Simulation of unsteady cavitation with a two-equations turbulence model including compressibility effects

Unsteady effects associated with cavitation were investigated by numerical simulations in three configurations. The simplest one was a Venturi-type section in which the cavitation sheet oscillates periodically with vapour cloud shedding. The second one was a hydrofoil whose unsteady cavitating behaviour depends on the angle of attack, and the most complex one was a cascade of three hydrofoils. In this last configuration, in addition to the unsteadiness associated with each cavity, a coupling between the three channels was also observed. These cavitating flows were simulated by 2D computations. Resolution of Reynolds-averaged Navier-Stokes equations was based on a finite-volume discretization associated with a pressure correction algorithm. Cavitation was simulated by using a barotropic vapour/liquid state law that links the fluid density evolution to the pressure variations. As standard k–ϵ RNG or k–ω turbulence models were found to be weakly efficient to simulate unsteady cavitation, influence of the compressibility of the two-phase medium on turbulence was considered. Both k–ϵ RNG and k–ω turbulence models, including corrections of these compressibility effects, were applied and results obtained were consistent with experiments: in the three configurations, the oscillation frequencies, the cavity length, the void ratio and the velocity fields obtained by numerical simulation were in reliable agreement with the available experimental data