Numerical investigation of the cavitation dynamic parameters in a Francis turbine draft tube with columnar vortex rope

The cavitation developed in the Francis turbine draft tube is known to be a source of the hydraulic instability,especially under the conditions with columnar cavitation vortex rope occurring in the draft tube.The hydraulic system will suffer from the risk of the self-excitation and the high pressure pulsations because of the dynamic features of the complex cavitation vortex rope.The links between the cavitation dynamic characteristics and the hydraulic system stability are important for an accurate system instability prediction.For this purpose,the cavitating flows in a Francis turbine operating under the overload conditions are simulated by using the Zwart-Gerber-Belamri(ZGB)cavitation model.The cavitation dynamic parameters in different cavitation development stages and the evolutions under various overload conditions are analyzed and compared in this paper.It is shown that the cavitation dynamic parameters,including the cavitation compliance,the mass flow gain factor and the wave speed,can well represent the cavitation characteristics with the vortex rope evolution.The predicted cavitation dynamic parameters are in a reasonable agreement with other available results,with an obvious dependency on the loads.The results obtained in this study are relevant to the system stability analysis.