Hydrodynamic characteristics of lateral withdrawal with effects of the slope ratio

unit mass force vector (N)

vertical height of the slope (m)

turbulent kinetic energy (J)

lateral length of the slope (m)

intake bottom layer

intake middle layer

intake surface layer

pressure (Pa)

pressure of section b–b (Pa)

time (s)

fluid velocity vector (m/s)

velocity vector (m/s)

fluid kinematic viscosity (m²/s)

helix-shaped recirculation width (cm)

the widest surface vortex width (cm)

volume fraction

dissipation rate (%)

slope ratio

fluid density (kg/m³)

ratio of recirculation to the width of the layer (%)

ratio of the widest surface vortex to the width of the layer (%)

vorticity vector

Lateral withdrawal is commonly performed as the first link of water supply or water transfer projects to optimize the allocation of water resources. Lateral intakes are built on the bank of the river mainstream, so that the water flow can be introduced from the mainstream into the pipeline system for water treatment and transportation. The hydrodynamic characteristics of lateral withdrawal are significant for the safe and stable operation of the whole project.

In lateral withdrawal, under the effects of lateral intake and inertia, the direction of mainstream flow is gradually changed and the water flow enters into the water intake at a certain angle (Neary et al. 1999; Chuang & Hsiao 2011). Therefore, due to centrifugal force and vertical velocity gradient, complex hydrodynamic characteristics and secondary flow will occur at the intake entrance. And secondary flow such as helix-shaped recirculation and vortex has significant three-dimensional (3-D) characteristics (He et al. 2021a). The location of the recirculation area in the main channel is completely different from a lateral open channel intake. The separation zones are located in the main channel after the intersection with the lateral open channel, near the internal wall of the diversion channel and just after the entrance of the lateral intake (Rahmani Firozjaei et al. 2020). A clockwise secondary motion cell is along the outer wall of the branch channel and a counterclockwise secondary motion cell in the main channel occurs after the intake and along the inner wall (Montaseri et al. 2019). Two recirculation structures in the lateral flow occurred, and the recirculation structures are helix-shaped and closed (Momplot et al. 2017).

These hydrodynamic phenomena affect withdrawal efficacy. They are closely related to the withdrawal conditions (He et al. 2021b) and water intake structure parameters (Yousefi et al. 2010; Shen et al. 2020), such as the intake width depth ratio, withdrawal angle, intake type and water diversion ratio. Effects of bank slope on the flow patterns in river intakes were studied, and it was found that the inclining bank causes the bottom stream tube width to be greater than at the surface (Seyedian et al. 2014). The coefficient of the discharge depends mainly on the approach flow Froude number and the ratio of width of orifice and bed width of the channel (Hashid et al. 2015). Flow patterns are identified considering the location and length of the hydraulic jumps that develop across the main and lateral channels. The discharge division ratio–Froude number relationship is proposed for subcritical dividing flows (Abderrezzak et al. 2014). Moreover, the intake structure with submerged vane is used to optimize the hydrodynamic characteristics and control the sediment (Rahmani Firozjaei et al. 2019; Baltazar et al. 2021).

Additionally, lateral withdrawal is the open channel flow of natural rivers. Some researchers studied many aspects of the open channel, among which numerical simulation methods were widely used (Retsinis et al. 2020; Maranzoni & Tomirotti 2021). Flow characteristics of the open channel were observed under different conditions and schemes. Moreover, turbulent characteristics and turbulence models were significant to accurately simulate hydrodynamic characteristics (Eringen 2003). Multiple turbulence models were compared to obtain more accurate flow characteristics in different hydraulic engineering (Zambrano et al. 2015; Yoon 2020). As the basis of numerical simulation, 3-D modeling was always applied in different open channel models. The framework of model establishment, the form of grid division and the solution setting provided references for practical simulation of the open channel (Sharifipour et al. 2015; Dvorak & Zhang 2017). Meanwhile, numerical simulation and experiment methods are commonly suitable in open channel flow studies (Rostami et al. 2012; Xu & Li 2020). The results of the volume of fluid (VOF) simulation model and experiment can achieve a good fit. The free surface flow of an open channel triangular weir (Aydin 2012) and an open channel dam-overtopping event (Xiao & Lin 2016) were modeled using the VOF simulation method to describe the flow characteristics, and good agreements were obtained between the simulation and experimental results. A comparison between the experimental data and the results of the numerical model showed that the VOF method is capable of simulating the flow pattern in the curved open channel bends (Ramamurthy et al. 2013; Gholami et al. 2014). And the VOF numerical simulation method with a high-resolution interface capturing scheme was used for free surface tracking (Jesudhas et al. 2018).

However, existing research, on the one hand, focuses on the hydrodynamic characteristics generated by the lateral withdrawal process itself. On the other hand, although the influence of different withdrawal parameters on characteristics in lateral withdrawal is studied, research on the effects of the intake structure, especially the intake slope, is scarce. And the effects of adding the intake slope and the influence of changing slope ratio on recirculation and surface vortex are rarely studied. Meanwhile, numerical simulation combined with experimental tests is applicable and has advantages. With the increase in lateral withdrawal projects and the emphasis on engineering safety, it is necessary to improve the secondary flow of the intake. And the effects of intake structure on hydrodynamic characteristics of lateral withdrawal require urgent study.

Based on a lateral withdrawal project in a river channel of east Guangdong Province, China, a 3-D numerical VOF model was established and validated by experimental tests. This work aims to study the hydrodynamic characteristics and improve the secondary flow of the lateral intake under the effects of the slope ratio. The remaining research is organized as follows. The second section briefly presents the methodology of numerical simulation and experimental test, including the numerical modeling, experimental test modeling and model scenarios. The results of lateral withdrawal under different slope ratios are described and discussed in the third section, and the main conclusions from this research are drawn in the fourth section.

Based on actual measured data of the lateral intake in a river channel of east Guangdong Province, China, the prototype river channel was relatively straight, so that a 3-D lateral withdrawal hydrodynamic numerical generalized model was established based on ANSYS FLUENT. The model scale was 30:1 and a similar gravity theory was followed. As shown in Figure 1(a), the computational domain covered the river mainstream and water intake. The mainstream scope was 120 m long and 100 m wide from the intake, and the intake elevation was −3.5 m (in the prototype). The cross-section of the model is shown in Figure 1(b). The cross-section could help understand the two-phase structure of the lateral intake, H was the vertical height of the slope, L was the lateral length of the slope and the slope ratio was defined. When changing the slope ratio ⁠, the withdrawal flow rate and the width of the intake water surface were kept constant.

Structured grids were generated as shown in Figure 2(a), which could not only ensure the quality of the grids but also ensure an adequate adaption to the complex geometry (Zhou et al. 2019). To validate the size of the grids used, a sensitivity analysis was conducted. Grids of different element numbers were generated, and the pressure of section b–b on the upstream was extracted and compared. As shown in Figure 2(b), the results confirmed that when the grids element number reached about 4 million, the pressure did not change significantly with an increase in grids’ element number. Considering the calculation accuracy and duration, about 4 million grids’ element number was selected for further model calculations. Moreover, the quality of the grids, whose value ranges from 0 (worst) to 1 (best), was checked to ensure that the quality of all grid values was higher than 0.3.

The 3-D numerical simulation of lateral withdrawal was based on the incompressible continuity and momentum equations. The governing equations are as follows (Park et al. 2006; Zhao et al. 2020):

Reynolds averaged Navier–Stokes turbulence models offer the most economic approach for computing complex turbulent industrial flows. The realizable turbulence model, which is a typical example of Reynolds averaged Navier–Stokes turbulence models, was selected to deal with turbulence in this work. The model simplifies a problem to the solution of two additional transport equations and introduces an eddy-viscosity (turbulent viscosity) to compute the Reynolds stresses. The transport equations for the turbulent kinetic energy (⁠⁠) and the dissipation rate (⁠⁠) are solved to close the Reynolds averaged Navier–Stokes equation, and models allow the determination of both a turbulent length and time scale by solving two separate transport equations. The model has been proved to be suitable for many engineering applications, and typically provides the level of accuracy required.

The semi-implicit method for pressure-linked equations-consistent (SIMPLEC) algorithm was selected for pressure–velocity coupling. According to pressure and mass fluxes values, the momentum equation and continuity equation were discretized in integral form, and the solution variables in the governing equations were solved. The updated velocity field and the mass-flux were used to solve the pressure correction equation and turbulent quantities equations.

The water level was fixed as the designed operation level of the lateral withdrawal, and the water level was −0.31 m in the prototype. The water boundary of the lateral intake model was set as velocity inlet and outlet, while the air boundary was set as the pressure boundary. The domain above the water surface was defined as the air phase, and the domain below the water surface was defined as the water phase initially.

An experimental model was built to validate the numerical simulation. The size of the experimental model was the same as that of the numerical simulation model, and the length of the mainstream channel was extended to stabilize water flow and ensure smooth water flow into the study area. The experimental model is shown in Figure 3(a), and the model covered the river mainstream and the water intake.

The plexiglass with a roughness of 0.008 was selected as experimental material for the water intake to meet the resistance similarity requirements. Multiple pumps were used to jointly control the inlet water flow. Another pump connected with flowmeters was used to control the withdrawal flow. An overflow weir and a needle water level gauge were installed for water level control and observation. The water velocity was tested using an LGY-III automatic velocity meter. The flow streamlines were observed using permanganate. At the beginning of the test, multiple pumps were used to adjust the mainstream and withdrawal flow rate. After the water level was fixed and flow fluctuation was small, the flow pattern and flow velocity were observed when the water flow was relatively stable. All data were taken as the average value of multiple measurements.

To validate the numerical simulation results by experiment, two monitoring planes C1 and C2 were set and each monitoring point was 4 cm below the water surface. As shown in Figure 3(b), 11 monitoring points at the upstream and water intake were displayed, which would be used to measure and compare velocities.

To study the effects of slope ratio on the intake hydrodynamic characteristics in lateral withdrawal, model scenarios were set according to different slope ratios. As shown in Table 1, the range of slope ratio was from 0 (vertical) to 1:2.5. The flow rates of mainstream and lateral intake were converted based on prototype measured data, and all model scenarios were simulated under the same withdrawal condition.

Under the model scenario S4 with a slope ratio, the numerical simulation model was validated through the experimental test. The verification results are shown in Figure 4(a). The lateral withdrawal process was carried out, and the monitoring point velocities of numerical simulation and experimental test were compared. It could be seen that the changing trend of velocity at monitoring points was the same, and the velocity values at each monitoring point were similar, which could illustrate the accuracy of numerical simulation. Additionally, helix-shaped recirculation and surface vortex appeared at the water intake in the experimental test (Figure 4(b)), which was also consistent with the observation of subsequent numerical simulation. The feasibility and effectiveness of lateral withdrawal prediction were validated.

Under the model scenario S1, the slope was vertical and the water intake was rectangular. The intake hydrodynamic results were analyzed through three water layers, namely, the bottom layer ⁠, the middle layer and the surface layer ⁠. Under the effects of lateral withdrawal, the flow direction near the side bank changes towards the intake, and secondary flow occurred. The velocity distribution contours are shown in Figure 5(a). The flow velocity was higher at the inlet of the water intake and the downstream side of the water intake, while there were local low-velocity areas near the upstream side of the water intake. The velocity distribution had an obvious circulation trend and the secondary flow was observed. Under different water layers, the velocity distribution was almost the same. However, with the decreased water depth, the overall velocity was slightly decreased.

As shown in Figure 5(b), streamlines of the intake in lateral withdrawal illustrated that part of the mainstream near the side bank flowed into the intake, and helix-shaped recirculation was generated near the upstream side of the intake. As the mainstream of lateral withdrawal gradually changed flow direction by 90°, the flow separated from the side wall, and the recirculation was generated under the effects of turbulent shear stress, inertia and gravity compensation. The recirculation area of each water layer was large, and the helix-shaped recirculation width of each water layer was basically the same. So, a 3-D cylindrical recirculation in the direction of the water depth could be inferred.

Due to the state change from acceleration and decompression to deceleration, the kinetic energy could no longer be converted into pressure energy when the water flowed into the water intake, and the mainstream would be forced to follow the original flow direction. This meant the downstream water would flow to the vacated zone of the mainstream, and the vortex would be formed. In lateral withdrawal, the vorticity method is the most direct and simple method to describe the turbulent vortex. Therefore, to save computing resources, vorticity magnitude was extracted to represent the surface vortex after numerical simulation by the turbulent model. The vorticity magnitude of the surface layer is shown in Figure 5(c). It could be seen that, besides a large vorticity magnitude zone at the recirculation center, an obvious long strip-shaped vortex was generated at the intersection of the mainstream and the intake, and the vortex gradually offset to the water intake.

As shown in Table 2, the helix-shaped recirculation width and the widest surface vortex width were measured through the three water layers ⁠, and ⁠. The ratio of recirculation to the width of the layer and the ratio of the widest surface vortex to the width of the layer were calculated. From bottom to surface layer, increased from 39.2 to 44.6 cm, and also increased from 48.94% to 55.75%. It could be proved that the recirculation of water surface was more serious and the flow patterns were worse than that of water bottom. In addition, of was low and of explained that the vortex accounted for a small proportion, which showed that, under the S1 scenario, the surface vortex range was relatively small.

Under the scenarios with a slope ratio (S2–S5), lateral withdrawal was simulated under the same withdrawal condition. The velocity distribution contours are shown in Figure 6. It could be seen that, compared with the vertical slope scenario (S1), the velocity distribution trend was roughly the same, which showed that there were high-velocity areas on the water intake side of the mainstream and the downstream side of the water intake, while there were low-velocity areas on the upstream side of the water intake. When the slope ratio was lower, the section area of the water intake was also lower, so the overall velocity of each layer was increased. With the decrease in the slope ratio, the high-velocity area significantly increased and the range of adverse effects of the low-velocity area was reduced, which was conducive to the improvement of water intake efficiency. In addition, the central position of the local low-velocity area was relatively stable and did not move with the change of the slope ratio, which was conducive to taking engineering measures to optimize the local low-velocity area.

As shown in Figure 7, streamlines of the intake in lateral withdrawal illustrated that the change of slope ratio had a great impact on the helix-shaped recirculation of water intake. Compared with the vertical slope scenario, the overall shape of the streamline was basically the same, and the shape of the recirculation area was oval. The mainstream near the side bank flowed into the intake and an obvious recirculation area on the upstream side of the water intake was generated. The recirculation area would decrease with the increase in the water depth. The recirculation width in scenarios with the vertical slope was less than that in scenarios with a slope ratio. In addition, through the three water layer streamlines in scenarios with a slope ratio, it could be found that, due to the limited boundary conditions, the location and size of the recirculation area were not much different. With the increase in the water depth, the recirculation area was gradually decreasing. There were also differences with different slope ratios, with the most significant difference appearing near the bottom of water layer ⁠. With the decrease in the slope ratio, the recirculation width also decreased especially in layer ⁠. It could be concluded that the slope with a slope ratio would restrict the generation and development of recirculation. The center of the helix-shaped recirculation did not move significantly, which corresponded to the center of the local low-velocity area. Meanwhile, from the 3-D perspective in the direction of the water depth, the recirculation gradually changed from cylinder to inverted cone with the decrease in the slope ratio.

As shown in Table 3, compared with the S1 scenario, the helix-shaped recirculation width and the ratio of recirculation to the width of the layer were all lower. From bottom to surface layer, and increased under the same scenario. With the decrease in the slope ratio, and of each layer decreased, and the minimum value was at layer under S5 scenario. It could be proved that the scenario with a slope ratio was beneficial to inhibit the development of recirculation. The lower the slope ratio was, the greater the inhibition effects were. Especially near the intake bottom, the optimization of flow patterns was more obvious.

The vorticity magnitude of the surface layer is shown in Figure 8. It could be seen that, compared with the S1 scenario, an obvious long strip-shaped vortex was also generated at the intersection of the mainstream and the intake under all scenarios, and the vorticity distribution of the water intake was almost the same. With the decrease in the slope ratio, the length and position of vortex strip were not significantly different. However, due to the increase in the velocity, the vorticity magnitude and the surface vortex width increased.

As shown in Table 4, compared with the S1 scenario, the widest surface vortex width and the ratio of the widest surface vortex to the width of the layer were all lower. and of surface vortex increased with the decrease in the slope ratio, and the maximum value appeared under the S5 scenario. It could be found that the scenarios with a slope ratio would aggravate the surface vortex. The lower the slope ratio was, the less conducive it was to the prevention of surface vortex. The decrease in the slope ratio had little effect on the length and position of the vortex strip, but increased the vorticity magnitude and vortex width.

To study the influence of the slope ratio on lateral withdrawal secondary flow, the model of this paper was simplified to a certain extent. Under the determined river mainstream flow rate and withdrawal flow rate, small flow fluctuation was ensured and the water level remained stable. Moreover, we assumed that temperature, density and other uncertainties remain constant, so that the only variable in this study was the slope ratio. Meanwhile, the error of the test was controlled in a small range, and all data were taken as the average value of multiple measurements. Therefore, the numerical and experimental tests were much idealized, and the comparison and verification results were consistent. However, there are uncertainties in practice influencing the conclusions in lateral withdrawal, and the real river would be much more complicated. The variation of water level and flow rate in river mainstream caused by tidal rivers and different water withdrawal conditions are the primary uncertainties in practice of lateral withdrawal. For lateral withdrawal projects with the same ratio of withdrawal velocity and mainstream velocity, the conclusions of this work are applicable. The velocity changes of mainstream and withdrawal would affect the width and length values of actual recirculation and surface vortex. It is considered that increasing the mainstream velocity and decreasing the withdrawal velocity would increase the width of secondary flow in different water layers. However, the qualitative analysis of the conclusions and the influence of the intake slope on secondary flow would still be applicable. The influence of more uncertainties on secondary flow in practice would be studied in future research.

For practical application, according to the findings in this work, adding an intake slope and decreasing the slope ratio are beneficial to improving the flow patterns and recirculation, while it is not conducive to the prevention of the surface vortex. Therefore, when the withdrawal velocity is much smaller than that of the mainstream or the recirculation problem is serious, it can be considered to change the vertical slope to the slope with a slope ratio and decrease the slope ratio as much as possible, which is conducive to improving the intake recirculation. However, if there are other facilities on the water surface of a river intake and the surface vortex has a great impact, the slope with a slope ratio should not be considered. If it is necessary to comprehensively consider the intake recirculation and surface vortex, finding an appropriate slope ratio value to adapt to the complex situation was feasible. In practical projects with the same withdrawal flow ratio and different intake terrain size, the dimensionless and could provide support. Moreover, to improve the generalization of the findings in this work, the variation trend of secondary flow parameters and slope ratio is proposed as shown in Figure 9. was the average value of the three water layers. It could be seen that there was an obvious exponential trend. In other words, in practical projects with different working conditions, the slope ratio could be appropriately selected according to the exponential distribution characteristics.

For air–water two-phase simulations, the energy equation of the air phase generally needs to be considered. However, in this work, the water flow pattern was the focus, and the heat and energy exchange was almost negligible. The change of temperature was small and the water flow changes caused by temperature were even smaller. So the temperature change was not considered, and the energy equation was neglected. In addition, the water surface was relatively stable and the air compression was minimal. Only the pressure and velocity through the mass conservation and momentum conservation of the VOF model needed to be solved, and it was unnecessary to bring the velocity field to the energy equation to solve the temperature field. After the verification of cases with or without energy equation, as mentioned above, it was also found that the energy equation would only increase the computing resources and would not affect the conclusions. The research, which considers the influence of heat exchange, temperature change and fluid compressibility on lateral withdrawal, would be conducted in future work. For turbulent vortex generated in lateral withdrawal, it was possible to simulate turbulent vortex more accurately through more advanced identification and simulation methods. However, in this study, we wanted to know how the slope ratio changes affected the range of surface vortex at the lateral intake connection, and we did not pay attention to the detailed 3-D characteristics of the vortex. Therefore, the vorticity method, which is the most direct and simple method, was used. The variation of turbulent kinetic energy, velocity and pressure gradient distribution characteristics are considered to affect the turbulent vortex, so the vortex width was defined and vorticity magnitude was extracted from the above characteristics by the vorticity method. Through more accurate turbulence models, such as Large-Eddy simulation, or more detailed vortex identification methods, such as Q criterion and method, turbulent vortex analysis and 3-D vortex research for the whole domain of lateral withdrawal will be done in future works.

The hydrodynamic characteristics of lateral intake are crucial to the water withdrawal efficiency and pipeline stable operation. By combining numerical simulation and experimental tests, this study revealed the hydrodynamic characteristics of lateral withdrawal with effects of the slope ratio. The VOF numerical model and experimental model of lateral withdrawal were established and validated. Velocity distribution, helix-shaped recirculation and surface vortex of the intake were analysed. The main conclusions are as follows:

• 1.

  Under the scenario with a vertical slope, the helix-shaped recirculation and surface vortex are always generated at the intake. Adding a slope ratio is beneficial to improve the flow patterns and recirculation, while it is not conducive to the prevention of surface vortex. Under the scenarios with a slope ratio, the flow patterns are more optimized, the low-velocity area decreases and the recirculation range and width (especially at the bottom layer) decrease, while the vortex width and vorticity magnitude increase.

• 2.

  With the decrease in the slope ratio, helix-shaped recirculation width and the ratio of recirculation to the width of the layer decrease. The lower the slope ratio is, especially near the intake bottom, the greater recirculation inhibition effects are. The minimum is 9.19 cm and the minimum is 22.97% at the bottom layer under the scenario with a slope ratio of 1:2.5.

• 3.

  The decrease in the slope ratio has little effect on the length and position of the vortex strip, but increases the vorticity magnitude and vortex width. The lower the slope ratio, the more serious the surface vortex.

This study enhances the understanding of lateral withdrawal hydrodynamic characteristics, and provides a technical guide for the design of water intakes. With more water withdrawal utilization in estuaries and coastal areas, intake structure research considering more parameters should continue.

This study was supported by the Fundamental Research Funds for the Central Universities (Grant No. B200203064), the Postgraduate Research & Innovation Program of Jiangsu Province (Grant No. KYCX20_0477) and the National Natural Science Foundation of China (Grant Nos. 51879087 and 51839008).

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