Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows

Clerc, Sébastien

doi:10.1006/jcph.2000.6515

Cited by 83 publications

(54 citation statements)

References 24 publications

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“…An elegant hierarchy of reduced models exists, with the numbers of equations ranging from six to three only. Examples of the latter are the homogeneous equilibrium model [5] and the barotropic model described in [26]. For a clear and compact overview over existing reduced two-fluid flow models, we refer to [6].…”

Section: Introductionmentioning

confidence: 99%

A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment

Kreeft

Koren

2010

Journal of Computational Physics

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a b s t r a c tA new formulation of Kapila's five-equation model for inviscid, non-heat-conducting, compressible two-fluid flow is derived, together with an appropriate numerical method. The new formulation uses flow equations based on conservation laws and exchange laws only. The two fluids exchange momentum and energy, for which exchange terms are derived from physical laws. All equations are written as a single system of equations in integral form. No equation is used to describe the topology of the two-fluid flow. Relations for the Riemann invariants of the governing equations are derived, and used in the construction of an Osher-type approximate Riemann solver. A consistent finite-volume discretization of the exchange terms is proposed. The exchange terms have distinct contributions in the cell interior and at the cell faces. For the exchange-term evaluation at the cell faces, the same Riemann solver as used for the flux evaluation is exploited. Numerical results are presented for two-fluid shock-tube and shock-bubble-interaction problems, the former also for a two-fluid mixture case. All results show good resemblance with reference results.

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Section: Introductionmentioning

confidence: 99%

A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment

Kreeft

Koren

2010

Journal of Computational Physics

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“…The PDE set to be solved is the usual Navier-Stokes equation set for CFD with thermal exchanges and variable density (dilatable flow) (Obry et al, 1990;Grandotto and Obry, 1996;Aubry et al, 1989;Clerc, 2000): two-phase mixture mass, energy and momentum balance equations, see Equations (1)-(3). In our application, the stationary flow regime is reached by means of a pseudo-time marching (or similarly by the outer iterations of a relaxed Picard iterative method (Ferziger and Peric, 1996)).…”

Section: Two-phase Flow Modellingmentioning

confidence: 99%

Multigrid preconditioning of steam generator two-phase mixture balance equations in the Genepi software

Belliard¹

2006

PCFD

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Within the framework of averaged two-phase mixture flow simulations of PWR Steam Generators (SG), this paper provides a geometric version of a pseudo-FMG FAS preconditioning of the balance equations used in the CEA Genepi code. The 3D steady-state flow is reached by a transient computation using a fractional step algorithm and a projection method. Our application is based on the PVM package. The difficulties of applying geometric FAS multigrid methods to the balance equations solver are addressed. The effects on the convergence behaviour of the numerical parameters are investigated. An original parallel red-black pseudo-FMG FAS multigrid algorithm is also presented. The use of dynamic multigrid cycles leads to perceptible improvements in the computation convergences. Numerical tests (academic and industrial simulations) underline a noticeable computation speed-up, essentially for a large number of freedom degrees: the speed-up reached for 2 or 3 grids ranges between 2 and 3.

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“…In this paper, we are interested in modelisations of the type described for instance in [13], [10] in which the convective part of the model is described by an hyperbolic system. This includes a large variety of different modelisations ranging from simple homogeneous [3] or drift flux models to sophisticated two pressure, two velocity models [10], [1], [11]. With a few exceptions, from a theoritical poinf of view, the behaviour for vanishing Mach number of these two-phase flows models is unknown.…”

Section: Introductionmentioning

confidence: 99%

“…There is no reason to believe that the situation is different for hyperbolic two-phase flow models and that in the low Mach number regime, standard discretization can be used safely to compute these flows. Actually, for one of the simplest two-phase flows model, namely the Homogeneous Equilibrium Model, it has been shown in [3] and [16] that FV upwind schemes exhibit the same type of accuracy problems than in the one phase context. In this paper, we investigate this situation for a more complex two-phase flow model, namely the five-equation model introduced in [7] and [9].…”

Section: Introductionmentioning

confidence: 99%

Behavior of upwind scheme in the low Mach number limit: III. Preconditioned dissipation for a five equation two phase model

Murrone

Guillard

2008

Computers & Fluids

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For single phase fluid models, like the Euler equations of compressible gas dynamics, upwind finite volume schemes suffer from a loss of accuracy when computing flows in the near incompressible regime. Preconditioning of the numerical dissipation is necessary to recover results consistent with the asymptotic behaviour of the continuous model. In this paper, we examine this situation for a two phase flow model. We show that as in the single phase case, the numerical approximation has to be done carefully in the near incompressible regime. We propose to adapt the preconditioning strategy used for single phase problems and present numerical results that show the efficiency of this approach

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Numerical Simulation of the Homogeneous Equilibrium Model for Two-Phase Flows

Cited by 83 publications

References 24 publications

A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment

A new formulation of Kapila’s five-equation model for compressible two-fluid flow, and its numerical treatment

Multigrid preconditioning of steam generator two-phase mixture balance equations in the Genepi software

Behavior of upwind scheme in the low Mach number limit: III. Preconditioned dissipation for a five equation two phase model

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