Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia

Gavrilyuk, Sergey; Saurel, Richard

doi:10.1006/jcph.2001.6951

Cited by 134 publications

(150 citation statements)

References 36 publications

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“…A challenging issue is to retain the validity of this asymptotic behavior from a numerical point of view, by means of an asymptotic-preserving scheme for the seven-equation model. In other words, such a scheme is expected to provide a consistent approximation of the drift-flux model (22), (23) in the asymptotic regime ε → 0. The rest of the paper is precisely devoted to the derivation of a numerical scheme for the seven-equation model.…”

Section: Asymptotic Propertiesmentioning

confidence: 99%

“…Then, the model (and related ones, see among others Stewart & Wendroff [41], Abgrall & Saurel [37], [38]...) has gained interest for the modelling and computation of two phase flows. See for instance, in a non-exhaustive way, Kapila et al [29], Glimm et al [23], Abgrall & Saurel [37], Gavrilyuk & Saurel [22], Gallouët, Hérard & Seguin [21], Coquel, Gallouët, Hérard & Seguin [13], and more recently Ambroso, Chalons, Coquel & Galié [1], Tokareva & Toro [42], and the references therein. One of the main features of this model is to involve two distinct velocities u 1 and u 2 and two pressures p 1 and p 2 associated with the two phases.…”

Section: Introductionmentioning

confidence: 99%

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A Godunov-type method for the seven-equation model of compressible two-phase flow

2012

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We are interested in the numerical approximation of the solutions of the compressible seven-equation two-phase flow model. We propose a numerical srategy based on the derivation of a simple, accurate and explicit approximate Riemann solver. The source terms associated with the external forces and the drag force are included in the definition of the Riemann problem, and thus receive an upwind treatment. The objective is to try to preserve, at the numerical level, the asymptotic property of the solutions of the model to behave like the solutions of a drift-flux model with an algebraic closure law when the source terms are stiff. Numerical simulations and comparisons with other strategies are proposed.

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Section: Asymptotic Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Godunov-type method for the seven-equation model of compressible two-phase flow

2012

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“…where p * andp * are the exact star states defined by the pair of equations in (21). For |ᾱ R −ᾱ L | small, we seek a solution to the jump conditions about an intermediate volume fractionᾱ m , say, in the form…”

Section: Linearized Solid Contactmentioning

confidence: 99%

“…Finite volume methods for the model equations, or similar forms, have been considered by Gonthier and Powers [16,17], Saurel and Abgrall [18], Andrianov et al [19], Saurel and Lemetayer [20], Gavrilyuk and Saurel [21] and by Abgrall and Saurel [22], among others. Gonthier and Powers, for example, develop a Godunov-type method for a two-phase flow model and use it to compute solutions to a number of reactive flow problems.…”

Section: Introductionmentioning

confidence: 99%

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

Schwendeman

Wahle

Kapila

2006

Journal of Computational Physics

172

188

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“…Then, dissipation terms which are compatible with the entropy inequality, are introduced (see examples of such a derivation in Gavrilyuk & Gouin (1999), and Gavrilyuk & Saurel (2002)). The model generalizes the capillary model of Perigaud & Saurel (2005) with the introduction of heat and mass transfer relaxation terms to describe phase transition.…”

Section: Introductionmentioning

confidence: 99%

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

Berry¹,

Saurel²,

Petitpas³

et al. 2008

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8 MotivationIn nuclear reactor safety and optimization there are key issues that rely on in-depth understanding of basic two-phase flow phenomena with heat and mass transfer. Within the context of multiphase flows, two bubble-dynamic phenomena -boiling (heterogeneous) and flashing or cavitation (homogeneous boiling), with bubble collapse, are technologically very important to nuclear reactor systems. The main difference between boiling and flashing is that bubble growth (and collapse) in boiling is inhibited by limitations on the heat transfer at the interface, whereas bubble growth (and collapse) in flashing is limited primarily by inertial effects in the surrounding liquid. The flashing process tends to be far more explosive (and implosive), and is more violent and damaging (at least in the near term) than the bubble dynamics of boiling. However, other problematic phenomena, such as crud deposition, appear to be intimately connecting with the boiling process. In reality, these two processes share many details.Flashing occurs in flowing liquid systems when the pressure falls sufficiently low in some region of the flow, reaching a metastable state where the temperature is higher than the saturated one at the reduced pressure of this expanded state. Then the superheated liquid releases its metastable energy (stored as internal energy) very quickly, even explosively, producing either pure vapor (bubble) or liquid-vapor mixture at high velocity, [2]. Expansion effects in nuclear reactor systems are often due to geometrical effects, as for example in nozzles where flashing appears at locations where the pressure is relatively low and the liquid superheated. In the case of twophase blowdown (from the superheated liquid state), bubble collapse is usually not important, but the flashing of superheated liquid strongly influences critical flow rates. In other cases, besides the performance limitations which this cavitation may cause in flow systems, subsequent bubble collapse may be responsible for damage to nearby solid surfaces.Many nuclear reactor applications rely on convective nucleate boiling to efficiently remove high heat fluxes from heated surfaces. Nucleate boiling is a very effective heat transfer mechanism, however it is well known that there exists a critical value of the heat flux at which nucleate boiling transitions to film boiling (departure from nucleate boiling (DNB) and boiling crisis), a very poor heat transfer mechanism. In most practical applications it is imperative to maintain the operating heat flux below such critical value, which is called the Critical Heat Flux (CHF). In this case, the presence of a nearby solid surface is necessary for the rapid supply of the latent heat inherent in the phase change. The presence of these surfaces is known to modify the flow patterns and other characteristics of these multiphase flows, and therefore must be interactively coupled with analyses of these phenomena. And again, as mentioned above, DNB is believed to play an integral role in performance degradatio...

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Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia

Cited by 134 publications

References 36 publications

A Godunov-type method for the seven-equation model of compressible two-phase flow

A Godunov-type method for the seven-equation model of compressible two-phase flow

The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

Progress in the Development of Compressible, Multiphase Flow Modeling Capability for Nuclear Reactor Flow Applications

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