## 4 Result and Discussion
### Water Hammer Change Rule of End Valve Under Different Influencing Factors  
Based on the above research results, during the first-stage linear valve closure process at the power station, when the shutdown time for large units is 12 s and for small units is 10 s, the valve closure program at the terminal valve meets the safety requirements outlined in the design and the water hammer pressure complies with the relevant standards. Furthermore, the study indicates that the maximum water hammer pressure occurs at the terminal valve in gravity-flow power stations. Based on the results of a previous study, during the linear shutdown process at the power plant, a shutdown time of 12 s for the large unit and 10 s for the small unit ensures that the terminal valve closure procedure meets the design safety requirements, and the water hammer pressure complies with the relevant standards. Additionally, it was found that in gravity-flow power plants, the maximum water hammer pressure occurs at the terminal valve. To further explore the relationship between the valve diameter, distance, and quantity, this study compared and analyzed the closure of large- and small-diameter valves to assess their effect on the water hammer phenomenon at power stations [44]. To ensure the consistency of the research variables, we first conducted simulations using two-dimensional computational software under a 12 s single-stage linear valve closure scenario for fully closed conditions. The comparative results indicate minimal differences. Consequently, in the three-dimensional simulations, the valve closure strategies for all scenarios were standardized to a 12 s single-stage linear closure to better align the computational results with real-world conditions. Moreover, the study investigated the impact of valve quantity on the water hammer pressure by analyzing the closure of 2, 3, and 4 valves. Finally, three-dimensional flow patterns within the pipeline were simulated using CFD to provide a theoretical foundation for optimizing the valve closing procedure and mitigating the water hammer effect. The pipeline geometry in the CFD analysis was based on the actual conditions. The main pipeline diameter was 4.1 m, whereas the valve and upstream pipeline diameters corresponded to the unit size, with the valve diameter set to 1.9 m for the large units and 1.1 m for the small units. An unstructured mesh generation method was employed to ensure the computational accuracy of the complex pipeline geometry. The material properties of the pressure steel pipes, including an elastic modulus of 2.06 GPa and Poisson's ratio of 0.3, were based on the conditions at the New Longkou Hydropower Station and were used as boundary condition inputs to reflect the actual material characteristics. Additionally, the valve opening and closing processes were precisely controlled using user-defined function (UDF) technology, enabling the accurate simulation of various valve closure strategies. 3.1 Analysis of the Effect of Different Diameters of the Turn-Off Pipe on the Change of Water Hammer Pressure  
Positions a1, b1, c1, and d1 correspond to the centerline locations of the pipelines upstream of valves D1, D2, X1, and X2, respectively. For ease of detection, all monitoring points were positioned 2 m upstream of their respective valves. The specific locations are shown in Figure 3.  
This figure illustrates the water hammer pressure responses for different pipeline diameters and valve closure configurations. Each subplot (I-IV) corresponds to different valve closure strategies, with conditions 1 and 2 in the figure representing the water hammer pressure curves at the terminal valves of pipelines with different diameters. In each subplot, curves a1, b1, c1, and d1 represent the pressure variations at the terminal valve monitoringpoints, whereas curves a, b, c, and d indicate the pressure variations at the monitoring points with the valve open.