Optimization of flow division pier distribution for a sedimentation tank in the Oujiang Water Diversion Project

Sedimentation tank design is of key importance in a water diversion project. Both physical and numerical models are used to study the hydrodynamics and sediment transport in the sedimentation tank of the Oujiang Water Diversion Project. The water inlet central axis is inclined sharply against the sedimentation tank central axis. The physical model adheres to the principle of gravitational similarity, with a geometric scale of 1:20. Four rows of division piers are designed and optimized to effectively separate the flow, ensure efficient sedimentation, and prevent sediment re-suspension. The numerical model simulates the graded sediments. The simulations are carried out under designed low, standard, and high water levels. The numerical results are in good agreement with the experimental measurements. The main flow is focused on the left bank of the tank due to the large angle between the inlet gate and the tank axis. Consequently, a large-scale backflow region forms on the right bank. After optimizing the flow division piers at the tank inlet, the main flow velocity significantly decreases, becoming smoother and more uniform, with no reversal flow areas. As a result, the sediment concentration distribution becomes more uniform, and the sedimentation rate increases notably.

1 Introduction

Water division projects provide essential infrastructure for life, agriculture, industry, and hydroelectric power generation in water resource management. Water division projects are often confronted with sedimentation challenges (Biswas, 1989; Wang et al., 2023) that significantly impact their efficiency, longevity, and overall functionality. Among the various strategies to address sedimentation, sedimentation tanks have emerged as a critical component in water division projects (Guo et al., 2023). Sedimentation refers to the process by which particles are deposited in water bodies due to reduced flow velocity or gravitational settling (Khanam and Biswal, 2024). In a water division project, sedimentation leads to the accumulation of sediments in reservoirs, channels, and pipelines, which causes many problems (Razad et al., 2018; Aliyev and Shukurov, 2024). These include reduced storage capacity of reservoirs, increased maintenance costs, decreased efficiency of hydro-turbines, and impaired water quality. Over time, sedimentation shortens the lifespan of water division projects, making it a critical issue that requires proactive management.

A sedimentation tank is a structure for reducing flow velocity and trapping sediment particles to allow them to settle at the bottom of the water. The tank is typically constructed upstream of critical infrastructure to prevent sediment from entering and causing damage. Tanks may be temporary or permanent (Wren et al., 2025). A temporary tank is often used during construction or land development projects to control sediment-laden runoff. In contrast, a permanent tank is integrated into water division projects as a long-term part of sediment management. The design is influenced by several factors, including the flow velocity, sediment characteristics, and the desired amount of sediment removal. Key factors (Guo et al., 2023) include: (1) hydraulic factors (tank’s length, width, and depth determined by the flow rate and sediment load) to ensure that velocity is reduced sufficiently to allow sediment particles to settle. (2) Sediment storage capacity is adequate to accommodate the expected sediment load over a specified period, and regular maintenance (periodic dredging) is necessary to prevent the tank from becoming full and losing its effectiveness. (3) Outlet and overflow structures are designed to regulate flow into and out of the tank, such that only water, but not sediment, exits the tank. (4) Turbulence is minimized, and smooth flow is ensured to prevent scour from re-suspending sediment and carrying it downstream.

The Oujiang Water Diversion Project is located in the urban area of Wenzhou City in China. As a newly added provincial key construction project in the 2020s, this project is the largest water diversion project in terms of flow rate, the longest water conveyance tunnel, and the largest investment in Wenzhou City to date. Figure 1 shows the location of the project on the WGS-84 coordinate system (Aliyev and Shukurov, 2024). The water inlet gate is located at the north and is divided into two sides by National Road G330: the riverbank side and the mountain side. The riverbank side is adjacent to the Oujiang ecological protection line, and the mountain side is adjacent to the control line of National Road G330. A 69.3° angle exists between the inlet central axis and the sedimentation tank central axis. Therefore, the inlet flow easily rushes to the south bank to form a large backflow region near the entrance, which reduces flow uniformity and sedimentation rate. Flow division structures should be optimized to achieve uniform flow in the tank.

Figure 1

Figure 1. Location of the sedimentation tank in the Oujiang Water Diversion Project.

The sedimentation tank is an essential component offering a practical method to the sedimentation issue in the Oujiang Water Division projects. The tank helps safeguard water resources, enhance project efficiency, and protect downstream ecosystems by effectively trapping and storing sediment. Flow division structures (piers) are used to overcome the mountain-land limitations and the influence of ecological protection red lines; that is, the entrance is nearly perpendicular to the central axis of the sedimentation tank and easily leads to uneven water flow and poor sedimentation effect. As water resource management evolves to meet increasing environmental challenges, the division piers are vital structures in ensuring the sustainability and resilience of the sedimentation tank. Physical experiments (Wang et al., 2024) and numerical models (Ye et al., 2023) are both utilized in the optimization of the flow division piers. A physical model can visually demonstrate the flow patterns within sedimentation tanks, such as dead zones, surface eddies, and sedimentation patterns. Among numerical models (Wu et al., 2023), FLUENT is widely used in three-dimensional situations (Lak et al., 2020; Debessai and Debessai, 2020), while MIKE21 is frequently used in two-dimensional cases (Jayanti and Narayanan, 2004; Simon et al., 2020). MIKE21 is adopted because the depth is much smaller than the length and width in this study. The following analysis addresses the hydrodynamics from the physical model and sediment transport from the numerical model and supplies a recommendation for the division piers for the sedimentation tank of the Oujiang Water Diversion Project.

2 Methods

The present sedimentation tank is permanent. This section introduces the physical and numerical models.

2.1 Physical model

The bottom elevation of the water intake channel is −7.0 m. Considering four factors in the introduction, a sediment barrier is set at the entrance of the water intake channel (Figure 2), with the top elevation of −5.0 m. A box culvert of 49.5 m is inclined at 69.3° to link the water intake channel and the sedimentation tank. The sedimentation tank is 220.85 m long and 55.4 m wide, with a bottom elevation of −7.5 m. At a distance of 14.0 m from the pump station, the bottom elevation of the sedimentation tank gradually decreases to −9.4 m to connect to the bottom of the pump station, and a second sediment barrier (top elevation is −4.5 m) is set up to prevent sediment from entering. The designed intake flow rate of the pump station is Q = 50 m³/s. Five pumps are installed, with a unit spacing of 8.0 m. Four rows of division piers (1.2 m width and 14 m long) separate the flow for efficient separation of sediment from water while minimizing overflow or sediment re-suspension. The distribution of division piers is optimized by the physical experiment and the numerical model.

Figure 2

Figure 2. Physical model for the sedimentation tank in the Oujiang Water Diversion Project.

A physical model holds significant value for diagnosing operational issues in existing sedimentation tanks and optimizing the design of channels and division piers. The physical model is located at the project premises prior to construction. Experimental water is directly obtained from the Oujiang River. The present physical model is conducted using the standard overall model of hydraulic engineering. It was designed based on geometric Froude similarity following the principle of gravitational similarity. According to the space and test requirements, the geometric scale of the model is λ_L = L_P/L_m = 1:20, but the sediment is a prototype. The conversion of the similarity criterion scale is shown in Table 1, where L denotes the length and subscripts p and m denote the prototype and model, respectively. Froude similarity is applicable to open-channel flows, wave motions, and other free-surface flow scenarios. It is reasonable for this study to use a physical model with Froude similarity to the prototype. However, Froude similarity requires the Froude numbers of the model and prototype to be equal, which also necessitates scaling down the sediment settling velocity. The settling velocity of sediment primarily depends on particle size, density, and fluid viscosity, but these properties of sediment are not changed with the reduction in model scale because it is difficult to find matching graded materials under cost-effective conditions. Therefore, prototype sediment in the model can only achieve approximate similarity, resulting in some discrepancies between the model’s settling results and the prototype. Consequently, the present physical model is not suitable for high-precision quantitative predictions. However, it can serve as an auxiliary tool for numerical simulations, providing a means to calibrate smooth and uniform velocity distribution and to overcome any shortcomings from the large, inclined inlet central axis.

Table 1

Table 1. Similarity criterion scale conversion.

The main measurements include flow rate, flow velocity, flow pattern (state), water level, water depth, sediment size, and concentration. The division piers are set to obtain regular and smooth flow, as shown in Figure 3. The flow velocity and water level are measured at the sections of the B0 series, as shown in Figure 3, and B0+000 m is set at the pump station. The flow rate is measured after each pump station using an LDY-100S electromagnetic flow meter, with an accuracy of approximately 0.01 L/s. The water levels upstream and downstream are observed using a conventional probe with a resolution of 0.1 mm (2.0 mm for the prototype), and the zero point of the probe is determined using a Nikon AS-2 and a precision level. The flow velocity is measured using an acoustic Doppler velocity (ADV) meter and a photoelectric propeller velocity meter at the B0 series sections. The measurement accuracy of the ADV meter is 0.01 cm/s (the prototype is 0.045 cm/s), and the critical flow velocity of the photoelectric propeller flow meter is approximately 1.7 cm/s (the prototype is 7.6 cm/s). At the pump station’s entrance (Section B-003.7), velocities are measured at five vertical positions, corresponding to 0.1, 0.3, 0.5, 0.7, and 0.9 of the water depth. At the remaining sections, velocities are measured at three vertical positions: 0.1, 0.5, and 0.9 of the water depth. The water depth is the difference between the measured water level and the tank bottom level. The flow (rotation) pattern is recorded and photographed under each test condition. Sediment samples are processed through sedimentation and analyzed using an MS2000 laser particle size analyzer for size distribution, with a grain size range of 0.2–2000 μm and an error margin of less than 1%. The installation for the suspended sediment sampler bottle is the same as that for the ADV. To minimize measurement errors in sediment concentration, three measurements are taken at each sampling point, with the error range controlled within 1%, and the average value is used. The inlet flow rate is kept stable to ensure the repeatability of the experiment.

Figure 3

Figure 3. Measurement sections and grid system for the simulation of the originally designed division piers.

2.2 Numerical model

The primary flow direction in the sedimentation tank is from the inlet to the outlet, with significantly smaller variations in velocity across the depth than along the length. In cases where the objective focuses on macroscopic flow patterns, the use of a two-dimensional model is sufficient to meet the requirements. The primary objective of this study is to optimize the distribution of division piers and investigate their impact on the macroscopic flow field, aiming to achieve a smooth and uniform velocity distribution. Therefore, employing a two-dimensional model is reasonable for the present tank. At the same time, we acknowledge the limitations of the two-dimensional model near the inlet and outlet, where a three-dimensional flow pattern is observed in the physical model. When the research objective involves local flow patterns or higher precision is required, a three-dimensional model should be utilized. The Mud Transport module of MIKE21 software is applied in the numerical study. The depth-integrated governing equations for water flow are

$\frac{\mathrm{\partial }h}{\mathrm{\partial }t}+\frac{\mathrm{\partial }hu}{\mathrm{\partial }x}+\frac{\mathrm{\partial }hv}{\mathrm{\partial }y}=0,(1)$

$\begin{array}{l}\frac{\mathrm{\partial }hu}{\mathrm{\partial }t}+\frac{\mathrm{\partial }h{u}^2}{\mathrm{\partial }x}+\frac{\mathrm{\partial }hvu}{\mathrm{\partial }y}=-gh\frac{\mathrm{\partial }\eta }{\mathrm{\partial }x}-\frac{h}{{\rho }_0}\frac{\mathrm{\partial }{p}_a}{\mathrm{\partial }x}-\frac{g{h}^2}{2{\rho }_0}\frac{\mathrm{\partial }\rho }{\mathrm{\partial }x}+\frac{{\tau }_{sx}}{{\rho }_0}-\frac{{\tau }_{bx}}{{\rho }_0}\\ -\frac{1}{{\rho }_0}\left(\frac{\mathrm{\partial }{s}_{xx}}{\mathrm{\partial }x}+\frac{\mathrm{\partial }{s}_{xy}}{\mathrm{\partial }y}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(h{T}_{xx}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }y}\left(h{T}_{xy}\right)\end{array},(2)$

$\begin{array}{l}\frac{\mathrm{\partial }hv}{\mathrm{\partial }t}+\frac{\mathrm{\partial }huv}{\mathrm{\partial }x}+\frac{\mathrm{\partial }h{v}^2}{\mathrm{\partial }y}=-gh\frac{\mathrm{\partial }\eta }{\mathrm{\partial }y}-\frac{h}{{\rho }_0}\frac{\mathrm{\partial }{p}_a}{\mathrm{\partial }y}-\frac{g{h}^2}{2{\rho }_0}\frac{\mathrm{\partial }\rho }{\mathrm{\partial }y}+\frac{{\tau }_{sy}}{{\rho }_0}-\frac{{\tau }_{by}}{{\rho }_0}\\ -\frac{1}{{\rho }_0}\left(\frac{\mathrm{\partial }{s}_{yx}}{\mathrm{\partial }x}+\frac{\mathrm{\partial }{s}_{yy}}{\mathrm{\partial }y}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(h{T}_{xy}\right)+\frac{\mathrm{\partial }}{\mathrm{\partial }y}\left(h{T}_{yy}\right)\end{array},(3)$

where x and y are the coordinates, with x = 0 at B0+000 m and y = 0 at the center of five pumps; t is the time; η is the water elevation; u and v are the depth-averaged velocities in the x and y directions, respectively; h is the water depth; d is the initial water depth; h = η+d is the total water depth; g is the gravity acceleration; ρ is the water density; ρ₀ is the relative density; (τ_sx and τ_sy) and (τ_bx and τ_by) are the surface wind stresses and bottom friction forces, respectively; s_xx, s_xy, s_yx, and s_yy are the radiation stresses; and T_xx, T_xy, and T_yy are the side stresses. The wind and radiation stresses are closed because there was neither wind nor waves during the test. The bottom friction force is given by τ_bx = ρn²u²h^-1/3 and τ_by = ρn²v²h^-1/3. n is the bottom roughness.

The suspended sediment transport and the bed change equations are as follows:

$\frac{\mathrm{\partial }{S}_i}{\mathrm{\partial }t}+u\frac{\mathrm{\partial }{S}_i}{\mathrm{\partial }x}+v\frac{\mathrm{\partial }{S}_i}{\mathrm{\partial }y}=\frac{1}{h}\frac{\mathrm{\partial }}{\mathrm{\partial }x}\left(h{D}_i\frac{S_i}{\mathrm{\partial }x}\right)+\frac{1}{h}\frac{\mathrm{\partial }}{\mathrm{\partial }y}\left(h{D}_i\frac{S_i}{\mathrm{\partial }y}\right)+\frac{F_{Si}}{h},(4)$

${\gamma }_d\frac{\mathrm{\partial }{\eta }_b}{\mathrm{\partial }t}-\sum F_{Si}=0,(5)$

where S_i is the suspended sediment concentration of the ith fraction; D_i is the mixing coefficient; F_si is the scour and siltation function; γ_d (=1700 kg/m³) is the dry density of sediment; and η_b is the vertical displacement of the bed. In a siltation problem, F_si = −ρω_i (S_i−S_i*), S_i* is the sediment-laden capacity, where ω_i is the sediment settling velocity. D_i = α $\sqrt{u^2+v^2}$ h, where α (=0.2) is an empirical parameter.

According to the prototype measured sediment size accumulation curve and the suggestion of Hu and Chen (2023), four sediment fractions are set in the numerical study, as provided in Table 2; Figure 4. The physical model was conducted from 7 May to 27 May 2020. The sediment exhibited small variation patterns over the 21 days. The sediment diameter and percentage are averaged values. For Fraction 1 (125–1000 μm), ω_i is calculated using the modified Wentworth formula with a diameter of 562.5 μm. For Fraction 2 (16–125 μm), ω_i is calculated using the modified Soulsby formula with a diameter of 70.5 μm. For Fraction 3 (4–16 μm), ω_i is calculated using Stokes law (particle Reynolds number <1) using a diameter of 10 μm. For Fraction 4 (0–4 μm), ω_i is calculated using the viscosity-modified Stokes law with a diameter of 2 μm. The motion of fine sediment particles is influenced by both interparticle cohesive forces (such as van der Waals and electrostatic forces) and fluid dynamics. It is generally considered that particles with a diameter <63 μm undergo flocculation and settling (the fourth fraction), but the critical particle size is significantly affected by environmental conditions (e.g., salinity, sediment concentration, and flow shear stress) and the mineral composition of the sediment. MIKE21 assumes that when the flow shear stress falls below a critical value, cohesive forces dominate, causing particles to floc and settle as larger aggregates. In this study, the flocculation is accounted for in Fractions 2, 3, and 4.

Table 2

Table 2. Four sediment fractions in the numerical study.

Figure 4

Figure 4. Observed sediment diameter distribution between 7 and 27 May 2020.

In the simulation, the moving boundary technique is employed to handle the dry–wet boundary. Regions with h < 0.01 m are classified as “dry regions” to prevent numerical oscillation in the dry region grids. The water level relaxation factor is 0.8, and the velocity relaxation factor is 0.7. The simulated area includes the intake gate, sedimentation tank, and pump station inlet. The model adopts unstructured triangular grids. The grid dependence is checked, and the final grid system is shown in Figure 3. Three sets of grids with different sizes are tested in Table 3, with their global average areas being 1.2 m² (coarse grid), 0.6 m² (medium grid), and 0.3 m² (fine grid). Comparing the water level time series and the velocity in the key section reveals that the discrepancies between the medium and fine grid results are significantly reduced, indicating that the solution for the medium grid has essentially converged. Therefore, the medium grid is selected to ensure computational accuracy while effectively controlling computational costs. To ensure the simulation accuracy, the grid is moderately increased in areas with relatively large changes in velocity and terrain. The time step Δt requires Δt (u_max+ $\sqrt{g{h}_{\max }}$)≤Δx_min, where Δx_min is the minimum grid size, u_max is the maximum velocity, and h_max is the maximum water depth. The total number of grids exceeds 20,000, with the maximum size of 5 m and the minimum size of 0.3 m. The time step is Δt = 0.05 s. Based on the experience of similar projects, the roughness of 0.02–0.025 is selected in the simulation. The inlet boundary adopts the water level, with a measured, averaged concentration of approximately 0.13–0.14 kg/m³. The outlet is located at the inlet of the pump station. According to the number of units in the pump station, it is divided into five parts, each of which adopts the averaged flow rate and is controlled by a zero gradient of sediment concentration.

Table 3

Table 3. Alternative grid resolutions for the standard water level using the originally designed division piers.

3 Results of hydrodynamics

Special water levels of designed operations are tested and simulated. The designed lowest, standard, and highest water levels are −2.53 m, 1.41 m, and 5.56 m, respectively. This section demonstrates the hydrodynamics results of the originally designed division piers and optimizes the division piers.

3.1 Originally designed division piers

The whole sections are validated. The value 4.47(λ_V) × ω_i is used in the validation to fit the physical model. Table 4 only shows the velocity and sediment concentration under the standard water level using the originally designed division piers in some points (Channel 2), as shown in Figure 3. The 95% confidence interval is [−0.024, 0.020] for velocity bias and [0.0046, 0.0076] for concentration bias. For overall velocity, the statistical metrics show that bias (−0.002 m/s), RMSE (0.02 m/s), and NRMSE (0.08) are all very small, and NSE (0.9) is close to 1. The statistical metrics simulate velocity well. For the whole concentration range, the simulated value is larger than the measured value, and the simulated sedimentation rate (81.6%) is slightly lower than the measured rate (84.9%), with similar decrease tendencies along Channel 2. The concentration validation generates relatively large errors (RMSE = 0.007 kg/m³, NRMSE = 0.145) and overestimation (bias = 0.006 kg/m³ > 0) and is worse than velocity validation (NSE = 0.86 < 0.9). Figure 5 shows the standard water level, where the black line is the bottom bed level. The simulated water level is basically consistent with the measured value, indicating that the roughness of the model and the terrain simulation are reasonable.

Table 4

Table 4. Validation of the numerical model in Channel 2 under the standard water level.

Figure 5

Figure 5. Validation of the numerical model for the standard water level.

Figure 6 shows the measured across-section velocity under the original division piers condition. From south to north, flows are separated into channels 1 to 5 by four rows of piers (Figure 6a). Due to the large angle (69.3°) between the inlet flow and the axis of the sedimentation tank, the main flow is restricted on the left (south) bank after the flow enters the tank, and the greatest velocity is in Channel 1. The main flow direction is reversed slightly toward the north from Sections B0-107.8 to B0-018.0 by the large-angled inlet flow. On the right (north) bank of the sedimentation tank, a large-scale backflow region is mainly formed in channels 4 and 5, with a small velocity. The main forward flow velocity beneath the lowest water level is 0.36–0.84 m/s, the designed standard water level is 0.23–0.57 m/s, and the highest water level is 0.14–0.48 m/s. The main velocity decreases as the water level increases while keeping the flow rates the same at 50 m³/s. The maximum velocity in the backflow region reaches 0.20 m/s when the lowest water level is operated. At the highest water level, the velocity is less than 0.10 m/s for most areas of the tank from channels 1 to 3. At the highest water level, the vertical water flow structure is blocked by beam structures at the top 2 m near the pump entrance, which results in a stratification of velocity in the vertical direction. Meanwhile, the lateral velocity is restricted by the piers in the sedimentation tank. As a result, the velocity at the end of the sedimentation tank is not adjusted evenly, and the velocity on the left bank is significantly higher than that on the right bank. When the designed standard water level is operated, the backflow region is 180 m long (almost covering B0-018.0 to B0-200.0) and 8–20 m wide, with approximately 3,120 m² accounting for approximately 30% of the entire sedimentation tank. The large-scale backflow region squeezes the cross-section and results in a main flow velocity that is too fast. Only a small part of the sediment-laden flow enters the low-velocity backflow region on the right bank, which reduces the sedimentation rate in the sedimentation tank. The division pier distribution must be optimized to achieve a lower velocity distribution without a backflow region.

Figure 6

Figure 6. Measured velocity based on the original division piers, with intake Q = 50 m³/s: (a) the lowest water level, (b) the standard water level, and (c) the highest water level.

Figure 7 shows the simulated velocity field under the original division pier condition, where the red color denotes a large velocity magnitude and the blue color denotes a small velocity magnitude. The simulated velocity vector generally agrees with that in Figure 6 for all the lowest, standard, and highest water level cases. The simulation reveals the backflow region at the right (north) bank, the main flow restriction in channels 1 and 2 on the left (south) bank after the flow enters the tank, and the greatest velocity is in Channel 1. The decreased velocity from the left (south) to the right (north) bank is obvious. The reasonable simulation indicates that the numerical model should be used for further optimization of the division pier distribution.

Figure 7

Figure 7. Simulated velocity field based on the original division piers, with intake Q = 50 m³/s: (a) the lowest water level, (b) the standard water level, and (c) the highest water level.

3.2 Recommended division piers

The key issue of optimization is flow division in the tank inlet, and thus, five inlet distributions of the division piers are designed. The first four distributions are shown in Figure 8 as optimization cases 1–4. The red line represents the optimized inlet piers. In Case 1, the inlet pier is extended along the central axis of the sedimentation tank to Section B0-218.8 by a circular arc section (radius = 7.5 m) and an 8.0 m straight section. Four piers near Sections B0-162.0 and B0-188.8 are rotated by ±5° to the left bank and the right bank, respectively, to make them generally parallel to the wall. Case 2 is set based on Case 1, and the inlet circular arc pier is shortened to ensure extension of the straight part reaching the front of the pier at the right (north) bank. In Case 3, the inlet pier is extended 5.4 m toward the right (north) pier after the inlet, based on Case 2. In Case 4, the inlet pier is fully extended to connect to the right pier after the inlet, based on Case 3. The flow patterns of all inlet pier distributions are observed (Supplementary Appendix A.1), and the velocity data at the cross-section are compared in Supplementary Table A1 of Supplementary Appendix A.2.

Figure 8

Figure 8. Four optimizations of the division pier distribution in the tank inlet.

The final recommended division pier distribution is set following the optimization of cases 1–4 and is shown in Figure 9. The shaded area represents the optimized piers, and the dashed line represents the original piers. First, the right (north) pier after the inlet is shifted 1.65 m to the left (south) bank, with an extension to connect to the water inlet gate, and the left (south) pier after the inlet is shifted 1.10 m to the left (south) bank. Second, two inclined piers are rotated by 2.3° to the left bank and the right bank, respectively, to make them parallel to the wall. Third, two new piers parallel to the axis are added at the left bank of the sedimentation tank to separate the inlet flow for channels 1, 2, and 3. The uniformity parameter is introduced to represent the quantitative adjustment of the flow pattern in the sedimentation tank for the cross-section velocity distribution, that is,

$N_0=\left[1-\sqrt{\frac{1}{n}{{\sum }_{i=1}^n\left(\frac{V_i}{V}-1\right)}^2}\right]\times 100\%,(6)$

where V_i is the absolute velocity at each point of the cross-section, V is the average velocity across the section, and N₀ is the uniformity parameter of velocity distribution.

Figure 9

Figure 9. Final recommended division pier distribution in the tank inlet.

Figure 10 shows the measured velocity of the optimal division of cases 1–4 within working Sections B0-018 and B0-150, with intake Q = 50 m³/s under the standard water level. The uniformity parameter of the velocity is N₀ = 16%–31% at cross-sections within the working sections (from B0-150.0 to B0-018.0) in the previous Figure 6 under the original division pier condition. In Case 1, the backflow region on the right bank is significantly reduced, but the main flow is still restricted on the left bank, with maximum V = 0.35 m/s. The velocity distribution remains uneven across the working sections, and N₀ = 24%–41%. In Case 2, the backflow region on the right bank is reduced further than in Case 1, and the main flow is moved toward the right bank by a shortened inlet circular arc pier, with maximum V = 0.31 m/s. The uneven velocity distribution is improved somewhat, and N₀ = 32%–49%. In Case 3, the velocity in the previous backflow region is fully reversed forward, but the value is relatively small. The velocity at the left bank decreases compared to Case 3 (maximum V = 0.27 m/s), but the improved velocity distribution remains uneven across the working sections with N₀ = 42%–58%. In Case 4, no backflow occurs again. Velocity near the left bank decreases (maximum V = 0.25 m/s), and that near the right bank increases. Therefore, velocity distribution across the working sections is relatively uniform, with N₀ = 55%–72%. Division piers should be constructed gradually, similar to Figure 8, to improve the velocity uniformity in other diversion projects with different geometries or flow conditions.

Figure 10

Figure 10. Measured velocity of the optimal cases 1–4, with intake Q = 50 m³/s under the standard water level.

Figure 11 shows the measured velocities for the final recommended case, where the red lines denote the final recommended division piers. After entering the sedimentation tank, the flow shows a small three-dimensional characteristic near the inlet. The angle between the surface flow and the bottom flow is relatively large due to the bottom slope and sudden section expansion near the inlet (Jiang et al., 2024). At the highest water level, the bottom velocity is even reversed, opposite to the surface velocity. However, the flow becomes smooth through the adjustment of the inlet piers. No backflow is observed in the working sections, and the velocity distribution across the section is relatively uniform at the standard and highest water levels (Figures 11b,c). At the lowest water level, there are very small backflow regions close to the left and right banks (channels 1 and 5 in Figure 11a) between Sections B0-100.0 and B0-150.0. The backflow region will be increased by the intake Q (velocity). Under the designed Q = 50 m³/s, the backflow region reaches Section B0-107.8 at the lowest water level.

Figure 11

Figure 11. Measured velocity based on the final recommended division piers, with intake Q = 50 m³/s: (a) the lowest water level, (b) the standard water level, and (c) the highest water level.

The velocity distribution is uneven near the inlet under all water levels. The averaged cross-section velocity decreases as the water level increases. The maximum velocity occurs on the right side of the inlet pier, which reaches 0.92 m/s, 0.56 m/s, and 0.28 m/s near the B0-213.4 section under the lowest, standard, and highest water levels, respectively. Subsequently, the velocity gradually decreases with the symmetrical expansion of the cross-section and the adjustment of the division piers. The velocity is continuously adjusted from cross-section B0-100.0 to B0-050.0, and the uniformity is further improved. At the highest water level (Figure 11c), the maximum velocity is decreased to less than 0.10 m/s, and the uniformity parameter of the velocity at each cross-section is N₀ = 78%–81% within the working sections. At the designed standard water level (Figure 11b), the maximum velocity is decreased to approximately 0.15 m/s within the working sections. The area of velocity less than 0.10 m/s accounts for more than 4/5th of the tank, and the uniformity parameter of the velocity is N₀ = 62%–78% at each cross-section, that is, the recommended division piers improve N₀ a great deal. If the intake Q is decreased to 37.5 m³/s, the velocity is reduced to 0.06–0.10 m/s within the working sections, and the uniformity parameter of the velocity increases to N₀ = 63%–82%. If the intake flow rate is further decreased to 25 m³/s, the velocity is 0.04–0.07 m/s within the working sections, and the uniformity parameter of the velocity further increases to N₀ = 76%–86%. At the lowest water level (Figure 11a), the maximum velocity is greater than 0.10 m/s in the working sections. The velocity is increased to approximately 0.17–0.36 m/s in channels 2, 3, and 4, and the velocity uniformity parameter is N₀ = 55%–77%. If the intake flow rate is decreased to 25 m³/s, the velocity is 0.03–0.06 m/s in channels 1 and 5, and that in the other channels is slightly greater than 0.10 m/s. The uniformity parameter of velocity is increased to N₀ = 68%–77%.

Figure 12 shows the simulated velocities for the final recommended case. The simulated velocity vector reasonably agrees with the result in Figure 11 for all three water level cases. The simulation shows an obvious velocity decrease from the lowest to the highest water level and an increase in velocity uniformity. Generally, as there are numerous division piers in the sedimentation tank, they effectively restrict the lateral velocity. The flow is basically along the axis of the sedimentation tank, and the angle between the flow and the pump station inlet is relatively small. It can be observed that the velocity distribution in the working sections of the sedimentation tank is mainly affected by the upstream inlet connection section, while the decrease in the intake flow rate has a significant improvement on the velocity uniformity parameter in the tank.

Figure 12

Figure 12. Simulated velocity field based on the final recommended division piers, with intake Q = 50 m³/s: (a) the lowest water level, (b) the standard water level, and (c) the highest water level.

4 Sedimentation rate

Following the above results of hydrodynamics, the simulated suspended sediment concentration distribution is shown in Figure 13 under standard water level conditions. The result is not compared to the physical model because ω_i in the simulation does not fit the physical prototype. The concentration distribution corresponds to the velocity distribution in Figures 6, 11. The main suspended sediment concentration (>0.07 kg/m³) is distributed to the outlet following the main velocity direction under the original division piers condition (Figure 13a); that is, after entering the sedimentation tank, it is carried north from Sections B0-107.8 to B0-018.0 by the large angled inlet flow. The concentration is the greatest at the inlet and decreases toward the outlet and the two side banks. The concentration distribution becomes more uniform through the adjustment of the recommended division piers in Figure 13b. The large concentration (>0.07 kg/m³) area is restricted near the inlet by the recommended division piers, and the concentration color contour is almost parallel to the division piers in the working sections. Sedimentation benefits from a uniform concentration distribution and low velocity. Table 5 shows the simulated sedimentation rate. Flocculation is triggered for fractions 2–4 in this simulation. The simulated total sedimentation rate is 56.7% under the original division piers condition, and it is 83.4% under the recommended division piers condition. More sediment is left in the tank, and the overall concentration at the pump station inlet is small under the recommended division pier condition.

Figure 13

Figure 13. Simulated sediment concentration distribution, with designed intake Q = 50 m³/s. (a) Original division piers. (b) Recommended division piers.

Table 5

Table 5. Simulated sedimentation rate under standard water level and Q = 50 m³/s.

Sediments are divided into four size fractions in the numerical study (Hu and Chen, 2023), as provided in Table 2. Figures 14–17 show the simulated amount of sedimentation in 24 h for all four fractions. The flocculation of Fractions 2, 3, and 4 generates extra sedimentation. The sedimentation amount of Fraction 1 (0.125–1 mm) mainly occurs in the inlet velocity expansion area following the main flow direction (Figure 14A) under the original division pier condition, and the maximum value reaches 9 kg/m³. The sedimentation rate of Fraction 2 (0.016–0.125 mm) is 60.8% under the original division pier condition in Figure 15a, and the maximum sedimentation amount reaches 36 kg/m³. The sedimentation mainly occurs along the left (south) bank of the tank following the inlet velocity, as shown in Figure 15a. The sedimentation rate of Fraction 3 (0.004–0.016 mm) is 55.2% under the original division pier condition, and this fraction is mainly flocculation deposited along the vector of main velocity (Figure 16a), almost matching the concentration distribution in Figure 13a. The sedimentation distribution of Fraction 4 in Figure 17a is similar to that of Fraction 3 in Figure 16a, but flocculation sedimentation occurs more toward the left (south) bank under the original division pier condition. Fractions 2 and 3 contribute to the major sedimentation due to the large inlet percentage and relatively large sedimentation rate. The sedimentation rate of Fraction 4 (<0.004 mm) is only 4.7% even when the flocculation effect is considered, and it is much smaller than fractions 1–3 because the large main velocity (uneven velocity distribution) is not helpful for flocculation.

Figure 14

Figure 14. Simulated sedimentation amount of Fraction 1 in 24 h. (a) Original division piers. (b) Recommended division piers.

Figure 15

Figure 15. Simulated sedimentation amount of Fraction 2 in 24 h. (a) Original division piers. (b) Recommended division piers.

Figure 16

Figure 16. Simulated sedimentation amount of Fraction 3 in 24 h. (a) Original division piers. (b) Recommended division piers.

Figure 17

Figure 17. Simulated sedimentation amount of Fraction 4 in 24 h. (a) Original division piers. (b) Recommended division piers.

The sedimentation rate and amount are much improved under the recommended division pier condition because the velocity distribution becomes uniform, and the main velocity magnitude is much reduced. The sedimentation rate of Fraction 1 (0.125–1 mm) is increased to 100%, and the sediment mainly settles in the inlet connection sections in Figure 14b. The sedimentation rate of Fraction 2 (0.016–0.125 mm) is also increased to 100%, and this fraction mainly settles uniformly in the inlet connection sections toward the working sections, as shown in Figure 15b. The sedimentation rates of Fraction 3 (0.004–0.016 mm) and Fraction 4 (<0.004 mm) are increased to 70.5% and 43.5%, respectively, and the main sediment deposition occurs in the low velocity areas on both the left and right banks and middle channels (Figures 16b, 17b). The simulated sedimentation of Fraction 4 is dominated by flocculation, and the distribution is very similar to that of Fraction 3.

5 Sensitivity of velocity and sedimentation to changes in key parameters

Table 6 shows the effect of changes in key parameters on velocity and sedimentation compared to the default case n = 0.022, inlet S = 0.14 kg/m³, water level = 1.41 m, Q = 50 m³/s, and recommended inlet division piers. The replaced (varied) parameters include roughness, inlet sediment concentration, flow rate, water level, and small changes in pier placement. The flow resistance decreases with reduced roughness (n). The range already stated is 0.025–0.02, resulting in a slight decrease in velocity uniformity. Therefore, N₀ slightly decreases, while the sedimentation rate of the coarse fraction still approaches 100% and that of the fine fraction slightly decreases. The sedimentation rates for all size fractions and velocity remain relatively stable, and the overall sensitivity to changes in n is low. With reduced inlet sediment concentration (S), the sedimentation amount decreases, but the sedimentation rate remains stable for the coarse fraction. At high inlet S, the sedimentation amount increases, and local flocculation increases the sedimentation rate for the fine fraction. The sedimentation rate matches the velocity uniformity and inlet S. N₀ is unaffected by concentration, with low sensitivity compared to the default case.

Table 6

Table 6. Sensitivity of velocity and sedimentation to changes in key parameters, compared to the default case n = 0.022, inlet S = 0.14 kg/m³, standard water level = 1.41 m, Q = 50 m³/s, and recommended inlet division piers.

At a small inlet flow rate (Q), the overall velocity decreases, and velocity uniformity (N₀) is significantly improved. The sedimentation rate increases because residence time increases and bottom shear stress decreases. Under medium flow conditions, both N₀ and sedimentation rate are at moderate levels. The sensitivity of velocity and sedimentation rate to changes in Q is large. At a low water level, velocity increases, and the velocity distribution becomes uneven. Both N₀ and the sedimentation rate decrease. At high water level, velocity slows, and velocity uniformity is improved. Both N₀ and the sedimentation rate increase. The sensitivity of velocity and sedimentation rate to changes in water level is also large. Under the original inlet division piers condition, the main flow is restricted near the south bank, and a large velocity and backflow region exists (Figure 6). Therefore, velocity uniformity is weak (N₀ = 16%–31%), and total sedimentation rate is low (56.7%). Under the optimal inlet division pier cases 1–4, the local flow fields all change gradually, and the maximum velocity and backflow region are reduced. N₀ and sedimentation rate increase gradually. The final N₀ and sedimentation rate are both significantly improved toward the ideal smooth and uniform velocity and efficient sedimentation. The effect of changes in the inlet division pier distribution on velocity and sedimentation rate is also substantial.

6 Conclusion

This study utilizes physical model experiments and numerical simulation to study hydrodynamics and sediment transport in the permanent sedimentation tank of the Oujiang Water Diversion Project. The physical model follows the principle of gravitational similarity, and the geometric scale is given as 1:20. A box culvert of 49.5 m is inclined at a very large angle (69.3°) to link the water intake channel and the sedimentation tank. Four rows of division piers are set to separate the flow into five channels. Pier distribution is optimized for smooth and uniform velocity distribution, efficient sedimentation, and prevention of sediment resuspension. The numerical model is adopted from MIKE21 software, and simulated sediments are divided into four size fractions, with flocculation accounting for cohesive fractions. A three-dimensional flow pattern is not performed near the inlet and outlet because the objective is the optimization of pier distribution for smooth and uniform velocity.

Water depth, averaged velocity, and sediment concentration are obtained by the numerical model. Experimental hydrodynamics and simulated sediment transport are shown under operation conditions of the designed lowest, standard, and highest water levels. The simulation is basically consistent with the measurement, indicating that the roughness of the model and the terrain simulation are reasonable and reliable. Under the originally designed division pier condition, the main flow of high velocity is focused on the left bank of the tank due to the large angle between the inlet gate and the tank axis, while a large-scale backflow region is formed against the right bank. Five inlet distributions of division piers are designed, and the effects of changes in key parameters are tested on the velocity distribution and sedimentation rate. Under the recommended division pier condition in the tank inlet, the main flow of high velocity is much decreased, while the reversal flow area is largely eliminated. The uniformity parameter of the velocity is much increased at each cross-section within the working sections under all operation conditions of the designed lowest, standard, and highest water levels. In addition, the sediment concentration distribution becomes uniform along the cross-section of the sedimentation tank, and the sedimentation rate obviously increases. More sediment is left in the tank, and the concentration at the pump station inlet is small. In turn, the optimized design of the division piers effectively enhances velocity uniformity and improves the overall sedimentation process.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.

Author contributions

JC: Conceptualization, Investigation, Validation, Writing – original draft. LZ: Methodology, Resources, Software, Writing – original draft. XW: Conceptualization, Formal analysis, Investigation, Methodology, Supervision, Writing – original draft. XT: Data curation, Writing – review and editing. JZ: Funding acquisition, Methodology, Validation, Writing – review and editing. RZ: Formal analysis, Visualization, Writing – review and editing. HQ: Formal analysis, Project administration, Writing – review and editing.

Funding

The authors declare that financial support was received for the research and/or publication of this article. This research was funded by the National Natural Science Foundation of China (grant number 41961144014).

Conflict of interest

Authors JC and XT were employed by Wenzhou Water Conservancy Survey and Design Institute Co., Ltd. Authors XW, RZ, and HQ were employed by Wenzhou Oujiang Water Diversion Development Co., Ltd.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Generative AI statement

The authors declare that no Generative AI was used in the creation of this manuscript.

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Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/feart.2025.1686407/full#supplementary-material

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