Computation of Flashing Flows In Variable Cross-Section Ducts

Faucher, Eric; Herardc, Jean-Marc; Barret, Michel; Toulemonde, Charles

doi:10.1080/10618560008940907

Cited by 28 publications

(24 citation statements)

References 13 publications

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“…It nonetheless requires schemes to compute Euler equations which enable computing strong rarefaction waves, shocks and contact discontinuities. Many schemes have been proposed to deal with that kind of system with reasonable success [6,13,14,16,47], which rely on "standard" upwinding techniques such as those developed to cope with aerodynamics [22,23,36,39,46]. Another physically relevant approach relies on the Homogeneous Relaxation Model, which in addition requires computing an extra mass balance equation including (stiff) source terms in order to account for mass transfer terms between phases (see for instance the work of Bilicki and co-workers [7][8][9]).…”

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confidence: 99%

A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

Gallouët¹,

Hérard²,

Seguin³

2002

ESAIM: M2AN

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Abstract. The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional variables are exhibited. It is shown first that a standard conservative formulation of above mentioned schemes enables to predict "perfectly" unsteady contact discontinuities on coarse meshes, when the equation of state (EOS) belongs to the first class. On the basis of previous work issuing from literature, an almost conservative though modified version of the scheme is proposed to deal with EOS in the second or third class. Numerical evidence shows that the accuracy of approximations of discontinuous solutions of standard Riemann problems is strengthened on coarse meshes, but that convergence towards the right shock solution may be lost in some cases involving complex EOS in the third class. Hence, a blend scheme is eventually proposed to benefit from both properties ("perfect" representation of contact discontinuities on coarse meshes, and correct convergence on finer meshes). Computational results based on an approximate Godunov scheme are provided and discussed.Mathematics Subject Classification. 65M99, 76M15, 76N15, 80A10.

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confidence: 99%

A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

Gallouët¹,

Hérard²,

Seguin³

2002

ESAIM: M2AN

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“…As may be observed, upon initiation of the problem a shock propagates to the right and is accompanied by an evaporation jump (such behaviour is typical of two-phase shock tube problems (Faucher et al, 2000)). This is followed by a slower moving contact discontinuity.…”

Section: Two-phase Testsmentioning

confidence: 89%

“…The governing equations for one-dimensional single-fluid flow in a rigid duct of variable crosssectional area are based on the Euler equations with an additional non-conservative term, (Faucher et al, 2000):…”

Section: Fluid Dynamicsmentioning

confidence: 99%

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Simulation of two-phase flow through ducts with discontinuous cross-section

2015

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The development of an AUSM+-up based scheme for simulating transient single or two-phase flows through ducts with discontinuous or abrupt changes in area is presented. The non-conservative terms in the governing equations arising from the variation in the duct area are discretised to maintain exactly states at rest. An additional scaling of the pressure based dissipation is added to ensure numerical stability across the area change. The extensive application of the scheme to ideal gas and two-phase CO 2 based on the Homogeneous Equilibrium Model (HEM) for both shock tube and other transient flow problems indicate the scheme's capability to resolve such problems accurately and robustly.

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“…Such a non-conservative hyperbolic problem is similar to the flow of compressible gas in a variable cross section duct model [4,5,10], where the cross section variation is considered as a discontinuous change in the 0021-9991/$ -see front matter Ó 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.jcp.2006.03.013 material porosity.…”

Section: Introductionmentioning

confidence: 99%