A Phase Transition Model for Cavitating Flows

A general formulation for cavitation, boiling and evaporating flows is first studied where liquid water and gaseous water are included. The model was originally derived for the numerical simulation of multi-phase flows with phase transition. The model arises from the classical multi-component Euler equations but is associated to a non-classical thermodynamic closure: each phase is compressible and evolves in its own sub-volume, with sharing pressure, velocity, and temperature, leading to non-trivial thermodynamic relations for the mixture. The hyperbolic four-equation is first solved. Then the phase transition state is obtained by invoking the Gibbs free energy equilibrium. Another formulation is then implemented. Compared to the first model, the thermodynamic and pressure equilibrium conditions are considered among liquid water, gaseous water, and ideal gas. Several one-dimensional shock tube and cavitating results are shown with the two models. Then the second model with three phases is implemented in a general three-dimensional code (FEFLO).