Multiphase flows with compressible and incompressible phases

TL;DR

This paper introduces a coupled compressible-incompressible SPH method to model gas-liquid multiphase flows, validating it against the Rayleigh--Plesset equation through simulations of bubble dynamics under pressure variations.

Contribution

A novel coupling of SPH for compressible and incompressible phases is proposed and validated against classical bubble dynamics models.

Findings

The coupled SPH method accurately reproduces RP equation results.

The model effectively captures bubble deformation under pressure variations.

Validation across different density ratios demonstrates robustness.

Abstract

Gas bubbles immersed in a liquid and flowing through a large pressure gradient undergoes volumetric deformation in addition to possible deviatoric deformation. While the high density liquid phase can be assumed to be an incompressible fluid, the gas phase needs to be modelled as a compressible fluid for such bubble flow problems. The Rayleigh--Plesset (RP) equation describes such a bubble undergoing volumetric deformation due to changes in pressure in the ambient incompressible fluid, assuming axisymmetric dynamics. We propose a compressible-incompressible coupling of Smoothed Particle Hydrodynamics (SPH) and validate this coupling against the RP model in two dimensions. For different density ratios, a sinusoidal pressure variation is applied to the ambient incompressible liquid and the response of the bubble is observed and compared with the solutions of the axisymmetric RP equation.