Investigations of Compressible Turbulent Flow in a High-Head Francis Turbine

Abstract

Dynamic stability of the high-head Francis turbines is one of the challenging problems. Unsteady rotor–stator interaction (RSI) develops dynamic stresses and leads to crack in the blades. In a high-head turbine, vaneless space is small and the amplitudes of RSI frequencies are very high. Credible estimation of the amplitudes is vital for the runner design. The current study is aimed to investigate the amplitudes of RSI frequencies considering a compressible flow. The hydro-acoustic phenomenon is dominating the turbines, and the compressibility effect should be accounted for accurate estimation of the pressure amplitudes. Unsteady pressure measurements were performed in the turbine during the best efficiency point (BEP) and part load (PL) operations. The pressure data were used to validate the numerical model. The compressible flow simulations showed 0.5–3% improvement in the time-averaged pressure and the amplitudes over incompressible flow. The maximum numerical errors in the vaneless space and runner were 6% and 10%, respectively. Numerical errors in the instantaneous pressure amplitudes at the vaneless space, runner, and draft tube were ±1.6%, ±0.9%, and ±1.8%, respectively. In the draft tube, the incompressible flow study showed the pressure amplitudes up to eight times smaller than those of the compressible. Unexpectedly, the strong effect of RSI was seen in the upper and lower labyrinth seals, which was absent for the incompressible flow.