Simulation and Analysis of Real-Time Coupling of Free-Surface Flow and Pressure Flow in Hydropower Station Tailrace Tunnels Based on the Finite Volume Method

Accurate water hammer calculations are crucial for hydraulic safety and unit stability in hydropower systems with free-surface tailrace tunnels. However, existing models often neglect hydraulic variations in free-surface sections, while the commonly used method of characteristics tends to cause numerical instability and dissipation due to interpolation or wave speed adjustments, leading to significant computational errors. Aiming at the transient process of hydropower stations with free-surface tailrace tunnels and fully considering the influence between pressure and free-surface conditions, this study employs the second-order Godunov scheme to solve the governing flow equations for pressurized and free-surface flows. A generalized boundary of the regulating pool and a variable time step calculation method were proposed to solve the problem of real-time coupling calculation in the pressure–free-surface transition area. The results show that during the large fluctuation transient process, the hydraulic characteristics of the free-surface flow have little impact on the inlet pressure of the unit’s volute and the unit’s rotational speed but have a significant impact on the fluctuation period and extreme value of the inlet pressure of the draft tube. During the small fluctuation transient process, the hydraulic characteristics of open channel flow are beneficial for improving the unit’s regulation quality. This indicates that considering the hydraulic characteristics of free-surface flow is of great significance for realizing an accurate simulation of the transient process of hydropower stations.