A simple HLLC-type Riemann solver for compressible non-equilibrium two-phase flows

Furfaro, Damien; Saurel, Richard

doi:10.1016/j.compfluid.2015.01.016

Cited by 53 publications

(58 citation statements)

References 31 publications

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“…These two models are thus well posed in the sense that they are thermodynamically consistent, frame invariant and hyperbolic. Both models can be solved by Godunov type methods as the Riemann problem has been addressed for both (Saurel et al, 1994, Saurel and Abgrall, 1999, Schwendeman et al, 2006, Deledicque and Papalexandris, 2010, Furfaro and Saurel, 2015. However, well posedness is a necessary condition but not a sufficient one for physical validity.…”

Section: A) Bn Type Model (1986)mentioning

confidence: 99%

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Modelling compressible dense and dilute two-phase flows

Saurel

Chinnayya

Carmouze³

2017

Physics of Fluids

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Many two-phase flow situations, from engineering science to astrophysics, deal with transition from dense (high concentration of the condensed phase) to dilute concentration (low concentration of the same phase), covering the entire range of volume fractions. Some models are now well accepted at the two limits, but none is able to cover accurately the entire range, in particular regarding waves propagation. In the present work an alternative to the Baer and Nunziato (1986) (BN for short) model, initially designed for dense flows, is built. The corresponding model is hyperbolic and thermodynamically consistent. Contrarily to the BN model that involves 6 wave speeds, the new formulation involves 4 waves only, in agreement with the Marble (1963) model based on pressureless Euler equations for the dispersed phase, a well-accepted model for low particle volume concentrations. In the new model, the presence of pressure in the momentum equation of the particles and consideration of volume fractions in the two phases render the model valid for large particle concentrations. A symmetric version of the new model is derived as well for liquids containing gas bubbles. This model version involves 4 wave speeds as well, but with different wave's speeds. Last, the two sub-models with 4 waves are combined in a unique formulation, valid for the full range of volume fractions. It involves the same 6 wave's speeds as the BN model, but at a given point of space 4 waves only emerge, depending on the local volume fractions. The non-linear pressure waves propagate only in the phase with dominant volume fraction. The new model is tested numerically on various test problems ranging from separated phases in a shock tube to shock -particle cloud interaction. Its predictions are compared to BN and Marble models as well as against experimental data.Key words: hyperbolic, two-phase, compressible, shocks Emails: Richard.Saurel@univ-amu.fr; Ashwin.Chinnayya@ensma.fr; Quentin.Carmouze@rs2n.eu 2 I. IntroductionIt is well accepted that hyperbolic models are mandatory to deal with phenomena involving wave propagation. This is the case for multiphase flow mixtures in many situations such as in particular shocks and detonations propagation in granular explosives and in fuel suspensions, as well as liquid-gas mixtures with bubbles, cavitation and flashing, as soon as motion is intense and governed by pressure gradients. This is thus the case of most unsteady two-phase flows situations. Wave propagation is important as it carries pressure, density and velocity disturbances. Sound propagation is also very important as it determines critical (choked) flow conditions and associated mass flow rates. It has also fundamental importance on sonic conditions of detonation waves when the twophase mixture is exothermically reacting (Petitpas et al., 2009). Hyperbolicity is also related to the causality principle, meaning that initial and boundary conditions are responsible of time evolution of the solution. When dealing with first-order partial different...

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Section: A) Bn Type Model (1986)mentioning

confidence: 99%

“…-It involves an extra wave, not aligned with the condensed phase velocity, this property having benefits at least for numerical resolution (Ambroso et al, 2012, Furfaro andSaurel, 2015). This system admits the following mixture entropy equation:…”

Section: A) Bn Type Model (1986)mentioning

confidence: 99%

Modelling compressible dense and dilute two-phase flows

Saurel

Chinnayya

Carmouze³

2017

Physics of Fluids

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“…We propose here to repeat the explosive liquid water dispersal test presented in Furfaro and Saurel (2015) [16] with the 4 and 7-equation models. The test consists in a cylindrical gas-liquid explosion schematically represented in Fig 11. The results are given in Fig 12. Nearly pure gas (1 kg/m 3 ) Atmospheric pressure (0.1 Mpa)…”

Section: Explosive Liquid Water Dispersal Into Airmentioning

confidence: 99%

A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows

2017

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To cite this version:Alexandre Chiapolino, Pierre Boivin, Richard Saurel. A simple and fast phase transition relaxation solver for compressible multicomponent two-phase flows. Computers and Fluids, Elsevier, 2017, 150, pp.31 -45. <10.1016/j.compfluid.2017 AbstractThe present paper aims at building a fast and accurate phase transition solver dedicated to unsteady multiphase flow computations. In a previous contribution (Chiapolino et al. 2017), such a solver was successfully developed to compute thermodynamic equilibrium between a liquid phase and its corresponding vapor phase. The present work extends the solver's range of application by considering a multicomponent gas phase instead of pure vapor, a necessary improvement in most practical applications. The solver proves easy to implement compared to common iterative procedures, and allows systematic CPU savings over 50%, at no cost in terms of accuracy. It is validated against solutions based on an accurate but expensive iterative solver.Its capability to deal with cavitating, evaporating and condensing two-phase flows is highlighted on severe test problems both 1D and 2D.

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“…In all tests that follow, the hyperbolic part of the two-phase flow model (1), (2) is solved with the method given in [6]. A one-meter long shock tube contains gas and liquid phases with uniform volume fraction everywhere.…”

Section: Shock Tube With Dropletsmentioning

confidence: 99%

“…The equilibrium state is correctly reached at the end of the evaporation process (6). The Ridders' method is used to solve f ðY g;wat;I Þ ¼ 0 in the domain ½Y a ; Y b resulting in the determination of Y g;wat;I .…”

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confidence: 99%