A thermal equilibrium approach to modelling multiple solid–fluid interactions with phase transitions, with application to cavitation

Abstract

This paper presents a new approach to model phase transitions in multi-material problems based on the assumption of thermal equilibrium. The method is used to construct an equation of state for water which captures the liquid–vapour phase transition and is suitable for simulating cavitating flows. A key advantage of this approach is that the physics of the phase transition is entirely encoded within the equation of state. Complex multi-physics models can therefore be augmented to include the physics of phase transitions without further complicating the partial evolution equations. This is substantiated by integrating the model within a diffuse interface scheme for coupled solid–fluid dynamics, and implemented using a structured adaptive mesh refinement (SAMR) strategy. The combined model facilitates the fully-coupled simulation of complex multi-material, multi-physics problems featuring elastoplastic solids, gases, cavitating liquids and reactive materials. Evaluation of the model is shown to add little overhead – for parts of the domain without cavitation the equations reduce to those of the underpinning model with simple stiffened gas equation of state for liquid components; for parts of the domain where cavitation does occur, it requires a non-linear relaxation with only one degree of freedom. The method is applied to several strenuous test cases for cavitating flows and shown to be in good agreement with previously published works.