A compressible solver for two phase-flows with phase change for bubble cavitation

Abstract

The present work describes the development of a novel fully compressible solver for two-phase flows with liquid-vapour phase change. Phase change phenomena in compressible two-phase flows are driving mechanisms for a multitude of phenomena including cavitation, droplet evaporation in acoustic fields, phase change in closed environments. Those are fundamental for a large number of technological applications including combustion chambers, propellant management in space and submarine engine design. The accurate simulation of phase change phenomena in compressible flows requires a direct numerical solver thermodynamically consistent and able to describe the smallest driving scales and to handle capillary effects. The present solver has these characteristics. It solves the full system of conservation equations for real fluid compressible flows of single species written in primitive variables using a semi-implicit pressure based solver. It leads to the energy equation being a Screened Poisson equation for the pressure that can be solved as a linear system. For the sake of thermodynamic consistency, several cubic equations of state are proposed to describe liquid and vapour phases as well as evolving saturation conditions at the interface. The proposed solver can be considered as an extension of classical incompressible solvers for nucleate boiling based on sharp interface approaches towards configurations with temporally and spatially evolving saturation conditions at the interface. It enables a complete coupling between local liquid-vapour phase change at the interface and pressure variations due to local flow features or time evolving thermodynamic conditions. Its interest is demonstrated with several benchmarks of increasing complexity with an ultimate configuration involving bubble cavitation due to the pressure drop in a convergent pipe.