Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques

Métayer, Olivier Le; Massoni, Jacques; Saurel, Richard

doi:10.1016/j.ijthermalsci.2003.09.002

Cited by 126 publications

(73 citation statements)

References 19 publications

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“…This is not surprising as these two equations, (A12) (a)-(b), are precisely Equations (4) and (23), which are the basis of the theoretical derivations. Equations (A6) and (40) being now considered, the following partial derivatives are obtained:…”

Section: Appendix B Maxwell's Relationsmentioning

confidence: 91%

“…In the present approach, as in Le Métayer et al [23] and Le Métayer and Saurel [14], each fluid, liquid and gas, is governed by the same EOS, here Equation (16) but with different parameters unlike cubic EOSs. The term p ∞ (T) is important for the liquid state whereas the second attractive term…”

Section: Thermal and Caloric Eossmentioning

confidence: 99%

“…As the thermodynamic definition of entropy and specific volume implies s = − ∂g ∂T p and v = ∂g ∂p T , identity (23) transforms to a more convenient expression,…”

Section: Expression Of the Entropymentioning

confidence: 99%

“…Building of appropriate EOSs in this direction was done by Le Métayer et al [23] and Le Métayer and Saurel [14] with extended "Stiffened-Gas" (SG) formulations. In the present contribution, the proposed EOS is also meant to describe transitions from pure fluids to supercritical state.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Chiapolino

Saurel

2018

Fluids

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Abstract:The Noble-Abel Stiffened-Gas (NASG) equation of state (Le Métayer, O. and Saurel, R. proposed in 2016) is extended to variable attractive and repulsive effects to improve the liquid phase accuracy when large temperature and pressure variation ranges are under consideration. The transition from pure phase to supercritical state is of interest as well. The gas phase is considered through the ideal gas assumption with variable specific heat rendering the formulation valid for high temperatures. The liquid equation-of-state constants are determined through the saturation curves making the formulation suitable for two-phase mixtures at thermodynamic equilibrium. The overall formulation is compared to experimental characteristic curves of the phase diagram showing good agreement for various fluids (water, oxygen). Compared to existing cubic equations of state, the present one is convex, a key feature for computations with hyperbolic flow models.

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Section: Appendix B Maxwell's Relationsmentioning

confidence: 91%

Section: Thermal and Caloric Eossmentioning

confidence: 99%

“…As the thermodynamic definition of entropy and specific volume implies s = − ∂g ∂T p and v = ∂g ∂p T , identity (23) transforms to a more convenient expression,…”

Section: Expression Of the Entropymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Chiapolino

Saurel

2018

Fluids

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“…The constant parameters for the specified equation of state are found from the experimental saturation curves for the enthalpies, densities and pressure in the fixed range of the temperatures [11,12]. Calculations related to the influence of capillary effects in two-phase flows are presented in [13].…”

Section: Introductionmentioning

confidence: 99%

Direct numerical simulation of two-phase gas dynamic flows with phase transition for water and for liquid sodium

et al. 2017

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On the modeling and simulation of a laser‐induced cavitation bubble

Zein

Hantke

Warnecke

2013

Numerical Methods in Fluids

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SUMMARYSingle cavitation bubbles exhibit severe modeling and simulation difficulties. This is due to the small scales of time and space as well as due to the involvement of different phenomena in the dynamics of the bubble. For example, the compressibility, phase transition, and the existence of a noncondensable gas inside the bubble have strong effects on the dynamics of the bubble. Moreover, the collapse of the bubble involves the occurrence of critical conditions for the pressure and temperature. This adds extra difficulties to the choice of equations of state. Even though several models and simulations have been used to study the dynamics of the cavitation bubbles, many details are still not clearly accounted for.Here, we present a numerical investigation for the collapse and rebound of a laser‐induced cavitation bubble in liquid water. The compressibility of the liquid and vapor are involved. In addition, great focus is devoted to study the effects of phase transition and the existence of a noncondensable gas on the dynamics of the collapsing bubble. If the bubble contains vapor only, we use the six‐equation model for two‐phase flows that was modified in our previous work [A. Zein, M. Hantke, and G. Warnecke, J. Comput. Phys., 229(8):2964‐2998, 2010]. This model is an extension to the six‐equation model with a single velocity of Kapila et al. (Phys. Fluid, 13:3002‐3024, 2001) taking into account the heat and mass transfer.To study the effect of a noncondensable gas inside the bubble, we add a third phase to the original model. In this case, the phase transition is considered only at interfaces that separate the liquid and its vapor. The stiffened gas equations of state are used as closure relations. We use our own method to determine the parameters to obtain reasonable equations of state for a wide range of temperatures and make them suitable for the phase transition effects. We compare our results with experimental ones. Also our results confirm some expected physical phenomena. Copyright © 2013 John Wiley & Sons, Ltd.

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Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques

Cited by 126 publications

References 19 publications

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Extended Noble–Abel Stiffened-Gas Equation of State for Sub-and-Supercritical Liquid-Gas Systems Far from the Critical Point

Direct numerical simulation of two-phase gas dynamic flows with phase transition for water and for liquid sodium

On the modeling and simulation of a laser‐induced cavitation bubble

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