Finite mass transfer effects in cavitation modelling

Abstract

One of the key aspects classifying the various approaches in numerical simulation of cavitating flows is the equilibrium flow assumption. It states that internal processes in the flow always occur instantaneously compared to the time scale of the flow (s. Sezal (2009)). As a consequence, the density-pressure trajectory in a barotropic flow may follow a unique curve. Contrary to the equilibrium flow assumption, one may assume that the time to achieve a new state is governed by the magnitude of a finite mass transfer source term in a volume fraction transport equation (s. Asnaghi et al. (2015)). In this case, the set of possible density-pressure states is not predefined, but strongly depends on the rate at which pressure changes. Although it has been pointed out by Koukouvinis and Gavaises (2015) that the equilibrium assumption for a barotropic flow would theoretically be mimicked by the mass transfer model if the finite transfer rate tended to infinity, the model parameters triggering the finite transfer rate are generally considered as empirical (s. Frikha et al. (2008)).
In this paper, effects of the finite mass transfer rate with special focus on condensation will be studied in detail. First, a cavity collapse will be considered to demonstrate how the finite transfer source term must be modified to satisfy the equilibrium flow assumption. Second, a single bubble collapse is studied
numerically and effects of the finite mass transfer rate will be discussed.