Development and application of modified partially averaged Navier Stokes in the internal flow field of a Francis turbine

The load regulation capability of hydropower station ensures power system efficiency and stability while supporting the development of renewable energy-integrated smart grids. Seeking a better way to study internal fluid characteristic and performance of turbine is a long-standing subject, numerical simulation demonstrates significant advantages due to its cost-effectiveness and fully visualization capabilities, with turbulence models playing a pivotal role in ensuring simulation precision. A dynamically defined MPANS (Modified Partially Averaged Navier Stokes) turbulence model is developed in this work by integrating considerations of real-time turbulence scale and mesh size. Comparative analyses between experimental data and numerical results reveal that the MPANS model exhibits a higher degree of agreement with experimental data. Compared with RNG (Renormalization Group) k-ε model, MPANS significantly reduces the maximum deviations in torque, efficiency, and water head. Under steady conditions, the vortex volumes captured in the runner and draft tube are increased by 18% and 126% with MPANS, respectively, relative to those predicted by the RNG k-ε model. Under load-increasing condition, the vortex volumes in the runner and draft tube show increases of approximately 6% and 87% with MPANS, respectively. Parameter like eddy viscosity is considered based on flow characteristic, MPANS demonstrates enhanced capability in resolving intricate details of vortex structure and offers a more comprehensive depiction of dynamic vortex evolution, under both steady and transient condition of Francis turbine.