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A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium


Re, Barbara; Abgrall, Rémi (2022). A pressure‐based method for weakly compressible two‐phase flows under a Baer–Nunziato type model with generic equations of state and pressure and velocity disequilibrium. International Journal for Numerical Methods in Fluids, 94(8):1183-1232.

Abstract

Within the framework of diffuse interface methods, we derive a pressure-based Baer–Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state—stiffened gas and Peng–Robinson—were investigated.

Abstract

Within the framework of diffuse interface methods, we derive a pressure-based Baer–Nunziato type model well-suited to weakly compressible multiphase flows. The model can easily deal with different equation of states and it includes relaxation terms characterized by user-defined finite parameters, which drive the pressure and velocity of each phase toward the equilibrium. There is no clear notion of speed of sound, and thus, most of the classical low Mach approximation cannot easily be cast in this context. The proposed solution strategy consists of two operators: a semi-implicit finite-volume solver for the hyperbolic part and an ODE integrator for the relaxation processes. Being the acoustic terms in the hyperbolic part integrated implicitly, the stability condition on the time step is lessened. The discretization of nonconservative terms involving the gradient of the volume fraction fulfills by construction the nondisturbance condition on pressure and velocity to avoid oscillations across the multimaterial interfaces. The developed simulation tool is validated through one-dimensional simulations of shock-tube and Riemann-problems, involving water-aluminum and water-air mixtures, vapor-liquid mixture of water and of carbon dioxide, and almost pure flows. The numerical results match analytical and reference ones, except some expected discrepancies across shocks, which however remain acceptable (errors within some percentage points). All tests were performed with acoustic CFL numbers greater than one, and no stability issues arose, even for CFL greater than 10. The effects of different values of relaxation parameters and of different amount equations of state—stiffened gas and Peng–Robinson—were investigated.

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Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Computational Mechanics
Physical Sciences > Mechanics of Materials
Physical Sciences > Mechanical Engineering
Physical Sciences > Computer Science Applications
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Applied Mathematics, Computer Science Applications, Mechanical Engineering, Mechanics of Materials, Computational Mechanics ; Baer–Nunziato type model, compressible two-phase flows, Peng–Robinson equation of state, pressure and velocity relaxation with finite parameters, pressure formulation, semi-implicit finite-volume schem
Language:English
Date:1 August 2022
Deposited On:02 Aug 2022 15:23
Last Modified:27 Feb 2024 02:42
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0271-2091
OA Status:Green
Publisher DOI:https://doi.org/10.1002/fld.5087
Project Information:
  • : FunderNorges Forskningsråd NCCS Centre
  • : Grant ID
  • : Project Title
  • : FunderUniversity of Zürich
  • : Grant IDFK-20-121
  • : Project Title
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)