kazuhiro KOBAYASHI & Masataka NISHI

Abstract

일본원자력연구소(JAERI) 산하 삼중수소공정연구소(TPL)에서는 핵융합로의 안전성 확인 및 강화를 위해 12m3의 대형 밀폐용기(Caisson)로 삼중수소 안전 연구(CATS)용 케이슨 조립체를 제작하여 추정 삼중수소 누출 이벤트가 발생해야 하는 경우 삼중수소 거동. 본 연구의 주요 목적 중 하나는 환기실에서 삼중수소 누출 사건이 발생한 후 삼중수소 거동을 예측하기 위한 시뮬레이션 방법을 확립하는 것입니다.

RNG 모델은 허용 가능한 엔지니어링 정밀도로 50m3/h 환기 케이슨에서 맴돌이 흐름 계산에 유효한 것으로 밝혀졌습니다. 의도된 삼중수소 방출 후 계산된 초기 및 제거 삼중수소 농도 이력은 50m3/h 환기 케이슨에서 실험 관찰과 일치했습니다.

환기실의 삼중수소 수송에는 벽 근처의 흐름이 중요한 역할을 하는 것으로 밝혀졌다. 한편, 3,000m3의 삼중수소 취급실에서 의도적으로 방출된 삼중수소 거동은 미일 협력하에 실험적으로 조사되었습니다. 동일한 방법으로 계산된 삼중수소 농도 이력은 실험적 관찰과 일치하였으며, 이는 현재 개발된 방법이 삼중수소 취급실의 실제 규모에 적용될 수 있음을 입증한다.

At the Tritium Process Laboratory (TPL) at the Japan Atomic Energy Research Institute (JAERI), Caisson Assembly for Tritium Safety study (CATS) with 12 m3 of large airtight vessel (Caisson) was fabricated for confirmation and enhancement of fusion reactor safety to estimate tritium behavior in the case where a tritium leak event should happen. One of the principal objectives of the present studies is the establishment of simulation method to predict the tritium behavior after the tritium leak event should happen in a ventilated room. The RNG model was found to be valid for eddy flow calculation in the 50m3/h ventilated Caisson with acceptable engineering precision. The calculated initial and removal tritium concentration histories after intended tritium release were consistent with the experimental observations in the 50 m3/h ventilated Caisson. It is found that the flow near a wall plays an important role for the tritium transport in the ventilated room. On the other hand, tritium behavior intentionally released in the 3,000 m3 of tritium handling room was investigated experimentally under a US-Japan collaboration. The tritium concentration history calculated with the same method was consistent with the experimental observations, which proves that the present developed method can be applied to the actual scale of tritium handling room.

KEYWORDS: 

Fig. 1 Geometrical 3D model of Caisson
Fig. 1 Geometrical 3D model of Caisson
Fig. 2 Geometrical 3D model of "main cell" of TSTA
Fig. 2 Geometrical 3D model of “main cell” of TSTA

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Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Development of macro-defect-free PBF-EB-processed Ti–6Al–4V alloys with superior plasticity using PREP-synthesized powder and machine learning-assisted process optimization

Yunwei GuiabKenta Aoyagib Akihiko Chibab
aDepartment of Materials Processing, Graduate School of Engineering, Tohoku University, 6-6 Aramaki Aza Aoba, Aoba-ku, Sendai, 980-8579, Japan
bInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

Received 14 October 2022, Revised 23 December 2022, Accepted 3 January 2023, Available online 5 January 2023.Show lessAdd to MendeleyShareCite

https://doi.org/10.1016/j.msea.2023.144595Get rights and content

Abstract

The elimination of internal macro-defects is a key issue in Ti–6Al–4V alloys fabricated via powder bed fusion using electron beams (PBF-EB), wherein internal macro-defects mainly originate from the virgin powder and inappropriate printing parameters. This study compares different types powders by combining support vector machine techniques to determine the most suitable powder for PBF-EB and to predict the processing window for the printing parameters without internal macro-defects. The results show that powders fabricated via plasma rotating electrode process have the best sphericity, flowability, and minimal porosity and are most suitable for printing. Surface roughness criterion was also applied to determine the quality of the even surfaces, and support vector machine was used to construct processing maps capable of predicting a wide range of four-dimensional printing parameters to obtain macro-defect-free samples, offering the possibility of subsequent development of Ti–6Al–4V alloys with excellent properties. The macro-defect-free samples exhibited good elongation, with the best overall mechanical properties being the ultimate tensile strength and elongation of 934.7 MPa and 24.3%, respectively. The elongation of the three macro-defect-free samples was much higher than that previously reported for additively manufactured Ti–6Al–4V alloys. The high elongation of the samples in this work is mainly attributed to the elimination of internal macro-defects.

Introduction

Additive manufacturing (AM) technologies can rapidly manufacture complex or custom parts, reducing process steps and saving manufacturing time [[1], [2], [3], [4]], and are widely used in the aerospace, automotive, and other precision industries [5,6]. Powder bed fusion using an electron beam (PBF-EB) is an additive manufacturing method that uses a high-energy electron beam to melt metal powders layer by layer to produce parts. In contrast to selective laser melting, PBF-EB involves the preparation of samples in a high vacuum environment, which effectively prevents the introduction of impurities such as O and N. It also involves a preheating process for the print substrate and powder, which reduces residual thermal stress on the sample and subsequent heat treatment processes [[2], [3], [4],7]. Due to these features and advantages, PBF-EB technology is a very important AM technology with great potential in metallic materials. Moreover, PBF-EB is the ideal AM technology for the manufacture of complex components made of many alloys, such as titanium alloys, nickel-based superalloys, aluminum alloys and stainless steels [[2], [3], [4],8].

Ti–6Al–4V alloy is one of the prevalent commercial titanium alloys possessing high specific strength, excellent mechanical properties, excellent corrosion resistance, and good biocompatibility [9,10]. It is widely used in applications requiring low density and excellent corrosion resistance, such as the aerospace industry and biomechanical applications [11,12]. The mechanical properties of PBF-EB-processed Ti–6Al–4V alloys are superior to those fabricated by casting or forging, because the rapid cooling rate in PBF-EB results in finer grains [[12], [13], [14], [15], [16], [17], [18]]. However, the PBF-EB-fabricated parts often include internal macro-defects, which compromises their mechanical properties [[19], [20], [21], [22]]. This study focused on the elimination of macro-defects, such as porosity, lack of fusion, incomplete penetration and unmelted powders, which distinguishes them from micro-defects such as vacancies, dislocations, grain boundaries and secondary phases, etc. Large-sized fusion defects cause a severe reduction in mechanical strength. Smaller defects, such as pores and cracks, lead to the initiation of fatigue cracking and rapidly accelerate the cracking process [23]. The issue of internal macro-defects must be addressed to expand the application of the PBF-EB technology. The main studies for controlling internal macro-defects are online monitoring of defects, remelting and hot isostatic pressing (HIP). The literatures [24,25] report the use of infrared imaging or other imaging techniques to identify defects, but the monitoring of smaller sized defects is still not adequate. And in some cases remelting does not reduce the internal macro-defects of the part, but instead causes coarsening of the macrostructure and volatilization of some metal elements [23]. The HIP treatment does not completely eliminate the internal macro-defects, the original defect location may still act as a point of origin of the crack, and the subsequent treatment will consume more time and economic costs [23]. Therefore, optimizing suitable printing parameters to avoid internal macro-defects in printed parts at source is of great industrial value and research significance, and is an urgent issue in PBF-EB related technology.

There are two causes of internal macro-defects in the AM process: gas pores trapped in the virgin powder and the inappropriate printing parameters [7,23]. Gui et al. [26] classify internal macro-defects during PBF-EB process according to their shape, such as spherical defects, elongated shape defects, flat shape defects and other irregular shape defects. Of these, spherical defects mainly originate from raw material powders. Other shape defects mainly originate from lack of fusion or unmelted powders caused by unsuitable printing parameters, etc. The PBF-EB process requires powders with good flowability, and spherical powders are typically chosen as raw materials. The prevalent techniques for the fabrication of pre-alloyed powders are gas atomization (GA), plasma atomization (PA), and the plasma rotating electrode process (PREP) [27,28]. These methods yield powders with different characteristics that affect the subsequent fabrication. The selection of a suitable powder for PBF-EB is particularly important to produce Ti–6Al–4V alloys without internal macro-defects. The need to optimize several printing parameters such as beam current, scan speed, line offset, and focus offset make it difficult to eliminate internal macro-defects that occur during printing [23]. Most of the studies [11,12,22,[29], [30], [31], [32], [33]] on the optimization of AM processes for Ti–6Al–4V alloys have focused on samples with a limited set of parameters (e.g., power–scan speed) and do not allow for the guidance and development of unknown process windows for macro-defect-free samples. In addition, process optimization remains a time-consuming problem, with the traditional ‘trial and error’ method demanding considerable time and economic costs. The development of a simple and efficient method to predict the processing window for alloys without internal macro-defects is a key issue. In recent years, machine learning techniques have increasingly been used in the field of additive manufacturing and materials development [[34], [35], [36], [37]]. Aoyagi et al. [38] recently proposed a novel and efficient method based on a support vector machine (SVM) to optimize the two-dimensional process parameters (current and scan speed) and obtain PBF-EB-processed CoCr alloys without internal macro-defects. The method is one of the potential approaches toward effective optimization of more than two process parameters and makes it possible for the machine learning techniques to accelerate the development of alloys without internal macro-defects.

Herein, we focus on the elimination of internal macro-defects, such as pores, lack of fusion, etc., caused by raw powders and printing parameters. The Ti–6Al–4V powders produced by three different methods were compared, and the powder with the best sphericity, flowability, and minimal porosity was selected as the feedstock for subsequent printing. The relationship between the surface roughness and internal macro-defects in the Ti–6Al–4V components was also investigated. The combination of SVM and surface roughness indices (Sdr) predicted a wider four-dimensional processing window for obtaining Ti–6Al–4V alloys without internal macro-defects. Finally, we investigated the tensile properties of Ti–6Al–4V alloys at room temperature with different printing parameters, as well as the corresponding microstructures and fracture types.

Section snippets

Starting materials

Three types of Ti–6Al–4V alloy powders, produced by GA, PA, and PREP, were compared. The particle size distribution of the powders was determined using a laser particle size analyzer (LS230, Beckman Coulter, USA), and the flowability was measured using a Hall flowmeter (JIS-Z2502, Tsutsui Scientific Instruments Co., Ltd., Japan), according to the ASTM B213 standard. The powder morphology and internal macro-defects were determined using scanning electron microscopy (SEM, JEOL JCM-6000) and X-ray 

Comparison of the characteristics of GA, PA, and PREP Ti–6Al–4V powders

The particle size distributions (PSDs) and flowability of the three types of Ti–6Al–4V alloy powders produced by GA, PA, and PREP are shown in Fig. 2. Although the average particle sizes are similar (89.4 μm for GA, 82.5 μm for PA, and 86.1μm for PREP), the particle size range is different for the three types of powder (6.2–174.8 μm for GA, 27.3–139.2 μm for PA, and 39.4–133.9 μm for PREP). The flowability of the GA, PA, and PREP powders was 30.25 ± 0.98, 26.54 ± 0.37, and 25.03 ± 0.22 (s/50

Conclusions

The characteristics of the three types of Ti–6Al–4V alloy powders produced via GA, PA, and PREP were compared. The PREP powder with the best sphericity, flowability, and low porosity was found to be the most favorable powder for subsequent printing of Ti–6Al–4V alloys without internal macro-defects. The quantitative criterion of Sdr <0.015 for even surfaces was also found to be applicable to Ti–6Al–4V alloys. The process maps of Ti–6Al–4V alloys include two regions, high beam current/scan speed 

Uncited references

[55]; [56]; [57]; [58]; [59]; [60]; [61]; [62]; [63]; [64]; [65].

CRediT authorship contribution statement

Yunwei Gui: Writing – original draft, Visualization, Validation, Investigation. Kenta Aoyagi: Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Conceptualization. Akihiko Chiba: Supervision, Funding acquisition.

Declaration of competing interest

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

Acknowledgments

This study was based on the results obtained from project JPNP19007, commissioned by the New Energy and Industrial Technology Development Organization (NEDO). This work was also supported by JSPS KAKENHI (Proposal No. 21K03801) and the Inter-University Cooperative Research Program (Proposal nos. 18G0418, 19G0411, and 20G0418) of the Cooperative Research and Development Center for Advanced Materials, Institute for Materials Research, Tohoku University. It was also supported by the Council for

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Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

Flow-3D를 사용하여 전산유체역학(CFD)을 적용한 빠른 단계의 플러시 유동 수치 모델링

Numerical Modeling of Flush Flow in a Rapid Step Applying Computational Fluid Dynamics (CFD) Using Flow-3D.

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이 프로젝트의 주요 목표는 FLOW-3D를 사용하여 계단식 여수로에서 스키밍 흐름의 수치 모델링을 개발하는 것입니다. 이러한 구조의 설계는 물리적 모델링에서 얻은 경험적 표현과 CFD 코드를 지원하는 계단식 여수로를 통한 흐름의 수치 모델링에서 보완 연구를 기반으로 합니다. 수치 모델은 균일한 영역의 유속과 계단 여수로의 마찰 계수를 추정하는 데 사용됩니다(ϴ = 45º, Hd=4.61m). 흐름에 대한 자동 통기의 표현은 복잡하므로 프로그램은 공기 연행 모델을 사용하여 특정 제한이 있는 솔루션에 근접합니다.

The main objective of this project is to develop the numerical modeling of the skimming flow in a stepped spillway using FLOW-3D. The design of these structures is based on the use of empirical expressions obtained from physical modeling and complementary studies in the numerical modeling of flow over the stepped spillway with support of CFD code. The numerical model is used to estimate the flow velocity in the uniform region and the friction coefficient of the stepped spillway (ϴ = 45º, Hd=4.61m). The representation of auto aeration a flow is complex, so the program approximates the solution with certain limitations, using an air entrainment model; drift flux model and turbulence model k-ԑ RNG. The results obtained with numerical modeling and physical modeling at the beginning of natural auto aeration of flow and depth of the biphasic flow in the uniform region presents deviations above to 10% perhaps the flow is highly turbulent.

Keywords : Stepped spillway; skimming flow; air entrainment; drift flux; numerical modeling; FLOW-3D.

Keywords : 계단식 여수로; 스키밍 흐름; 공기 연행; 드리프트 플럭스; 수치 모델링; 흐름-3D.· 

스페인어로 된 초록 · 스페인어 로 된 텍스트 · 스페인어로 된 텍스트( pdf 

Figure 1. Grazing flow over a rapid step.
Figure 1. Grazing flow over a rapid step.
Figura 2. Principales regiones existentes en un flujo rasante.
Figura 2. Principales regiones existentes en un flujo rasante.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 3. Dimensions of the El Batán stepped rapid.
Figure 4. 3D physical model of the El Batán stepped rapid
Figure 4. 3D physical model of the El Batán stepped rapid
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.
Figura 7. Influencia del modelo de turbulencia. Qmodelo=27.95l/s.

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Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D

Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D

As part of the National Aero-Space Plane (NASP) project, the multi-dimensional effects of gravitational force, initial tank pressure, initial ullage temperature, and heat transfer rate on the 2-D temperature profiles were studied. FLOW-3D, a commercial finite difference fluid flow model, was used for the evaluation. These effects were examined on the basis of previous liquid hydrogen experimental data with gaseous hydrogen pressurant. FLOW-3D results were compared against an existing 1-D model. In addition, the effects of mesh size and convergence criteria on the analytical results were investigated. Suggestions for future modifications and uses of FLOW-3D for modeling of a NASP tank are also presented.

Document ID : 19900016844

Document Type : Technical Memorandum (TM)

AuthorsHardy, Terry L.

(NASA Lewis Research Center Cleveland, OH, United States)Tomsik, Thomas M.
(NASA Lewis Research Center Cleveland, OH, United States)

Date Acquired : September 6, 2013

Publication Date : July 1, 1990

Subject CategoryPropellants And Fuels : Report/Patent NumberNASA-TM-103217E-5629NAS 1.15:103217

Funding Number(s)PROJECT: RTOP 763-01-21

Distribution Limits : Public

Copyright : Work of the US Gov. Public Use Permitted.

Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D
Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D
Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D
Prediction of the ullage gas thermal stratification in a NASP vehicle propellant tank experimental simulation using FLOW-3D

Available Downloads

19900016844.pdf

Figure 2. Different PKW Types.

A review of Piano Key Weir as a superior alternative for dam rehabilitation

댐 복구를 위한 우수한 대안으로서의 Piano Key Weir에 대한 검토

Amiya Abhash &

K. K. Pandey

Pages 541-551 | Received 03 Mar 2020, Accepted 07 May 2020, Published online: 21 May 2020

ABSTRACT

Dams fall in ‘installations containing dangerous forces’ because of their massive impact on the environment and civilian life and property as per International humanitarian law. As such, it becomes vital for hydraulic engineers to refurbish various solutions for dam rehabilitation. This paper presents a review of a new type of weir installation called Piano Key Weir (PKW), which is becoming popular around the world for its higher spillway capacity both for existing and new dam spillway installations. This paper reviews the geometry along with structural integrity, discharging capacity, economic aspects, aeration requirements, sediment transport and erosion aspects of Piano Key Weir (PKW) as compared with other traditional spillway structures and alternatives from literature. The comparison with other alternatives shows PKW to be an excellent alternative for dam risk mitigation owing to its high spillway capabilities and economy, along with its use in both existing and new hydraulic structures.

댐은 국제 인도법에 따라 환경과 민간인 생활 및 재산에 막대한 영향을 미치기 때문에 ‘위험한 힘을 포함하는 시설물’에 속합니다. 따라서 유압 엔지니어는 댐 복구를 위한 다양한 솔루션을 재정비해야 합니다.

이 백서에서는 PKW(Piano Key Weir)라는 새로운 유형의 둑 설치에 대한 검토를 제공합니다. PKW는 기존 및 신규 댐 방수로 설치 모두에서 더 높은 방수로 용량으로 전 세계적으로 인기를 얻고 있습니다.

이 백서에서는 구조적 무결성, 배출 용량, 경제적 측면, 폭기 요구 사항, 퇴적물 운반 및 PKW(Piano Key Weir)의 침식 측면과 함께 다른 전통적인 여수로 구조 및 문헌의 대안과 비교하여 기하학을 검토합니다.

다른 대안과의 비교는 PKW가 높은 여수로 기능과 경제성으로 인해 댐 위험 완화를 위한 탁월한 대안이며 기존 및 새로운 수력 구조물 모두에 사용됨을 보여줍니다.

KEYWORDS: 

Figure 2. Different PKW Types.
Figure 2. Different PKW Types.

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Serife Yurdagul Kumcu−2−KSCE Journal of Civil Engineeringthe use of CFD for the assessment of a design, as well as screeningand optimizing of hydraulic structures and cofferdam layouts. Theyconclude that CFD has been successful in optimizing the finalconceptual configuration for the hydraulics design of the project,but recommend that physical modeling still be used as a finalconfirmation.This paper provides experimental studies performed on Kav akDam and analyses the stability of spillway design by usingFLOW-3D model. It compares the hydraulic model tests withFLOW-3D simulation results and gives information on howaccurately a commercially available Computational Fluid Dynamic(CFD) model can predict the spillway discharge capacity andpressure distribution along the spillway bottom surface. 2. Physical ModelA 1/50-scaled undistorted physical model of the Kavsak Damspillway and stilling basin was built and tested at the HydraulicModel Laboratory of State Hydraulic Works of Turkey (DSI).The model was constructed of plexiglas and was fabricated toconform to the distinctive shape of an ogee crest. The spillwayhas 45.8 m in width and 57 m long with a bottom slope of 125%.The length of the stilling basin is about 90 m. During model tests,flow velocities were measured with an ultrasonic flow meter.Pressures on the spillway were measured using a piezometerssçTable 1. Upstream and Downstream Operating Conditions of theKavsak DamRun Upstream reservoir elevation (m)Downstream tailwater elevation (m)1 306.55 168.002 311.35 174.503 314.00 178.904 316.50 182.55Fig. 1. (a) Original Project Design and Final Project Design after Experimental Investigations and Flow Measurement Sections at theApproach, (b) Top View Experimentally Modified Approach in the Laboratory, (c) Side View of the Experimentally Modified Approachin the Laboratory

Investigation of flow over spillway modeling and comparison between experimental data and CFD analysis

여수로 모델링 및 실험 데이터와 CFD 해석의 비교에 대한 조사

DOI:10.1007/s12205-016-1257-z

Authors:

Serife Yurdagul Kumcu at Necmettin Erbakan Üniversitesi

Serife Yurdagul Kumcu

Abstract and Figures

As a part of design process for hydro-electric generating stations, hydraulic engineers typically conduct some form of model testing. The desired outcome from the testing can vary considerably depending on the specific situation, but often characteristics such as velocity patterns, discharge rating curves, water surface profiles, and pressures at various locations are measured. Due to recent advances in computational power and numerical techniques, it is now also possible to obtain much of this information through numerical modeling. In this paper, hydraulic characteristics of Kavsak Dam and Hydroelectric Power Plant (HEPP), which are under construction and built for producing energy in Turkey, were investigated experimentally by physical model studies. The 1/50-scaled physical model was used in conducting experiments. Flow depth, discharge and pressure data were recorded for different flow conditions. Serious modification was made on the original project with the experimental study. In order to evaluate the capability of the computational fluid dynamics on modeling spillway flow a comparative study was made by using results obtained from physical modeling and Computational Fluid Dynamics (CFD) simulation. A commercially available CFD program, which solves the Reynolds-averaged Navier-Stokes (RANS) equations, was used to model the numerical model setup by defining cells where the flow is partially or completely restricted in the computational space. Discharge rating curves, velocity patterns and pressures were used to compare the results of the physical model and the numerical model. It was shown that there is reasonably good agreement between the physical and numerical models in flow characteristics.

수력 발전소 설계 프로세스의 일부로 수력 엔지니어는 일반적으로 어떤 형태의 모델 테스트를 수행합니다. 테스트에서 원하는 결과는 특정 상황에 따라 상당히 다를 수 있지만 속도 패턴, 방전 등급 곡선, 수면 프로파일 및 다양한 위치에서의 압력과 같은 특성이 측정되는 경우가 많습니다. 최근 계산 능력과 수치 기법의 발전으로 인해 이제는 수치 모델링을 통해 이러한 정보의 대부분을 얻을 수도 있습니다.

본 논문에서는 터키에서 에너지 생산을 위해 건설 중인 Kavsak 댐과 수력발전소(HEPP)의 수력학적 특성을 물리적 모델 연구를 통해 실험적으로 조사하였다. 1/50 스케일의 물리적 모델이 실험 수행에 사용되었습니다. 다양한 흐름 조건에 대해 흐름 깊이, 배출 및 압력 데이터가 기록되었습니다. 실험 연구를 통해 원래 프로젝트에 대대적인 수정이 이루어졌습니다.

배수로 흐름 모델링에 대한 전산유체역학의 능력을 평가하기 위해 물리적 모델링과 전산유체역학(CFD)