Analysis and optimization of flow pattern in the forebay of shaft-inflow pumping station based on response surface method

Shaft-inflow pumping stations have frequently been constrained to the urban and rural planning, as well as the land use. For instance, the mainstream deviation and backflow are prone to occur, leading to poor inflow conditions in the design-constrained shaft-inflow pumping station, particularly harmful to the safe, stable, and efficient operation. The shaft-inflow pumping station can distribute the water into the forebay through the bottom pipe culvert and the inlet shaft, thus resulting in the complex flow in the forebay. The water flow in the forebay and inlet sump is often characterized by the concentrated mainstream and uneven velocity distribution in the vertical direction. This study aims to improve the flow pattern of the shaft-inflow pumping stations. Numerical simulation and physical model tests were also adopted to determine the low flow pattern in the forebay of a shaft-inflow pumping station under the rated operating flow rate of 28.92 m³/s. Among them, the inlet boundary was set as the pressure inlet, while the outlet boundary was set as the mass flow outlet, and the walls were set as the non-slip wall. On the water surface, the numerical simulation of the volume of fluid (VOF) and the rigid-lid hypothesis were compared to consider the calculation cost and efficiency. The rigid lid hypothesis was ultimately adopted to simulate the water surface. Qualitative and quantitative analysis was conducted using the rotation correction factor, velocity uniformity, and global reflux coefficient. The various types of diversion pier were rectified on the flow pattern in the forebay. The final optimization of the diversion pier was recommended using the response surface method (RSM). The results show that a significant mainstream diversion appeared in the forebay, and then a large-scale reflux zone was formed, due to the bottom inflow and excessive diffusion angle. The hydraulic performance of the pumping station was obtained after optimization. Compared with the vorticity, the rotation correction factor was used to effectively characterize the large-scale reflux zone in the forebay of the pumping station. A comparison was also made on the rectification of the diversion piers configuration in front of the forebay and inside the box culvert. The diversion piers were used to adjust the flow pattern, where the mainstream was guided to uniformly spread in the forebay. Diversion piers were arranged inside the box culvert in order to improve the flow pattern in the forebay. The diversion pier configuration was then optimized in the box culvert using RSM. There was a relatively strong correlation between the distance between the head of diversion pier and the outlet of box culvert X and the angle between the diversion pier and the pumping station θ. The objective function S was solved within the ranges of 1.619 75D ≤ X ≤ 1.835 01D, 0.660 369D ≤ b ≤ 0.665 309D, and 7.475 56β ≤ θ ≤ 8.25 672β. The optimal combination of the diversion pier was obtained: the distance between the head of the diversion pier and the outlet of box culvert X was 1.740D, while the distance between the head of the diversion pier and the inner wall of box culvert b was 0.662 5D, and the angle between the diversion pier and the pumping station θ was 0.333β. The uniform velocity and the global reflux coefficient of the optimal scheme increased by 28.02% and 13.72%, respectively, compared with the scheme without a diversion pier. Finally, the numerical simulation was verified through physical model tests. The surface flow pattern after numerical simulation was similar to the physical test. The relative errors of the hydraulic loss and mean velocity in the forebay were less than 5% and 9%, respectively, indicating the accurate simulation and the reliable optimization scheme. The finding can also provide the theoretical and technical support to the safe and stable operation of the shaft-inflow pumping station.