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

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

Abstract

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

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

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

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

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

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

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

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

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

1 Introduction

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

Various fish ladders/fishways include vertical slots, denil, rock ramps, and pool weirs [1]. The choice of fish ladder usually depends on many factors, including water elevation, space available for construction, and fish species. Pool and weir structures are among the most important fish ladders that help fish overcome obstacles in streams or rivers and swim upstream [1]. Because they are easy to construct and maintain, this type of fish ladder has received considerable attention from researchers and practitioners. Such a fish ladder consists of a sloping-floor channel with series of pools directly separated by a series of weirs [4]. These fish ladders, with or without underwater openings, are generally well-suited for slopes of 10% or less [12]. Within these pools, flow velocities are low and provide resting areas for fish after they enter the fish ladder. After resting in the pools, fish overcome these weirs by blasting or jumping over them [2]. There may also be an opening in the flooded portion of the weir through which the fish can swim instead of jumping over the weir. Design parameters such as the length of the pool, the height of the weir, the slope of the bottom, and the water discharge are the most important factors in determining the hydraulic structure of this type of fish ladder [3]. The flow over the weir depends on the flow depth at a given slope S0 and the pool length, either “plunging” or “streaming.” In plunging flow, the water column h over each weir creates a water jet that releases energy through turbulent mixing and diffusion mechanisms [5]. The dimensionless discharges for plunging (Q+) and streaming (Q*) flows are shown in Fig. 1, where Q is the total discharge, B is the width of the channel, w is the weir height, S0 is the slope of the bottom, h is the water depth above the weir, d is the flow depth, and g is the acceleration due to gravity. The maximum velocity occurs near the top of the weir for plunging flow. At the water’s surface, it drops to about half [6].

figure 1
Fig. 1

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

Considering the beneficial characteristics reported in the limited studies of researchers on the labyrinth weir in the pool-weir-type fishway, and knowing that the characteristics of flow in pool-weir-type fishways are highly dependent on the geometry of the weir, an alternative design of the rectangular labyrinth weir instead of the straight weirs in the pool-weir-type fishway is investigated in this study [79]. Kim [10] conducted experiments to compare the hydraulic characteristics of three different weir types in a pool-weir-type fishway. The results show that a straight, rectangular weir with a notch is preferable to a zigzag or trapezoidal weir. Studies on natural fish passes show that pass ability can be improved by lengthening the weir’s crest [7]. Zhong et al. [11] investigated the semi-rigid weir’s hydraulic performance in the fishway’s flow field with a pool weir. The results showed that this type of fishway performed better with a lower invert slope and a smaller radius ratio but with a larger pool spacing.

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

2 Materials and Methods

2.1 Physical Model Configuration

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

figure 2
Fig. 2

Table 1 Experimental conditions considered for calibration

Full size table

2.2 Numerical Models

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

figure 3
Fig. 3

2.3 Governing Equations

FLOW-3D® software solves the Navier–Stokes–Reynolds equations for three-dimensional analysis of incompressible flows using the fluid-volume method on a gridded domain. FLOW -3D® uses an advanced free surface flow tracking algorithm (TruVOF) developed by Hirt and Nichols [12], where fluid configurations are defined in terms of a VOF function F (xyzt). In this case, F (fluid fraction) represents the volume fraction occupied by the fluid: F = 1 in cells filled with fluid and F = 0 in cells without fluid (empty areas) [413]. The free surface area is at an intermediate value of F. (Typically, F = 0.5, but the user can specify a different intermediate value.) The equations in Cartesian coordinates (xyz) applicable to the model are as follows:

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

(1)

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

(2)

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

(3)

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

(4)

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

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

(5)

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

(6)

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

2.4 Meshing and the Boundary Conditions in the Model Setup

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

Full size table

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

figure 4
Fig. 4

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

�=ln⁡(�3−�2)(�2−�1)/ln⁡(�)

(7)

f1f2, and f3 are the hydraulic parameters obtained from the numerical simulation (f1 corresponds to the small mesh), and r is the refinement ratio. The following equation defines the convergence index of the fine mesh:

GCIfine=1.25|ε|��−1

(8)

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

GCI12=1.25|�2−�1�1|��−1

(9)

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

Full size table

figure 5
Fig. 5

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

figure 6
Fig. 6

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

figure 7
Fig. 7

3 Results

3.1 Verification of Numerical Results

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

MAPE(%)100×1�∑1�|�exp−�num�exp|

(10)

RMSE(−)1�∑1�(�exp−�num)2

(11)

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

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

3.2 Flow Regime and Discharge-Depth Relationship

Depending on the geometric shape of the fishway, including the distance of the weir, the slope of the bottom, the height of the weir, and the flow conditions, the flow regime in the fishway is divided into three categories: dipping, transitional, and flow regimes [4]. In the plunging flow regime, the flow enters the pool through the weir, impacts the bottom of the fishway, and forms a hydraulic jump causing two eddies [220]. In the streamwise flow regime, the surface of the flow passing over the weir is almost parallel to the bottom of the channel. The transitional regime has intermediate flow characteristics between the submerged and flow regimes. To predict the flow regime created in the fishway, Ead et al. [6] proposed two dimensionless parameters, Qt* and L/w, where Qt* is the dimensionless discharge, L is the distance between weirs, and w is the height of the weir:

��∗=���0���

(12)

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

figure 11
Fig. 11

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

�+=��ℎ�ℎ=23�d�

(13)

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

�d=0.57+0.075ℎ�

(14)

figure 12
Fig. 12

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

figure 13
Fig. 13

3.3 Depth-Averaged Velocity Distributions

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

figure 14
Fig. 14
figure 15
Fig. 15

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

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

figure 16
Fig. 16

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

figure 17
Fig. 17

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

figure 18
Fig. 18

3.4 Turbulence Characteristics

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

�=12(�x′2+�y′2+�z′2)

(15)

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

figure 19
Fig. 19

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

figure 20
Fig. 20
figure 21
Fig. 21

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

figure 22
Fig. 22

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

figure 23
Fig. 23

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

figure 24
Fig. 24
figure 25
Fig. 25

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

figure 26
Fig. 26

3.5 Energy Dissipation

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

�=����0��

(16)

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

figure 27
Fig. 27

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

ε=�1−�2�1

(17)

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

figure 28
Fig. 28
figure 29
Fig. 29

4 Discussion

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

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

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

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

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

5 Conclusions

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

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

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비선형 파력의 영향에 따른 잔해 언덕 방파제 형상의 효과에 대한 수치 분석

비선형 파력의 영향에 따른 잔해 언덕 방파제 형상의 효과에 대한 수치 분석

Numerical Analysis of the Effects of Rubble Mound Breakwater Geometry Under the Effect of Nonlinear Wave Force

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Abstract

Assessing the interaction of waves and porous offshore structures such as rubble mound breakwaters plays a critical role in designing such structures optimally. This study focused on the effect of the geometric parameters of a sloped rubble mound breakwater, including the shape of the armour, method of its arrangement, and the breakwater slope. Thus, three main design criteria, including the wave reflection coefficient (Kr), transmission coefficient (Kt), and depreciation wave energy coefficient (Kd), are discussed. Based on the results, a decrease in wavelength reduced the Kr and increased the Kt and Kd. The rubble mound breakwater with the Coreloc armour layer could exhibit the lowest Kr compared to other armour geometries. In addition, a decrease in the breakwater slope reduced the Kr and Kd by 3.4 and 1.25%, respectively. In addition, a decrease in the breakwater slope from 33 to 25° increased the wave breaking height by 6.1% on average. Further, a decrease in the breakwater slope reduced the intensity of turbulence depreciation. Finally, the armour geometry and arrangement of armour layers on the breakwater with its different slopes affect the wave behaviour and interaction between the wave and breakwater. Thus, layering on the breakwater and the correct use of the geometric shapes of the armour should be considered when designing such structures.

파도와 잔해 더미 방파제와 같은 다공성 해양 구조물의 상호 작용을 평가하는 것은 이러한 구조물을 최적으로 설계하는 데 중요한 역할을 합니다. 본 연구는 경사진 잔해 둔덕 방파제의 기하학적 매개변수의 효과에 초점을 맞추었는데, 여기에는 갑옷의 형태, 배치 방법, 방파제 경사 등이 포함된다. 따라서 파동 반사 계수(Kr), 투과 계수(Kt) 및 감가상각파 에너지 계수(Kd)에 대해 논의합니다. 결과에 따르면 파장이 감소하면 K가 감소합니다.r그리고 K를 증가시켰습니다t 및 Kd. Coreloc 장갑 층이 있는 잔해 언덕 방파제는 가장 낮은 K를 나타낼 수 있습니다.r 다른 갑옷 형상과 비교했습니다. 또한 방파제 경사가 감소하여 K가 감소했습니다.r 및 Kd 각각 3.4%, 1.25% 증가했다. 또한 방파제 경사가 33°에서 25°로 감소하여 파도 파쇄 높이가 평균 6.1% 증가했습니다. 또한, 방파제 경사의 감소는 난류 감가상각의 강도를 감소시켰다. 마지막으로, 경사가 다른 방파제의 장갑 형상과 장갑 층의 배열은 파도 거동과 파도와 방파제 사이의 상호 작용에 영향을 미칩니다. 따라서 이러한 구조를 설계 할 때 방파제에 층을 쌓고 갑옷의 기하학적 모양을 올바르게 사용하는 것을 고려해야합니다.

Keywords

  • Rubble mound breakwater
  • Computational fluid dynamics
  • Armour layer
  • Wave reflection coefficient
  • Wave transmission coefficient
  • Wave energy dissipation coefficient

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Effects of surface roughness on overflow discharge of embankment weirs

표면 거칠기가 제방 둑의 오버플로 배출에 미치는 영향

Effects of surface roughness on overflow discharge of embankment weirs

Abstract

A numerical study was performed on the embankment weir overflows with various surface roughness and tailwater submergence, to better understand the effects of weir roughness on discharge performances under the free and submerged conditions. The variation of flow regime is captured, from the free overflow, submerged hydraulic jump, to surface flow with increasing tailwater depth. A roughness factor is introduced to reflect the reduction in discharge caused by weir roughness. The roughness factor decreases with the roughness height, and it also depends on the tailwater depth, highlighting various relations of the roughness factor with the roughness height between different flow regimes, which is linear for the free overflow and submerged hydraulic jump while exponential for the surface flow. Accordingly, the effects of weir roughness on overflow discharge appear nonnegligible for the significant roughness height and the surface flow regime occurring under considerable tailwater submergence. The established empirical expressions of discharge coefficient and submergence and roughness factors make it possible to predict the discharge over embankment weirs considering both tailwater submergence and surface roughness.

자유 및 침수 조건에서 방류 성능에 대한 둑 거칠기의 영향을 더 잘 이해하기 위해 다양한 표면 거칠기와 테일워터 침수를 갖는 제방 둑 범람에 대한 수치 연구가 수행되었습니다.

자유 범람, 수중 수압 점프, 테일워터 깊이가 증가하는 표면 유동에 이르기까지 유동 체제의 변화가 캡처됩니다. 위어 거칠기로 인한 배출 감소를 반영하기 위해 거칠기 계수가 도입되었습니다.

조도 계수는 조도 높이와 함께 감소하고, 또한 테일워터 깊이에 따라 달라지며, 서로 다른 흐름 영역 사이의 조도 높이와 조도 계수의 다양한 관계를 강조합니다.

이는 자유 범람 및 수중 수압 점프에 대해 선형인 반면 표면에 대해 지수적입니다. 흐름. 따라서 월류 방류에 대한 웨어 조도의 영향은 상당한 조도 높이와 상당한 방수 침수 하에서 발생하는 표면 흐름 체제에 대해 무시할 수 없는 것으로 보입니다.

방류계수와 침수 및 조도계수의 확립된 실증식은 방류수 침수와 지표조도를 모두 고려한 제방보 위의 방류량을 예측할 수 있게 합니다.

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Figure 2 Modeling the plant with cylindrical tubes at the bottom of the canal.

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

열린 운하에서 홍수 흐름의 에너지를 분산시키기 위해 최적화된 식생 밀도

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

Abstract

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

Abstract

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

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [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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Figure 4. Field gate discharge experiment.

FLOW-3D Model Development for the Analysis of the Flow Characteristics of Downstream Hydraulic Structures

하류 유압 구조물의 유동 특성 분석을 위한 FLOW-3D 모델 개발

Beom-Jin Kim 1, Jae-Hong Hwang 2 and Byunghyun Kim 3,*
1 Advanced Structures and Seismic Safety Research Division, Korea Atomic Energy Research Institute,
Daejeon 34057, Korea
2 Korea Water Resources Corporation (K-Water), Daejeon 34350, Korea
3 Department of Civil Engineering, Kyungpook National University, Daegu 41566, Korea

  • Correspondence: bhkimc@knu.ac.kr; Tel.: +82-53-950-7819

Abstract

Hydraulic structures installed in rivers inevitably create a water level difference between upstream and downstream regions. The potential energy due to this difference in water level is converted into kinetic energy, causing high-velocity flow and hydraulic jumps in the river. As a result, problems such as scouring and sloping downstream may occur around the hydraulic structures. In this study, a FLOW-3D model was constructed to perform a numerical analysis of the ChangnyeongHaman weir in the Republic of Korea. The constructed model was verified based on surface velocity measurements from a field gate operation experiment. In the simulation results, the flow discharge differed from the measured value by 9–15 m3/s, from which the accuracy was evaluated to be 82–87%. The flow velocity was evaluated with an accuracy of 92% from a difference of 0.01 to 0.16 m/s. Following this verification, a flow analysis of the hydraulic structures was performed according to boundary conditions and operation conditions for numerous scenarios. Since 2018, the ChangnyeongHaman weir gate has been fully opened due to the implementation of Korea’s eco-environmental policy; therefore, in this study, the actual gate operation history data prior to 2018 was applied and evaluated. The evaluation conditions were a 50% open gate condition and the flow discharge of two cases with a large difference in water level. As a result of the analysis, the actual operating conditions showed that the velocity and the Froude number were lower than the optimal conditions, confirming that the selected design was appropriate. It was also found that in the bed protection section, the average flow velocity was high when the water level difference was large, whereas the bottom velocity was high when the gate opening was large. Ultimately, through the reviewed status survey data in this study, the downstream flow characteristics of hydraulic structures along with adequacy verification techniques, optimal design techniques such as procedures for design, and important considerations were derived. Based on the current results, the constructed FLOW-3D-based model can be applied to creating or updating flow analysis guidelines for future repair and reinforcement measures as well as hydraulic structure design.

하천에 설치되는 수력구조물은 필연적으로 상류와 하류의 수위차를 발생시킨다. 이러한 수위차로 인한 위치에너지는 운동에너지로 변환되어 하천의 고속유동과 수압점프를 일으킨다. 그 결과 수력구조물 주변에서 하류의 세굴, 경사 등의 문제가 발생할 수 있다.

본 연구에서는 대한민국 창녕함안보의 수치해석을 위해 FLOW-3D 모델을 구축하였다. 구축된 모델은 현장 게이트 작동 실험에서 표면 속도 측정을 기반으로 검증되었습니다.

시뮬레이션 결과에서 유량은 측정값과 9~15 m3/s 차이가 나고 정확도는 82~87%로 평가되었다. 유속은 0.01~0.16m/s의 차이에서 92%의 정확도로 평가되었습니다.

검증 후 다양한 시나리오에 대한 경계조건 및 운전조건에 따른 수리구조물의 유동해석을 수행하였다. 2018년부터 창녕함안보 문은 한국의 친환경 정책 시행으로 전면 개방되었습니다.

따라서 본 연구에서는 2018년 이전의 실제 게이트 운영 이력 데이터를 적용하여 평가하였다. 평가조건은 50% open gate 조건과 수위차가 큰 2가지 경우의 유수방류로 하였다. 해석 결과 실제 운전조건은 속도와 Froude수가 최적조건보다 낮아 선정된 설계가 적합함을 확인하였다.

또한 베드보호구간에서는 수위차가 크면 평균유속이 높고, 수문개구가 크면 저저유속이 높은 것으로 나타났다. 최종적으로 본 연구에서 검토한 실태조사 자료를 통해 적정성 검증기법과 함께 수력구조물의 하류 유동특성, 설계절차 등 최적 설계기법 및 중요 고려사항을 도출하였다.

현재의 결과를 바탕으로 구축된 FLOW-3D 기반 모델은 수력구조 설계뿐만 아니라 향후 보수 및 보강 조치를 위한 유동해석 가이드라인 생성 또는 업데이트에 적용할 수 있습니다.

Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.
Figure 1. Effect of downstream riverbed erosion according to the type of weir foundation.
Figure 2. Changnyeong-Haman weir depth survey results (June 2015)
Figure 2. Changnyeong-Haman weir depth survey results (June 2015)
Figure 4. Field gate discharge experiment.
Figure 4. Field gate discharge experiment.
Figure 16. Analysis results for Case 7 and Case 8
Figure 16. Analysis results for Case 7 and Case 8

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Numerical analysis of energy dissipator options using computational fluid dynamics modeling — a case study of Mirani Dam

전산 유체 역학 모델링을 사용한 에너지 소산자 옵션의 수치적 해석 — Mirani 댐의 사례 연구

Arabian Journal of Geosciences volume 15, Article number: 1614 (2022) Cite this article

Abstract

이 연구에서 FLOW 3D 전산 유체 역학(CFD) 소프트웨어를 사용하여 파키스탄 Mirani 댐 방수로에 대한 에너지 소산 옵션으로 미국 매립지(USBR) 유형 II 및 USBR 유형 III 유역의 성능을 추정했습니다. 3D Reynolds 평균 Navier-Stokes 방정식이 해결되었으며, 여기에는 여수로 위의 자유 표면 흐름을 캡처하기 위해 공기 유입, 밀도 평가 및 드리프트-플럭스에 대한 하위 그리드 모델이 포함되었습니다. 본 연구에서는 5가지 모델을 고려하였다. 첫 번째 모델에는 길이가 39.5m인 USBR 유형 II 정수기가 있습니다. 두 번째 모델에는 길이가 44.2m인 USBR 유형 II 정수기가 있습니다. 3번째와 4 번째모델에는 길이가 각각 48.8m인 USBR 유형 II 정수조와 39.5m의 USBR 유형 III 정수조가 있습니다. 다섯 번째 모델은 네 번째 모델과 동일하지만 마찰 및 슈트 블록 높이가 0.3m 증가했습니다. 최상의 FLOW 3D 모델 조건을 설정하기 위해 메쉬 민감도 분석을 수행했으며 메쉬 크기 0.9m에서 최소 오차를 산출했습니다. 세 가지 경계 조건 세트가 테스트되었으며 최소 오류를 제공하는 세트가 사용되었습니다. 수치적 검증은 USBR 유형 II( L = 48.8m), USBR 유형 III( L = 35.5m) 및 USBR 유형 III 의 물리적 모델 에너지 소산을 0.3m 블록 단위로 비교하여 수행되었습니다( L= 35.5m). 통계 분석 결과 평균 오차는 2.5%, RMSE(제곱 평균 제곱근 오차) 지수는 3% 미만이었습니다. 수리학적 및 경제성 분석을 바탕으로 4 번째 모델이 최적화된 에너지 소산기로 밝혀졌습니다. 흡수된 에너지 백분율 측면에서 물리적 모델과 수치적 모델 간의 최대 차이는 5% 미만인 것으로 나타났습니다.

In this study, the FLOW 3D computational fluid dynamics (CFD) software was used to estimate the performance of the United States Bureau of Reclamation (USBR) type II and USBR type III stilling basins as energy dissipation options for the Mirani Dam spillway, Pakistan. The 3D Reynolds-averaged Navier–Stokes equations were solved, which included sub-grid models for air entrainment, density evaluation, and drift–flux, to capture free-surface flow over the spillway. Five models were considered in this research. The first model has a USBR type II stilling basin with a length of 39.5 m. The second model has a USBR type II stilling basin with a length of 44.2 m. The 3rd and 4th models have a USBR type II stilling basin with a length of 48.8 m and a 39.5 m USBR type III stilling basin, respectively. The fifth model is identical to the fourth, but the friction and chute block heights have been increased by 0.3 m. To set up the best FLOW 3D model conditions, mesh sensitivity analysis was performed, which yielded a minimum error at a mesh size of 0.9 m. Three sets of boundary conditions were tested and the set that gave the minimum error was employed. Numerical validation was done by comparing the physical model energy dissipation of USBR type II (L = 48.8 m), USBR type III (L =35.5 m), and USBR type III with 0.3-m increments in blocks (L = 35.5 m). The statistical analysis gave an average error of 2.5% and a RMSE (root mean square error) index of less than 3%. Based on hydraulics and economic analysis, the 4th model was found to be an optimized energy dissipator. The maximum difference between the physical and numerical models in terms of percentage energy absorbed was found to be less than 5%.

Keywords

  • Numerical modeling
  • Spillway
  • Hydraulic jump
  • Energy dissipation
  • FLOW 3D

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Flow Field in a Sloped Channel with Damaged and Undamaged Piers: Numerical and Experimental Studies

Flow Field in a Sloped Channel with Damaged and Undamaged Piers: Numerical and Experimental Studies

Ehsan OveiciOmid Tayari & Navid Jalalkamali
KSCE Journal of Civil Engineering volume 25, pages4240–4251 (2021)Cite this article

Abstract

본 논문은 경사가 완만한 수로에서 손상되거나 손상되지 않은 교각 주변의 유동 패턴을 분석했습니다. 실험은 길이가 12m이고 기울기가 0.008인 직선 수로에서 수행되었습니다. Acoustic Doppler Velocimeter(ADV)를 이용하여 3차원 유속 데이터를 수집하였고, 그 결과를 PIV(Particle Image Velocimetry) 데이터와 분석하여 비교하였습니다.

다중 블록 옵션이 있는 취수구의 퇴적물 시뮬레이션(SSIIM)은 이 연구에서 흐름의 수치 시뮬레이션을 위해 통합되었습니다. 일반적으로 비교에서 얻은 결과는 수치 데이터와 실험 데이터 간의 적절한 일치를 나타냅니다. 결과는 모든 경우에 수로 입구에서 2m 거리에서 기복적 수압 점프가 발생했음을 보여주었습니다.

경사진 수로의 최대 베드 전단응력은 2개의 손상 및 손상되지 않은 교각을 설치하기 위한 수평 수로의 12배였습니다. 이와 같은 경사수로 교각의 위치에 따라 상류측 수위는 수평수로의 유사한 조건에 비해 72.5% 감소한 반면, 이 감소량은 경사면에서 다른 경우에 비해 8.3% 감소하였다. 채널 또한 두 교각이 있는 경우 최대 Froude 수는 수평 수로의 5.7배였습니다.

This paper analyzed the flow pattern around damaged and undamaged bridge piers in a channel with a mild slope. The experiments were carried out on a straight channel with a length of 12 meters and a slope of 0.008. Acoustic Doppler velocimeter (ADV) was employed to collect three-dimensional flow velocity data, and the results were analyzed and compared with particle image velocimetry (PIV) data. Sediment Simulation in Intakes with Multiblock option (SSIIM) was incorporated for the numerical simulation of the flow in this study. Generally, the results obtained from the comparisons referred to the appropriate agreement between the numerical and the experimental data. The results showed that an undular hydraulic jump occurred at a distance of two meters from the channel entrance in every case; the maximum bed shear stress in the sloped channel was 12 times that in a horizontal channel for installing two damaged and undamaged piers. With this position of the piers in the sloped channel, the upstream water level underwent a 72.5% reduction compared to similar conditions in a horizontal channel, while the amount of this water level decrease was equal to 8.3% compared to the other cases in a sloped channel. In addition, with the presence of both piers, the maximum Froude number was 5.7 times that in a horizontal channel.

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Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.

Hybrid modeling on 3D hydraulic features of a step-pool unit

Chendi Zhang1
, Yuncheng Xu1,2, Marwan A Hassan3
, Mengzhen Xu1
, Pukang He1
1State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, China. 2
College of Water Resources and Civil Engineering, China Agricultural University, Beijing, 100081, China.
5 3Department of Geography, University of British Columbia, 1984 West Mall, Vancouver BC, V6T1Z2, Canada.
Correspondence to: Chendi Zhang (chendinorthwest@163.com) and Mengzhen Xu (mzxu@mail.tsinghua.edu.cn)

Abstract

스텝 풀 시스템은 계류의 일반적인 기반이며 전 세계의 하천 복원 프로젝트에 활용되었습니다. 스텝 풀 장치는 스텝 풀 기능의 형태학적 진화 및 안정성과 밀접하게 상호 작용하는 것으로 보고된 매우 균일하지 않은 수력 특성을 나타냅니다.

그러나 스텝 풀 형태에 대한 3차원 수리학의 자세한 정보는 측정의 어려움으로 인해 부족했습니다. 이러한 지식 격차를 메우기 위해 SfM(Structure from Motion) 및 CFD(Computational Fluid Dynamics) 기술을 기반으로 하이브리드 모델을 구축했습니다. 이 모델은 CFD 시뮬레이션을 위한 입력으로 6가지 유속의 자연석으로 만든 인공 스텝 풀 장치가 있는 침대 표면의 3D 재구성을 사용했습니다.

하이브리드 모델은 스텝 풀 장치에 대한 3D 흐름 구조의 고해상도 시각화를 제공하는 데 성공했습니다. 결과는 계단 아래의 흐름 영역의 분할, 즉 수면에서의 통합 점프, 침대 근처의 줄무늬 후류 및 그 사이의 고속 제트를 보여줍니다.

수영장에서 난류 에너지의 매우 불균일한 분포가 밝혀졌으며 비슷한 용량을 가진 두 개의 에너지 소산기가 수영장에 공존하는 것으로 나타났습니다. 흐름 증가에 따른 풀 세굴 개발은 점프 및 후류 와류의 확장으로 이어지지만 이러한 증가는 스텝 풀 실패에 대한 임계 조건에 가까운 높은 흐름에서 점프에 대해 멈춥니다.

음의 경사면에서 발달된 곡물 20 클러스터와 같은 미세 지반은 국부 수력학에 상당한 영향을 주지만 이러한 영향은 수영장 바닥에서 억제됩니다. 스텝 스톤의 항력은 가장 높은 흐름이 사용되기 전에 배출과 함께 증가하는 반면 양력은 더 큰 크기와 더 넓은 범위를 갖습니다. 우리의 결과는 계단 풀 형태의 복잡한 흐름 특성을 조사할 때 물리적 및 수치적 모델링을 결합한 하이브리드 모델 접근 방식의 가능성과 큰 잠재력을 강조합니다.

Step-pool systems are common bedforms in mountain streams and have been utilized in river restoration projects around the world. Step-pool units exhibit highly non-uniform hydraulic characteristics which have been reported to closely 10 interact with the morphological evolution and stability of step-pool features. However, detailed information of the threedimensional hydraulics for step-pool morphology has been scarce due to the difficulty of measurement. To fill in this knowledge gap, we established a hybrid model based on the technologies of Structure from Motion (SfM) and computational fluid dynamics (CFD). The model used 3D reconstructions of bed surfaces with an artificial step-pool unit built by natural stones at six flow rates as inputs for CFD simulations. The hybrid model succeeded in providing high-resolution visualization 15 of 3D flow structures for the step-pool unit. The results illustrate the segmentation of flow regimes below the step, i.e., the integral jump at the water surface, streaky wake vortexes near the bed, and high-speed jets in between. The highly non-uniform distribution of turbulence energy in the pool has been revealed and two energy dissipaters with comparable capacity are found to co-exist in the pool. Pool scour development under flow increase leads to the expansion of the jump and wake vortexes but this increase stops for the jump at high flows close to the critical condition for step-pool failure. The micro-bedforms as grain 20 clusters developed on the negative slope affect the local hydraulics significantly but this influence is suppressed at pool bottom. The drag forces on the step stones increase with discharge before the highest flow is used while the lift force has a larger magnitude and wider varying range. Our results highlight the feasibility and great potential of the hybrid model approach combining physical and numerical modeling in investigating the complex flow characteristics of step-pool morphology.

Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 1: Workflow of the hybrid modeling. SfM-MVS refers to the technology of Structure from Motion with Multi View Stereo. DSM is short for digital surface model. RNG-VOF is short for Renormalized Group (RNG) k-ε turbulence model coupled with Volume of Fluid method.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 2: Flume experiment settings in Zhang et al., (2020): (a) the artificially built-up step-pool model using natural stones, with stone number labelled; (b) the unsteady hydrograph of the run of CIFR (continually-increasing-flow-rate) T2 used in this study.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 3: Setup of the CFD model: (a) three-dimensional digital surface model (DSM) of the step-pool unit by structure from motion with multi view stereo (SfM-MVS) method as the input to the 3D computational fluid dynamics (CFD) modeling; (b) extruded bed 160 surface model connected to the extra downstream component (in purple blue) and rectangular columns to fill leaks (in green), with the boundary conditions shown on mesh planes; (c) recognized geometry with mesh grids of two mesh blocks shown where MS is short for mesh size; (d) sampling volumes to capture the flow forces acting on each step stone at X, Y, and Z directions; and (e) an example for the simulated 3D flow over the step-pool unit colored by velocity magnitude at the discharge of 49.9 L/s. The abbreviations for boundary conditions in (b) are: V for specified velocity; C for continuative; P for specific pressure; and W for wall 165 condition. The contraction section in Figure (e) refers to the edge between the jet and jump at water surface.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with 265 lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 4: Distribution of time-averaged velocity magnitude (VM_mean) and vectors in three longitudinal sections. The section at Y = 0 cm goes across the keystone while the other two (Y = -18 and 13.5 cm) are located at the step stones beside the keystone with lower top elevations. Q refers to the discharge at the inlet of the computational domain. The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 5: Distribution of time-averaged flow velocity at five cross sections which are set according to the reference section (x0). The reference cross section x0 is located at the downstream end of the keystone (KS). The five sections are located at 18 cm and 6 cm upstream of the reference section (x0-18 and x0-6), and 2 cm, 15 cm and 40 cm downstream of the reference section (x0+2, x0+15, x0+40). The spacing for X, Y, and Z axes are all 10 cm in the plots.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 6: Distribution of the time-averaged turbulence kinetic energy (TKE) at the five cross sections same with Figure 3.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 7: Boxplots for the distributions of the mass-averaged flow kinetic energy (KE, panels a-f), turbulence kinetic energy (TKE, panels g-l), and turbulent dissipation (εT, panels m-r) in the pool for all the six tested discharges (the plots at the same discharge are in the same row). The mass-averaged values were calculated every 2 cm in the streamwise direction. The flow direction is from left to right in all the plots. The general locations of the contraction section for all the flow rates are marked by the dashed lines, except for Q = 5 L/s when the jump is located too close to the step. The longitudinal distance taken up by negative slope in the pool for the inspected range is shown by shaded area in each plot.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 8: Instantaneous flow structures extracted using the Q-criterion (Qcriterion=1200) and colored by the magnitude of flow velocity.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 9: Time-averaged dynamic pressure (DP_mean) on the bed surface in the step-pool model under the two highest discharges, with the step numbers marked. The negative values in the plots result from the setting of standard atmospheric pressure = 0 Pa, whose absolute value is 1.013×105 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 10: Time-averaged shear stress (SS_mean) on bed surface in the step-pool model, with the step numbers marked. The standard atmospheric pressure is set as 0 Pa.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 11: Variation of fluid force components and magnitude of resultant flow force acting on step stones with flow rate. The stone 4 is the keystone. Stone numbers are consistent with those in Fig. 9-10. The upper limit of the sampling volumes for flow force calculation is higher than water surface while the lower limit is set at 3 cm lower than the keystone crest.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 12: Variation of drag (CD) and lift (CL) coefficient of the step stones along with flow rate. Stone numbers are consistent with those in Fig. 8-9. KS is short for keystone. The negative values of CD correspond to the drag forces towards the upstream while the negative values of CL correspond to lift forces pointing downwards.
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure 13: Longitudinal distributions of section-averaged and -integral turbulent kinetic energy (TKE) for the jump and wake vortexes at the largest three discharges. The flow direction is from left to right in all the plots. The general locations of the contraction sections under the three flow rates are marked by dashed lines in figures (d) to (f).
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A1: Water surface profiles of the simulations with different mesh sizes at the discharge of 43.6 L/s at the longitudinal sections at: (a) Y = 24.5 cm (left boundary); (b) Y = 0.3 cm (middle section); (c) Y = -24.5 cm (right boundary). MS is short for mesh size. The flow direction is from left to right in each plot.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A2: Contours of velocity magnitude in the longitudinal section at Y = 0 cm at different mesh sizes (MSs) under the flow condition with the discharge of 43.6 L/s: (a) 0.50 cm; (b) 0.375 cm; (c) 0.30 cm; (d) 0.27 cm; (e) 0.25 cm; (f) 0.24 cm. The flow direction is from left to right.
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A3: Measurements of water surfaces (orange lines) used in model verification: (a) water surface profiles from both sides of the flume; (b) upstream edge of the jump regime from top view. KS refers to keystone in figure (b).
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A15. Figure (a) shows the locations of the cross sections and target coarse grains at Q = 49.9 L/s. Figures (b) to (e) show the distribution of velocity magnitude (VM_mean) in the four chosen cross sections: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5. G1 to G6 refer to 6 protruding grains in the micro-bedforms in the pool.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.
Figure A16. The distribution of turbulent kinetic energy (TKE) in the same cross sections as in figure S15: (a) x0+8.0; (b) x0+14.0; (c) x0+21.5; (d) x0+42.5.

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그림 1 하천횡단구조물 하류부 횡단구조물 파괴

유입조건에 따른압력변이로 인한하천횡단구조물 하류물받이공 및 바닥보호공설계인자 도출최종보고서

주관연구기관 / 홍익대학교 산학협력단
공동연구기관 / 한국건설기술연구원
공동연구기관 / 주식회사 지티이

연구의 목적 및 내용

하천횡단구조물이 하천설계기준(2009)대로 설계되었음에도 불구하고, 하류부에서 물받이공 및 바닥보호공의 피해가 발생하여, 구조물 본체에 대한 안전성이 현저하 게 낮아지고 있는 실정이다. 하천설계기준이 상류부의 수리특성을 반영하였다고 하나 하류부의 수리특성인 유속의 변동 성분 또는 압력의 변동성분까지 고려하고 있지는 않다. 현재 많은 선행연구에서 이러한 난류적 특성이 구조물에 미치는 영 향에 대해 제시하고 있는 실정이며, 국내 하천에서의 피해 또한 이와 관련이 있다 고 판단된다. 이에 본 연구에서는 난류성분 특히 압력의 변동성분이 물받이공과 바닥보호공에 미치는 영향을 정량적으로 분석하여, 하천 횡단구조물의 치수 안전 성 증대에 기여하고자 한다. 물받이공과 바닥보호공에 미치는 압력의 변동성분 (pressure fluctuation) 영향을 분석하기 위해 크게 3가지로 연구내용을 분류하였 다. 첫 번째는 압력의 변동으로 순간적인 음압구배(adversed pressure gradient) 가 발생할 경우 바닥보호공의 사석 및 블록이 이탈하는 것이다. 이를 확인하기 위 해 정밀한 압력 측정장치를 통해 압력변이를 측정하여, 사석의 이탈 가능성을 검 토할 것이며, 최종적으로 이탈에 대한 한계조건을 도출할 것이다. 두 번째는 압력 의 변동이 물받이공의 진동을 유발시켜 이를 지지하고 있는 지반에 다짐효과를 가 져와 물받이공과 지반사이에 공극이 발생하는 경우이다. 이러한 공극으로 물받이 공은 자중 및 물의 압력을 받게 되어, 결국 휨에 의한 파괴가 발생할 가능성이 있 게 된다. 본 연구에서는 실험을 통하여 압력의 변동과 물받이공의 진동을 동시에 측정하여, 진동이 발생하지 않을 최소 두께를 제시할 것이다. 세 번째는 압력변이 로 인한 물받이공의 진동이 피로파괴로 연결되는 경우이다. 이 현상 또한 수리실 험을 통해 압력변이-피로파괴의 관계를 정량적으로 분석하여, 한계 조건을 제시할 것이다. 본 연구는 국내 보 및 낙차공에서 발생하는 다양한 Jet의 특성을 수리실 험으로 재현해야 하며, 이를 위해 평면 Jet 분사기(plane Jet injector)를 고안/ 제작하여, 효율적인 수리실험을 수행할 것이다. 또한 3차원 수치해석을 통해 실제 스케일에 적용함으로써 연구결과의 활용도 및 적용성을 높이고자 한다.

Keywords

압력변이, 물받이공, 바닥보호공, 난류, 진동

 그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 1 하천횡단구조물 하류부 횡단구조물 파괴
그림 2. 시간에 따른 압력의 변동 양상 및 정의
그림 2. 시간에 따른 압력의 변동 양상 및 정의
 그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
그림 3. 하천횡단구조물 하류부 도수현상시 발생하는 압력변이 분포도, Fr=8.0 상태이며, 바닥(slab)에 양압과 음압이 지속적으로 작용한다. (Fiorotto & Rinaldo, 2010)
 그림 4. 파괴 개념
그림 4. 파괴 개념
그림 6. PIV 측정 원리(www.photonics.com)
그림 6. PIV 측정 원리(www.photonics.com)
그림 7. LED회로판 및 BIV기법 기본개념
그림 7. LED회로판 및 BIV기법 기본개념
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 8. BIV측정기법을 적용한 순간이미지 (Lin et al., 2012)
그림 9. 감세공의 분류
그림 9. 감세공의 분류
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 17 수리실헐 수로시설: (a) 전체수로전경, (b) Weir 보를 포함한 측면도, (c) 도수조건 실험전경
그림 18 수리실험 개요도
그림 18 수리실험 개요도
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 127 난류모형별 압력 Data (측정위치는 그림 125 참조)
그림 128 RNG 모형을 이용한 수치모의 결과
그림 128 RNG 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 129 LES 모형을 이용한 수치모의 결과
그림 130 압력 Data의 필터링
그림 130 압력 Data의 필터링
그림 134 Case 1의 흐름특성 분포도 및 그래프
그림 134 Case 1의 흐름특성 분포도 및 그래프

참고문헌

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태.

국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서. 국토해양부 (2010). 낙동강 살리기 사업 24공구(성주칠곡지구) 실시설계보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인.

국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기준. 류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999).

류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.

배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.

우효섭 (2001). 하천수리학. 청문각.

한국수자원학회 (2009). 하천설계기준해설.

한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발

한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
기법에 대한 원천기술개발

국토기술연구센터 (1998) 하상유지공의 구조설계 지침.

감사원 (2013) 감사원 결과보고서- 4대강살리기 사업 주요시설물 품질 밑 수질관리 실태. 국토해양부 (2009) 전국 하천횡단 구조물 설치현황 및 어도 실태조사 보고서.

국토해양부 (2012) 보도자료-준공대비 점검결과, 4대강 보 안전 재확인. 국토해양부 (2012) 국가 및 지방하천 종합정비 마스터플랜.

국토교통성 (2008) 하천사방기술기준.

농림부 (1996). 농업생산기반정비사업계획 설계기

류권규(역자) (2009). 난류의 수치모의(원저자 : 梶島岳夫, 1999).
류권규, 마리안 머스테, 로버트 에테마, 윤병만 (2006). “난류 중 부유사의 속도 지체 측정.” 한국수자원학회논문집, 제39권, 제2호, pp.99-108.
배재현, 이경훈, 신종근, 양용수, 이주희 (2011). “입자영상유속계를 이용한 은어의 유영능력 측정.” 제47권, 제4호, pp.411-418.
우효섭 (2001). 하천수리학. 청문각. 한국수자원학회 (2009). 하천설계기준해설. 한국건설기술연구원 (2014) 입자영상유속계(PIV)를 이용한 하천구조물 주변 유동해석 기법 개발
한국건설기술연구원 (2017) 보와 하상유지공의 안전성 확보를 위한 물받이와 바닥보호공의 성능평가
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원본 보기
Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.

스키밍 흐름 영역에서 계단형 여수로의 수리 성능에 대한 삼각형 프리즘 요소의 영향: 실험 연구 및 수치 모델링

The effect of triangular prismatic elements on the hydraulic performance of stepped spillways in the skimming flow regime: an experimental study and numerical modeling 

Kiyoumars RoushangarSamira AkhgarSaman Shahnazi

계단식 여수로는 댐의 여수로 위로 흐르는 큰 물의 에너지를 분산시키는 비용 효율적인 유압 구조입니다. 이 연구에서는 삼각주형 요소(TPE)가 계단식 배수로의 수력 성능에 미치는 영향에 초점을 맞췄습니다. 9개의 계단식 배수로 모델이 TPE의 다양한 모양과 레이아웃으로 실험 및 수치적으로 조사되었습니다. 적절한 난류 모델을 채택하려면 RNG k – ε 및 표준 k – ε모델을 활용했습니다. 계산 모델 결과는 계단 표면의 속도 분포 및 압력 프로파일을 포함하여 실험 사례의 계단 여수로에 대한 복잡한 흐름을 만족스럽게 시뮬레이션했습니다. 결과는 계단식 여수로에 TPE를 설치하는 것이 캐비테이션 효과를 줄이는 효과적인 방법이 될 수 있음을 나타냅니다. 계단식 여수로에 TPE를 설치하면 에너지 소실률이 최대 54% 증가했습니다. 계단식 배수로의 성능은 TPE가 더 가깝게 배치되었을 때 개선되었습니다. 또한, 실험 데이터를 이용하여 거칠기 계수( f )와 임계 깊이 대 단차 거칠기( yc / k )의 비율 사이의 관계를 높은 정확도로 얻었다.

Keywords

energy dissipationFlow-3Droughness coefficientstepped spillwaytriangular prismatic elements

에너지 소산 , Flow-3D , 거칠기 계수 , 계단식 배수로 , 삼각형 프리즘 요소

Figure 1 | General schematics of laboratory flume facilities.
Figure 1 | General schematics of laboratory flume facilities.
Figure 2 | Different layouts of the selected TPE in the experimental study (y1 and y2 are initial, and sequent depths of hydraulic jump).
Figure 2 | Different layouts of the selected TPE in the experimental study (y1 and y2 are initial, and sequent depths of hydraulic jump).
Figure 3 | Geometry and alignment of TPE in the numerical study.
Figure 3 | Geometry and alignment of TPE in the numerical study.
Figure 5 | Comparison of turbulence models in Flow-3D.
Figure 5 | Comparison of turbulence models in Flow-3D.
Figure 6 | Sequent water depths versus unit flow rate in standard stepped spillways and stepped spillways with triangular TPEs of types A and B.
Figure 6 | Sequent water depths versus unit flow rate in standard stepped spillways and stepped spillways with triangular TPEs of types A and B.
Figure 7 | Energy dissipation for the standard stepped spillway and the stepped spillway with TPEs.
Figure 7 | Energy dissipation for the standard stepped spillway and the stepped spillway with TPEs.
Figure 8 | Positions of measurement points to investigate the pressure and velocity distributions on the stepped spillway
Figure 8 | Positions of measurement points to investigate the pressure and velocity distributions on the stepped spillway
Figure 9 | Velocity distributions on the vertical surface of step number 4.
Figure 9 | Velocity distributions on the vertical surface of step number 4.
Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.
Figure 10 | Contour lines of the static pressure (Pa) for the standard form of the stepped spillway with discharge of 60 liters/second.
Figure 11 | Pressure distribution on the vertical surface of the fourth step.
Figure 11 | Pressure distribution on the vertical surface of the fourth step.
Figure 12 | Horizontal profile of the pressure distribution on the floor of step 4.
Figure 12 | Horizontal profile of the pressure distribution on the floor of step 4.
Figure 13 | Roughness coefficient changes with various unit discharges for stepped spillways.
Figure 13 | Roughness coefficient changes with various unit discharges for stepped spillways.
Figure 14 | Variations of sequent depth of downstream with various unit discharges for stepped spillways.
Figure 14 | Variations of sequent depth of downstream with various unit discharges for stepped spillways.
Figure 15 | Energy dissipation rate changes with various unit discharges for different stepped spillways.
Figure 15 | Energy dissipation rate changes with various unit discharges for different stepped spillways.
Figure 16 | Roughness coefficients (f ) versus the critical depth to the step roughness ratio (yc/K).
Figure 16 | Roughness coefficients (f ) versus the critical depth to the step roughness ratio (yc/K).

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Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

지속 가능한 해안 보호 구조로서 굴절식 콘크리트 블록 매트리스의 손상 메커니즘의 수치적 모델링

Numerical Modeling of Failure Mechanisms in Articulated Concrete Block Mattress as a Sustainable Coastal Protection Structure

Author

Ramin Safari Ghaleh(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Omid Aminoroayaie Yamini(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

S. Hooman Mousavi(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Mohammad Reza Kavianpour(Department of Civil Engineering, K. N. Toosi University of Technology, Tehran 19967-15433, Iran)

Abstract

해안선 보호는 전 세계적인 우선 순위로 남아 있습니다. 일반적으로 해안 지역은 석회암과 같은 단단하고 비자연적이며 지속 불가능한 재료로 보호됩니다. 시공 속도와 환경 친화성을 높이고 개별 콘크리트 블록 및 보강재의 중량을 줄이기 위해 콘크리트 블록을 ACB 매트(Articulated Concrete Block Mattress)로 설계 및 구현할 수 있습니다. 이 구조물은 필수적인 부분으로 작용하며 방파제 또는 해안선 보호의 둑으로 사용할 수 있습니다. 물리적 모델은 해안 구조물의 현상을 추정하고 조사하는 핵심 도구 중 하나입니다. 그러나 한계와 장애물이 있습니다. 결과적으로, 본 연구에서는 이러한 구조물에 대한 파도의 수치 모델링을 활용하여 방파제에서의 파도 전파를 시뮬레이션하고, VOF가 있는 Flow-3D 소프트웨어를 통해 ACB Mat의 불안정성에 영향을 미치는 요인으로는 파괴파동, 옹벽의 흔들림, 파손으로 인한 인양력으로 인한 장갑의 변위 등이 있다. 본 연구의 가장 중요한 목적은 수치 Flow-3D 모델이 연안 호안의 유체역학적 매개변수를 모사하는 능력을 조사하는 것입니다. 콘크리트 블록 장갑에 대한 파동의 상승 값은 파단 매개변수( 0.5 < ξ m – 1 , 0 < 3.3 )가 증가할 때까지(R u 2 % H m 0 = 1.6) ) 최대값에 도달합니다. 따라서 차단파라미터를 증가시키고 파괴파(ξ m − 1 , 0 > 3.3 ) 유형을 붕괴파/해일파로 변경함으로써 콘크리트 블록 호안의 상대파 상승 변화 경향이 점차 증가합니다. 파동(0.5 < ξ m − 1 , 0 < 3.3 )의 경우 차단기 지수(표면 유사성 매개변수)를 높이면 상대파 런다운의 낮은 값이 크게 감소합니다. 또한, 천이영역에서는 파단파동이 쇄도파에서 붕괴/서징으로의 변화( 3.3 < ξ m – 1 , 0 < 5.0 )에서 상대적 런다운 과정이 더 적은 강도로 발생합니다.

Shoreline protection remains a global priority. Typically, coastal areas are protected by armoring them with hard, non-native, and non-sustainable materials such as limestone. To increase the execution speed and environmental friendliness and reduce the weight of individual concrete blocks and reinforcements, concrete blocks can be designed and implemented as Articulated Concrete Block Mattress (ACB Mat). These structures act as an integral part and can be used as a revetment on the breakwater body or shoreline protection. Physical models are one of the key tools for estimating and investigating the phenomena in coastal structures. However, it does have limitations and obstacles; consequently, in this study, numerical modeling of waves on these structures has been utilized to simulate wave propagation on the breakwater, via Flow-3D software with VOF. Among the factors affecting the instability of ACB Mat are breaking waves as well as the shaking of the revetment and the displacement of the armor due to the uplift force resulting from the failure. The most important purpose of the present study is to investigate the ability of numerical Flow-3D model to simulate hydrodynamic parameters in coastal revetment. The run-up values of the waves on the concrete block armoring will multiply with increasing break parameter ( 0.5 < ξ m − 1 , 0 < 3.3 ) due to the existence of plunging waves until it ( R u 2 % H m 0 = 1.6 ) reaches maximum. Hence, by increasing the breaker parameter and changing breaking waves ( ξ m − 1 , 0 > 3.3 ) type to collapsing waves/surging waves, the trend of relative wave run-up changes on concrete block revetment increases gradually. By increasing the breaker index (surf similarity parameter) in the case of plunging waves ( 0.5 < ξ m − 1 , 0 < 3.3 ), the low values on the relative wave run-down are greatly reduced. Additionally, in the transition region, the change of breaking waves from plunging waves to collapsing/surging ( 3.3 < ξ m − 1 , 0 < 5.0 ), the relative run-down process occurs with less intensity.

Figure 1.  Armor  geometric  characteristics  and  drawing  three-dimensional  geometry  of  a  breakwater section  in SolidWorks software.
Figure 1. Armor geometric characteristics and drawing three-dimensional geometry of a breakwater section in SolidWorks software.
Figure  5.  Wave  overtopping on  concrete block  mattress in (a)  laboratory  and (b)  numerical  model.
Figure 5. Wave overtopping on concrete block mattress in (a) laboratory and (b) numerical model.
Figure  7.  Mesh  block  for  calibrated  numerical  model  with  686,625  cells  and  utilization  of  FAVOR  tab to assess figure geometry.
Figure 7. Mesh block for calibrated numerical model with 686,625 cells and utilization of FAVOR tab to assess figure geometry.
Figure  10.  How to place different layers  (core, filter,  and revetment)  of the structure on slope.
Figure 10. How to place different layers (core, filter, and revetment) of the structure on slope.

Suggested Citation

Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
Figure 11. Wave run-up on ACB Mat blocks in (a) laboratory model and (b) numerical modeling.
Figure  15.  Localized  deformations  on  revetment  due  to  run-down  and  sliding  of  armor  from  body  laboratory  model  (left) and  numerical  modeling (right).
Figure 15. Localized deformations on revetment due to run-down and sliding of armor from body laboratory model (left) and numerical modeling (right).

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Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s.

Optimization Algorithms and Engineering: Recent Advances and Applications

Mahdi Feizbahr,1 Navid Tonekaboni,2Guang-Jun Jiang,3,4 and Hong-Xia Chen3,4Show moreAcademic Editor: Mohammad YazdiReceived08 Apr 2021Revised18 Jun 2021Accepted17 Jul 2021Published11 Aug 2021

Abstract

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


강의 식생은 거칠기를 증가시키고 평균 유속을 감소시키며, 유속 에너지를 감소시키고 강의 단면에서 유속 프로파일을 변경합니다. 자연의 많은 운하와 강은 홍수 동안 초목으로 덮여 있습니다. 운하의 조도는 식물의 영향을 많이 받으므로 홍수시 유동저항에 큰 영향을 미칩니다. 식물로 인한 흐름에 대한 거칠기 저항은 흐름 조건 및 식물에 따라 다르므로 모델은 유속, 흐름 깊이 및 운하를 따라 식생 유형의 영향을 고려하여 현재 속도를 시뮬레이션해야 합니다. 근관의 거칠기의 영향을 조사하기 위해 총 48개의 모델이 시뮬레이션되었습니다. 결과는 유속을 높임으로써 유속을 감소시키는 식생의 영향은 무시할 수 있는 반면, 해류가 더 낮은 유속일 때 유속을 감소시키는 식생의 영향은 분명히 상당함을 나타냈다.

1. Introduction

Considering the impact of each variable is a very popular field within the analytical and statistical methods and intelligent systems [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.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 4 Flow velocity profiles for canals with a depth of 1 m and flow velocities of 3–3.3 m/s. Canal with a depth of 1 meter and a flow velocity of (a) 3 meters per second, (b) 3.1 meters per second, (c) 3.2 meters per second, and (d) 3.3 meters per second.

Figure 5 Canal diagram with a depth of 1 meter and a flow rate of 3 meters per second.

Figure 6 Canal diagram with a depth of 1 meter and a flow rate of 3.1 meters per second.

Figure 7 Canal diagram with a depth of 1 meter and a flow rate of 3.2 meters per second.

Figure 8 Canal diagram with a depth of 1 meter and a flow rate of 3.3 meters per second.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 9 Flow velocity profiles for canals with a depth of 2 m and flow velocities of 4–4.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

Figure 10 Canal diagram with a depth of 2 meters and a flow rate of 4 meters per second.

Figure 11 Canal diagram with a depth of 2 meters and a flow rate of 4.1 meters per second.

Figure 12 Canal diagram with a depth of 2 meters and a flow rate of 4.2 meters per second.

Figure 13 Canal diagram with a depth of 2 meters and a flow rate of 4.3 meters per second.(a)
(a)(b)
(b)(c)
(c)(d)
(d)(a)
(a)(b)
(b)(c)
(c)(d)
(d)Figure 14 Flow velocity profiles for canals with a depth of 3 m and flow velocities of 5–5.3 m/s. Canal with a depth of 2 meters and a flow rate of (a) 4 meters per second, (b) 4.1 meters per second, (c) 4.2 meters per second, and (d) 4.3 meters per second.

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

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

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

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

According to Figure 11, we see that, with increasing Manning’s coefficient, the canal bed speed decreases. But this deceleration is more noticeable than the deceleration of Figures 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.(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 19 Comparison of velocity profiles with the same plant densities (depth 1 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 1 m; (b) plant densities of 50%, depth 1 m; and (c) plant densities of 75%, depth 1 m.

According to Figure 20, by increasing the speed of vegetation, the effect of vegetation on reducing the flow rate becomes more noticeable. And the role of input current does not have much effect in reducing speed.(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 20 Comparison of velocity profiles with the same plant densities (depth 2 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 2 m; (b) plant densities of 50%, depth 2 m; and (c) plant densities of 75%, depth 2 m.

According to Figure 21, it can be seen that, with increasing speed, the effect of vegetation on reducing the bed flow rate becomes more noticeable and the role of the input current does not have much effect. In general, it can be seen that, by increasing the speed of the input current, the slope of the profiles increases from the bed to the water surface and due to the fact that, in software, the roughness coefficient applies to the channel floor only in the boundary conditions, this can be perfectly justified. Of course, it can be noted that, due to the flexible conditions of the vegetation of the bed, this modeling can show acceptable results for such grasses in the canal floor. In the next directions, we may try application of swarm-based optimization methods for modeling and finding the most effective factors in this research [27815188994]. In future, we can also apply the simulation logic and software of this research for other domains such as power engineering [9599].(a)
(a)(b)
(b)(c)
(c)(a)
(a)(b)
(b)(c)
(c)Figure 21 Comparison of velocity profiles with the same plant densities (depth 3 m). Comparison of velocity profiles with (a) plant densities of 25%, depth 3 m; (b) plant densities of 50%, depth 3 m; and (c) plant densities of 75%, depth 3 m.

3. Conclusion

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

Nomenclature

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

Data Availability

All data are included within the paper.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

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

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Fig. 1. Hydraulic jump flow structure.

Performance assessment of OpenFOAM and FLOW-3D in the numerical modeling of a low Reynolds number hydraulic jump

낮은 레이놀즈 수 유압 점프의 수치 모델링에서 OpenFOAM 및 FLOW-3D의 성능 평가

ArnauBayona DanielValerob RafaelGarcía-Bartuala Francisco ​JoséVallés-Morána P. AmparoLópez-Jiméneza

Abstract

A comparative performance analysis of the CFD platforms OpenFOAM and FLOW-3D is presented, focusing on a 3D swirling turbulent flow: a steady hydraulic jump at low Reynolds number. Turbulence is treated using RANS approach RNG k-ε. A Volume Of Fluid (VOF) method is used to track the air–water interface, consequently aeration is modeled using an Eulerian–Eulerian approach. Structured meshes of cubic elements are used to discretize the channel geometry. The numerical model accuracy is assessed comparing representative hydraulic jump variables (sequent depth ratio, roller length, mean velocity profiles, velocity decay or free surface profile) to experimental data. The model results are also compared to previous studies to broaden the result validation. Both codes reproduced the phenomenon under study concurring with experimental data, although special care must be taken when swirling flows occur. Both models can be used to reproduce the hydraulic performance of energy dissipation structures at low Reynolds numbers.

CFD 플랫폼 OpenFOAM 및 FLOW-3D의 비교 성능 분석이 3D 소용돌이치는 난류인 낮은 레이놀즈 수에서 안정적인 유압 점프에 초점을 맞춰 제시됩니다. 난류는 RANS 접근법 RNG k-ε을 사용하여 처리됩니다.

VOF(Volume Of Fluid) 방법은 공기-물 계면을 추적하는 데 사용되며 결과적으로 Eulerian-Eulerian 접근 방식을 사용하여 폭기가 모델링됩니다. 입방체 요소의 구조화된 메쉬는 채널 형상을 이산화하는 데 사용됩니다. 수치 모델 정확도는 대표적인 유압 점프 변수(연속 깊이 비율, 롤러 길이, 평균 속도 프로파일, 속도 감쇠 또는 자유 표면 프로파일)를 실험 데이터와 비교하여 평가됩니다.

모델 결과는 또한 결과 검증을 확장하기 위해 이전 연구와 비교됩니다. 소용돌이 흐름이 발생할 때 특별한 주의가 필요하지만 두 코드 모두 실험 데이터와 일치하는 연구 중인 현상을 재현했습니다. 두 모델 모두 낮은 레이놀즈 수에서 에너지 소산 구조의 수리 성능을 재현하는 데 사용할 수 있습니다.

Keywords

CFDRANS, OpenFOAM, FLOW-3D ,Hydraulic jump, Air–water flow, Low Reynolds number

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Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.

Numerical Simulations of the Flow Field of a Submerged Hydraulic Jump over Triangular Macroroughnesses

Triangular Macroroughnesses 대한 잠긴 수압 점프의 유동장 수치 시뮬레이션

by Amir Ghaderi 1,2,Mehdi Dasineh 3,Francesco Aristodemo 2 andCostanza Aricò 4,*1Department of Civil Engineering, Faculty of Engineering, University of Zanjan, Zanjan 537138791, Iran2Department of Civil Engineering, University of Calabria, Arcavacata, 87036 Rende, Italy3Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Maragheh 8311155181, Iran4Department of Engineering, University of Palermo, Viale delle Scienze, 90128 Palermo, Italy*Author to whom correspondence should be addressed.Academic Editor: Anis YounesWater202113(5), 674; https://doi.org/10.3390/w13050674

Abstract

The submerged hydraulic jump is a sudden change from the supercritical to subcritical flow, specified by strong turbulence, air entrainment and energy loss. Despite recent studies, hydraulic jump characteristics in smooth and rough beds, the turbulence, the mean velocity and the flow patterns in the cavity region of a submerged hydraulic jump in the rough beds, especially in the case of triangular macroroughnesses, are not completely understood. The objective of this paper was to numerically investigate via the FLOW-3D model the effects of triangular macroroughnesses on the characteristics of submerged jump, including the longitudinal profile of streamlines, flow patterns in the cavity region, horizontal velocity profiles, streamwise velocity distribution, thickness of the inner layer, bed shear stress coefficient, Turbulent Kinetic Energy (TKE) and energy loss, in different macroroughness arrangements and various inlet Froude numbers (1.7 < Fr1 < 9.3). To verify the accuracy and reliability of the present numerical simulations, literature experimental data were considered.

Keywords: submerged hydraulic jumptriangular macroroughnessesTKEbed shear stress coefficientvelocityFLOW-3D model

수중 유압 점프는 강한 난류, 공기 동반 및 에너지 손실로 지정된 초임계에서 아임계 흐름으로의 급격한 변화입니다. 최근 연구에도 불구하고, 특히 삼각형 거시적 거칠기의 경우, 평활 및 거친 베드에서의 수압 점프 특성, 거친 베드에서 잠긴 수압 점프의 공동 영역에서 난류, 평균 속도 및 유동 패턴이 완전히 이해되지 않았습니다.

이 논문의 목적은 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 두께를 포함하여 서브머지드 점프의 특성에 대한 삼각형 거시 거칠기의 영향을 FLOW-3D 모델을 통해 수치적으로 조사하는 것이었습니다.

내부 층의 층 전단 응력 계수, 난류 운동 에너지(TKE) 및 에너지 손실, 다양한 거시 거칠기 배열 및 다양한 입구 Froude 수(1.7 < Fr1 < 9.3). 현재 수치 시뮬레이션의 정확성과 신뢰성을 검증하기 위해 문헌 실험 데이터를 고려했습니다.

 Introduction

격렬한 난류 혼합과 기포 동반이 있는 수압 점프는 초임계에서 아임계 흐름으로의 변화 과정으로 간주됩니다[1]. 자유 및 수중 유압 점프는 일반적으로 게이트, 배수로 및 둑과 같은 수력 구조 아래의 에너지 손실에 적합합니다. 매끄러운 베드에서 유압 점프의 특성은 널리 연구되었습니다[2,3,4,5,6,7,8,9].

베드의 거칠기 요소가 매끄러운 베드와 비교하여 수압 점프의 특성에 어떻게 영향을 미치는지 예측하기 위해 거시적 거칠기에 대한 자유 및 수중 수력 점프에 대해 여러 실험 및 수치 연구가 수행되었습니다. Ead와 Rajaratnam[10]은 사인파 거대 거칠기에 대한 수리학적 점프의 특성을 조사하고 무차원 분석을 통해 수면 프로파일과 배출을 정규화했습니다.

Tokyayet al. [11]은 두 사인 곡선 거대 거칠기에 대한 점프 길이 비율과 에너지 손실이 매끄러운 베드보다 각각 35% 더 작고 6% 더 높다는 것을 관찰했습니다. Abbaspur et al. [12]는 6개의 사인파형 거대 거칠기에 대한 수력학적 점프의 특성을 연구했습니다. 그 결과, 꼬리수심과 점프길이는 평상보다 낮았고 Froude 수는 점프길이에 큰 영향을 미쳤습니다.

Shafai-Bejestan과 Neisi[13]는 수압 점프에 대한 마름모꼴 거대 거칠기의 영향을 조사했습니다. 결과는 마름모꼴 거시 거칠기를 사용하면 매끄러운 침대와 비교하여 꼬리 수심과 점프 길이를 감소시키는 것으로 나타났습니다. Izadjoo와 Shafai-Bejestan[14]은 다양한 사다리꼴 거시 거칠기에 대한 수압 점프를 연구했습니다.

그들은 전단응력계수가 평활층보다 10배 이상 크고 점프길이가 50% 감소하는 것을 관찰하였습니다. Nikmehr과 Aminpour[15]는 Flow-3D 모델 버전 11.2[16]를 사용하여 사다리꼴 블록이 있는 거시적 거칠기에 대한 수력학적 점프의 특성을 조사했습니다. 결과는 거시 거칠기의 높이와 거리가 증가할수록 전단 응력 계수뿐만 아니라 베드 근처에서 속도가 감소하는 것으로 나타났습니다.

Ghaderi et al. [17]은 다양한 형태의 거시 거칠기(삼각형, 정사각형 및 반 타원형)에 대한 자유 및 수중 수력 점프 특성을 연구했습니다. 결과는 Froude 수의 증가에 따라 자유 및 수중 점프에서 전단 응력 계수, 에너지 손실, 수중 깊이, 미수 깊이 및 상대 점프 길이가 증가함을 나타냅니다.

자유 및 수중 점프에서 가장 높은 전단 응력과 에너지 손실은 삼각형의 거시 거칠기가 존재할 때 발생했습니다. Elsebaie와 Shabayek[18]은 5가지 형태의 거시적 거칠기(삼각형, 사다리꼴, 2개의 측면 경사 및 직사각형이 있는 정현파)에 대한 수력학적 점프의 특성을 연구했습니다. 결과는 모든 거시적 거칠기에 대한 에너지 손실이 매끄러운 베드에서보다 15배 이상이라는 것을 보여주었습니다.

Samadi-Boroujeni et al. [19]는 다양한 각도의 6개의 삼각형 거시 거칠기에 대한 수력 점프를 조사한 결과 삼각형 거시 거칠기가 평활 베드에 비해 점프 길이를 줄이고 에너지 손실과 베드 전단 응력 계수를 증가시키는 것으로 나타났습니다.

Ahmed et al. [20]은 매끄러운 베드와 삼각형 거시 거칠기에서 수중 수력 점프 특성을 조사했습니다. 결과는 부드러운 침대와 비교할 때 잠긴 깊이와 점프 길이가 감소했다고 밝혔습니다. 표 1은 다른 연구자들이 제시한 과거의 유압 점프에 대한 실험 및 수치 연구의 세부 사항을 나열합니다.

Table 1. Main characteristics of some past experimental and numerical studies on hydraulic jumps.

ReferenceShape Bed-Channel Type-
Jump Type
Channel Dimension (m)Roughness (mm)Fr1Investigated Flow
Properties
Ead and Rajaratnam [10]-Smooth and rough beds-Rectangular channel-Free jumpCL1 = 7.60
CW2 = 0.44
CH3 = 0.60
-Corrugated sheets (RH4 = 13 and 22)4–10-Upstream and tailwater depths-Jump length-Roller length-Velocity-Water surface profile
Tokyay et al. [11]-Smooth and rough beds-Rectangular channel-Free jumpCL = 10.50
CW = 0.253
CH = 0.432
-Two sinusoidal corrugated (RH = 10 and 13)5–12-Depth ratio-Jump length-Energy loss
Izadjoo and Shafai-Bejestan [14]-Smooth and rough beds-Two rectangular-channel-Free jumpCL = 1.2, 9
CW = 0.25, 0.50
CH = 0.40
Baffle with trapezoidal cross section
(RH: 13 and 26)
6–12-Upstream and tailwater depths-Jump length-Velocity-Bed shear stress coefficient
Abbaspour et al. [12]-Horizontal bed with slope 0.002-Rectangular channel—smooth and rough beds-Free jumpCL = 10
CW = 0.25
CH = 0.50
-Sinusoidal bed (RH = 15,20, 25 and 35)3.80–8.60-Water surface profile-Depth ratio-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
Shafai-Bejestan and Neisi [13]-Smooth and rough beds-Rectangular channel-Free jumpCL = 7.50
CW = 0.35
CH = 0.50
Lozenge bed4.50–12-Sequent depth-Jump length
Elsebaie and Shabayek [18]-Smooth and rough beds-Rectangular channel-With side slopes of 45 degrees for two trapezoidal and triangular macroroughnesses and of 60 degrees for other trapezoidal macroroughnesses-Free jumpCL = 9
CW = 0.295
CH = 0.32
-Sinusoidal-Triangular-Trapezoidal with two side-Rectangular-(RH = 18 and corrugation wavelength = 65)50-Water surface profile-Sequent depth-Jump length-Bed shear stress coefficient
Samadi-Boroujeni et al. [19]-Rectangular channel-Smooth and rough beds-Free jumpCL = 12
CW = 0.40
CH = 0.40
-Six triangular corrugated (RH = 2.5)6.10–13.10-Water surface profile-Sequent depth-Jump length-Energy loss-Velocity profiles-Bed shear stress coefficient
Ahmed et al. [20]-Smooth and rough beds-Rectangular channel-Submerged jumpCL = 24.50
CW = 0.75
CH = 0.70
-Triangular corrugated sheet (RH = 40)1.68–9.29-Conjugated and tailwater depths-Submerged ratio-Deficit depth-Relative jump length-Jump length-Relative roller jump length-Jump efficiency-Bed shear stress coefficient
Nikmehr and Aminpour [15]-Horizontal bed with slope 0.002-Rectangular channel-Rough bed-Free jumpCL = 12
CW = 0.25
CH = 0.50
-Trapezoidal blocks (RH = 2, 3 and 4)5.01–13.70-Water surface profile-Sequent depth-Jump length-Roller length-Velocity
Ghaderi et al. [17]-Smooth and rough beds-Rectangular channel-Free and submerged jumpCL = 4.50
CW = 0.75
CH = 0.70
-Triangular, square and semi-oval macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Horizontal velocity distributions-Bed shear stress coefficient-Sequent depth ratio and submerged depth ratio-Jump length-Energy loss
Present studyRectangular channel
Smooth and rough beds
Submerged jump
CL = 4.50
CW = 0.75
CH = 0.70
-Triangular macroroughnesses (RH = 40 and distance of roughness of I = 40, 80, 120, 160 and 200)1.70–9.30-Longitudinal profile of streamlines-Flow patterns in the cavity region-Horizontal velocity profiles-Streamwise velocity distribution-Bed shear stress coefficient-TKE-Thickness of the inner layer-Energy loss

CL1: channel length, CW2: channel width, CH3: channel height, RH4: roughness height.

이전에 논의된 조사의 주요 부분은 실험실 접근 방식을 기반으로 하며 사인파, 마름모꼴, 사다리꼴, 정사각형, 직사각형 및 삼각형 매크로 거칠기가 공액 깊이, 잠긴 깊이, 점프 길이, 에너지 손실과 같은 일부 자유 및 수중 유압 점프 특성에 어떻게 영향을 미치는지 조사합니다.

베드 및 전단 응력 계수. 더욱이, 저자[17]에 의해 다양한 형태의 거시적 거칠기에 대한 수력학적 점프에 대한 이전 발표된 논문을 참조하면, 삼각형의 거대조도는 가장 높은 층 전단 응력 계수 및 에너지 손실을 가지며 또한 가장 낮은 잠긴 깊이, tailwater를 갖는 것으로 관찰되었습니다.

다른 거친 모양, 즉 정사각형 및 반 타원형과 부드러운 침대에 비해 깊이와 점프 길이. 따라서 본 논문에서는 삼각형 매크로 거칠기를 사용하여(일정한 거칠기 높이가 T = 4cm이고 삼각형 거칠기의 거리가 I = 4, 8, 12, 16 및 20cm인 다른 T/I 비율에 대해), 특정 캐비티 영역의 유동 패턴, 난류 운동 에너지(TKE) 및 흐름 방향 속도 분포와 같은 연구가 필요합니다.

CFD(Computational Fluid Dynamics) 방법은 자유 및 수중 유압 점프[21]와 같은 복잡한 흐름의 모델링 프로세스를 수행하는 중요한 도구로 등장하며 수중 유압 점프의 특성은 CFD 시뮬레이션을 사용하여 정확하게 예측할 수 있습니다 [22,23 ].

본 논문은 초기에 수중 유압 점프의 주요 특성, 수치 모델에 대한 입력 매개변수 및 Ahmed et al.의 참조 실험 조사를 제시합니다. [20], 검증 목적으로 보고되었습니다. 또한, 본 연구에서는 유선의 종방향 프로파일, 캐비티 영역의 유동 패턴, 수평 속도 프로파일, 내부 층의 두께, 베드 전단 응력 계수, TKE 및 에너지 손실과 같은 특성을 조사할 것입니다.

Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.
Figure 1. Definition sketch of a submerged hydraulic jump at triangular macroroughnesses.

Table 2. Effective parameters in the numerical model.

Bed TypeQ
(l/s)
I
(cm)
T (cm)d (cm)y1
(cm)
y4
(cm)
Fr1= u1/(gy1)0.5SRe1= (u1y1)/υ
Smooth30, 4551.62–3.839.64–32.101.7–9.30.26–0.5039,884–59,825
Triangular macroroughnesses30, 454, 8, 12, 16, 20451.62–3.846.82–30.081.7–9.30.21–0.4439,884–59,825
Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).
Figure 2. Longitudinal profile of the experimental flume (Ahmed et al. [20]).

Table 3. Main flow variables for the numerical and physical models (Ahmed et al. [20]).

ModelsBed TypeQ (l/s)d (cm)y1 (cm)u1 (m/s)Fr1
Numerical and PhysicalSmooth4551.62–3.831.04–3.701.7–9.3
T/I = 0.54551.61–3.831.05–3.711.7–9.3
T/I = 0.254551.60–3.841.04–3.711.7–9.3
Figure 3. The boundary conditions governing the simulations.
Figure 3. The boundary conditions governing the simulations.
Figure 4. Sketch of mesh setup.
Figure 4. Sketch of mesh setup.

Table 4. Characteristics of the computational grids.

MeshNested Block Cell Size (cm)Containing Block Cell Size (cm)
10.551.10
20.651.30
30.851.70

Table 5. The numerical results of mesh convergence analysis.

ParametersAmounts
fs1 (-)7.15
fs2 (-)6.88
fs3 (-)6.19
K (-)5.61
E32 (%)10.02
E21 (%)3.77
GCI21 (%)3.03
GCI32 (%)3.57
GCI32/rp GCI210.98
Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
Figure 5. Time changes of the flow discharge in the inlet and outlet boundaries conditions (A): Q = 0.03 m3/s (B): Q = 0.045 m3/s.
Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
Figure 6. The evolutionary process of a submerged hydraulic jump on the smooth bed—Q = 0.03 m3/s.
Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
Figure 7. Numerical versus experimental basic parameters of the submerged hydraulic jump. (A): y3/y1; and (B): y4/y1.
Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
Figure 8. Velocity vector field and flow pattern through the gate in a submerged hydraulic jump condition: (A) smooth bed; (B) triangular macroroughnesses.
Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
Figure 9. Velocity vector distributions in the x–z plane (y = 0) within the cavity region.
Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
Figure 10. Typical vertical distribution of the mean horizontal velocity in a submerged hydraulic jump [46].
Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
Figure 11. Typical horizontal velocity profiles in a submerged hydraulic jump on smooth bed and triangular macroroughnesses.
Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
Figure 12. Horizontal velocity distribution at different distances from the sluice gate for the different T/I for Fr1 = 6.1
Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
Figure 13. Stream-wise velocity distribution for the triangular macroroughnesses with T/I = 0.5 and 0.25.
Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
Figure 14. Dimensionless horizontal velocity distribution in the submerged hydraulic jump for different Froude numbers in triangular macroroughnesses.
Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
Figure 15. Spatial variations of (umax/u1) and (δ⁄y1).
Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
Figure 16. The shear stress coefficient (ε) versus the inlet Froude number (Fr1).
Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
Figure 17. Longitudinal turbulent kinetic energy distribution on the smooth and triangular macroroughnesses: (A) Y/2; (B) Y/6.
Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).
Figure 18. The energy loss (EL/E3) of the submerged jump versus inlet Froude number (Fr1).

Conclusions

  • 본 논문에서는 유선의 종방향 프로파일, 공동 영역의 유동 패턴, 수평 속도 프로파일, 스트림 방향 속도 분포, 내부 층의 두께, 베드 전단 응력 계수, 난류 운동 에너지(TKE)를 포함하는 수중 유압 점프의 특성을 제시하고 논의했습니다. ) 및 삼각형 거시적 거칠기에 대한 에너지 손실. 이러한 특성은 FLOW-3D® 모델을 사용하여 수치적으로 조사되었습니다. 자유 표면을 시뮬레이션하기 위한 VOF(Volume of Fluid) 방법과 난류 RNG k-ε 모델이 구현됩니다. 본 모델을 검증하기 위해 평활층과 삼각형 거시 거칠기에 대해 수치 시뮬레이션과 실험 결과를 비교했습니다. 본 연구의 다음과 같은 결과를 도출할 수 있다.
  • 개발 및 개발 지역의 삼각형 거시 거칠기의 흐름 패턴은 수중 유압 점프 조건의 매끄러운 바닥과 비교하여 더 작은 영역에서 동일합니다. 삼각형의 거대 거칠기는 거대 거칠기 사이의 공동 영역에서 또 다른 시계 방향 와류의 형성으로 이어집니다.
  • T/I = 1, 0.5 및 0.33과 같은 거리에 대해 속도 벡터 분포는 캐비티 영역에서 시계 방향 소용돌이를 표시하며, 여기서 속도의 크기는 평균 유속보다 훨씬 작습니다. 삼각형 거대 거칠기(T/I = 0.25 및 0.2) 사이의 거리를 늘리면 캐비티 영역에 크기가 다른 두 개의 소용돌이가 형성됩니다.
  • 삼각형 거시조도 사이의 거리가 충분히 길면 흐름이 다음 조도에 도달할 때까지 속도 분포가 회복됩니다. 그러나 짧은 거리에서 흐름은 속도 분포의 적절한 회복 없이 다음 거칠기에 도달합니다. 따라서 거시 거칠기 사이의 거리가 감소함에 따라 마찰 계수의 증가율이 감소합니다.
  • 삼각형의 거시적 거칠기에서, 잠수 점프의 지정된 섹션에서 최대 속도는 자유 점프보다 높은 값으로 이어집니다. 또한, 수중 점프에서 두 가지 유형의 베드(부드러움 및 거친 베드)에 대해 깊이 및 와류 증가로 인해 베드로부터의 최대 속도 거리는 감소합니다. 잠수 점프에서 경계층 두께는 자유 점프보다 얇습니다.
  • 매끄러운 베드의 난류 영역은 게이트로부터의 거리에 따라 생성되고 자유 표면 롤러 영역 근처에서 발생하는 반면, 거시적 거칠기에서는 난류가 게이트 근처에서 시작되어 더 큰 강도와 제한된 스위프 영역으로 시작됩니다. 이는 반시계 방향 순환의 결과입니다. 거시 거칠기 사이의 공간에서 자유 표면 롤러 및 시계 방향 와류.
  • 삼각 거시 거칠기에서 침지 점프의 베드 전단 응력 계수와 에너지 손실은 유입구 Froude 수의 증가에 따라 증가하는 매끄러운 베드에서 발견된 것보다 더 큽니다. T/I = 0.50 및 0.20에서 최고 및 최저 베드 전단 응력 계수 및 에너지 손실이 평활 베드에 비해 거칠기 요소의 거리가 증가함에 따라 발생합니다.
  • 거의 거칠기 요소가 있는 삼각형 매크로 거칠기의 존재에 의해 주어지는 점프 길이와 잠긴 수심 및 꼬리 수심의 감소는 결과적으로 크기, 즉 길이 및 높이가 감소하는 정수조 설계에 사용될 수 있습니다.
  • 일반적으로 CFD 모델은 다양한 수력 조건 및 기하학적 배열을 고려하여 잠수 점프의 특성 예측을 시뮬레이션할 수 있습니다. 캐비티 영역의 흐름 패턴, 흐름 방향 및 수평 속도 분포, 베드 전단 응력 계수, TKE 및 유압 점프의 에너지 손실은 수치적 방법으로 시뮬레이션할 수 있습니다. 그러나 거시적 차원과 유동장 및 공동 유동의 변화에 ​​대한 다양한 배열에 대한 연구는 향후 과제로 남아 있다.

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Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow

Numerical Methods in Civil Engineering

Rasoul Daneshfaraz*, Ehsan Aminvash**, Silvia Di Francesco***, Amir Najibi**, John Abraham****

토목공학의 수치해석법

Abstract

The main purpose of this study is to provide a method to increase energy dissipation on an inclined drop. Therefore, three types of rough elements with cylindrical, triangular and batshaped geometries are used on the inclined slope in the relative critical depth range of 0.128 to 0.36 and the effect of the geometry of these elements is examined using Flow 3D software. The results showed demonstrate that the downstream relative depth obtained from the numerical analysis is in good agreement with the laboratory results. The application of rough elements on the inclined drop increased the downstream relative depth and also the relative energy dissipation. The application of rough elements on the sloping surface of the drop significantly reduced the downstream Froude number, so that the Froude number in all models ranging from 4.7~7.5 to 1.45~3.36 also decreased compared to the plain drop. Bat-shaped elements are structurally smaller in size, so the use of these elements, in addition to dissipating more energy, is also economically viable.

이 연구의 주요 목적은 경사진 낙하에서 에너지 소산을 증가시키는 방법을 제공하는 것입니다. 따라서 0.128 ~ 0.36의 상대 임계 깊이 범위에서 경사면에 원통형, 삼각형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거친 요소가 사용되며 이러한 요소의 형상의 영향은 Flow 3D 소프트웨어를 사용하여 조사됩니다. 결과는 수치 분석에서 얻은 하류 상대 깊이가 실험실 결과와 잘 일치함을 보여줍니다. 경 사진 낙하에 거친 요소를 적용하면 하류 상대 깊이와 상대 에너지 소산이 증가했습니다. 낙차 경사면에 거친 요소를 적용하면 하류의 Froude 수를 크게 감소시켜 4.7~7.5에서 1.45~3.36 범위의 모든 모델에서 Froude 수도 일반 낙차에 비해 감소했습니다. 박쥐 모양의 요소는 구조적으로 크기가 더 작기 때문에 더 많은 에너지를 분산시키는 것 외에도 이러한 요소를 사용하는 것이 경제적으로도 가능합니다.

Keywords: Downstream depth, Energy dissipation, Froude number, Inclined drop, Roughness elements

Introduction

급수 네트워크 시스템, 침식 수로, 수처리 시스템 및 경사가 큰 경우 흐름 에너지를 더 잘 제어하기 위해 경사 방울을 사용할 수 있습니다. 낙하 구조는 지반의 자연 경사를 설계 경사로 변환하여 에너지 소산, 유속 감소 및 수심 증가를 유발합니다. 따라서 흐름의 하류 에너지를 분산 시키기 위해 에너지 분산 구조를 사용할 수 있습니다. 난기류와 혼합된 물과 공기의 형성은 에너지 소비를 증가 시키는 효과적인 방법입니다. 흐름 경로에서 거칠기 요소를 사용하는 것은 에너지 소산을 위한 알려진 방법입니다. 이러한 요소는 흐름 경로에 배치됩니다. 그들은 종종 에너지 소산을 증가시키기 위해 다른 기하학적 구조와 배열을 가지고 있습니다. 이 연구의 목적은 직사각형 경사 방울에 대한 거칠기 요소의 영향을 조사하는 것입니다.

Fig. 1: Model made in Ardabil, Iran
Fig. 1: Model made in Ardabil, Iran
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 2: Geometric and hydraulic parameters of an inclined drop equipped with roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 3: Views of the incline with (a) Bat-shaped, (b) Cylindrical, (c) Triangular roughness elements
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 4: Geometric profile of inclined drop and boundary conditions with the bat-shape roughness element
Fig. 5: Variation of the RMSE varying cell size
Fig. 5: Variation of the RMSE varying cell size
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 6: Numerical and laboratory comparison of the downstream relative depth
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 7: Flow profile on inclined drop in discharge of 5 L/s: (a) Without roughness elements; (b) Bat-shaped roughness element; (c) Cylindrical roughness element; (d) Triangular roughness element
Fig. 8: Relative edge depth versus the relative critical depth
Fig. 8: Relative edge depth versus the relative critical depth
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Flow on the inclined drop with bat-shaped elements: (a) Non-submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 9: Flow on the inclined drop with bat-shaped elements: (b) Submerged flow
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 10: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth
Fig. 11: Relative downstream depth versus the relative critical depth

Conclusions

현재 연구에서 FLOW-3D 소프트웨어를 사용하여 한 높이, 한 각도, 밀도 15% 및 지그재그 배열에서 삼각형, 원통형 및 박쥐 모양의 형상을 가진 세 가지 유형의 거칠기 요소를 사용하여 경사 낙하 수리학적 매개변수에 대한 거칠기 요소 형상의 영향 평가되었다. VOF 방법을 사용하여 자유 표면 흐름을 시뮬레이션하고 초기에 3개의 난류 모델 RNG, k-ɛ 및 kω를 검증에 사용하고 이를 검토한 후 RNG 방법을 사용하여 다른 모델을 시뮬레이션했습니다. 1- 수치 결과에서 얻은 부드러운 경사 방울의 하류 상대 깊이는 실험실 데이터와 매우 좋은 상관 관계가 있으며 원통형 요소가 장착 된 경사 방울의 상대 에지 깊이 값이 가장 높았습니다. 2- 하류 상대깊이는 임계상대깊이가 증가함에 따라 상승하는 경향을 나타내어 박쥐형 요소를 구비한 경사낙하와 완만한 경사낙하가 각각 하류상대깊이가 가장 높고 가장 낮았다. 3- 하류 깊이의 증가로 인해 상대적 임계 깊이가 증가함에 따라 상대적 에너지 소산이 감소합니다. 한편, 가장 높은 에너지 소산은 박쥐 모양의 요소가 장착된 경사 낙하와 관련이 있으며 가장 낮은 에너지 소산은 부드러운 낙하와 관련이 있습니다. 삼각형, 원통형 및 박쥐 모양의 거친 요소가 장착된 드롭은 부드러운 드롭보다 각각 65%, 76% 및 85% 더 많은 흐름 에너지를 소산합니다. 4- 낙차의 경사면에 거친 요소를 적용하여 다운 스트림 Froude 수를 크게 줄여 4.7 ~ 7.5에서 1.45 ~ 3.36까지의 모든 모델에서 Froude 수가 부드러운 낙하에 비해 감소했습니다. 또한, 다른 원소보다 부피가 작은 박쥐 모양의 거칠기의 부피로 인해 이러한 유형의 거칠기를 사용하는 것이 경제적입니다.

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Numerical simulation of energy dissipation in crescent-shaped contraction of the flow path

Numerical simulation of energy dissipation in crescent-shaped contraction of the flow path

Authors

1 Professor, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran.
2 M.sc student, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran.
3 M.sc student, Department of Civil Engineering, Faculty of Engineering, University of Maragheh, Iran

Abstract

One of the methods of controlling and reducing flow energy is the use of energy dissipating structures and the formation of hydraulic jumps. One of these types of structures is the constriction elements in the flow path, which leads to a decrease in the energy of the passing flow. In the present study, the effect of crescent-shaped contraction as an energy dissipating structure in the supercritical flow path has been investigated using FLOW-3D software. Examining the simulation results, the RNG turbulence model due to its higher accuracy and lower relative error and absolute error percentage than other models, among the RNG turbulence models, k-ε, k-ω and LES was selected. In this study, the amplitude of the Froude number after the gate as the most effective dimensionless parameter in energy dissipation varied from 2.8 to 7.5 and the values of stenosis on both sides are 5 and 7.5 cm. The results show that in all cases of using the crescent-shaped contractions, the energy consumption due to the contraction is 5 and 7.5 cm, respectively, based on the energy drop relative to the upstream of 24.62% and 29.84% and compared to the downstream 46.14% and 48.42% more than the classic free jump. Also, by examining the obtained results, it was observed that the crescent-shaped contractions have a better performance in terms of energy loss compared to the sudden contraction, obtained from the studies of previous researchers. Based on the simulation results, with increasing the upstream Froude number, the relative energy dissipation to the upstream and downstream crescent-shaped contraction increased so that the use of contraction elements reduces the downstream Froude number of the contracted section in the range of 1.6 to 3/2.

흐름 에너지를 제어하고 줄이는 방법 중 하나는 에너지 소산 구조를 사용하고 유압 점프를 형성하는 것입니다. 이러한 유형의 구조 중 하나는 흐름 경로의 수축 요소로, 통과하는 흐름의 에너지를 감소시킵니다. 현재 연구에서는 초 임계 유동 경로에서 에너지 소산 구조로서 초승달 모양의 수축 효과가 FLOW-3D 소프트웨어를 사용하여 조사되었습니다. 시뮬레이션 결과를 살펴보면 RNG 난류 모델 중 k-ε, k-ω, LES 중에서 다른 모델보다 정확도가 높고 상대 오차와 절대 오차 비율이 낮은 RNG 난류 모델을 선택했습니다. 이 연구에서 에너지 소산에서 가장 효과적인 무 차원 매개 변수 인 게이트 뒤의 Froude 수의 진폭은 2.8에서 7.5까지 다양했으며 양쪽의 협착 값은 5cm와 7.5cm입니다. 결과는 초승달 모양의 수축을 사용하는 모든 경우에서 수축으로 인한 에너지 소비는 각각 5cm와 7.5cm로 상류에 비해 에너지 강하가 24.62 % 및 29.84 %이고 하류와 비교됩니다. 고전적인 자유 점프보다 46.14 % 및 48.42 % 더 많습니다. 또한 얻어진 결과를 살펴보면 초승달 모양의 수축이 이전 연구자들의 연구에서 얻은 갑작스런 수축에 비해 에너지 손실 측면에서 더 나은 성능을 보이는 것으로 나타났습니다. 시뮬레이션 결과에 따르면 상류 Froude 수를 증가 시키면 상류 및 하류 초승달 모양의 수축에 대한 상대적 에너지 소산이 증가하여 수축 요소를 사용하면 수축 된 부분의 하류 Froude 수가 1.6 ~ 3/2 범위에서 감소합니다. .

Keywords

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Numerical investigation of flow characteristics over stepped spillways

Güven, Aytaç
Mahmood, Ahmed Hussein
Water Supply (2021) 21 (3): 1344–1355.
https://doi.org/10.2166/ws.2020.283Article history

Abstract

Spillways are constructed to evacuate flood discharge safely so that a flood wave does not overtop the dam body. There are different types of spillways, with the ogee type being the conventional one. A stepped spillway is an example of a nonconventional spillway. The turbulent flow over a stepped spillway was studied numerically by using the Flow-3D package. Different fluid flow characteristics such as longitudinal flow velocity, temperature distribution, density and chemical concentration can be well simulated by Flow-3D. In this study, the influence of slope changes on flow characteristics such as air entrainment, velocity distribution and dynamic pressures distribution over a stepped spillway was modelled by Flow-3D. The results from the numerical model were compared with an experimental study done by others in the literature. Two models of a stepped spillway with different discharge for each model were simulated. The turbulent flow in the experimental model was simulated by the Renormalized Group (RNG) turbulence scheme in the numerical model. A good agreement was achieved between the numerical results and the observed ones, which are exhibited in terms of graphics and statistical tables.

배수로는 홍수가 댐 몸체 위로 넘치지 않도록 안전하게 홍수를 피할 수 있도록 건설되었습니다. 다른 유형의 배수로가 있으며, ogee 유형이 기존 유형입니다. 계단식 배수로는 비 전통적인 배수로의 예입니다. 계단식 배수로 위의 난류는 Flow-3D 패키지를 사용하여 수치적으로 연구되었습니다.

세로 유속, 온도 분포, 밀도 및 화학 농도와 같은 다양한 유체 흐름 특성은 Flow-3D로 잘 시뮬레이션 할 수 있습니다. 이 연구에서는 계단식 배수로에 대한 공기 혼입, 속도 분포 및 동적 압력 분포와 같은 유동 특성에 대한 경사 변화의 영향을 Flow-3D로 모델링 했습니다.

수치 모델의 결과는 문헌에서 다른 사람들이 수행한 실험 연구와 비교되었습니다. 각 모델에 대해 서로 다른 배출이 있는 계단식 배수로의 두 모델이 시뮬레이션되었습니다. 실험 모델의 난류 흐름은 수치 모델의 Renormalized Group (RNG) 난류 계획에 의해 시뮬레이션되었습니다. 수치 결과와 관찰 된 결과 사이에 좋은 일치가 이루어졌으며, 이는 그래픽 및 통계 테이블로 표시됩니다.

HIGHLIGHTS

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  • A numerical model was developed for stepped spillways.
  • The turbulent flow was simulated by the Renormalized Group (RNG) model.
  • Both numerical and experimental results showed that flow characteristics are greatly affected by abrupt slope change on the steps.

Keyword

CFDnumerical modellingslope changestepped spillwayturbulent flow

INTRODUCTION

댐 구조는 물 보호가 생활의 핵심이기 때문에 물을 저장하거나 물을 운반하는 전 세계에서 가장 중요한 프로젝트입니다. 그리고 여수로는 댐의 가장 중요한 부분 중 하나로 분류됩니다. 홍수로 인한 파괴 나 피해로부터 댐을 보호하기 위해 여수로가 건설됩니다.

수력 발전, 항해, 레크리에이션 및 어업의 중요성을 감안할 때 댐 건설 및 홍수 통제는 전 세계적으로 매우 중요한 문제로 간주 될 수 있습니다. 많은 유형의 배수로가 있지만 가장 일반적인 유형은 다음과 같습니다 : ogee 배수로, 자유 낙하 배수로, 사이펀 배수로, 슈트 배수로, 측면 채널 배수로, 터널 배수로, 샤프트 배수로 및 계단식 배수로.

그리고 모든 여수로는 입구 채널, 제어 구조, 배출 캐리어 및 출구 채널의 네 가지 필수 구성 요소로 구성됩니다. 특히 롤러 압축 콘크리트 (RCC) 댐 건설 기술과 더 쉽고 빠르며 저렴한 건설 기술로 분류 된 계단식 배수로 건설과 관련하여 최근 수십 년 동안 많은 계단식 배수로가 건설되었습니다 (Chanson 2002; Felder & Chanson 2011).

계단식 배수로 구조는 캐비테이션 위험을 감소시키는 에너지 소산 속도를 증가시킵니다 (Boes & Hager 2003b). 계단식 배수로는 다양한 조건에서 더 매력적으로 만드는 장점이 있습니다.

계단식 배수로의 흐름 거동은 일반적으로 낮잠, 천이 및 스키밍 흐름 체제의 세 가지 다른 영역으로 분류됩니다 (Chanson 2002). 유속이 낮을 때 nappe 흐름 체제가 발생하고 자유 낙하하는 낮잠의 시퀀스로 특징 지워지는 반면, 스키밍 흐름 체제에서는 물이 외부 계단 가장자리 위의 유사 바닥에서 일관된 흐름으로 계단 위로 흐릅니다.

또한 주요 흐름에서 3 차원 재순환 소용돌이가 발생한다는 것도 분명합니다 (예 : Chanson 2002; Gonzalez & Chanson 2008). 계단 가장자리 근처의 의사 바닥에서 흐름의 방향은 가상 바닥과 가상으로 정렬됩니다. Takahashi & Ohtsu (2012)에 따르면, 스키밍 흐름 체제에서 주어진 유속에 대해 흐름은 계단 가장자리 근처의 수평 계단면에 영향을 미치고 슈트 경사가 감소하면 충돌 영역의 면적이 증가합니다. 전이 흐름 체제는 나페 흐름과 스키밍 흐름 체제 사이에서 발생합니다. 계단식 배수로를 설계 할 때 스키밍 흐름 체계를 고려해야합니다 (예 : Chanson 1994, Matos 2000, Chanson 2002, Boes & Hager 2003a).

CFD (Computational Fluid Dynamics), 즉 수력 공학의 수치 모델은 일반적으로 물리적 모델에 소요되는 총 비용과 시간을 줄여줍니다. 따라서 수치 모델은 실험 모델보다 빠르고 저렴한 것으로 분류되며 동시에 하나 이상의 목적으로 사용될 수도 있습니다. 사용 가능한 많은 CFD 소프트웨어 패키지가 있지만 가장 널리 사용되는 것은 FLOW-3D입니다. 이 연구에서는 Flow 3D 소프트웨어를 사용하여 유량이 서로 다른 두 모델에 대해 계단식 배수로에서 공기 농도, 속도 분포 및 동적 압력 분포를 시뮬레이션합니다.

Roshan et al. (2010)은 서로 다른 수의 계단 및 배출을 가진 계단식 배수로의 두 가지 물리적 모델에 대한 흐름 체제 및 에너지 소산 조사를 연구했습니다. 실험 모델의 기울기는 각각 19.2 %, 12 단계와 23 단계의 수입니다. 결과는 23 단계 물리적 모델에서 관찰 된 흐름 영역이 12 단계 모델보다 더 수용 가능한 것으로 간주되었음을 보여줍니다. 그러나 12 단계 모델의 에너지 손실은 23 단계 모델보다 더 많았습니다. 그리고 실험은 스키밍 흐름 체제에서 23 단계 모델의 에너지 소산이 12 단계 모델보다 약 12 ​​% 더 적다는 것을 관찰했습니다.

Ghaderi et al. (2020a)는 계단 크기와 유속이 다른 정련 매개 변수의 영향을 조사하기 위해 계단식 배수로에 대한 실험 연구를 수행했습니다. 그 결과, 흐름 체계가 냅페 흐름 체계에서 발생하는 최소 scouring 깊이와 같은 scouring 구멍 치수에 영향을 미친다는 것을 보여주었습니다. 또한 테일 워터 깊이와 계단 크기는 최대 scouring깊이에 대한 실제 매개 변수입니다. 테일 워터의 깊이를 6.31cm에서 8.54 및 11.82cm로 늘림으로써 수세 깊이가 각각 18.56 % 및 11.42 % 증가했습니다. 또한 이 증가하는 테일 워터 깊이는 scouring 길이를 각각 31.43 % 및 16.55 % 감소 시킵니다. 또한 유속을 높이면 Froude 수가 증가하고 흐름의 운동량이 증가하면 scouring이 촉진됩니다. 또한 결과는 중간의 scouring이 횡단면의 측벽보다 적다는 것을 나타냅니다. 계단식 배수로 하류의 최대 scouring 깊이를 예측 한 후 실험 결과와 비교하기 위한 실험식이 제안 되었습니다. 그리고 비교 결과 제안 된 공식은 각각 3.86 %와 9.31 %의 상대 오차와 최대 오차 내에서 scouring 깊이를 예측할 수 있음을 보여주었습니다.

Ghaderi et al. (2020b)는 사다리꼴 미로 모양 (TLS) 단계의 수치 조사를 했습니다. 결과는 이러한 유형의 배수로가 확대 비율 LT / Wt (LT는 총 가장자리 길이, Wt는 배수로의 폭)를 증가시키기 때문에 더 나은 성능을 갖는 것으로 관찰되었습니다. 또한 사다리꼴 미로 모양의 계단식 배수로는 더 큰 마찰 계수와 더 낮은 잔류 수두를 가지고 있습니다. 마찰 계수는 다양한 배율에 대해 0.79에서 1.33까지 다르며 평평한 계단식 배수로의 경우 대략 0.66과 같습니다. 또한 TLS 계단식 배수로에서 잔류 수두의 비율 (Hres / dc)은 약 2.89이고 평평한 계단식 배수로의 경우 약 4.32와 같습니다.

Shahheydari et al. (2015)는 Flow-3D 소프트웨어, RNG k-ε 모델 및 VOF (Volume of Fluid) 방법을 사용하여 배출 계수 및 에너지 소산과 같은 자유 표면 흐름의 프로파일을 연구하여 스키밍 흐름 체제에서 계단식 배수로에 대한 흐름을 조사했습니다. 실험 결과와 비교했습니다. 결과는 에너지 소산 율과 방전 계수율의 관계가 역으로 실험 모델의 결과와 잘 일치 함을 보여 주었다.

Mohammad Rezapour Tabari & Tavakoli (2016)는 계단 높이 (h), 계단 길이 (L), 계단 수 (Ns) 및 단위 폭의 방전 (q)과 같은 다양한 매개 변수가 계단식 에너지 ​​소산에 미치는 영향을 조사했습니다. 방수로. 그들은 해석에 FLOW-3D 소프트웨어를 사용하여 계단식 배수로에서 에너지 손실과 임계 흐름 깊이 사이의 관계를 평가했습니다. 또한 유동 난류에 사용되는 방정식과 표준 k-ɛ 모델을 풀기 위해 유한 체적 방법을 적용했습니다. 결과에 따르면 스텝 수가 증가하고 유량 배출량이 증가하면 에너지 손실이 감소합니다. 얻은 결과를 다른 연구와 비교하고 경험적, 수학적 조사를 수행하여 결국 합격 가능한 결과를 얻었습니다.

METHODOLOGY

ListenReadSpeaker webReader: ListenFor all numerical models the basic principle is very similar: a set of partial differential equations (PDE) present the physical problems. The flow of fluids (gas and liquid) are governed by the conservation laws of mass, momentum and energy. For Computational Fluid Dynamics (CFD), the PDE system is substituted by a set of algebraic equations which can be worked out by using numerical methods (Versteeg & Malalasekera 2007). Flow-3D uses the finite volume approach to solve the Reynolds Averaged Navier-Stokes (RANS) equation, by applying the technique of Fractional Area/Volume Obstacle Representation (FAVOR) to define an obstacle (Flow Science Inc. 2012). Equations (1) and (2) are RANS and continuity equations with FAVOR variables that are applied for incompressible flows.

formula

(1)

formula

(2)where  is the velocity in xi direction, t is the time,  is the fractional area open to flow in the subscript directions,  is the volume fraction of fluid in each cell, p is the hydrostatic pressure,  is the density, is the gravitational force in subscript directions and  is the Reynolds stresses.

Turbulence modelling is one of three key elements in CFD (Gunal 1996). There are many types of turbulence models, but the most common are Zero-equation models, One-equation models, Two-equation models, Reynolds Stress/Flux models and Algebraic Stress/Flux models. In FLOW-3D software, five turbulence models are available. The formulation used in the FLOW-3D software differs slightly from other formulations that includes the influence of the fractional areas/volumes of the FAVORTM method and generalizes the turbulence production (or decay) associated with buoyancy forces. The latter generalization, for example, includes buoyancy effects associated with non-inertial accelerations.

The available turbulence models in Flow-3D software are the Prandtl Mixing Length Model, the One-Equation Turbulent Energy Model, the Two-Equation Standard  Model, the Two-Equation Renormalization-Group (RNG) Model and large Eddy Simulation Model (Flow Science Inc. 2012).In this research the RNG model was selected because this model is more commonly used than other models in dealing with particles; moreover, it is more accurate to work with air entrainment and other particles. In general, the RNG model is classified as a more widely-used application than the standard k-ɛ model. And in particular, the RNG model is more accurate in flows that have strong shear regions than the standard k-ɛ model and it is defined to describe low intensity turbulent flows. For the turbulent dissipation  it solves an additional transport equation:

formula

(3)where CDIS1, CDIS2, and CDIS3 are dimensionless parameters and the user can modify them. The diffusion of dissipation, Diff ɛ, is

formula

(4)where uv and w are the x, y and z coordinates of the fluid velocity; ⁠, ⁠,  and ⁠, are FLOW-3D’s FAVORTM defined terms;  and  are turbulence due to shearing and buoyancy effects, respectively. R and  are related to the cylindrical coordinate system. The default values of RMTKE, CDIS1 and CNU differ, being 1.39, 1.42 and 0.085 respectively. And CDIS2 is calculated from turbulent production (⁠⁠) and turbulent kinetic energy (⁠⁠).The kinematic turbulent viscosity is the same in all turbulence transport models and is calculated from

formula

(5)where ⁠: is the turbulent kinematic viscosity.  is defined as the numerical challenge between the RNG and the two-equation k-ɛ models, found in the equation below. To avoid an unphysically large result for  in Equation (3), since this equation could produce a value for  very close to zero and also because the physical value of  may approach to zero in such cases, the value of  is calculated from the following equation:

formula

(6)where ⁠: the turbulent length scale.

VOF and FAVOR are classifications of volume-fraction methods. In these two methods, firstly the area should be subdivided into a control volume grid or a small element. Each flow parameter like velocity, temperature and pressure values within the element are computed for each element containing liquids. Generally, these values represent the volumetric average of values in the elements.Numerous methods have been used recently to solve free infinite boundaries in the various numerical simulations. VOF is an easy and powerful method created based on the concept of a fractional intensity of fluid. A significant number of studies have confirmed that this method is more flexible and efficient than others dealing with the configurations of a complex free boundary. By using VOF technology the Flow-3D free surface was modelled and first declared in Hirt & Nichols (1981). In the VOF method there are three ingredients: a planner to define the surface, an algorithm for tracking the surface as a net mediator moving over a computational grid, and application of the boundary conditions to the surface. Configurations of the fluids are defined in terms of VOF function, F (x, y, z, t) (Hirt & Nichols 1981). And this VOF function shows the volume of flow per unit volume

formula

(7)

formula

(8)

formula

(9)where  is the density of the fluid, is a turbulent diffusion term,  is a mass source,  is the fractional volume open to flow. The components of velocity (u, v, w) are in the direction of coordinates (x, y, z) or (r, ⁠).  in the x-direction is the fractional area open to flow,  and  are identical area fractions for flow in the y and z directions. The R coefficient is based on the selection of the coordinate system.

The FAVOR method is a different method and uses another volume fraction technique, which is only used to define the geometry, such as the volume of liquid in each cell used to determine the position of fluid surfaces. Another fractional volume can be used to define the solid surface. Then, this information is used to determine the boundary conditions of the wall that the flow should be adapted for.

Case study

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In this study, the experimental results of Ostad Mirza (2016) was simulated. In a channel composed of two 4 m long modules, with a transparent sidewall of height 0.6 m and 0.5 m width. The upstream chute slope (i.e. pseudo-bottom angle) Ɵ1 = 50°, the downstream chute slope Ɵ2 = 30° or 18.6°, the step heights h = 0.06 m, the total number of steps along the 50° chute 41 steps, the total number of steps along the 30° chute 34 steps and the total number of steps along the 18.6° chute 20 steps.

The flume inflow tool contained a jetbox with a maximum opening set to 0.12 meters, designed for passing the maximum unit discharge of 0.48 m2/s. The measurements of the flow properties (i.e. air concentration and velocity) were computed perpendicular to the pseudo-bottom as shown in Figure 1 at the centre of twenty stream-wise cross-sections, along the stepped chute, (i.e. in five steps up on the slope change and fifteen steps down on the slope change, namely from step number −09 to +23 on 50°–30° slope change, or from −09 to +15 on 50°–18.6° slope change, respectively).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).
Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Sketch of the air concentration C and velocity V measured perpendicular to the pseudo-bottom used by Mirza (Ostad Mirza 2016).

Pressure sensors were arranged with the x/l values for different slope change as shown in Table 1, where x is the distance from the step edge, along the horizontal step face, and l is the length of the horizontal step face. The location of pressure sensors is shown in Table 1.Table 1

Location of pressure sensors on horizontal step faces

Θ(°)L(m)x/l (–)
50.0 0.050 0.35 0.64 – – – 
30.0 0.104 0.17 0.50 0.84 – – 
18.6 0.178 0.10 0.30 0.50 0.7 0.88 
Location of pressure sensors on horizontal step faces
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.
Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Inlet boundary condition for Q = 0.235 m3/s and fluid elevation 4.21834 m.

Numerical model set-up

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A 3D numerical model of hydraulic phenomena was simulated based on an experimental study by Ostad Mirza (2016). The water surcharge and flow pressure over the stepped spillway was computed for two models of a stepped spillway with different discharge for each model. In this study, the package was used to simulate the flow parameters such as air entrainment, velocity distribution and dynamic pressures. The solver uses the finite volume technique to discretize the computational domain. In every test run, one incompressible fluid flow with a free surface flow selected at 20̊ was used for this simulation model. Table 2 shows the variables used in test runs.Table 2

Variables used in test runs

Test no.Θ1 (°)Θ2 (°)h(m)d0q (m3s1)dc/h (–)
50 18.6 0.06 0.045 0.1 2.6 
50 18.6 0.06 0.082 0.235 4.6 
50 30.0 0.06 0.045 0.1 2.6 
50 30.0 0.06 0.082 0.235 4.6 
Table 2 Variables used in test runs

For stepped spillway simulation, several parameters should be specified to get accurate simulations, which is the scope of this research. Viscosity and turbulent, gravity and non-inertial reference frame, air entrainment, density evaluation and drift-flux should be activated for these simulations. There are five different choices in the ‘viscosity and turbulent’ option, in the viscosity flow and Renormalized Group (RNG) model. Then a dynamical model is selected as the second option, the ‘gravity and non-inertial reference frame’. Only the z-component was inputted as a negative 9.81 m/s2 and this value represents gravitational acceleration but in the same option the x and y components will be zero. Air entrainment is selected. Finally, in the drift-flux model, the density of phase one is input as (water) 1,000 kg/m3 and the density of phase two (air) as 1.225 kg/m3. Minimum volume fraction of phase one is input equal to 0.1 and maximum volume fraction of phase two to 1 to allow air concentration to reach 90%, then the option allowing gas to escape at free surface is selected, to obtain closer simulation.

The flow domain is divided into small regions relatively by the mesh in Flow-3D numerical model. Cells are the smallest part of the mesh, in which flow characteristics such as air concentration, velocity and dynamic pressure are calculated. The accuracy of the results and simulation time depends directly on the mesh block size so the cell size is very important. Orthogonal mesh was used in cartesian coordinate systems. A smaller cell size provides more accuracy for results, so we reduced the number of cells whilst including enough accuracy. In this study, the size of cells in x, y and z directions was selected as 0.015 m after several trials.

Figure 3 shows the 3D computational domain model 50–18.6 slope change, that is 6.0 m length, 0.50 m width and 4.23 m height. The 3D model of the computational domain model 50–30 slope changes this to 6.0 m length, 0.50 m width and 5.068 m height and the size of meshes in x, y, and z directions are 0.015 m. For the 50–18.6 slope change model: both total number of active and passive cells = 4,009,952, total number of active cells = 3,352,307, include real cells (used for solving the flow equations) = 3,316,269, open real cells = 3,316,269, fully blocked real cells equal to zero, external boundary cells were 36,038, inter-block boundary cells = 0 (Flow-3D report). For 50–30 slope change model: both total number of active and passive cells = 4,760,002, total number of active cells equal to 4,272,109, including real cells (used for solving the flow equations) were 3,990,878, open real cells = 3,990,878 fully blocked real cells = zero, external boundary cells were 281,231, inter-block boundary cells = 0 (Flow-3D report).

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.
Figure3 The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

Figure 3VIEW LARGEDOWNLOAD SLIDE

The 3D computational domain model (50–18.6) slope change, and boundary condition for (50–30 slope change) model.

When solving the Navier-Stokes equation and continuous equations, boundary conditions should be applied. The most important work of boundary conditions is to create flow conditions similar to physical status. The Flow-3D software has many types of boundary condition; each type can be used for the specific condition of the models. The boundary conditions in Flow-3D are symmetry, continuative, specific pressure, grid overlay, wave, wall, periodic, specific velocity, outflow, and volume flow rate.

There are two options to input finite flow rate in the Flow-3D software either for inlet discharge of the system or for the outlet discharge of the domain: specified velocity and volume flow rate. In this research, the X-minimum boundary condition, volume flow rate, has been chosen. For X-maximum boundary condition, outflow was selected because there is nothing to be calculated at the end of the flume. The volume flow rate and the elevation of surface water was set for Q = 0.1 and 0.235 m3/s respectively (Figure 2).

The bottom (Z-min) is prepared as a wall boundary condition and the top (Z-max) is computed as a pressure boundary condition, and for both (Y-min) and (Y-max) as symmetry.

RESULTS AND DISCUSSION

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The air concentration distribution profiles in two models of stepped spillway were obtained at an acquisition time equal to 25 seconds in skimming flow for both upstream and downstream of a slope change 50°–18.6° and 50°–30° for different discharge as in Table 2, and as shown in Figure 4 for 50°–18.6° slope change and Figure 5 for 50°–30° slope change configuration for dc/h = 4.6. The simulation results of the air concentration are very close to the experimental results in all curves and fairly close to that predicted by the advection-diffusion model for the air bubbles suggested by Chanson (1997) on a constant sloping chute.

Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.
Figure 4 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6. VIEW LARGEDOWNLOAD SLIDE Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure 4VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 4.6.

Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.
Figure5 Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 5VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated air concentration distribution for steps number −5, +1, +5, +11, +19 and +22 along the 50°–30° slope change, for dc/h = 4.6.

Figure 6VIEW LARGEDOWNLOAD SLIDE

Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.
Figure 6 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5, +8, +11 and +15 along the 50°–18.6° slope change for dc/h = 2.6.

Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.
Figure 7 Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

Figure 7VIEW LARGEDOWNLOAD SLIDE

Experimental and simulated dimensionless velocity distribution for steps number −5, −1, +1, +5. +11, +15 and +22 along the 50°–30° slope change for dc/h = 2.6.

But as is shown in all above mentioned figures it is clear that at the pseudo-bottom the CFD results of air concentration are less than experimental ones until the depth of water reaches a quarter of the total depth of water. Also the direction of the curves are parallel to each other when going up towards the surface water and are incorporated approximately near the surface water. For all curves, the cross-section is separate between upstream and downstream steps. Therefore the (-) sign for steps represents a step upstream of the slope change cross-section and the (+) sign represents a step downstream of the slope change cross-section.

The dimensionless velocity distribution (V/V90) profile was acquired at an acquisition time equal to 25 seconds in skimming flow of the upstream and downstream slope change for both 50°–18.6° and 50°–30° slope change. The simulation results are compared with the experimental ones showing that for all curves there is close similarity for each point between the observed and experimental results. The curves increase parallel to each other and they merge near at the surface water as shown in Figure 6 for slope change 50°–18.6° configuration and Figure 7 for slope change 50°–30° configuration. However, at step numbers +1 and +5 in Figure 7 there are few differences between the simulated and observed results, namely the simulation curves ascend regularly meaning the velocity increases regularly from the pseudo-bottom up to the surface water.

Figure 8 (50°–18.6° slope change) and Figure 9 (50°–30° slope change) compare the simulation results and the experimental results for the presented dimensionless dynamic pressure distribution for different points on the stepped spillway. The results show a good agreement with the experimental and numerical simulations in all curves. For some points, few discrepancies can be noted in pressure magnitudes between the simulated and the observed ones, but they are in the acceptable range. Although the experimental data do not completely agree with the simulated results, there is an overall agreement.

Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 8 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 8VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 +3 and +20 on the horizontal step faces of 50°–18.6° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number  −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.
Figure 9 Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

Figure 9VIEW LARGEDOWNLOAD SLIDE

Comparison between simulated and experimental results for the dimensionless pressure for steps number −1, −2, −3 and +1, +2 and +30, +31 on the horizontal step face of 50°–30° slope change configuration, for dc/h = 4.6, x is the distance from the step edge.

The pressure profiles were acquired at an acquisition time equal to 70 seconds in skimming flow on 50°–18.6°, where p is the measured dynamic pressure, h is step height and ϒ is water specific weight. A negative sign for steps represents a step upstream of the slope change cross-section and a positive sign represents a step downstream of the slope change cross-section.

Figure 10 shows the experimental streamwise development of dimensionless pressure on the 50°–18.6° slope change for dc/h = 4.6, x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute compared with the numerical simulation. It is obvious from Figure 10 that the streamwise development of dimensionless pressure before slope change (steps number −1, −2 and −3) both of the experimental and simulated results are close to each other. However, it is clear that there is a little difference between the results of the streamwise development of dimensionless pressure at step numbers +1, +2 and +3. Moreover, from step number +3 to the end, the curves get close to each other.

Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.
Figure 10 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 10VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–18.6° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.3 on 18.6° sloping chute.

Figure 11 compares the experimental and the numerical results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute. It is apparent that the outcomes of the experimental work are close to the numerical results, however, the results of the simulation are above the experimental ones before the slope change, but the results of the simulation descend below the experimental ones after the slope change till the end.

Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.
Figure 11 Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

Figure 11VIEW LARGEDOWNLOAD SLIDE

Comparison between experimental and simulated results for the streamwise development of the dimensionless pressure on the 50°–30° slope change, for dc/h = 4.6, and x/l = 0.35 on 50° sloping chute and x/l = 0.17 on 30° sloping chute.

CONCLUSION

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In this research, numerical modelling was attempted to investigate the effect of abrupt slope change on the flow properties (air entrainment, velocity distribution and dynamic pressure) over a stepped spillway with two different models and various flow rates in a skimming flow regime by using the CFD technique. The numerical model was verified and compared with the experimental results of Ostad Mirza (2016). The same domain of the numerical model was inputted as in experimental models to reduce errors as much as possible.

Flow-3D is a well modelled tool that deals with particles. In this research, the model deals well with air entrainment particles by observing their results with experimental results. And the reason for the small difference between the numerical and the experimental results is that the program deals with particles more accurately than the laboratory. In general, both numerical and experimental results showed that near to the slope change the flow bulking, air entrainment, velocity distribution and dynamic pressure are greatly affected by abrupt slope change on the steps. Although the extent of the slope change was relatively small, the influence of the slope change was major on flow characteristics.

The Renormalized Group (RNG) model was selected as a turbulence solver. For 3D modelling, orthogonal mesh was used as a computational domain and the mesh grid size used for X, Y, and Z direction was equal to 0.015 m. In CFD modelling, air concentration and velocity distribution were recorded for a period of 25 seconds, but dynamic pressure was recorded for a period of 70 seconds. The results showed that there is a good agreement between the numerical and the physical models. So, it can be concluded that the proposed CFD model is very suitable for use in simulating and analysing the design of hydraulic structures.

이 연구에서 수치 모델링은 두 가지 다른 모델과 다양한 유속을 사용하여 스키밍 흐름 영역에서 계단식 배수로에 대한 유동 특성 (공기 혼입, 속도 분포 및 동적 압력)에 대한 급격한 경사 변화의 영향을 조사하기 위해 시도되었습니다. CFD 기술. 수치 모델을 검증하여 Ostad Mirza (2016)의 실험 결과와 비교 하였다. 오차를 최대한 줄이기 위해 실험 모형과 동일한 수치 모형을 입력 하였다.

Flow-3D는 파티클을 다루는 잘 모델링 된 도구입니다. 이 연구에서 모델은 실험 결과를 통해 결과를 관찰하여 공기 혼입 입자를 잘 처리합니다. 그리고 수치와 실험 결과의 차이가 작은 이유는 프로그램이 실험실보다 입자를 더 정확하게 다루기 때문입니다. 일반적으로 수치 및 실험 결과는 경사에 가까워지면 유동 벌킹, 공기 혼입, 속도 분포 및 동적 압력이 계단의 급격한 경사 변화에 크게 영향을받는 것으로 나타났습니다. 사면 변화의 정도는 상대적으로 작았지만 사면 변화의 영향은 유동 특성에 큰 영향을 미쳤다.

Renormalized Group (RNG) 모델이 난류 솔버로 선택되었습니다. 3D 모델링의 경우 계산 영역으로 직교 메쉬가 사용되었으며 X, Y, Z 방향에 사용 된 메쉬 그리드 크기는 0.015m입니다. CFD 모델링에서 공기 농도와 속도 분포는 25 초 동안 기록되었지만 동적 압력은 70 초 동안 기록되었습니다. 결과는 수치 모델과 물리적 모델간에 좋은 일치가 있음을 보여줍니다. 따라서 제안 된 CFD 모델은 수력 구조물의 설계 시뮬레이션 및 해석에 매우 적합하다는 결론을 내릴 수 있습니다.

DATA AVAILABILITY STATEMENT

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

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© 2021 The Authors
This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/).

Figure 1. Experimental flume used (a) Side view of the flume; (b) Pool detail.

Modelling of Pool-Type Fishways Flows: Efficiency and Scale Effects Assessment

by Ana L. Quaresma *OrcID andAntónio N. PinheiroOrcID
CERIS—Civil Engineering for Research and Innovation for Sustainability, Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa, Portugal*
Author to whom correspondence should be addressed.
Academic Editor: Bommanna Krishnappan
Water 2021, 13(6), 851; https://doi.org/10.3390/w13060851
Received: 16 January 2021 / Revised: 8 March 2021 / Accepted: 18 March 2021 / Published: 20 March 2021
(This article belongs to the Special Issue Ecohydraulics of Pool-Type Fishways)

Abstract

이 연구에서는 전산 유체 역학 (CFD) 소프트웨어 (FLOW-3D®)를 사용하여 바닥 오리피스가 있는 풀형 어로에서 흐름의 3D 수치 모델링을 수행했습니다. 수치 결과는 음향 도플러 속도계 (ADV) 및 입자 이미지 속도계 (PIV) 측정에서 얻은 실험 데이터와 비교되었습니다.

흐름 깊이, 흐름 패턴, 수속, 난류 운동 에너지, Reynolds 수직 응력 및 바닥 구성 요소에 평행한 Reynolds 전단 응력과 같이 어로 효율에 영향을 미치는 여러 유체 역학적 변수를 정성 및 정량적으로 비교했습니다.

수치 모델은 복잡한 유동장을 정확하게 재현하여 수치 모델 예측과 분석 된 변수에 대한 실험 데이터 사이에 전반적으로 좋은 일치를 보여줍니다. 분석중인 모든 매개 변수에 대한 수치 모델 검증 수행의 중요성이 강조되었습니다.

또한 프로토 타입 어로의 업 스케일 된 수치 모델을 실행하여 스케일링 효과를 분석했습니다. 스케일 효과의 증거없이 실제 모델과 프로토 타입 치수 모두에 대해 유사한 정확도로 모델을 수행했습니다.

현재 연구는 CFD 모델 (즉, FLOW-3D®)이 새로운 수영장 유형 어로 형상을 위한 적절하고 효율적인 설계 및 분석 도구로 사용될 수 있으며 물리적 모델 테스트를 줄이고 보완 할 수 있다고 결론지었습니다.

In this study, the 3D numerical modelling of flow in a pool-type fishway with bottom orifices was performed using computational fluid dynamics (CFD) software (FLOW-3D®). Numerical results were compared with experimental data obtained from acoustic Doppler velocimetry (ADV) and particle image velocimetry (PIV) measurements. Several hydrodynamic variables that influence fishways efficiencies, such as flow depths, flow patterns, water velocity, turbulent kinetic energy, Reynolds normal stresses, and Reynolds shear stress parallel to the bottom component, were qualitatively and quantitatively compared. The numerical model accurately reproduced the complex flow field, showing an overall good agreement between the numerical model predictions and the experimental data for the analysed variables. The importance of performing a numerical model validation for all the parameters under analyses was highlighted. Additionally, scaling effects were analysed by running an upscaled numerical model of the prototype fishway. The model performed with similar accuracy for both physical model and prototype dimensions with no evidence of scale effects. The present study concludes that CFD models (namely FLOW-3D®) may be used as an adequate and efficient design and analysis tool for new pool-type fishways geometries, reducing and complementing physical model testing.Keywords: pool-type fishways3D numerical modellingLESscale effectsflow patternsCFD model assessment

Introduction

강의 종단 연결성을 복원하는 것은 담수 생태계의 회복에있어 여전히 중요한 문제입니다 [1,2]. 잘 설계되고 건설된 경우 어로는 물고기가 댐과 둑을 지나 계속 이동할 수 있는 경로를 제공합니다.

물고기 통과 효율성에 대한 검토에서 Noonan et al. [3]은 기존의 많은 어로의 설계 특성이 어종의 요구를 적절하게 충족시키지 못했지만, 풀형 어로가 모든 어류 그룹에 대해 가장 높은 효율성을 보여 주었다는 것을 발견했습니다.
여러 어종에 적합한 수영 조건을 제공하는 것은 어항의 흐름과 난류 패턴이 성공에 중요한 역할을 하기 때문에 다소 어려운 일입니다 [2,4,5,6,7,8,9,10,11,12].

물리적 모델링은 풀형 유형 어로의 유체 역학을 연구하기 위한 주요 접근 방식이었습니다 (예 : [13,14,15,16,17,18,19,20,21,22]). 그러나 물리적 실험은 비용과 시간이 많이 소요됩니다. 따라서 컴퓨터 기술의 발전으로 인해 물리적 모델 테스트를 줄이기 위해 복잡한 기하학적 구조를 가진 유압 구조의 흐름 패턴을 분석하는 데 전산 유체 역학 (CFD) 3 차원 (3D) 모델이 점점 더 많이 사용되고 있습니다 [23,24].

따라서 이러한 모델은 어로 유체 역학 연구 및 효율적인 어로 설계에 필수적인 역할을 할 수 있습니다.
어로에 대한 수치 모델링 연구는 주로 수직 슬롯 어로에 초점을 맞추고 있습니다 [12,25,26,27,28,29,30,31,32,33,34,35,36,37]. 수영장의 주요 부분에서 수직 슬롯 어로 흐름은 거의 2 차원 (2D)이고 수직 속도 구성 요소가 수평 요소 [26]보다 훨씬 작기 때문에 이러한 연구의 대부분은 2D 모델을 사용했습니다.

바닥 오리피스가있는 수영장 유형 어로에서는 흐름이 매우 복잡하고 3D이므로 정확한 유동장 특성화를 얻기 위해 3D 모델을 사용해야합니다. 이 어로 구성을 모델링하는 것은 높은 속도 구배, 높은 와도 및 높은 전단 영역을 포함하기 때문에 다소 어렵습니다.

이 연구에서는 FLOW-3D® (Flow Science, Inc., Santa Fe, NM, USA)를 사용하여 바닥 오리피스가 있는 수영장 유형 어로의 3D 수치 시뮬레이션을 수행하여 흐름 깊이, 속도 및 난류 패턴을 예측하는 능력을 평가했습니다. .

최근 몇 년 동안 실내에 가까운 프로토 타입 수영장 형 어로가 사이프 린드 종의 행동과 움직임을 연구하는데 사용되었습니다 [1,7,8,11,38,39,40,41,42,43]. Silva et al. [38]은 노치, 급락 및 스트리밍에 대한 두 가지 다른 유동 체제와 관련하여 조정 가능한 치수를 가진 침수된 오리피스와 표면 노치의 동시 존재에 대한 Iberian barbel Luciobarbus bocagei (Steindachner, 1864)의 반응을 평가했습니다.

이 연구의 결과는 이베리아 바벨이 어로를 협상하기 위해 오리피스 (76 %)를 선호했으며 어로에 들어가는 데 걸리는 시간도 오리피스에 비해 훨씬 적다는 것을 보여주었습니다.

Silva et al. [39] 오프셋 및 직선 오리피스가있는 수영장 유형 어로의 이베리아 바벨에 대한 적합성을 테스트했습니다. 이 연구는 오프셋 구성이 직선 오리피스 레이아웃 (28 %)에 비해 물고기 통과 성공률 (68 %)이 훨씬 더 높음을 발견했습니다. 어로를 성공적으로 협상하는 데 걸리는 시간도 오프셋 구성, 특히 작은 성인의 경우 훨씬 더 낮았습니다.

이 연구에서는 유속과 난류 매개 변수가 물고기 수영 성능에 미치는 영향을 분석했습니다. 수영장의 유동장을 특성화하기 위해 음향 도플러 속도계가 사용되었습니다.

이 연구의 결과에 따르면 레이놀즈 전단 응력은 어로 내 이베리아 미늘의 움직임에 가장 큰 영향을 미치는 매개 변수임이 입증되었습니다. Branco et al. [40] 두 가지 다른 흐름을 가진 오리피스와 노치가 있는 풀형 유형 어로에서 형태 학적 및 생태학적 특성이 다른 두 종, 바닥 지향 이베리아 바벨 Luciobarbus bocagei 및 물기둥 수영 자 Iberian chub Squalius pyrenaicus의 거동과 성능을 평가했습니다.

풀의 유체 역학을 특성화하기 위해 음향 도플러 속도계가 사용되었습니다. 결과는 두 종 모두 흐름 흐름이있는 노치를 선호했으며 이 흐름 체제로 상류로 이동하는데 더 성공적이었습니다.
이 연구에서는 이 시설의 1 : 2.5 스케일 어로 모델을 사용하여 Silva et al.에 의해 테스트된 바닥 오리피스 구성이 있는 풀형 유형 어로의 속도와 난류를 측정했습니다.

[7,38] 효과가 입증된 바벨 사용. 2D 입자 이미지 속도계 (PIV) 시스템 및 음향 도플러 속도계 (ADV)를 사용하여 순간 속도의 광범위한 측정을 수행하고, 후 처리하고, 수치 모델 정확도를 평가하는 데 사용했습니다.

Haque et al. [44] 대부분의 경우 수치 모델의 검증에 사용할 수있는 실험 데이터 세트에 높은 측정 오류가 있고 / 또는 측정 메시가 너무 거칠어 서 이들의 예측 기능을 올바르게 평가할 수없는 문제를 언급했습니다.

모델. Blocken과 Gualtieri [23]는 검증 및 검증 연구가 필수적이며 CFD 연구를 검증하기위한 데이터를 제공하기 위해 고품질 실험이 필요하다고 언급합니다.

Fuentes-Pérez et al. [35]는 특히 난류 메트릭에 대한 어로 연구에서 수치 모델 검증 데이터를 찾는 데 어려움을 언급합니다. 두 가지 측정 기술을 사용하고 상당한 양의 실험 데이터를 얻었기 때문에 이 연구에서는 이러한 문제를 극복했습니다.

물리적 모델은 종종 Froude 수 유사성을 기반으로하며, 두 유사성 법칙을 모두 충족하는 데 어려움이있어 무시되는 레이놀즈 수 유사성입니다. 프로토 타입 레이놀즈 수가 일반적으로 훨씬 더 크기 때문에 레이놀즈 수 관련 스케일 효과가 도입될 수 있습니다.

레이놀즈 수 증가는 속도 분포와 경계층 속성에 영향을 미칠 수 있습니다 [45]. 척도 효과를 평가하기 위해 수치 시뮬레이션을 사용할 수 있습니다 [46,47]. 따라서 본 연구에서는 바닥 오리피스 흐름이있는 풀형어도에 대한 스케일 효과를 분석하기 위해 두 가지 크기의 수치 모델을 개발했습니다.

프로토 타입 치수의 대형 모델과 물리적 모델 치수의 스케일 된 소형 모델입니다. .
바닥 오리피스가있는 수영장 형 어로의 유동장은 수직 슬롯 어로 (VSF)의 유동장보다 매우 3 차원 적이며 훨씬 더 복잡합니다. 이는 어로 수치 모델 검증에 대한 이전 연구에서 더 자주 고려 된 설계입니다 [26, 27,28,29,35].

저자가 아는 한, 이것은 바닥 오리피스가있는 풀형 어로에 대한 최초의 CFD 연구이며, 여기에는 실험 속도 데이터와 풀형 어로에 대한 3 차원 수치 모델링 결과 간의 가장 광범위한 비교도 포함됩니다. 두 가지 다른 측정 기술 (PIV 및 ADV)이 사용되어 자세한 비교가 가능하고 이러한 유형의 유동장에 대한 CFD 시뮬레이션 결과에 대한 확신을 제공합니다.

이 연구는 다른 어로 유형의 이전 수치 모델 연구에서 제시되지 않았던 난류 매개 변수를 포함하여 수치 모델 결과와 측정 간의 일치에 대한 통계적 테스트를 통해 정성적 비교 뿐만 아니라 상세한 정량적 비교도 제공합니다. 스케일 효과도 다룹니다.

따라서 이 연구는 전 세계적으로 가장 많이 사용되는 풀 유형 어로의 CFD 모델 검증을 원활하게 할 것이며 [10] 설계자들의 사용을 장려 할 것입니다.
또한 새로운 풀 유형 어로 형상을 위한 설계 도구로 CFD 모델 (즉, FLOW 3D®)을 사용하는 방법에 대해 설명합니다.

Figure 1. Experimental flume used (a) Side view of the flume; (b) Pool detail.
Figure 1. Experimental flume used (a) Side view of the flume; (b) Pool detail.
Figure 2. Three dimensional representations of a pool showing the measurement planes and the acoustic Doppler velocimetry (ADV) measurement grid (a) measurement planes parallel to the flume bottom; (b) vertical measurement planes (ADV measurement grid is only shown in one plane).
Figure 2. Three dimensional representations of a pool showing the measurement planes and the acoustic Doppler velocimetry (ADV) measurement grid (a) measurement planes parallel to the flume bottom; (b) vertical measurement planes (ADV measurement grid is only shown in one plane).
Figure 3. Computational domain, showing Pool 3 mesh block.
Figure 3. Computational domain, showing Pool 3 mesh block.
Figure 4. Streamlines of time-averaged velocities (left: PIV; right: mesh Amodel): (a,b) plane 2 (z = 0.088 m); (c,d) plane 5 (y = 0.20 m).
Figure 4. Streamlines of time-averaged velocities (left: PIV; right: mesh Amodel): (a,b) plane 2 (z = 0.088 m); (c,d) plane 5 (y = 0.20 m).
Figure 5. Longitudinal variation of velocity components: (a,c,e) planes 1 and 6 intersection (y = 0.36 m and z = 0.04 m); (b,d,f) planes 2 and 5 intersection (y = 0.20 m and z = 0.088 m).
Figure 5. Longitudinal variation of velocity components: (a,c,e) planes 1 and 6 intersection (y = 0.36 m and z = 0.04 m); (b,d,f) planes 2 and 5 intersection (y = 0.20 m and z = 0.088 m).
Figure 6. Longitudinal variation of Reynolds normal stress components and Reynolds shear stress parallel to the bottom component: (a,c,e,g) planes 1 and 6 intersection (y = 0.36 m and z = 0.04m); (b,d,f,h) planes 2 and 5 intersection (y = 0.20 m and z = 0.088 m).
Figure 6. Longitudinal variation of Reynolds normal stress components and Reynolds shear stress parallel to the bottom component: (a,c,e,g) planes 1 and 6 intersection (y = 0.36 m and z = 0.04m); (b,d,f,h) planes 2 and 5 intersection (y = 0.20 m and z = 0.088 m).
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Figure 5. Flow pattern of operating condition 1: (a) Physical model flow diagram; (b) Simulation model flow.

Numerical Study of Fluctuating Pressure on Stilling Basin Slab with Sudden Lateral Enlargement and Bottom Drop

급격한 측면 확대 및 바닥 낙하에 따른 정류지(stilling basin) 슬래브의 변동 압력에 대한 수치 연구

by Yangliang Lu,Jinbu Yin *OrcID,Zhou Yang,Kebang Wei andZhiming Liu
College of Water Resources and Architectural Engineering, Northwest A&F University, Weihui Road, Yangling 712100, China*
Author to whom correspondence should be addressed.
Water 2021, 13(2), 238; https://doi.org/10.3390/w13020238
Received: 6 November 2020 / Revised: 7 January 2021 / Accepted: 11 January 2021 / Published: 19 January 2021
(This article belongs to the Special Issue Physical Modelling in Hydraulics Engineering)

Abstract

갑작스런 확장 및 바닥 낙하가 있는 고요한 정류지(stilling basin) 유역은 복잡한 수력 특성, 특히 3D 공간 수력 점프 아래에서 변동하는 압력 분포로 이어집니다.

이 논문은 FLOW-3D 소프트웨어를 기반으로 한 LES (Large Eddy Simulation) 모델과 TruVOF 방법을 사용하여 시간 평균 압력, 변동 압력의 RMS (Root Mean Square), 정물(stilling basin) 조 슬래브의 최대 및 최소 압력을 시뮬레이션했습니다.

실제 모델 결과와 비교하여 시뮬레이션 결과는 LES 모델이 정물 유역의 변동하는 수류 압력을 안정적으로 시뮬레이션 할 수 있음을 보여줍니다. 변동 압력의 RMS의 최대 값은 정수조 전면과 측벽의 연장선 부근에 나타납니다.

이 논문은 변동 압력의 생성 메커니즘과 Navier-Stokes 방정식에서 파생된 Poisson 방정식을 기반으로 영향 요인 (변동 속도, 속도 구배, 변동 와도)의 정량 분석과 특성의 정성 분석을 결합하는 연구 방법을 제공합니다.

변동하는 압력의. 정류 지의 소용돌이 영역과 벽에 부착 된 제트 영역의 변동 압력 분포는 주로 각각 와류 및 변동 유속의 영향을 받으며 충돌 영역의 분포는 변동 속도, 속도 구배 및 변동에 의해 발생합니다.

A stilling basin with sudden enlargement and bottom drop leads to complicated hydraulic characteristics, especially a fluctuating pressure distribution beneath 3D spatial hydraulic jumps. This paper used the large eddy simulation (LES) model and the TruVOF method based on FLOW-3D software to simulate the time-average pressure, root mean square (RMS) of fluctuating pressure, maximum and minimum pressure of a stilling basin slab. Compared with physical model results, the simulation results show that the LES model can simulate the fluctuating water flow pressure in a stilling basin reliably. The maximum value of RMS of fluctuating pressure appears in the vicinity of the front of the stilling basin and the extension line of the side wall. Based on the generating mechanism of fluctuating pressure and the Poisson Equation derived from the Navier–Stokes Equation, this paper provides a research method of combining quantitative analysis of influencing factors (fluctuating velocity, velocity gradient, and fluctuating vorticity) and qualitative analysis of the characteristics of fluctuating pressure. The distribution of fluctuating pressure in the swirling zone of the stilling basin and the wall-attached jet zone is mainly affected by the vortex and fluctuating flow velocity, respectively, and the distribution in the impinging zone is caused by fluctuating velocity, velocity gradient and fluctuating vorticity. 

Keywords: submerged jumpsudden lateral enlargement and bottom droplarge eddy simulationvortexfluctuating pressure

Figure 1. Schematic design of model test: (a) Sectional view; (b) Plan view.
Figure 1. Schematic design of model test: (a) Sectional view; (b) Plan view.
Figure 2. Model layout in laboratory: (a) Discharge chute; (b) The stilling basin.
Figure 2. Model layout in laboratory: (a) Discharge chute; (b) The stilling basin.

Table 1. Operating conditions.

ConditionFlow Discharge
(m3/s)
Inflow Froude NumberInflow Velocity (m/s)Inflow Water Depth (m)
10.9425.2955.6110.114
20.6434.5454.4890.097
30.2324.2273.0180.052
Figure 3. Schematic diagram of fluctuating pressure data-processing process.
Figure 3. Schematic diagram of fluctuating pressure data-processing process.
Figure 4. 3D simulation model: (a) Boundary conditions; (b) Grid mesh.
Figure 4. 3D simulation model: (a) Boundary conditions; (b) Grid mesh.

Table 2. Grid independence test.

GridContaining Block Cell Size (m)Nested Block Cell Size (m)Discharge
(m3/s)
Relative Error (%)
10.0500.0250.9905.10
20.0400.0200.9692.70
30.0300.0150.9561.49
40.0200.0100.9521.06
Figure 5. Flow pattern of operating condition 1: (a) Physical model flow diagram; (b) Simulation model flow.
Figure 5. Flow pattern of operating condition 1: (a) Physical model flow diagram; (b) Simulation model flow.
Figure 6. Numerical simulation of water surface profile and x-z plane flow rate vector.
Figure 6. Numerical simulation of water surface profile and x-z plane flow rate vector.
Figure 7. Comparison of bottom velocity.
Figure 7. Comparison of bottom velocity.
Figure 8. Comparison of pressure at 10 pressure measurement points: (a) Comparison of root mean square (RMS) of fluctuating and time-average pressure; (b) Comparison of maximum and minimum pressure.
Figure 8. Comparison of pressure at 10 pressure measurement points: (a) Comparison of root mean square (RMS) of fluctuating and time-average pressure; (b) Comparison of maximum and minimum pressure.
Figure 9. The distribution diagram of time-average pressure and RMS of fluctuating pressure of bottom of stilling basin under three cases.
Figure 9. The distribution diagram of time-average pressure and RMS of fluctuating pressure of bottom of stilling basin under three cases.
Figure 10. Speed vector in stilling basin at z = 40 cm horizontal plane and bottom plate plane in three cases.
Figure 10. Speed vector in stilling basin at z = 40 cm horizontal plane and bottom plate plane in three cases.
Figure 11. Distribution of fluctuating velocity and vorticity in the horizontal section of the stilling basin slab: (a) Distribution of fluctuating velocity; (b) Distribution of fluctuating vorticity.
Figure 11. Distribution of fluctuating velocity and vorticity in the horizontal section of the stilling basin slab: (a) Distribution of fluctuating velocity; (b) Distribution of fluctuating vorticity.
Figure 12. Distribution of root time-average square fluctuating pressure of x = 50 cm cross-section of bottom plate: (a) Distributions of fluctuating velocity and fluctuating pressure; (b) Distributions of fluctuating vorticity and fluctuating pressure.
Figure 12. Distribution of root time-average square fluctuating pressure of x = 50 cm cross-section of bottom plate: (a) Distributions of fluctuating velocity and fluctuating pressure; (b) Distributions of fluctuating vorticity and fluctuating pressure.
Figure 13. Variance of fluctuating pressure coefficient (Cp′).
Figure 13. Variance of fluctuating pressure coefficient (Cp′).

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ANSI/HI 9.8 Pump Intake Design

Hydraulic Jump in a Trench Type Pump Sump

트렌치 형 펌프 배수 조의 유압 점프

이 기사는 Ibis Group의 대표인 Steve Saunders가 기고했습니다.

유압 점프는 개방형 채널 애플리케이션으로 작업하는 사람들에게 친숙한 흐름 현상입니다. Wikipedia는 수력 점프를 “개방형 채널 흐름이 초-임계에서 아임계로 갑자기 변환되는 조건”으로 정의합니다. 점프가 발생하는 위치에서 속도 헤드가 수면 상승으로 거래되는 것을 관찰 할 수 있습니다. 방수로와 같은 흐름 제어 응용 분야에서 수압 점프는 침식을 완화하기 위해 에너지를 소산하는 수단으로 의도적으로 설정됩니다. 또한 레크리에이션 목적으로 사용됩니다. 유압 점프로 생성된 정상 파도는 어떤 바다에서든 수천 마일 떨어진 서핑 공원에서 타는 방법을 서퍼를 훈련시키는데 사용됩니다. 유압 점프의 새로운 응용 분야는 점프의 에너지 전달이 다시 중단되고 정상적인 펌핑 작업 중에 침전된 고형물을 제거하는 자가 세척 트렌치 유형 펌프 섬프(sump)입니다.

트렌치 유형 집수 펌프 시뮬레이션
FLOW-3D는 유압 점프 시뮬레이션에서 신뢰할 수 있는 도구로 입증되었으며 자가 세척 트렌치 유형 펌프 섬프의 설계 및 시연에 사용되었습니다. 트렌치 형 펌프 섬프는 펌프 흡입 라인이 있는 좁은 채널로 구성됩니다. 일반적인 응용 분야는 들어오는 물에서 모래와 자갈을 걸러내는 입구 스크린이 없는 빗물 수집입니다. 아래 회로도에 예가 나와 있습니다.

ANSI/HI 9.8 Pump Intake Design
ANSI/HI 9.8 Pump Intake Design

이 수치는 ANSI / HI 9.8 펌프 흡기 설계 매뉴얼에서 발췌한 것이며 4 개의 펌프가 설치된 섬프의 평면도 및 입면도를 보여줍니다. 유입 암거, 웅덩이 바닥 및 펌프 흡입 바닥을 벗어난 높이의 배열은 이 설계 유형의 자체 청소 기능에 매우 중요합니다. 유입 암거는 최소 작동 웅덩이 수위보다 높은 고도에 있습니다. 또한 유입단의 ​​트렌치 벽은 Ogee 모양입니다. 마지막으로, 트렌치의 맨 끝에 있는 펌프 흡입 벨은 상류 펌프의 절반 높이에 설정됩니다.

Designing for Storm Events

폭풍이 닥친 후 모래와 자갈이 웅덩이 바닥에 쌓입니다. 그들은 점진적인 유압 점프를 통해 다시 매달리고 빠져 나갑니다. 청소 주기 동안 물은 유입 암거를 통해 유입되는 것보다 더 빠른 속도로 트렌치의 맨 끝에 있는 하부 펌프에 의해 배출됩니다.

이 시퀀스 동안 유압 점프는 두 가지 중요한 역할을 수행합니다. 점프 업스트림의 초임계 부분은 섬프 바닥의 모래와 자갈을 휘감아 펌핑이 되도록 다시 일시 중단합니다. 애니메이션의 색상 스케일을 보면 ogee 바닥의 수색 속도가 약 9ft/sec에 가깝다는 것을 알 수 있습니다. 한편, 점프 하류의 계단식 수면 상승은 하단 펌프에 충분한 잠수를 제공하여 섬프가 펌핑 될 때까지 계속 작동합니다.

물이 최소 정상 작동 수준 아래로 떨어지면 유입이 Ogee 모양의 벽 아래로 가속되어 궁극적으로 초임계가됩니다. 섬프의 수위가 바닥에 가까워지면 수압 점프가 형성되고 하단 원단 펌프가 흡입력을 잃을 때까지 섬프를 따라 진행됩니다. 아래 애니메이션에서 이런 일이 일어나는 것을 관찰 할 수 있습니다.

The Magnolia Storm Water Pumping Station

이 자체 세척 섬프 응용 분야에 FLOW-3D를 사용하면 트렌치 형상을 쉽게 조정하여 유압 점프 동작을 최적화 할 수 있습니다. 텍사스 엘파소에있는 Magnolia Storm Water Pumping Station은 FLOW-3D가 설계 및 평가 도구로 사용 된 예입니다. 2016 년에 시운전 된 Magnolia Storm Water Pumping Station은 폭우시 고속도로 10 번의 홍수를 방지하기 위해 건설되었습니다.

Magnolia 스테이션은자가 세척 트렌치 유형 섬프에 3 개의 대형 수직 터빈 펌프로 구성됩니다. 섬프 설계 과정에서 FLOW-3D를 사용하여 몇 가지 기하학적 변형을 평가하여 자체 세척 기능을 통해 펌프 작동 효율성 및 유지 보수 용이성에 이상적인 구성에 도달했습니다.

수자원/수처리/환경분야

수자원 분야

Water & Environmental

FLOW-3D는 작은 하수 처리 시스템부터 대형 수력 발전 프로젝트까지 수처리 및 환경 산업에 직면한 광범위한 문제를 해결할 수 있는 뛰어난 CFD 소프트웨어 입니다. FLOW-3D는 시뮬레이션의 복잡성을 감소시키고 최적의 솔루션에 대해 노력을 집중할 수 있도록 해줍니다. 이를 통해 통해 파악된 가치 있는 통찰력은 귀하의 상당한 시간과 비용을 절약 할 수 있습니다.

실제 지형을 적용하여 3차원 shallow water hybrid model을 이용한 댐 붕괴 시뮬레이션

FLOW-3D는 자유표면 흐름이 있는 수치해석 알고리듬에 의해 유동의 표면이 시공간적으로 변하는 모사를 위한 이상적인 도구라고 할 수 있습니다. 자유 표면은 물과 공기 같은 높은 비율의 밀도 변화를 가지는 유체들 사이의 특정한 경계를 일컫습니다. 자유 표면 흐름을 모델링하는 것은 일반적인 유동방정식과 난류 모델이 결합된 고급 알고리즘을 필요로 합니다. 이 기능은 FLOW-3D로 하여금 침수 구조에 의해 형성된 방수, 수력 점프 및 수면 변화의 흐름의 궤적을 포착 할 수 있습니다.


Bibliography & Technical Data

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

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

Arash Ahmadi a, Amir H. Azimi b Abstract 험프 웨어는 수위 제어 및 배출 측정을 위한 기존의 수력 구조물 중 하나입니다. 상류 및 하류 경사로의 ...
그림 0 - 임계값의 다양한 위치에서 슬라이딩 밸브를 통과하는 흐름의 개략도: a) 밸브 아래, b) 밸브의 하류 측에 접선, c) 밸브의 상류 측에 접선

수직 슬라이딩 밸브의 토출 계수에 대한 형상 및 임계 위치 변화의 영향 평가

Abstract 본 연구의 목적은 다양한 위치에서 임계값을 갖는 슬라이딩 밸브의 유량계수를 조사하는 것입니다. 이 목표를 달성하기 위해 슬라이딩 밸브 아래 ...
Fig. 9 From: An Investigation on Hydraulic Aspects of Rectangular Labyrinth Pool and Weir Fishway Using FLOW-3D

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

Research Article-Civil Engineering Open access Published: 04 January 2024 Abstract 웨어의 두 가지 서로 다른 배열(즉, 직선형 웨어와 직사각형 미로 ...
Figura 1 – Mapa de localização da PCH Salto Paraopeba

하천 저수지 물리적 모델의 침적 과정에 대한 전산 유체 역학 모델링(CFD) 기준

Natália Melo da Silva1 1; Jorge Luis Zegarra Tarqui2,Edna Maria de Faria Viana 3 Abstract 저수지 침전은 수력 발전의 지속 ...
Open Channels Flow에서의 콘크리트 캔버스 거동 연구

Study of Concrete Canvas Behavior in Open Channels Flow

Document Type : Research Paper Authors Mohammad Fayyaz saeed ahmadi Mahdi Dehghannejad Sani 1 Imam Hosein Uni 2 Researcher of ...
Figure 4. Rectangular stepped spillway with (a) three baffle arrangement (b) five baffle arrangement

Prediction of Energy Dissipation over Stepped Spillwaywith Baffles Using Machine Learning Techniques

Saurabh Pujari*, Vijay Kaushik, S. Anbu KumarDepartment of Civil Engineering, Delhi Technological University, IndiaReceived February 23, 2023; Revised April 25, ...
Schematic view of the experimental set-up

Short-time numerical simulation of ultrasonically assisted electrochemical removal of strontium from water

September 2023 DOI:10.30955/gnc2023.00436 Conference: 18th International Conference on Environmental Science and Technology CEST2023, 30 August to 2 September 2023, Athens, ...
Study on the critical sediment concentration determining the optimal transport capability of submarine sediment flows with different particle size composition

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

Yupeng Ren abc, Huiguang Zhou cd, Houjie Wang ab, Xiao Wu ab, Guohui Xu cd, Qingsheng Meng cd Abstract 해저 퇴적물 흐름은 퇴적물을 심해로 운반하는 주요 수단 중 하나이며, 종종 장거리를 이동하고 수십 또는 수백 킬로미터에 걸쳐 ...
Figure 2-15: Système expérimental du plan incliné

새로운 콘크리트의 유체 흐름 모델링

Sous la direction de :Marc Jolin, directeur de rechercheBenoit Bissonnette, codirecteur de recherche Modélisation de l’écoulement du béton frais Abstract ...
Figure 1. US bath modified as an EC reactor

물에서 초음파를 이용한 전기화학적 스트론튬 제거에 대한 단시간 수치 시뮬레이션

전기화학 반응기에 대한 3D 수치 시뮬레이션 및 측정을 사용하여 동시 초음파 처리 유무에 관계없이 물에서 스트론튬 제거 효율을 분석했습니다. 초음파는 ...


FLOW-3D Water & Environmental Brochure (FSI) Bibliography

Models

  • Air Entrainment
  • Hybrid Shallow Water/3D Flow
  • Sediment Scour
  • Turbulence
  • More Modeling Capabilities

Case Studies

  • Evaluating Hydraulic Energy Losses and Total Hydraulic Head with FLOW-3D‘s Flux Baffles
  • Modeling Commercial Aquaculture Systems
  • Modeling Local Bridge Scour during Flood Event

Conference Proceedings

Design of a Sewer Transition

Design of a Sewer Transition | 하수도 전환 설계

This article was contributed by Daniel Valero, Rafael García-Bartual, Ignacio Andrés and Francisco Valles of the Polytechnic University of Valencia.

2010 년 12 월, 새로운 고속 열차 MADRID-VALENCIA (스페인)가 개통되었습니다. 건설 전에 극복해야 할 많은 기술적 문제 중 하나는 터널로 구성된 도심의 철도 입구로 발렌시아의 주요 남쪽 하수도를 벗어나게 했습니다. 이탈 도달 범위는 길이가 143 미터이며 아래에 자세히 설명된 복잡한 유압 설계를 포함하여 기존 경사와 관련하여 경사 및 단면의 중요한 변경을 포함합니다. 유압 성능은 FLOW-3D를 사용한 수치 시뮬레이션과   발렌시아 폴리 테크닉 대학교의 유압 실험실에서 물리적 모델을 통해 확인되었습니다. 최대 용량 100 m 3 / s에 대한 테스트가 수행되었습니다 .

The Sewer                          

그림 1은 하수도 기하학 설계의 주요 특징을 보여줍니다. 여기에는 철도 터널을 건넌 직후에 위치한 표준 WES 프로파일이 포함됩니다. 이 위어는 높은 유속으로 초 임계 흐름을 강제합니다. 하류에서 바람직하지 않은 흐름 조건이 설정되는 것을 방지하기 위해 둑 바로 하류에 정류 조를 설계했습니다. 이러한 장치는 연결 하류 하수도에서 높은 에너지 손실 및 임계 이하의 흐름 조건을 수반하는 유압 점프를 강제합니다. 서로 다른 배출 조건에서 흐름의 거동을 보장하기 위해 채널에 두 개의 세로 줄의 삼각형 블록이 포함되었으며, 이는 정수 조 길이에서 유압 점프를 국지화하기 위해 에너지 소산 기 역할을했습니다. 그 계단의 길이에서 수압 점프. 새로운 변형 채널과 기존 도달 지점(upstream and downstream)사이는 기하학적 요소로 부드럽게 연결합니다.(그림 2).

Figure 1. Geometry of the sewer

Figure 2. Reach 2 of the sewer

FLOW-3D Simulations

문제의 정확한 해결을 위해 계산 리소스를 최적화하기 위해 하수도를 여러 개의 중첩 된 범위로 분할하여 수력 솔루션의 연속성을 보장하고 고려 된 각 도달 범위에서 더 미세한 메시를 사용할 수 있습니다. 가장 복잡한 흐름이 정수 조에서 발생하기 때문에 이러한 도달 범위는 윤곽선과 바닥 블록에서 중앙 흐름 영역까지 점진적으로 다양한 셀 크기로 가장 높은 해상도 (6.000.000 셀)로 해결되었습니다. 유압 점프 시뮬레이션에 대한 비디오는 이 기사의 끝에 있습니다.

Figure 3. Velocity magnitude distribution

Figure 4. Turbulent kinetic energy distribution.

Figure 5. Air entrained prediction with turbulent air entrainment model

ke RNG 난류 모델이 선택되었으며, 이류에 대한 명시적인 2 차 단 조성 보존 체계가 있습니다. 자유 표면 표현에는 Split Lagrangian 방법이 사용되었습니다. 정상 상태 솔루션 이전의 과도 흐름은 더 거친 메쉬로 시뮬레이션되었습니다. 그림 3과 4는 수치 시뮬레이션의 관련 결과를 보여줍니다. 또한 수력 점프의 수치 시뮬레이션을 보여주는 비디오 가이드 기술 노트에 첨부되어 있습니다.

유압 점프에서 발생하는 공기 혼입, 특히 난류와 자유 표면 간의 상호 작용을 설명하기 위해 추가 시뮬레이션이 수행되었습니다. 그림 5는 가변 밀도 옵션을 선택하고 기본 계수 C air  = 0.5를 사용하는 FLOW-3D 의 공기 혼입 모델을 사용한 결과를 보여줍니다.

Comparison with the Physical Model

발렌시아 Polytechnic University의 수압 실험실에 실물 모형을 구축하였습니다. 모형에 사용된 척도는 1/20이었습니다. 그림 6은 weir 상단 바로 위에 있는 임계 단면의 프로파일을 보여 줍니다. 발견된 평균 깊이의 오차는 1.3% 였습니다. 유동의 다른 구조적 특성은 FLOW-3D에 의해 적절하게 재현되었다. 예를 들어, 예를 들어, 하수도가 만곡된 범위에 따른 자유 표면의 형상과 Weir의 상류로의 흐르는 자유 표면의 현상입니다.

Figure 6. Relative error at the critical section. Comparison between FLOW-3D, physical model, and HEC-RAS (US Army Corps of Engineers).

Conclusions

실험실 결과와 FLOW-3D시뮬레이션 간의 약간의 차이가 확인되지만 연구 결과는 매우 만족스럽습니다. 아래 동영상을 통해 실험 및 수치해석 결과를 비교해 보시길 바랍니다.

FLOW-3D는 가능한 많은 형상 또는 유압 설계를 테스트할 때 실험실의 실험 횟수를 줄일 수 있습니다. 또한 FLOW-3D의 파일이 속도, 와도, 난류 등과 같은 관련 분야의 상세한 시공간 분포를 제공하므로 최종 설계와 관련하여 실험실에서 수행 된 결과와 측정을 확장하는 데 도움이 될 수 있습니다. 결합된 기술은 연구에서 언급한 것과 같은 유압 기반시설의 설계, 검증 및 최적화를 위한 강력한 도구입니다.

FLOW-3D CAST Bibliography

FLOW-3D CAST bibliography

아래는 FSI의 금속 주조 참고 문헌에 수록된 기술 논문 모음입니다. 이 모든 논문에는 FLOW-3D CAST 해석 결과가 수록되어 있습니다. FLOW-3D CAST를 사용하여 금속 주조 산업의 응용 프로그램을 성공적으로 시뮬레이션하는 방법에 대해 자세히 알아보십시오.

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

33-20     Eric Riedel, Martin Liepe Stefan Scharf, Simulation of ultrasonic induced cavitation and acoustic streaming in liquid and solidifying aluminum, Metals, 10.4; 476, 2020. doi.org/10.3390/met10040476

20-20   Wu Yue, Li Zhuo and Lu Rong, Simulation and visual tester verification of solid propellant slurry vacuum plate casting, Propellants, Explosives, Pyrotechnics, 2020. doi.org/10.1002/prep.201900411

17-20   C.A. Jones, M.R. Jolly, A.E.W. Jarfors and M. Irwin, An experimental characterization of thermophysical properties of a porous ceramic shell used in the investment casting process, Supplimental Proceedings, pp. 1095-1105, TMS 2020 149th Annual Meeting and Exhibition, San Diego, CA, February 23-27, 2020. doi.org/10.1007/978-3-030-36296-6_102

12-20   Franz Josef Feikus, Paul Bernsteiner, Ricardo Fernández Gutiérrez and Michal Luszczak , Further development of electric motor housings, MTZ Worldwide, 81, pp. 38-43, 2020. doi.org/10.1007/s38313-019-0176-z

09-20   Mingfan Qi, Yonglin Kang, Yuzhao Xu, Zhumabieke Wulabieke and Jingyuan Li, A novel rheological high pressure die-casting process for preparing large thin-walled Al–Si–Fe–Mg–Sr alloy with high heat conductivity, high plasticity and medium strength, Materials Science and Engineering: A, 776, art. no. 139040, 2020. doi.org/10.1016/j.msea.2020.139040

07-20   Stefan Heugenhauser, Erhard Kaschnitz and Peter Schumacher, Development of an aluminum compound casting process – Experiments and numerical simulations, Journal of Materials Processing Technology, 279, art. no. 116578, 2020. doi.org/10.1016/j.jmatprotec.2019.116578

05-20   Michail Papanikolaou, Emanuele Pagone, Mark Jolly and Konstantinos Salonitis, Numerical simulation and evaluation of Campbell running and gating systems, Metals, 10.1, art. no. 68, 2020. doi.org/10.3390/met10010068

102-19   Ferencz Peti and Gabriela Strnad, The effect of squeeze pin dimension and operational parameters on material homogeneity of aluminium high pressure die cast parts, Acta Marisiensis. Seria Technologica, 16.2, 2019. doi.org/0.2478/amset-2019-0010

94-19   E. Riedel, I. Horn, N. Stein, H. Stein, R. Bahr, and S. Scharf, Ultrasonic treatment: a clean technology that supports sustainability incasting processes, Procedia, 26th CIRP Life Cycle Engineering (LCE) Conference, Indianapolis, Indiana, USA, May 7-9, 2019. 

93-19   Adrian V. Catalina, Liping Xue, Charles A. Monroe, Robin D. Foley, and John A. Griffin, Modeling and Simulation of Microstructure and Mechanical Properties of AlSi- and AlCu-based Alloys, Transactions, 123rd Metalcasting Congress, Atlanta, GA, USA, April 27-30, 2019. 

84-19   Arun Prabhakar, Michail Papanikolaou, Konstantinos Salonitis, and Mark Jolly, Sand casting of sheet lead: numerical simulation of metal flow and solidification, The International Journal of Advanced Manufacturing Technology, pp. 1-13, 2019. doi.org/10.1007/s00170-019-04522-3

72-19   Santosh Reddy Sama, Eric Macdonald, Robert Voigt, and Guha Manogharan, Measurement of metal velocity in sand casting during mold filling, Metals, 9:1079, 2019. doi.org/10.3390/met9101079

71-19   Sebastian Findeisen, Robin Van Der Auwera, Michael Heuser, and Franz-Josef Wöstmann, Gießtechnische Fertigung von E-Motorengehäusen mit interner Kühling (Casting production of electric motor housings with internal cooling), Geisserei, 106, pp. 72-78, 2019 (in German).

58-19     Von Malte Leonhard, Matthias Todte, and Jörg Schäffer, Realistic simulation of the combustion of exothermic feeders, Casting, No. 2, pp. 28-32, 2019. In English and German.

52-19     S. Lakkum and P. Kowitwarangkul, Numerical investigations on the effect of gas flow rate in the gas stirred ladle with dual plugs, International Conference on Materials Research and Innovation (ICMARI), Bangkok, Thailand, December 17-21, 2018. IOP Conference Series: Materials Science and Engineering, Vol. 526, 2019. doi.org/10.1088/1757-899X/526/1/012028

47-19     Bing Zhou, Shuai Lu, Kaile Xu, Chun Xu, and Zhanyong Wang, Microstructure and simulation of semisolid aluminum alloy castings in the process of stirring integrated transfer-heat (SIT) with water cooling, International Journal of Metalcasting, Online edition, pp. 1-13, 2019. doi.org/10.1007/s40962-019-00357-6

31-19     Zihao Yuan, Zhipeng Guo, and S.M. Xiong, Skin layer of A380 aluminium alloy die castings and its blistering during solution treatment, Journal of Materials Science & Technology, Vol. 35, No. 9, pp. 1906-1916, 2019. doi.org/10.1016/j.jmst.2019.05.011

25-19     Stefano Mascetti, Raul Pirovano, and Giulio Timelli, Interazione metallo liquido/stampo: Il fenomeno della metallizzazione, La Metallurgia Italiana, No. 4, pp. 44-50, 2019. In Italian.

20-19     Fu-Yuan Hsu, Campbellology for runner system design, Shape Casting: The Minerals, Metals & Materials Series, pp. 187-199, 2019. doi.org/10.1007/978-3-030-06034-3_19

19-19     Chengcheng Lyu, Michail Papanikolaou, and Mark Jolly, Numerical process modelling and simulation of Campbell running systems designs, Shape Casting: The Minerals, Metals & Materials Series, pp. 53-64, 2019. doi.org/10.1007/978-3-030-06034-3_5

18-19     Adrian V. Catalina, Liping Xue, and Charles Monroe, A solidification model with application to AlSi-based alloys, Shape Casting: The Minerals, Metals & Materials Series, pp. 201-213, 2019. doi.org/10.1007/978-3-030-06034-3_20

17-19     Fu-Yuan Hsu and Yu-Hung Chen, The validation of feeder modeling for ductile iron castings, Shape Casting: The Minerals, Metals & Materials Series, pp. 227-238, 2019. doi.org/10.1007/978-3-030-06034-3_22

04-19   Santosh Reddy Sama, Tony Badamo, Paul Lynch and Guha Manogharan, Novel sprue designs in metal casting via 3D sand-printing, Additive Manufacturing, Vol. 25, pp. 563-578, 2019. doi.org/10.1016/j.addma.2018.12.009

02-19   Jingying Sun, Qichi Le, Li Fu, Jing Bai, Johannes Tretter, Klaus Herbold and Hongwei Huo, Gas entrainment behavior of aluminum alloy engine crankcases during the low-pressure-die-casting-process, Journal of Materials Processing Technology, Vol. 266, pp. 274-282, 2019. doi.org/10.1016/j.jmatprotec.2018.11.016

92-18   Fast, Flexible… More Versatile, Foundry Management Technology, March, 2018. 

82-18   Xu Zhao, Ping Wang, Tao Li, Bo-yu Zhang, Peng Wang, Guan-zhou Wang and Shi-qi Lu, Gating system optimization of high pressure die casting thin-wall AlSi10MnMg longitudinal loadbearing beam based on numerical simulation, China Foundry, Vol. 15, no. 6, pp. 436-442, 2018. doi: 10.1007/s41230-018-8052-z

80-18   Michail Papanikolaou, Emanuele Pagone, Konstantinos Salonitis, Mark Jolly and Charalampos Makatsoris, A computational framework towards energy efficient casting processes, Sustainable Design and Manufacturing 2018: Proceedings of the 5th International Conference on Sustainable Design and Manufacturing (KES-SDM-18), Gold Coast, Australia, June 24-26 2018, SIST 130, pp. 263-276, 2019. doi.org/10.1007/978-3-030-04290-5_27

64-18   Vasilios Fourlakidis, Ilia Belov and Attila Diószegi, Strength prediction for pearlitic lamellar graphite iron: Model validation, Metals, Vol. 8, No. 9, 2018. doi.org/10.3390/met8090684

51-18   Xue-feng Zhu, Bao-yi Yu, Li Zheng, Bo-ning Yu, Qiang Li, Shu-ning Lü and Hao Zhang, Influence of pouring methods on filling process, microstructure and mechanical properties of AZ91 Mg alloy pipe by horizontal centrifugal casting, China Foundry, vol. 15, no. 3, pp.196-202, 2018. doi.org/10.1007/s41230-018-7256-6

47-18   Santosh Reddy Sama, Jiayi Wang and Guha Manogharan, Non-conventional mold design for metal casting using 3D sand-printing, Journal of Manufacturing Processes, vol. 34-B, pp. 765-775, 2018. doi.org/10.1016/j.jmapro.2018.03.049

42-18   M. Koru and O. Serçe, The Effects of Thermal and Dynamical Parameters and Vacuum Application on Porosity in High-Pressure Die Casting of A383 Al-Alloy, International Journal of Metalcasting, pp. 1-17, 2018. doi.org/10.1007/s40962-018-0214-7

41-18   Abhilash Viswanath, S. Savithri, U.T.S. Pillai, Similitude analysis on flow characteristics of water, A356 and AM50 alloys during LPC process, Journal of Materials Processing Technology, vol. 257, pp. 270-277, 2018. doi.org/10.1016/j.jmatprotec.2018.02.031

29-18   Seyboldt, Christoph and Liewald, Mathias, Investigation on thixojoining to produce hybrid components with intermetallic phase, AIP Conference Proceedings, vol. 1960, no. 1, 2018. doi.org/10.1063/1.5034992

28-18   Laura Schomer, Mathias Liewald and Kim Rouven Riedmüller, Simulation of the infiltration process of a ceramic open-pore body with a metal alloy in semi-solid state to design the manufacturing of interpenetrating phase composites, AIP Conference Proceedings, vol. 1960, no. 1, 2018. doi.org/10.1063/1.5034991

41-17   Y. N. Wu et al., Numerical Simulation on Filling Optimization of Copper Rotor for High Efficient Electric Motors in Die Casting Process, Materials Science Forum, Vol. 898, pp. 1163-1170, 2017.

12-17   A.M.  Zarubin and O.A. Zarubina, Controlling the flow rate of melt in gravity die casting of aluminum alloys, Liteynoe Proizvodstvo (Casting Manufacturing), pp 16-20, 6, 2017. In Russian.

10-17   A.Y. Korotchenko, Y.V. Golenkov, M.V. Tverskoy and D.E. Khilkov, Simulation of the Flow of Metal Mixtures in the Mold, Liteynoe Proizvodstvo (Casting Manufacturing), pp 18-22, 5, 2017. In Russian.

08-17   Morteza Morakabian Esfahani, Esmaeil Hajjari, Ali Farzadi and Seyed Reza Alavi Zaree, Prediction of the contact time through modeling of heat transfer and fluid flow in compound casting process of Al/Mg light metals, Journal of Materials Research, © Materials Research Society 2017

04-17   Huihui Liu, Xiongwei He and Peng Guo, Numerical simulation on semi-solid die-casting of magnesium matrix composite based on orthogonal experiment, AIP Conference Proceedings 1829, 020037 (2017); doi.org/10.1063/1.4979769.

100-16  Robert Watson, New numerical techniques to quantify and predict the effect of entrainment defects, applied to high pressure die casting, PhD Thesis: University of Birmingham, 2016.

88-16   M.C. Carter, T. Kauffung, L. Weyenberg and C. Peters, Low Pressure Die Casting Simulation Discovery through Short Shot, Cast Expo & Metal Casting Congress, April 16-19, 2016, Minneapolis, MN, Copyright 2016 American Foundry Society.

61-16   M. Koru and O. Serçe, Experimental and numerical determination of casting mold interfacial heat transfer coefficient in the high pressure die casting of a 360 aluminum alloy, ACTA PHYSICA POLONICA A, Vol. 129 (2016)

59-16   R. Pirovano and S. Mascetti, Tracking of collapsed bubbles during a filling simulation, La Metallurgia Italiana – n. 6 2016

43-16   Kevin Lee, Understanding shell cracking during de-wax process in investment casting, Ph.D Thesis: University of Birmingham, School of Engineering, Department of Chemical Engineering, 2016.

35-16   Konstantinos Salonitis, Mark Jolly, Binxu Zeng, and Hamid Mehrabi, Improvements in energy consumption and environmental impact by novel single shot melting process for casting, Journal of Cleaner Production, doi.org/10.1016/j.jclepro.2016.06.165, Open Access funded by Engineering and Physical Sciences Research Council, June 29, 2016

20-16   Fu-Yuan Hsu, Bifilm Defect Formation in Hydraulic Jump of Liquid Aluminum, Metallurgical and Materials Transactions B, 2016, Band: 47, Heft 3, 1634-1648.

15-16   Mingfan Qia, Yonglin Kanga, Bing Zhoua, Wanneng Liaoa, Guoming Zhua, Yangde Lib,and Weirong Li, A forced convection stirring process for Rheo-HPDC aluminum and magnesium alloys, Journal of Materials Processing Technology 234 (2016) 353–367

112-15   José Miguel Gonçalves Ledo Belo da Costa, Optimization of filling systems for low pressure by FLOW-3D, Dissertação de mestrado integrado em Engenharia Mecânica, 2015.

89-15   B.W. Zhu, L.X. Li, X. Liu, L.Q. Zhang and R. Xu, Effect of Viscosity Measurement Method to Simulate High Pressure Die Casting of Thin-Wall AlSi10MnMg Alloy Castings, Journal of Materials Engineering and Performance, Published online, November 2015, doi.org/10.1007/s11665-015-1783-8, © ASM International.

88-15   Peng Zhang, Zhenming Li, Baoliang Liu, Wenjiang Ding and Liming Peng, Improved tensile properties of a new aluminum alloy for high pressure die casting, Materials Science & Engineering A651(2016)376–390, Available online, November 2015.

83-15   Zu-Qi Hu, Xin-Jian Zhang and Shu-Sen Wu, Microstructure, Mechanical Properties and Die-Filling Behavior of High-Performance Die-Cast Al–Mg–Si–Mn Alloy, Acta Metall. Sin. (Engl. Lett.), doi.org/10.1007/s40195-015-0332-7, © The Chinese Society for Metals and Springer-Verlag Berlin Heidelberg 2015.

82-15   J. Müller, L. Xue, M.C. Carter, C. Thoma, M. Fehlbier and M. Todte, A Die Spray Cooling Model for Thermal Die Cycling Simulations, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

81-15   M. T. Murray, L.F. Hansen, L. Chilcott, E. Li and A.M. Murray, Case Studies in the Use of Simulation- Improved Yield and Reduced Time to Market, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

80-15   R. Bhola, S. Chandra and D. Souders, Predicting Castability of Thin-Walled Parts for the HPDC Process Using Simulations, 2015 Die Casting Congress & Exposition, Indianapolis, IN, October 2015

76-15   Prosenjit Das, Sudip K. Samanta, Shashank Tiwari and Pradip Dutta, Die Filling Behaviour of Semi Solid A356 Al Alloy Slurry During Rheo Pressure Die Casting, Transactions of the Indian Institute of Metals, pp 1-6, October 2015

74-15   Murat KORU and Orhan SERÇE, Yüksek Basınçlı Döküm Prosesinde Enjeksiyon Parametrelerine Bağlı Olarak Döküm Simülasyon, Cumhuriyet University Faculty of Science, Science Journal (CSJ), Vol. 36, No: 5 (2015) ISSN: 1300-1949, May 2015

69-15   A. Viswanath, S. Sivaraman, U. T. S. Pillai, Computer Simulation of Low Pressure Casting Process Using FLOW-3D, Materials Science Forum, Vols. 830-831, pp. 45-48, September 2015

68-15   J. Aneesh Kumar, K. Krishnakumar and S. Savithri, Computer Simulation of Centrifugal Casting Process Using FLOW-3D, Materials Science Forum, Vols. 830-831, pp. 53-56, September 2015

59-15   F. Hosseini Yekta and S. A. Sadough Vanini, Simulation of the flow of semi-solid steel alloy using an enhanced model, Metals and Materials International, August 2015.

44-15   Ulrich E. Klotz, Tiziana Heiss and Dario Tiberto, Platinum investment casting material properties, casting simulation and optimum process parameters, Jewelry Technology Forum 2015

41-15   M. Barkhudarov and R. Pirovano, Minimizing Air Entrainment in High Pressure Die Casting Shot Sleeves, GIFA 2015, Düsseldorf, Germany

40-15   M. Todte, A. Fent, and H. Lang, Simulation in support of the development of innovative processes in the casting industry, GIFA 2015, Düsseldorf, Germany

19-15   Bruce Morey, Virtual casting improves powertrain design, Automotive Engineering, SAE International, March 2015.

15-15   K.S. Oh, J.D. Lee, S.J. Kim and J.Y. Choi, Development of a large ingot continuous caster, Metall. Res. Technol. 112, 203 (2015) © EDP Sciences, 2015, doi.org/10.1051/metal/2015006, www.metallurgical-research.org

14-15   Tiziana Heiss, Ulrich E. Klotz and Dario Tiberto, Platinum Investment Casting, Part I: Simulation and Experimental Study of the Casting Process, Johnson Matthey Technol. Rev., 2015, 59, (2), 95, doi.org/10.1595/205651315×687399

138-14 Christopher Thoma, Wolfram Volk, Ruben Heid, Klaus Dilger, Gregor Banner and Harald Eibisch, Simulation-based prediction of the fracture elongation as a failure criterion for thin-walled high-pressure die casting components, International Journal of Metalcasting, Vol. 8, No. 4, pp. 47-54, 2014. doi.org/10.1007/BF03355594

107-14  Mehran Seyed Ahmadi, Dissolution of Si in Molten Al with Gas Injection, ProQuest Dissertations And Theses; Thesis (Ph.D.), University of Toronto (Canada), 2014; Publication Number: AAT 3637106; ISBN: 9781321195231; Source: Dissertation Abstracts International, Volume: 76-02(E), Section: B.; 191 p.

99-14   R. Bhola and S. Chandra, Predicting Castability for Thin-Walled HPDC Parts, Foundry Management Technology, December 2014

92-14   Warren Bishenden and Changhua Huang, Venting design and process optimization of die casting process for structural components; Part II: Venting design and process optimization, Die Casting Engineer, November 2014

90-14   Ken’ichi Kanazawa, Ken’ichi Yano, Jun’ichi Ogura, and Yasunori Nemoto, Optimum Runner Design for Die-Casting using CFD Simulations and Verification with Water-Model Experiments, Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition, IMECE2014, November 14-20, 2014, Montreal, Quebec, Canada, IMECE2014-37419

89-14   P. Kapranos, C. Carney, A. Pola, and M. Jolly, Advanced Casting Methodologies: Investment Casting, Centrifugal Casting, Squeeze Casting, Metal Spinning, and Batch Casting, In Comprehensive Materials Processing; McGeough, J., Ed.; 2014, Elsevier Ltd., 2014; Vol. 5, pp 39–67.

77-14   Andrei Y. Korotchenko, Development of Scientific and Technological Approaches to Casting Net-Shaped Castings in Sand Molds Free of Shrinkage Defects and Hot Tears, Post-doctoral thesis: Russian State Technological University, 2014. In Russian.

69-14   L. Xue, M.C. Carter, A.V. Catalina, Z. Lin, C. Li, and C. Qiu, Predicting, Preventing Core Gas Defects in Steel Castings, Modern Casting, September 2014

68-14   L. Xue, M.C. Carter, A.V. Catalina, Z. Lin, C. Li, and C. Qiu, Numerical Simulation of Core Gas Defects in Steel Castings, Copyright 2014 American Foundry Society, 118th Metalcasting Congress, April 8 – 11, 2014, Schaumburg, IL

51-14   Jesus M. Blanco, Primitivo Carranza, Rafael Pintos, Pedro Arriaga, and Lakhdar Remaki, Identification of Defects Originated during the Filling of Cast Pieces through Particles Modelling, 11th World Congress on Computational Mechanics (WCCM XI), 5th European Conference on Computational Mechanics (ECCM V), 6th European Conference on Computational Fluid Dynamics (ECFD VI), E. Oñate, J. Oliver and A. Huerta (Eds)

47-14   B. Vijaya Ramnatha, C.Elanchezhiana, Vishal Chandrasekhar, A. Arun Kumarb, S. Mohamed Asif, G. Riyaz Mohamed, D. Vinodh Raj , C .Suresh Kumar, Analysis and Optimization of Gating System for Commutator End Bracket, Procedia Materials Science 6 ( 2014 ) 1312 – 1328, 3rd International Conference on Materials Processing and Characterisation (ICMPC 2014)

42-14  Bing Zhou, Yong-lin Kang, Guo-ming Zhu, Jun-zhen Gao, Ming-fan Qi, and Huan-huan Zhang, Forced convection rheoforming process for preparation of 7075 aluminum alloy semisolid slurry and its numerical simulation, Trans. Nonferrous Met. Soc. China 24(2014) 1109−1116

37-14    A. Karwinski, W. Lesniewski, P. Wieliczko, and M. Malysza, Casting of Titanium Alloys in Centrifugal Induction Furnaces, Archives of Metallurgy and Materials, Volume 59, Issue 1, doi.org/10.2478/amm-2014-0068, 2014.

26-14    Bing Zhou, Yonglin Kang, Mingfan Qi, Huanhuan Zhang and Guoming ZhuR-HPDC Process with Forced Convection Mixing Device for Automotive Part of A380 Aluminum Alloy, Materials 2014, 7, 3084-3105; doi.org/10.3390/ma7043084

20-14  Johannes Hartmann, Tobias Fiegl, Carolin Körner, Aluminum integral foams with tailored density profile by adapted blowing agents, Applied Physics A, doi.org/10.1007/s00339-014-8377-4, March 2014.

19-14    A.Y. Korotchenko, N.A. Nikiforova, E.D. Demjanov, N.C. Larichev, The Influence of the Filling Conditions on the Service Properties of the Part Side Frame, Russian Foundryman, 1 (January), pp 40-43, 2014. In Russian.

11-14 B. Fuchs and C. Körner, Mesh resolution consideration for the viability prediction of lost salt cores in the high pressure die casting process, Progress in Computational Fluid Dynamics, Vol. 14, No. 1, 2014, Copyright © 2014 Inderscience Enterprises Ltd.

08-14 FY Hsu, SW Wang, and HJ Lin, The External and Internal Shrinkages in Aluminum Gravity Castings, Shape Casting: 5th International Symposium 2014. Available online at Google Books

103-13  B. Fuchs, H. Eibisch and C. Körner, Core Viability Simulation for Salt Core Technology in High-Pressure Die Casting, International Journal of Metalcasting, July 2013, Volume 7, Issue 3, pp 39–45

94-13    Randall S. Fielding, J. Crapps, C. Unal, and J.R.Kennedy, Metallic Fuel Casting Development and Parameter Optimization Simulations, International Conference on Fast reators and Related Fuel Cycles (FR13), 4-7 March 2013, Paris France

90-13  A. Karwińskia, M. Małyszaa, A. Tchórza, A. Gila, B. Lipowska, Integration of Computer Tomography and Simulation Analysis in Evaluation of Quality of Ceramic-Carbon Bonded Foam Filter, Archives of Foundry Engineering, doi.org/10.2478/afe-2013-0084, Published quarterly as the organ of the Foundry Commission of the Polish Academy of Sciences, ISSN, (2299-2944), Volume 13, Issue 4/2013

88-13  Litie and Metallurgia (Casting and Metallurgy), 3 (72), 2013, N.V.Sletova, I.N.Volnov, S.P.Zadrutsky, V.A.Chaikin, Modeling of the Process of Removing Non-metallic Inclusions in Aluminum Alloys Using the FLOW-3D program, pp 138-140. In Russian.

85-13    Michał Szucki,Tomasz Goraj, Janusz Lelito, Józef S. Suchy, Numerical Analysis of Solid Particles Flow in Liquid Metal, XXXVII International Scientific Conference Foundryman’ Day 2013, Krakow, 28-29 November 2013

84-13  Körner, C., Schwankl, M., Himmler, D., Aluminum-Aluminum compound castings by electroless deposited zinc layers, Journal of Materials Processing Technology (2014), doi.org/10.1016/j.jmatprotec.2013.12.01483-13.

77-13  Antonio Armillotta & Raffaello Baraggi & Simone Fasoli, SLM tooling for die casting with conformal cooling channels, The International Journal of Advanced Manufacturing Technology, doi.org/10.1007/s00170-013-5523-7, December 2013.

64-13   Johannes Hartmann, Christina Blümel, Stefan Ernst, Tobias Fiegl, Karl-Ernst Wirth, Carolin Körner, Aluminum integral foam castings with microcellular cores by nano-functionalization, J Mater Sci, doi.org/10.1007/s10853-013-7668-z, September 2013.

46-13  Nicholas P. Orenstein, 3D Flow and Temperature Analysis of Filling a Plutonium Mold, LA-UR-13-25537, Approved for public release; distribution is unlimited. Los Alamos Annual Student Symposium 2013, 2013-07-24 (Rev.1)

42-13   Yang Yue, William D. Griffiths, and Nick R. Green, Modelling of the Effects of Entrainment Defects on Mechanical Properties in a Cast Al-Si-Mg Alloy, Materials Science Forum, 765, 225, 2013.

39-13  J. Crapps, D.S. DeCroix, J.D Galloway, D.A. Korzekwa, R. Aikin, R. Fielding, R. Kennedy, C. Unal, Separate effects identification via casting process modeling for experimental measurement of U-Pu-Zr alloys, Journal of Nuclear Materials, 15 July 2013.

35-13   A. Pari, Real Life Problem Solving through Simulations in the Die Casting Industry – Case Studies, © Die Casting Engineer, July 2013.

34-13  Martin Lagler, Use of Simulation to Predict the Viability of Salt Cores in the HPDC Process – Shot Curve as a Decisive Criterion, © Die Casting Engineer, July 2013.

24-13    I.N.Volnov, Optimizatsia Liteynoi Tekhnologii, (Casting Technology Optimization), Liteyshik Rossii (Russian Foundryman), 3, 2013, 27-29. In Russian

23-13  M.R. Barkhudarov, I.N. Volnov, Minimizatsia Zakhvata Vozdukha v Kamere Pressovania pri Litie pod Davleniem, (Minimization of Air Entrainment in the Shot Sleeve During High Pressure Die Casting), Liteyshik Rossii (Russian Foundryman), 3, 2013, 30-34. In Russian

09-13  M.C. Carter and L. Xue, Simulating the Parameters that Affect Core Gas Defects in Metal Castings, Copyright 2012 American Foundry Society, Presented at the 2013 CastExpo, St. Louis, Missouri, April 2013

08-13  C. Reilly, N.R. Green, M.R. Jolly, J.-C. Gebelin, The Modelling Of Oxide Film Entrainment In Casting Systems Using Computational Modelling, Applied Mathematical Modelling, http://dx.doi.org/10.1016/j.apm.2013.03.061, April 2013.

03-13  Alexandre Reikher and Krishna M. Pillai, A fast simulation of transient metal flow and solidification in a narrow channel. Part II. Model validation and parametric study, Int. J. Heat Mass Transfer (2013), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.061.

02-13  Alexandre Reikher and Krishna M. Pillai, A fast simulation of transient metal flow and solidification in a narrow channel. Part I: Model development using lubrication approximation, Int. J. Heat Mass Transfer (2013), http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12.060.

116-12  Jufu Jianga, Ying Wang, Gang Chena, Jun Liua, Yuanfa Li and Shoujing Luo, “Comparison of mechanical properties and microstructure of AZ91D alloy motorcycle wheels formed by die casting and double control forming, Materials & Design, Volume 40, September 2012, Pages 541-549.

107-12  F.K. Arslan, A.H. Hatman, S.Ö. Ertürk, E. Güner, B. Güner, An Evaluation for Fundamentals of Die Casting Materials Selection and Design, IMMC’16 International Metallurgy & Materials Congress, Istanbul, Turkey, 2012.

103-12 WU Shu-sen, ZHONG Gu, AN Ping, WAN Li, H. NAKAE, Microstructural characteristics of Al−20Si−2Cu−0.4Mg−1Ni alloy formed by rheo-squeeze casting after ultrasonic vibration treatment, Transactions of Nonferrous Metals Society of China, 22 (2012) 2863-2870, November 2012. Full paper available online.

109-12 Alexandre Reikher, Numerical Analysis of Die-Casting Process in Thin Cavities Using Lubrication Approximation, Ph.D. Thesis: The University of Wisconsin Milwaukee, Engineering Department (2012) Theses and Dissertations. Paper 65.

97-12 Hong Zhou and Li Heng Luo, Filling Pattern of Step Gating System in Lost Foam Casting Process and its Application, Advanced Materials Research, Volumes 602-604, Progress in Materials and Processes, 1916-1921, December 2012.

93-12  Liangchi Zhang, Chunliang Zhang, Jeng-Haur Horng and Zichen Chen, Functions of Step Gating System in the Lost Foam Casting Process, Advanced Materials Research, 591-593, 940, DOI: 10.4028/www.scientific.net/AMR.591-593.940, November 2012.

91-12  Hong Yan, Jian Bin Zhu, Ping Shan, Numerical Simulation on Rheo-Diecasting of Magnesium Matrix Composites, 10.4028/www.scientific.net/SSP.192-193.287, Solid State Phenomena, 192-193, 287.

89-12  Alexandre Reikher and Krishna M. Pillai, A Fast Numerical Simulation for Modeling Simultaneous Metal Flow and Solidification in Thin Cavities Using the Lubrication Approximation, Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, 63:2, 75-100, November 2012.

82-12  Jufu Jiang, Gang Chen, Ying Wang, Zhiming Du, Weiwei Shan, and Yuanfa Li, Microstructure and mechanical properties of thin-wall and high-rib parts of AM60B Mg alloy formed by double control forming and die casting under the optimal conditions, Journal of Alloys and Compounds, http://dx.doi.org/10.1016/j.jallcom.2012.10.086, October 2012.

78-12   A. Pari, Real Life Problem Solving through Simulations in the Die Casting Industry – Case Studies, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

77-12  Y. Wang, K. Kabiri-Bamoradian and R.A. Miller, Rheological behavior models of metal matrix alloys in semi-solid casting process, 2012 Die Casting Congress & Exposition, © NADCA, October 8-10, 2012, Indianapolis, IN.

76-12  A. Reikher and H. Gerber, Analysis of Solidification Parameters During the D