A unified algorithm for interfacial flows with incompressible and compressible fluids

TL;DR

This paper introduces a unified numerical algorithm capable of simulating interfacial flows involving both incompressible and compressible fluids across all Mach number regimes, improving computational efficiency and physical accuracy.

Contribution

A novel pressure-based finite-volume algorithm that handles mixed compressible-incompressible interfacial flows within a single framework, applicable from subsonic to supersonic regimes.

Findings

Successfully simulates flows with acoustic waves, shock waves, and rarefaction fans.

Reduces to existing frameworks for purely incompressible or compressible flows.

Validated through representative test cases demonstrating accuracy and robustness.

Abstract

The majority of available numerical algorithms for interfacial two-phase flows either treat both fluid phases as incompressible (constant density) or treat both phases as compressible (variable density). This presents a limitation for the prediction of many two-phase flows, such as subsonic fuel injection, as treating both phases as compressible is computationally expensive due to the very stiff pressure-density-temperature coupling of liquids. A framework with the capability of treating one phase compressible and the other phase incompressible, therefore, has a significant potential to improve the computational performance and still capture all important physical mechanisms. We propose a numerical algorithm that can simulate interfacial flows in all Mach number regimes, ranging from $M=0$ to $M > 1$, including interfacial flows in which compressible and incompressible fluids interact, within the same pressure-based framework and conservative finite-volume discretisation. For interfacial flows with only incompressible fluids or with only compressible fluids, the proposed pressure-based algorithm and finite-volume discretisation reduce to numerical frameworks that have already been presented in the literature. Representative test cases are used to validate the proposed algorithm, including mixed compressible-incompressible interfacial flows with acoustic waves, shock waves and rarefaction fans.