||A 3D numerical model is proposed to simulate complex unsteady cavitating flows. The final objective is to predict instabilities due to cavitation in turbopump inducers. It was previously applied to simpler two-dimensional simulations such as a Venturi type section [Int. J. Numer. Meth. Fluids, in press] and foil sections [Int. J. JSME B 45(3) (2002)].
The model is based on the code FineTurbo significantly modified to take into account the cavitation process. The numerical scheme consists in a time-marching algorithm initially devoted to compressible flows. A low-speed preconditioner is applied to treat low Mach number flows. This numerical resolution is coupled to a single-fluid model of cavitation. The evolution of the density is governed by a barotropic state law proposed and validated previously by Delannoy and Kueny [Proc 1990 ASME Cavitation Multiphase Flow Forum 98 (1990) p. 153] and Coutier-Delgosha et al. [Int. J. Numer. Meth. Fluids 42 (2003) 527].
The present work focuses on the numerical stability of the NavierStokes equations associated to the barotropic state law. Fourier footprint representations are applied to several two-dimensional non-cavitating and cavitating flow field configurations, and the influence of the numerical and physical parameters on the stability is investigated. The influence of the preconditioner is also discussed: a modification is proposed in the two-phase areas, and its effect is tested in a two-dimensional Venturi type section flow configuration. A significant improvement is obtained concerning both the convergence level and speed.