Mixture model for two-phase flows with high density ratios: A conservative and realizable SPH formulation

• Published in: International journal of multiphase flow Vol. 111; pp. 158 - 174
• Main Authors: Fonty, Thomas, Ferrand, Martin, Leroy, Agnès, Joly, Antoine, Violeau, Damien
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2019; Elsevier
• Subjects: Fluid mechanics; Large density ratios; Mechanics; Physics; Smoothed particle hydrodynamics; Two-phase mixture flows; Smoothed particle hydrodynamics; Large density ratios; Two-phase mixture flows
• ISSN: 0301-9322; 1879-3533
• DOI: 10.1016/j.ijmultiphaseflow.2018.11.007

•A two-phase flow mixture model is implemented in Smoothed Particle Hydrodynamics.•Special attention is paid to conservation and realizability properties.•The model is validated on separation cases and mixture plane Poiseuille flow.•Degeneration to multi-fluid SPH is ensured in case of non-miscible phases. The numerical modelling of two-phase mixture flows with high density ratios (e.g. water/air) is challenging. Multiphase averaged models with volume fraction representation encompass a simple way of simulating such flows: mixture models with relative velocity between phases. Such approaches were implemented in SPH (Smoothed Particle Hydrodynamics) using a mass-weighted definition of the mixture velocity, but with limited validation. Instead, to handle high density ratios, a mixture model with a volumetric mixture velocity is developed in this work. To avoid conservation issues raised by the discretization of the relative material displacement contribution in the volume fraction equation, a formulation on phase volumes is derived following a finite volume reasoning. Conservativity, realizability, limit behaviour for single-phase flow are the leading principles of this derivation. Volume diffusion is added to prevent development of instabilities due to the colocated nature of SPH. This model is adapted to the semi-analytical SPH wall boundary conditions. Running on GPU, this approach is successfully applied to the separation of phases in a settling tank with low to high density ratios. An analytical solution on a two-phase mixture Poiseuille flow is also used to check the accuracy of the numerical implementation. Then, a Rayleigh–Taylor instability test case is performed to compare with multi-fluid SPH. Finally, a comparison with experimental and numerical data is made on a sand dumping case; this highlights some limits of this mixture model.