Numerical Modeling of Aerated Cavitation Using Compressible Homogeneous Equilibrium Model

Abstract

Cavitation is a well-known physical phenomenon occurring in various technical applications such as hydraulic turbo-machines, pipe flows, and venturis. Coupling aeration in a cavitating flow is a recent technique to control the overall effect of the cavitation over the zone of interest. The aeration process is done by injecting spherical air bubbles into the fluid flow without having at the same time an interaction with it. The contact handling algorithm is based on the projection of the velocity field of the injected particles over the velocity field of the fluid flow, in such a manner that, at each time step the gradient of the distance between every two bubbles is kept non-negative as a guarantee of the non-overlapping. The collisions between the air bubbles are considered as inelastic. The differential equation system is composed of the Navier-Stokes equations, implemented with the Homogeneous Mixture Model. The latter accounts the three phases (liquid, vapor, and mixture) separately. In the mixture phase, the gas and liquid phases are considered in local thermodynamic equilibrium. A high-order Finite Volume solver based on Moving Least Squares approximations is used for this analysis. For the sake of the numerical simulations, structured and unstructured grids have been used. The code makes use of a SLAU-type Riemann solver for low Mach numbers in order to accurately calculate the numerical fluxes. To avoid any numerical oscillations in the zones of strong gradients, a slope limiter algorithm is coupled with a Moving Least Squares sensor detecting any discontinuities.