A weakly compressible free-surface flow solver for liquid-gas systems using the volume-of-fluid approach

  • Authors:

  • Johan A. Heyns;Arnaud G. Malan;Thomas M. Harms;Oliver F. Oxtoby

  • Affiliations:

  • Aerospace Systems Competency, Council for Scientific and Industrial Research, P.O. Box 395, Pretoria 0001, South Africa;Aerospace Systems Competency, Council for Scientific and Industrial Research, P.O. Box 395, Pretoria 0001, South Africa;Mechanical and Mechatronic Engineering, University of Stellenbosch, South Africa;Aerospace Systems Competency, Council for Scientific and Industrial Research, P.O. Box 395, Pretoria 0001, South Africa

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2013

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Abstract

This paper presents a weakly compressible volume-of-fluid formulation for modelling immiscible high density ratio two-fluid flow under low Mach number conditions. This follows findings of experimental analyses that concluded the compressibility of the gas has a noteworthy effect on predicted pressure loads in liquid-gas flow in certain instances. With the aim of providing a more accurate numerical representation of dynamic two-fluid flow, the solver is subsequently extended to account for variations in gas densities. A set of governing equations is proposed, which accounts for the compressible properties of the gas phase in a manner which allows for a computationally efficient numerical simulation. Furthermore, the governing equations are numerically expressed so that they allow for large variations in the material properties, without introducing notable non-physical oscillations over the interface. For the discretisation of the governing equations an edge-based vertex-centred finite volume approach is followed. The developed solver is applied to various test cases and demonstrated to be efficient and accurate.