For a water diversion hydropower system with a flat ceiling tail tunnel with high elevation, during transient states with relatively low tail water levels, free-surface-pressurized flow inevitably appears and its transient characteristics have obvious effects on the system’s operating stability. Using Newton–Raphson linearization in the characteristic implicit format for modeling of the free-surface-pressurized flow in the tail tunnel, the mathematical models for necessary boundary conditions were derived and linear algebraic equations with a band coefficient matrix were grouped for further transient simulation. Then, a unified mathematical model was established for hydraulic transient analysis of the hydropower system with free-surface-pressurized flow. Combined with experimental research and numerical simulation, the wave speed for the free-surface-pressurized flow was experimentally analyzed for further correctness in the unified model, and by comparative analysis the hydraulic characteristics of the free-surface-pressurized flow in the flat ceiling tail tunnel were investigated. It was found that the derived mathematical model can basically represent water behaviors in the water-surface-pressurized flow, the wave speed for the mixed water-surface-pressurized flow can be set to approximately 50m/s, and with this correctness the numerical results are in good agreement with the experimental results. Therefore, the obtained mathematical model combined with an experimental wave speed or a reference wave speed of 50 m/s for the free-surface-pressurized flow is preferable during the design stage of the hydropower system.
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