The numerical simulation of draft tube cavitation in Francis turbine at off-design conditions

Abstract

Purpose – The vortex ropes in draft tube of Francis turbine always cause fluctuation and vibration, which consequently threaten the safety and stability of hydro turbines. The purpose of this paper is to use a cavitation flow computational method to simulate spiral vortex ropes under part load conditions and columnar vortex ropes under high-load conditions in draft tube. The unsteady cavitating flow characteristics in draft tube and its interaction with runner cavitation were analyzed. Design/methodology/approach – The calculation method was verified by cavitation simulation around a 3D hydrofoil. The results show that the Large Eddy Simulation (LES) turbulence model with the Zwart-Gerber-Blemari cavitation model have comparative advantage in cavitation simulations whether from capture of cavity shape or prediction of pressure changes. So it was chosen to simulate the two-phase cavitation flow in Francis turbine. The boundary conditions for inlet and outlet were set to inlet total pressure and outlet static pressure. The finite volume method with the central difference was adopted to discretize the equations. Findings – The calculated Thoma number agreed well with the experimental data. The vortex rope diameter and length increased with the cavitation development for both of the two types of vortex ropes conditions. The maximum peak-to-peak values of pressure pulsations located in the draft tube elbow part under all of the Thoma numbers conditions. Under spiral vortex rope conditions, the pressure pulsation in the same section of draft tube cone show obviously phase shift. The vortex rope affects the development of runner cavitation, which induces the symmetric and axisymmetric cavitation region in the suction side of blades for spiral and columnar vortex rope condition, respectively. Research limitations/implications – The mesh independence had been checked only in non-cavitation flow; in addition, the mesh density did not well satisfy the requirements of LES due to the limitations of computing power. The higher mesh density on a simplified model with one blade flow path and the entire draft tube may be helpful for obtaining more precise results. Originality/value – The spiral and columnar vortex ropes in a Francis turbine were compared and analyzed. The annular hydraulic jump appeared in the columnar vortex rope conditions has little effects on the pressure pulsations. The uneven flow field caused by spiral vortex led to the asymmetric cavitation development.