Numerical Simulation of Nonlinear Self Oscillations of a Full Load Vortex Rope

Self excited instabilities or oscillations of a cavitating full load vortex rope occur due to an interaction between the gas volume and the acoustic waves. From the onset of the oscillations, the amplitudes grow until they reach a maximum, called the “limit cycle”. The aim of this paper is to predict and to simulate this full load instability with its corresponding “limit cycle”. The test case is a reduced scale model installed on test rig in the Laboratory for Hydraulic Machines at the EPFL. An advanced hydro acoustic vortex rope model is developed to take into account the energy dissipation due to thermodynamic exchange between the gas and the surrounding liquid. Three key hydro acoustic parameters are set up using both steady CFD simulations and analytical models. First of all, parameters are assumed to be constant and time domain simulation is divergent without reaching the limit cycle. However frequency of instability is well predicted. Then inclusion of nonlinear parameters is found to lead to a limit cycle of finite amplitude. Prediction is compared with results from experiments and is in good agreement. It is shown that nonlinearity of the viscoelastic damping parameter, modelling the energy dissipation, is decisive to reach the limit cycle. Moreover, an energy approach is developed to understand the interaction process between the mass source and the system dissipation to reach the equilibrium at the limit cycle. It brings out that over one period the dissipation can provide energy to the system whereas the mass source dissipates to ensure the equilibrium.