## 1 Introduction
Using two-dimensional vector field plots generated from three-dimensional simulations, this study further investigated the flow characteristics at specific cross sections of critical pipeline nodes. In addition to two-dimensional water hammer calculations, numerous studies have utilized computational fluid dynamics (CFD) to analyze the water hammer phenomenon. [PERSON] et al. demonstrated the advantages of combining the MOC and CFD for the dynamic analysis of pump station systems. The MOC effectively describes the fluid propagation characteristics within pipelines, whereas CFD can simulate the internal flow and cavitation phenomena within pumps. The integration of these methods allows for a more accurate analysis and prediction of the pump system performance under varying operational conditions [23]. Similarly, [PERSON] et al. described the accuracy and computational efficiency of using CFD for transient flow analysis [24]. Although CFD provides precise flow predictions, its computational requirements are significant. Therefore, optimizing the computational process and algorithms is critical for engineering applications. This study adopted a combined two- and three-dimensional approach to analyze the water hammer phenomenon at the Xinlongkou Hydropower Station. The aforementioned studies cover analyses of water hammers in long-distance pipelines and localized water hammers under laboratory conditions. However, in practical engineering applications, it is essential to consider factors such as the project characteristics and construction conditions. Therefore, experimental or simulation-based evaluations are necessary to guide engineering construction. In conclusion, the theoretical analyses and methodologies for local water hammer in pipelines under long-distance and laboratory conditions are well established. However, in practical engineering applications, it is crucial to consider various factors, such as the specific characteristics of the project and construction conditions, and conduct research tailored to the unique features of each case. For example, the Xinlongkou Power Station, which is part of the second-stage hydropower project of the Kuitun River diversion in Xinjiang, presents a pipeline layout with short distances and high drops. Additionally, the flow of the river is primarily sourced from snowmelt, which causes significant fluctuations in flow due to temperature changes. Consequently, turbine operation and shutdowns must be carefully managed to balance power generation with downstream agricultural water use. Therefore, valve closure methods and processes are of considerable importance. Moreover, because the plant design combines both large and small turbines, factors such as spacing, quantity, and diameter of valves play a significant role in influencing the water hammer effect during operation. [PERSON] [25] developed a valve closure function to investigate the impact of V-shaped notches on valve flow control and water hammer suppression, thereby providing valuable insights into the linear throttling behavior of gate valves during the closing process. [PERSON] [26] systematically analyzed the effects of progressive valve closure on water hammer pressure under various pipeline characteristics and operational conditions, offering useful guidance on optimal valve closing strategies. [PERSON] [27] employed CFD methods to examine the variations in water hammer pressure under different closure times and patterns for ball valves, demonstrating the correlation between the closing speed and water hammer intensity, and highlighting that extending the closing time can effectively reduce the maximum water hammer pressure. [PERSON] [28] combined physical experiments and computational methods and compared the water hammer processes for different pipe materials and valve types, emphasizing the critical influence of valve closure characteristics on the dynamic water hammer process.