The Influence of Geometric Parameters of Pump Installation on the Hydraulic Performance of a Prefabricated Pumping Station

: A prefabricated pumping station is a new type of pumping station that plays an important role in the construction of sponge cities in developing countries. It solves the problem of urban water-logging and makes great contributions to the sustainable development of water resources. In order to research the influence of different installation positions of pumps on the internal hydraulic performance of a prefabricated pumping station, based on ANSYS software, the computational fluid dynamics (CFD) numerical simulation method was used to analyze the internal flow state of the prefabricated pump station. In this research, the optimal geometric parameters of pump installation in a prefabricated pumping station are given. The results show that when the distance between the connecting line of two pumps and the center of the sump is L = 0.2 R , the distance between the two pumps is S = 0.6 R , and the suspension height of the two pumps is H = 0.6 D , the internal flow pattern of the prefabricated pump station is better. ( R is the cross-sectional radius of the sump and D is the diameter of the nozzle of the pump horn.) These research results have certain guiding significance for improvement of the hydraulic performance and operation efficiency of prefabricated pump stations. They also provide a theoretical basis for parameter selection for prefabricated pumping stations.


Introduction
With the acceleration of the urbanization process in developing countries, as well as the construction of various infrastructure, more and more wastewater needs to be lifted and transported by pumping stations. In the sewage treatment system, the sewage treatment plant is the "kidney", the pipelines are the "blood vessels", and the pumping stations all over the city are like "hearts", which continuously and stably transport the collected sewage to the treatment center after pretreatment. Traditional concrete pumping stations have the disadvantages of large area, difficult planning, long construction period, and high cost. When the concrete pump station is put into use, due to the low level of integration and automation, it needs to be manually kept on duty and maintained.
A prefabricated pumping station is a kind of pumping station which integrates the storage tank, pump, pipeline, control system, and ventilation system. The pre-installation and testing are completed before delivery [1]. The cylinder of the prefabricated pumping station is made of glass-fiber-reinforced plastics (GFRP) or high-density polyethylene (HDPE). It has the characteristics of light weight, high strength, and strong corrosion resistance. The prefabricated pumping station is equipped with two submersible sewage pumps, automatic coupling device, guide rod, lifting chain, inlet pipe, check valve, gate valve, and outlet pipe [2] (Figure 1). With the construction of sponge cities in developing countries, prefabricated pumping stations have gradually become the first choice for municipal drainage systems. As a substitute for small and medium-sized concrete pumping stations, prefabricated pumping stations contribute to the treatment of urban water-logging, which is of great significance to the sustainable development of water resources.
(a) (b) The working environment of the submersible sewage pump in a prefabricated pumping station is similar to that of the pump in a traditional pump station with closed intake sump [3][4][5]. Both of them have no free water surface, and the pump directly absorbs water without passing through the inlet pipe or channel. In this respect, domestic and foreign scholars have made great achievements in experimental research and optimization design [6,7]. Charles [8] put forward that the average velocity in the pool should be kept at about 0.3 m/s when the width of the inlet pool is designed. Iversen [9] gave the range of submergence depth of a high-specific-speed intake tank. Following from a tremendous number of experiments, Japan Association of Agricultural Engineering Enterprises [10] gave reference value ranges for the important dimensions of pump suspension height, submergence depth, back wall distance, pool width, and pool length. Fraser [11] studied the vortex problem in the intake pool of a pumping station and put forward a solution. Nsar [12] analyzed the flow pattern in a pump inlet tank with and without tangential reflux at the inlet of the rectangular inlet tank.
So far, many scholars have also conducted relevant research on prefabricated pumping stations. Liu Q.et al. [13] used computational fluid dynamics (CFD) methods to optimize the geometric parameters of storage tanks in prefabricated pumping stations. The relationship between tank bottom diameter and tank height was studied, and the basic mechanism of sediment deposition in prefabricated pumping stations was expounded. Based on the discrete solid-liquid two-phase flow model (DPM) and MATLAB image processing technology, Kang W.et al. [14] analyzed the settlement characteristics of a prefabricated pumping station under the action of a single pump and double pumps and measured the movement track of sediment particles at the bottom of the pump station. Qing L.et al. [15] revealed the flow characteristics of water and sediment in the prefabricated pumping station and optimized the geometric parameters of the water tank to reduce sand deposition. The results show that the risk of sediment (http://creativecommons.org/licenses /by/4.0/). deposition is high at the bottom side near the inlet of the pumping station, and the geometry of the pump bottom and the suction of the pump inlet are conducive to sand deposition. Due to the lack of suitable dispatching facilities in the drilling area of southern Mexico, Medina, A P [16] proposed a design scheme of a closed circulating prefabricated pumping station. Hu et al. [17] optimized the effective volume of the prefabricated pumping station through calculation. In order to reduce the volume of the integrated prefabricated pumping station, the minimum start-up and stop time interval of the pump was derived. Hu [18] proposed a self-cleaning solution to solve the problem of residual debris and deposition inside prefabricated pumping stations. Cheng Li et al. [19] invented a self-cleaning measure for the bottom of prefabricated pumping stations. An arc rib embedded in the bottom of the tank surface was used to realize self-cleaning.
Previous studies on integrated pumping stations focus on the submersible centrifugal pump and its specific applications in engineering. However, there are few studies on the influence of the geometric parameters of a submersible axial-flow pump on prefabricated pumping stations. Based on computational fluid dynamics (CFD), the influence of the geometric parameters of the submersible axial-flow pump installation position on the internal hydraulic performance of a prefabricated pump station is studied and analyzed herein. The optimal geometric parameters of pump installation are thus recommended. This can improve the pump station's internal flow pattern and improve its operation efficiency. At the same time, the research results also provide a theoretical basis for parameter selection for prefabricated pumping stations.

Hydrodynamic Equations
The Navier-Stokes (N-S) equation is a motion equation describing the momentum conservation of viscous and incompressible fluid. The N-S equation is composed of three equations of fluid flow: the mass conservation equation, momentum conservation equation, and energy conservation equation. These correspond to the three conservation laws, namely, the law of conservation of energy, the law of conservation of momentum, and the law of conservation of mass. The expression of the N-S equation in the rectangular coordinate system is [20,21] where i u is the three-dimensional velocity component, i x is the three-dimensional coordinate component, p is the pressure, i g ρ is the gravity term, and i F is the external source term. ij τ is the stress tensor, its expression is as follows: where ij μ is the dynamic viscosity and ij δ is the Kronecker dela sign (when i = j, ij δ =1; when i ≠ j, ij If the influence of gravity is neglected, the momentum equation can be simplified to The Reynolds averaged N-S (RANS) equation is based on the time-averaged treatment of the transient N-S equation and supplemented with other equations reflecting the turbulence characteristics. The turbulence model theory based on the Reynolds averaged N-S equation has become the mainstream theory in the calculation of pump internal flow fields [22,23].
The time mean and fluctuating values of velocity and pressure are decomposed as follows: where is the instantaneous velocity in direction i, is the average velocity in direction i, is the pulsating value of velocity in direction i, ̅ is the mean pressure, and is the pulsating pressure. By substituting the above two equations into (1) and (4), the timeaveraged N-S equation can be obtained.
Continuity equation: Momentum equation: Equations (7) and (8) are the mathematical expressions of the RANS equation. The internal flow of a prefabricated pumping station is unsteady viscous flow. Therefore, the RANS equation was used as the basic governing equation to describe the flow law.
In the process of numerical simulation, the meshing software ICEM CFD of ANSYS, the fluid analysis software ANSYS CFX, and the visualization post-processing software Tecplot were used.
ANSYS CFX is a mature commercial fluid computing software with the most advanced algorithm in the world, which adopts the full implicit algorithm. Its rich physical models and the perfection of preprocessing and post-processing give CFX excellent performance in terms of the accuracy, stability, speed, and flexibility of results [24][25][26]. It includes three parts: CFX-pre, CFX-solver, and CFX-post. Figure 2 shows the structure of the prefabricated pumping station model. The numerical calculation area includes one collecting basin, one water inlet, two outlet pipes, and two symmetrical submersible axial-flow pumps. The pump includes an impeller, guide vane, and two submersible motors. According to the relevant literature and the operation practice recommended by the manufacturer [27,28], the relationship between the effective volume of the storage tank and the flow rate of the prefabricated pumping station is V = Qb/4Zmax, where Qb is the pump flow and Zmax is the maximum number of starts and stops (10~30 times/hour). A Zmax value of 15 times/hour was used to match the relationship between the effective volume and the flow rate of the pump. The water body of the tank was selected as a cylinder with diameter and height of 1 m in the research. The design flow of each single pump was 198 m 3 /hour. The impeller diameter of the pump was 120 mm, the number of blades was 3, and the speed was 2400 rev/min. The two pumps were run at the same time.

Mesh Generation and Grid Independence Examination
The grid was divided into blocks. The prefabricated pumping station was divided into a sump, two pairs of impellers and guide vanes, two trumpet pipes, and two outlet pipes. As shown in Figure 3a, the impeller and guide vane were meshed using ICEM CFD. As shown in Figure 3b, an unstructured tetrahedral mesh was used in the mesh of the workbench for the sump and pipeline.
We mainly checked the grid independence of the main part of the sump. The number of grid cells ranged between 900,000 and 1,300,000, and the efficiency of Pump I was used as the evaluation index. As can be seen from Table 1, the total number of grid cells used was 1,213,025.

Turbulence Model
The standard − turbulence model was proposed by Lauder B E and Spalding D B [29]. Based on the turbulent kinetic energy ( ) equation, the turbulence dissipation rate ( ) equation is introduced into the turbulence model to form a two-equation model. The standard − turbulence model is the most widely used turbulence model at present and is suitable for the fully developed turbulence calculation model with high Reynolds number [30]. We chose the standard − turbulence model in this research. In the model, the turbulent dissipation rate is defined as The turbulent viscosity can be expressed as The equations of the turbulent kinetic energy and turbulent energy dissipation are as follows: where is the production term of turbulent kinetic energy caused by buoyancy: , , and are empirical constants, with = 0.09, = 1.44, and = 1.92; and are the Prandtl numbers corresponding to the turbulent kinetic energy and dissipation rate , respectively, where = 1.0 and = 1.3.

Boundary Conditions
The boundary conditions have a very important influence on the numerical calculation. The boundary conditions not only need to consider the influence of the turbulence model but also must be consistent with the physical model.
There are five boundary types in ANSYS CFX, which are inlet, outlet, opening, wall, and symmetry. The inlet boundary condition was set at the inlet section of the prefabricated pumping station. The outlet condition was set at the outlet section of the prefabricated pumping station. In this paper, the pump impeller is a rotating area, and the guide vane is a stationary area. The "Frozen rotor" was adopted for the type of dynamic and static interface. The specific conditions are shown in Table 2.

Geometric Parameters of Submersible Axial-Flow Pump Installation
The geometric parameters of pump installation include L (the distance between the connecting line of the two pumps and the center of the sump), S (the distance between the two pumps), and H (the suspension height of the two pumps).
As shown in Figure 4, Section 1-1 is the longitudinal section of the two pumps perpendicular to L. Section 2-2 is the left longitudinal section at the center of Pump I and the right longitudinal section at the center of Pump Ⅱ. The outlet pipe of Pump I is Pipe I, and that of Pump Ⅱ is Pipe Ⅱ. Section 3-3 is the cross section between the sump bottom and the pump inlet. Section 4-4 is the cross section of the pump suction.  The geometric parameters of the pump installation position in the prefabricated pumping station were researched by a single-factor analysis method. Using a single-factor analysis method means that when one factor is analyzed, the other factors are fixed. This method can reasonably arrange research schemes, reduce the required number of studies, and quickly find the best scheme. Table 3 shows the parameter settings of the research schemes. R is the cross-sectional radius of the sump and D is the diameter of the nozzle of the pump horn. Table 3. Single-factor geometric parameter schemes.

Influence of L on Hydraulic Performance
In order to explore the influence of different L values on the hydraulic performance of the prefabricated pumping station, we set the inlet mass flow to Q = 55 kg/s, the suspension height of the pump to H = 0.6 D, and the distance between the two pumps to S = 0.6 R. The respective internal flow characteristics of prefabricated pumping stations with L = 0.2 R, L = 0.4 R, and L = 0.6 R were then determined. Figure 5a shows the curve of the influence of L on the efficiency of the two pumps. According to the curve, the influence of L on pump efficiency is small. The efficiency of Pump I was about 4% higher than that of Pump II due to the influence of asymmetric flow and pump suction in the sump. Figure 5b shows the variation curve of inlet velocity uniformity of the pump impeller chamber with L. According to the curve, when L = 0.4 R, the uniformity of the flow rate at the pump inlet was the highest. The uniformity of flow velocity at the inlet of Pump I was 1~4% higher than that of Pump II. Figure 5c shows the curve of the weighted average angle of inlet velocity of the pump impeller chamber with L. It can be seen from the curve that the inlet velocity weighted average angle of the Pump I impeller chamber increased slowly with increasing L. However, the weighted average angle of the impeller chamber inlet velocity of Pump II showed a gradual downward trend with increasing L. The weighted average angle of inlet velocity of Pump I was higher than that of Pump II.   It can be seen from Figure 7; Figure 8 that vortices and high-speed zones appeared below the water inlet of the water pump. It can be seen from the velocity distribution diagram that the velocity in the central area of the sump was the highest, and the velocity gradually decreased with decreasing distance from the wall. When L = 0.2 R, the efficiency of the two pumps was the highest, and the weighted average angle of the impeller chamber inlet velocity was the largest.

Influence of S on Hydraulic Performance
The inlet condition was kept unchanged, the suspended height was set to H = 0.6 D, and the distance between the connecting line of the two pumps and the center of the sump was set to L = 0.2 R. The hydraulic performance of prefabricated pumping stations with S = 0.6 R, S = 0.8 R, and S = 1.0 R was then studied. Figure 9a shows the curve of the influence of S on the efficiency of the two pumps. According to the curve, the efficiency of Pump I was higher than that of Pump II. The efficiency of Pump I was the highest when S = 0.8 R, and the efficiency of Pump II decreased with increasing S. Figure 9b shows the variation curve of inlet velocity uniformity of the pump impeller chamber with S. It can be seen from the curve that with increasing S, the uniformity of flow velocity at the pump inlet decreased. Figure 9c shows the curve of the weighted average angle of the inlet velocity of the pump impeller chamber with S. It can be seen from the curve that the influence of S on the weighted average angle of the impeller inlet velocity in Pipe I was greater than that in Pipe II. The weighted average angle of the impeller inlet velocity of Pipe I was higher than that of the impeller inlet of Pipe II under the three schemes. It can be seen from Figure 13 that when S = 0.6 R and S = 0.8 R, the streamline distribution was relatively uniform. When the pump spacing S was increased to 1.0 R, the streamline curvature between the two pipes became slightly more serious, and a vortex appeared near the outlet pipe of Pump Ⅱ. It can be seen from Figure 11; Figure 12 that the two swirling currents converged in front of the two pumps. With increasing S, the rotation radius of the streamline increased gradually around the pipe. This made the streamline between the two pipes tend to be uniform and smooth. When S = 0.6 R, smaller vortices appeared in the lower area of the suction inlet of the two pumps, but the vortex disappeared at the suction section. At this time, the streamline and velocity distribution were symmetrical. For both S = 0.8 R and S = 1.0 R, an obvious vortex appeared in the sump near Pump II. This led to deterioration of the flow pattern near Pump II, and the efficiency of water Pump II was reduced. The distribution of the side streamline and velocity near the incoming direction was not uniform.

Influence of H on Hydraulic Performance
In order to explore the influence of different H values on the hydraulic performance of the prefabricated pumping station, we set the inlet mass flow to Q = 55 kg/s, the distance between the connecting line of the two pumps and the center of the sump to L = 0.2 R, and the distance between the two pumps to S = 0.6 R. The respective internal flow characteristics of three schemes with suspended heights of H = 0.3 D, H = 0.6 D, and H = 0.9 D were then studied. Figure 13a shows the curve of the influence of H on the efficiency of the two pumps. According to the curve, the efficiency of Pump I was higher than that of Pump II. Moreover, when H = 0.3~0.6 D, the efficiency difference between the two pumps was larger and larger, and the difference was smaller and smaller when H = 0.6~0.9 D. Figure 13b shows the variation curve of the inlet velocity uniformity of the pump impeller chamber with H. It can be seen from the curve that with increasing suspended height H, the uniformity of the flow velocity at the impeller inlet of Pipe I gradually decreased, while that of Pipe II increased gradually. The two curves intersect at H = 0.6~0.9 D. Figure 13c shows the curve of the weighted average angle of inlet velocity of the pump impeller chamber with H. It can be seen from the curve that the weighted average angle of the impeller inlet velocity in Pipe I decreased gradually and that of Pipe II increased gradually.  It can be seen from Figure 14 that when the suspended height was changed from H = 0.3 D to H = 0.9 D, the streamline curvature became larger and larger, and the degree of uniformity became worse and worse. Specifically, when H = 0.3 D, the streamline distribution was more uniform and the velocity distribution was more symmetrical. When H = 0.6 D and H = 0.9 D, it can be seen from the streamline diagram of the vertical section that the streamline curvature between the two pipelines changed greatly. A vortex gradually appeared between the two pipes, and the flow pattern was more chaotic. According to Figure 15; Figure 16, when H = 0.3 D, the streamline distribution was more symmetrical, and the velocity distribution was more symmetrical. When H = 0.6 D, the flow was no longer symmetrical to the left and right, and the convergence point of the flow shifted. When H = 0.9 D, the streamline was symmetrical and the velocity distribution was uneven. The velocity of water between the front of Pump II and the wall was higher than that of the symmetrical area, and a vortex appeared on the wall in front of Pump II.

Conclusions
In the research, CFD numerical simulation was used to explore the influence of L (the distance between the connecting line of two pumps and the center of the sump), S (the distance between the two pumps), and H (the suspension height of the two pumps) on the hydraulic performance of a prefabricated pumping station. It was observed that changes in these geometric parameters had an impact on the internal hydraulic performance of the prefabricated pump station, and the impact on the two symmetrical pumps was not the same.
(1). In this research, the optimal design parameters for the internal pumps of a prefabricated pump station were determined. When L = 0.2 R, S = 0.6 R, and H = 0.6 D, the hydraulic performance of the prefabricated pump station was better. (2). Change in L had little effect on the efficiency of the two pumps, but it had a greater impact on the inlet velocity uniformity and the velocity weighted average angle of the pump impeller chamber. When L = 0.2 R, the efficiency of the two pumps was the highest, and the weighted average angle of the impeller chamber inlet velocity was the largest. L = 0.2 R is thus recommended. (3). Change in S had little effect on the efficiency of the two pumps, but it had a greater impact on the inlet velocity uniformity and the velocity weighted average angle of the impeller chamber. When S = 0.6 R, the velocity uniformity of the impeller chamber inlet was the highest. S = 0.6 R is thus recommended. (4). Change in H had little effect on the efficiency of the two pumps, but it had a greater impact on the inlet velocity uniformity and the velocity weighted average angle of the two impeller chambers. When H = 0.6 D, the water velocity near the pump inlet was lower, but at H = 0.9 D, the inlet velocity of the pump was higher. Considering the discharge of a pumping station, the velocity of the bottom water should reach the starting speed of impurity particles. If the suspended height of the pump is too high, the bottom velocity will be low, which is not conducive to sewage discharge from the prefabricated pump station. H = 0.6 D is thus recommended.