Analysis of the internal flow behavior on S-shaped region of a Francis pump turbine on turbine mode

Purpose - The purpose of this paper is to numerically analyze the flow characteristic and to explore the hydrodynamic mechanism of the S-shaped region formation of a Francis pump-turbine. Design/methodology/approach - Three-dimensional steady and unsteady simulations were performed for a number of operating conditions at the optimal guide vanes opening. The steady Reynolds averaged Navier-Stokes equations with the SST turbulence model were solved to model the internal flow within the entire flow passage. The predicted discharge-speed curve agrees well with the model test at generating mode. This paper compared the hydrodynamic characteristics of for off-design cases in S-shaped region with the optimal operating case, and more analysis focusses particularly on very low positive and negative discharge cases with the same unit speed. Findings - At runaway case toward smaller discharge, the relative circumferential velocity becomes stronger in the vaneless, which generates the "water ring" and blocks the flow between guide vane and runner. The runner inlet attack angle becomes larger, and the runner blade passages nearly filled with flow separation and vortexes. The deterioration of runner blade flow leads to the dramatic decrease of runner torque, which tends to reduce the runner rotation speed. In this situation, the internal flow cannot maintain the larger rotating speed at very low positive discharge cases, so the unit discharge-speed curves bend to S-shaped near runaway case. Originality/value - The analysis method of four off-design cases on S-shaped region with the comparison of optimal operation case and the calculated attack angles are adopted to explore the mechanism of S characteristic. The flow characteristic and quantitative analysis all explain the bending of the unit discharge-speed curves.