Towards numerical simulation of high part load pulsations in Francis turbines

One of the most interesting operating points of Francis turbines is the high part load point, which is characterized by synchronous pressure pulsations of large amplitude. Physical mechanisms of these pulsations are not well understood. Experimental observations show that the frequency of the pulsations is 1.5 to 4 times higher than the runner rotation frequency and there exists a 180 degree phase shift of pressure signal measured in the spiral casing and in the draft tube. Numerical modeling this operating point is challenging as it has to account several complex phenomena: cavitation, rotating vortex rope and interaction of the turbine flow with the whole water system of the test rig. In the present paper we carried out a series of 1D-3D calculations of a model turbine in an attempt to simulate the high part load pulsations. 1D hydro-acoustic equations were used for the upstream waterways, while 3D Reynolds averaged Navier-Stokes model of two-phase mixture was used for the turbine. Although the main factors were taken into account, these computations were not able to capture the high part load pulsations. Namely, the frequency and amplitude of the pressure pulsations were significantly lower than those in the experiment, and there was no phase shift in turbine domain. In order to investigate the shortcomings of the present model, we considered a problem of propagation of disturbances in two-phase "liquid-gas" flows. Several 2D test cases were numerically investigated using both incompressible and compressible gaseous phase model. It was shown that in the absence of phase transfer the compressible model correctly represents the speed of sound in both homogeneous and stratified flow regimes. From the other hand, in case of phase transfer the model damps out propagation of pressure disturbances in upstream direction. This behavior explains the failure of the present 1D-3D model to correctly describe the acoustic properties of the two-phase flow in the draft tube, playing a crucial role in the development of high part load pulsations.