## 1 Introduction  
In recent years, China has made significant progress in addressing the supply-demand contradiction of water resources. For example, in long- and medium-distance pressurized water pipeline projects, the relatively low requirements of geological conditions and the external environment for pressurized water pipelines have led to their widespread application in practical engineering [1]. However, when a pump station or hydropower station in a water conveyance system unexpectedly experiences a load drop due to failure, the energy within the pipeline system can cause oscillations in the form of water hammer waves after the valves are closed [2; 3; 4]. The increase in pressure can result in pipe bursts. Moreover, the transient flow associated with the water hammer can create negative pressure within the pipeline, thereby jeopardizing the safe operation of the hydropower station. Therefore, the calculation and protection against water hammers in pipeline systems are common and critical aspects of water diversion engineering [5; 6; 7; 8; 9]. With the continuous expansion of hydraulic engineering projects, the water hammer effect and its associated transient pressure issues in pipelines have gradually become an active area of research. In recent years, several studies have been conducted domestically and internationally in areas such as fluid forces, hydraulic circuit design, and water hammer protection [10; 11; 12; 13]. For instance, [PERSON] et al. [14] employed configurable hydraulic circuits to comprehensively measure flow and pressure under conditions of fixed and variable delivery heads, providing valuable experimental data for subsequent studies. However, this study lacked an in-depth exploration of the mechanisms underlying water hammer wave propagation. Similarly, [PERSON] [15] demonstrated that water hammer pressure transients could cause severe damage to critical components of RCS supply pipelines, such as pressure sensors, and highlighted the potential risks and hazards of this phenomenon to water supply systems. Nevertheless, the study fell short in its computational analysis of the water hammer phenomena in multibranch pipelines. [PERSON] et al. [16] demonstrated that improving the single and double coefficients in the IAB friction model, along with increasing the rotational inertia and employing reasonable valve operation methods, helps to control transient pressure changes in the fluid. That approach can effectively reduce the severe impact of water hammer waves on valves and manage the water hammer without the need for additional protective devices. However, increasing the rotational inertia necessitates the introduction of more efficient turbines, which can lead to higher economic costs in practical engineering. Therefore, this study primarily focused on researching the effective control of water hammer through appropriate valve closure procedures. Some scholars [5; 17; 18; 19; 20; 21] have also investigated the use of guide vane closure to control a water hammer, which is regarded as a mainstream research method. However, in scenarios where hydraulic turbines experience load dumping, the effects of guide vane closure render this method less applicable. Consequently, this study focused on the closure procedure of the worm gear valve at the front end of the turbine to manage water hammer, as this approach is more conducive to addressing various conditions in practical engineering projects. Most research methods that utilize valve control to manage a water hammer involve calculations based on the method of characteristics (MOC), which effectively simulates the propagation process of a water hammer [22]. This study employed a two-dimensional simulation software to model the water hammer phenomenon at the Longkou Hydropower Station under various load rejection conditions. Additionally, three-dimensional simulations were utilized to perform a detailed analysis of the flow pattern variations within the pipeline.