THERE DIMENSIONAL VORTEX METHOD SIMULATION OF UNSTEADY FLOW IN HYDRAULIC TURBINE

A fast Lagrangian vortex method presented in this paper is employed to simulate the flow inside a francis turbine runner. The normal flux boundary condition is satisfied by superimposing a potential flow on the vortical field, which is solved by the boundary element method (BEM), while the no-slip boundary condition is by generating vortex tiles on solid boundaries. The generalized Biot-Savart's law is adopted to calculate the vortical field in the Lagrangian frame of reference and the adaptive fast multipole method is utilized to reduce the computation complexity. The calculation results of a sample Francis turbine on design condition and off-design conditions agrees adequately well with experiment data, which confirms that the method is verified and practicable to simulate the complex interior unsteady flow with high Re.