Influence of Different Lateral Bending Angles on the Flow Pattern of Pumping Station Lateral Inflow

Amodel of the pumping station lateral inflow forebay was established to explore the influence of different lateral bending angles of the pumping station lateral inflow. ,e lateral bending angles were set at 45° and 60°, and the two schemes were calculated separately. Analyzing the results of the numerical simulation showed that the flow patterns of the diversion passages of different schemes were good, but the advancing mainstream of the 1# inlet passage near the sidewall was seriously deviated after entering the forebay. Most of the water can flow smoothly into the inlet passage, while a small part of the water flowed into the sidewall and formed a backflow, resulting in a large-scale backflow zone near the left sidewall of the forebay. Moreover, the flow in the backflow zone was turbulent, which affected the water inlet conditions of the 1# water flow passage. Comparing the water inlet conditions of the water passage with the numerical simulation results of 45° and 60° bending angles showed that the larger the lateral bending angle of the forebay was, the worse the flow pattern of the water flow, and the more unfavorable the pump operation.


Introduction
Irrigation and drainage pumping stations have played a vital role in fighting drought and waterlogging, ensuring increased agricultural production and income and developing the rural economy. e arrangement of several pumping stations is often restricted by objective factors such as water flow conditions and actual topography, such that the arrangement of lateral water intake has to be adopted. When water enters laterally, a certain angle is observed between the water flow direction and the forebay water flow direction, which may cause serious cavitation and vibration and will affect the normal operation of the pump. In rivers with much sediment, it will cause sedimentation and erosion of the bottom of the front pond. erefore, taking effective rectification measures to improve the inlet flow pattern of the pumping station [1][2][3][4] is of great importance to the design and transformation of the pumping station as well as the economy and safety of the project operation.
For a long time, experts and scholars have carried out a large amount of rectification optimization research on the intake buildings of the pumping station and achieved fruitful results. Arboleda et al. [5] used the overall model test method, and the main rectification method was "block," which adjusted the flow velocity distribution of the section and weakened the lateral flow velocity in the incoming flow, thus obtaining a better rectification effect. Rajendran et al. [6] used Particle Image Velocimetry (PIV) flow field display technology to capture information such as the position of the vortex near the pump inlet and, for the first time, intuitively and quantitatively revealed the vortex's motion characteristics. Hou [7] used Computational Fluid Dynamic (CFD) methods to study the flow pattern of the pressure forebay of a pumping station, and the good agreement between the calculation results and the empirical formula showed the accuracy and reliability of the CFD calculation method. e numerical simulation results provided a basis for the hydraulic optimization design of the pressure forebay. Liu et al. [8] used gates to control the water levels of the fore and intake sump, numerically simulated the flow patterns of the fore and intake sump before and after the rectification, and concluded that a combination of several engineering measures such as a discontinuous sill and a pressure plate was adopted. ese methods can make the flow velocity distribution of the forebay uniform and effectively improve the efficiency of the pumping station. Ansar et al. [9] took the pumping station inlet tank as the research object, compared and analyzed the numerical simulation results and the test results, and verified that the results obtained by the two methods were the same regardless of whether the pumping station enters the water directly or sideways. Moreover, the numerical calculation results had a high degree of credibility and can satisfy practical applications. Cheng et al. [10] analyzed the turbulence of the forebay caused by the movement characteristics of the curved water flow in the lateral inlet pumping station, which affected the pump inlet conditions, and calculated the 3D flow field of the rectification measures with the combined bottom sill.
is approach effectively improved the water inlet conditions of the forebay. Liu et al. [11] proposed adding multiple sets of bottom sills in the forebay of a multiunit pumping station, using 3D turbulence numerical simulation calculations, and verifying them through hydraulic model tests, which largely eliminated the backflow and the vortex and substantially improved the flow pattern. e current research on hydraulic characteristics of pumping stations mainly includes theoretical analysis, numerical simulation, and model tests [12][13][14][15][16][17], each with its own advantages and disadvantages. With the rapid development of computer technology, numerical simulation has become more important in various research fields [18][19][20][21][22][23][24], and its research results have important reference value for practical engineering.

Calculation
Model. e pumping station studied in this article is a pumping station hub with a lateral water intake. ree pump units are installed in the pump room. e design flow rate of each pump is 4.0 m /s. e inlet size of the flow passage is 2.36 m (width) × 1.8 m (length). e intake level of the pumping station is 1.9 m, the elevation of the bottom of the drainage canal is 0.0 m, and the elevation of the forebay bottom is −1.0 m. e main functions of the project are flood prevention and drainage. e left side of the pumping station is a self-draining culvert. When the pumping station is operating, the self-draining culvert control gate is closed. e total width of the outlet of the forebay is B, and the length from the center of the inlet of the forebay to the center of the outlet is L. Figure 1 shows that the plan layout of the intake building of the pumping station is mainly based on the 3D modeling and numerical simulation of the original design with lateral bending angles of 45°a nd 60°.

Calculation Method and
Meshing. ANSYS CFX software is used for numerical simulation, the standard k-ε turbulence model is used for calculation, and the MESH software is used for unstructured meshing of the entire computational domain. e size of the grid is controlled. e selected grid shape is a tetrahedron to meet the calculation requirements. e 3D model grid diagram of the pumping station intake building when the lateral angle of 45°is obtained is shown in Figure 2.
Taking the model with 45°lateral bending angle and the hydraulic loss from the inlet of the approach passage to the outlet of the inlet passage as the characteristic parameter to select the appropriate grid number, the calculation formula is as follows: where h f is the hydraulic loss, P in is the total pressure at the inlet, P out is the total pressure at the outlet, ρ is the density of water at 4°C, and g is the acceleration of gravity. e calculation results under different grid numbers are shown in Table 1 and Figure 3. e analysis of grid independence reveals that the final number of grids is 3.58 million, which has a minimal effect.

Boundary Condition Setting.
e inlet of the entire calculation domain is taken from the prototype of the diversion river to the upstream diversion passage at a 10 m section, which is set as the boundary condition of the mass flow, the inlet flow rate is 12 m 3 /s, and the medium turbulence intensity Tu � 5%. e outlet of the water flow passage is taken as the outlet of the calculation domain. e number of outlets is three. e water flow direction is perpendicular to the outlet section. Each outlet has an average static pressure of standard atmospheric pressure (1 atm) as the outlet condition. e water surfaces of the lead passage and the forebay are free liquid surfaces, and the water level of the forebay does not vary much. e shear stress effect of air on the water surface is neglected. e "rigid cover assumption" is selected in the calculation; that is, the symmetry surface boundary is used. e rest is set as a wall, and a nonslip wall is used for processing.

Calculation Evaluation Index.
e uniformity of the axial velocity distribution on the inlet section of the flow passage is an important indicator reflecting the velocity distribution on each section. e uniformity of axial velocity distribution is used to characterize the uniformity of the axial (downstream flow direction) velocity distribution of the inlet section of the flow passage. e larger the value is, the closer it is to 100%. is finding shows that the more uniform the axial velocity distribution of the water flow at the inlet section of each flow passage is, the more in line it is with the pump inlet design conditions. e calculation formula is as follows: where V ai is the axial velocity of each node of the section, m/ s; V a is the average axial velocity of the section, m/s; n is the number of nodes; and V au is the uniformity of axial velocity distribution. e weighted average angle of the inlet section velocity of the passage is an important physical quantity that measures the lateral velocity of the inlet section of each passage. e velocity-weighted average angle is selected to measure the transverse velocity on the inlet section of each flow passage. e closer the value is to 90°, the closer the outlet water flow is perpendicular to the outlet section, and the better the water inlet condition of the pump. e calculation formula is as follows: where θ is the weighted average angle of velocity at the inlet section of the inlet flow passage; V ti is the lateral velocity of the i-th unit grid at the inlet section of the inlet flow passage, m/s; and V ai is the axial velocity of the i-th unit grid at the inlet section of the inlet flow passage, m/s.

Numerical Simulation Results of the 45°Lateral Angle
Scheme. Considering that the 3D flow field of numerical simulation is more complicated, the flow velocity vector diagram, streamline diagram, and velocity distribution cloud diagram of characteristic sections are drawn. It is conducive to reflect the flow field of the diversion passage, forebay, and water inlet passage of the lateral intake pump station threedimensionally and intuitively and facilitate the comparative analysis and study of the flow pattern of the entire intake structure. Figure 5 shows that the water flow in the diversion canal develops smoothly, and the flow pattern is good because the project is a side-inlet forebay. However, after entering the forebay, the main flow of the 1# inlet passage near the sidewall is severely deviated. While most of the water flows into the water inlet passage, a small part of the water is still in the left side of the forebay (this article uses the flow direction to determine the left and right sides) to form a backflow near the sidewall, touching the sidewall and forming a large-scale backflow area. e flow regime in the return zone is turbulent. erefore, considering that the water flow in the diversion canal is relatively smooth and the water flow in the forebay is more turbulent, the focus is only on the elaboration and analysis of the flow pattern in the forebay when the lateral angle is 45°.     forebay to the inlet passage, the flow velocity in the middle position of the forebay is relatively large and has a decreasing trend to both sides; most of the fluid can flow smoothly into the inlet passage, but at the left sidewall of the forebay, a backflow zone is evident, and the flow pattern of the reflux zone is extremely high. e reason for this finding is that the transverse velocity of the mainstream is large, and a small part of the fluid contacts the left sidewall, which forms a large range of backflow zone, thus forcing the inflow mainstream to deform and deflect. Comparing and analyzing the flow field maps of each horizontal section show that, during the process from the surface layer to bottom layer, the scope of the reflux area is gradually expanded, and the position of the reflux center is approximately the same. According to the coordinate diagram, the center of the surface layer and middle layer reflux area that is located at X is −2 m, Y is 11 m, the bottom layer reflux area center that is located at X is −3 m, and Y is 11 m. e influent condition of 1# inlet passage is affected by the backflow zone that occurs before the 1# inlet passage. Figure 7 is a 2-2 plane velocity vector diagram with a 45°b ending in the lateral direction. e profile position is X 2 � −0.5 m, close to the inlet of the flow passage. e water flow in the forebay has a certain angle of deviation to the left due to the influence of the lateral water inflow. e water flow in the forebay near the inlet of 1# inlet passage is the most skewed, and the flow is turbulent. Figure 8 is a 1-1 plane velocity cloud diagram with a 45°b ending in the lateral direction. e position of the profile is X 1 � 0.01 m. e inlet flow patterns of 2# and 3# inlet passages are better, the velocity distribution is relatively uniform, and the overall distribution is symmetrical. However, the water flow at the inlet of the 1# passage is severely skewed due to the influence of the backflow in front of the passage. e high-speed area occurs on the left side,

Numerical Simulation Results of the Lateral 60°Bending
Angle Scheme. e position of the characteristic section selected in the plan for a 60°lateral bending angle is the same as that for a 45°bending angle. Seven characteristic sections are selected for the analysis of the results. e coordinates of the surface layer, middle layer, and bottom layer are Z a � 1.85 m, Z b � 0.95 m, and Z c � 0.05 m, respectively; the coordinates of the section perpendicular to the mainstream direction are X 1 � 0.01 m and X 2 � −0.5 m, respectively. e selected 1-1 section is the three inlet sections of the inlet flow passage to analyze the uniformity and weighted average angle of the axial velocity distribution on the section. Figure 9 shows that the water flow in the diversion canal is good, but a large-scale backflow zone is observed before the 1# inlet passage near the left sidewall after entering the forebay. e flow pattern in the recirculation zone is turbulent, and the main flow of the inlet water in front of the 1# inlet passage is seriously deviated. e comparative analysis shows that the flow pattern of the water flow at a lateral angle of 60°is the same as that at a lateral angle of 45°, except that the recirculation zone in front of the 1# inlet passage is larger. erefore, considering that the water flow in the diversion passage is relatively smooth and the water flow in the forebay is more turbulent, the following only focuses on the elaboration and analysis of the flow pattern in the forebay when the lateral angle is 60°. Figure 10 shows the axial velocity flow field diagram of each horizontal section when the lateral angle is 60°. Most of the water can flow smoothly into the inlet passage, but a clear backflow zone can be seen on the left sidewall of the forebay. e flow pattern in the return zone is extremely turbulent, and the reason is the same as when the lateral direction is 45°b ecause the mainstream lateral velocity at this place is relatively large, and a small part of the water flow contacts the left sidewall to form a larger return zone, thereby forcing the main flow of water to deform and deflect. Comparing and analyzing the flow field diagrams of the surface layer, middle layer, and bottom layer show that, from the surface layer to the bottom layer, the scope and position of the recirculation zone are the same, but the center of the recirculation zone moves to the right and forward. According to the coordinate map, the center of the surface and middle recirculation zone is approximately located at X � −5 m and Y � 11 m. e bottom recirculation zone center is at X � −4 m and Y � 9 m. e flow velocity in the mainstream zone is always greater than that in the recirculation zone.     Figure 11 is a 2-2 plane velocity vector diagram. e profile position is X 2 � −0.5 m, near the entrance of the flow passage, and the water in the forebay has an angular deflection to the left due to the influence of the lateral water inflow. e water flow in the forebay near the inlet of 1# inlet passage is the most skewed, and the flow is turbulent. Figure 12 is a 1-1 plane velocity cloud diagram. e section location is X 1 � 0.01 m. e inlet flow patterns of 2# and 3# inlet passages are better, the velocity distribution is relatively uniform, and the overall distribution is symmetrical. However, the water flow at the inlet of the 1# passage is severely skewed due to the influence of the backflow in front of the passage. e high-speed area occurs on the left side, and the velocity distribution is extremely uneven. e uniformities of the flow velocity distribution of 1#, 2#, and 3# passages are 78.05%, 90.78%, and 91.38%, respectively. e weighted average angles of the inlet sections of 1#, 2#, and 3# passages are 63.90°, 71.37°, and 70.41°, respectively.
In summary, the bottom water flow backflow area is the largest for the forebay with 45°and 60°lateral angles due to the large lateral velocity of the mainstream at this location, and the large-scale recirculation it forms compresses the streamlines of the mainstream area outward. e recirculation area occurs before the 1# inlet passage. According to the location where the recirculation zone occurs, the water inlet conditions of the 1# inlet flow passage are affected, which may endanger the safety of the pump.

Conclusion
Numerical simulations, including model establishment, setting of boundary conditions, and grid independence analysis, are carried out on the design schemes of the forebay of the inlet pumping station at 45°and 60°lateral angles. e turbulence model used is the standard k-ε model. rough comparative analysis of the numerical simulation results, the following conclusions are drawn: (1) For the side-inlet pump station, the flow pattern of the water in the front tank is poor during operation, a large-scale return zone is observed, and the flow velocity distribution at the inlet of the 1# passage is extremely uneven. (2) Comparing the numerical simulation results of the 45°lateral bending angle and the lateral 60°bending angle reveals that the larger the lateral bending angle of the forebay is, the worse the flow pattern of the water flow, and the more unfavorable the pump operation. (3) Effective engineering measures must be taken to improve the flow pattern in the forebay of the pumping station and ensure the efficient operation of the pumping station.

Data Availability
e curve data used to support the findings of this study are available from the corresponding author upon request.