scholarly journals Admissible equations of state for immiscible and miscible mixtures

2019 ◽  
Vol 66 ◽  
pp. 1-21 ◽  
Author(s):  
Gloria Faccanoni ◽  
Hélène Mathis
Keyword(s):  
General Framework ◽  
Equations Of State ◽  
Two Phase ◽  
Geometrical Properties ◽  
Homogeneous Equilibrium ◽  
Phase Mixture ◽  
Gibbs Formalism ◽  
Relaxation Models

This paper addresses the construction of admissible Equations of State (EoS) for compressible two-phase ows. We investigate two approaches. In the first one, the mixture is treated as a single uid with a complex thermodynamic. Most of the time the available EoS are determined experimentally and are often incomplete EoS, i.e. we know only the pressure as a function of the volume and the temperature. We present here a general framework to compute a complete EoS based on such an incomplete EoS. In the second approach, each phase is depicted by its own EoS. Following the Gibbs formalism, the mixture entropy is the sum of the phasic entropies which achieves its maximum at equilibrium. Depending on the miscibility of the mixture, one gets different geometrical properties on the resulting mixture entropy. Eventually we address the coupling of mixture EoS with the dynamic of the uid. Homogeneous Equilibrium and Relaxation Models (HEM and HRM) are introduced for an immiscible and a miscible two-phase mixture. Hyperbolicity is ensured taking advantage of the concavity properties of the mixture entropies.

scholarly journals A thermodynamically consistent model of a liquid-vapor fluid with a gas

2019 ◽  
Vol 53 (1) ◽  
pp. 63-84 ◽  
Author(s):  
Hélène Mathis
Keyword(s):  
Phase Transition ◽  
Thermodynamical Equilibrium ◽  
Geometrical Properties ◽  
Consistent Model ◽  
Growth Criterion ◽  
Three Phase ◽  
Symmetric Constraint ◽  
Phase Mixture ◽  
Gibbs Formalism ◽  
Mass Volume

This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are miscible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs formalism, the study of the extensive equilibrium entropy of the system allows to recover the Dalton’s law between the two gaseous phases. In addition, we distinguish whether phase transition occurs or not between the liquid and its vapor. The thermodynamical equilibria are described both in extensive and intensive variables. In the latter case, we focus on the geometrical properties of equilibrium entropy. The consistent characterization of the thermodynamics of the three-phase mixture is used to introduce two Homogeneous Equilibrium Models (HEM) depending on mass transfer is taking into account or not. Hyperbolicity is investigated while analyzing the entropy structure of the systems. Finally we propose two Homogeneous Relaxation Models (HRM) for the three-phase mixtures with and without phase transition. Supplementary equations on mass, volume and energy fractions are considered with appropriate source terms which model the relaxation towards the thermodynamical equilibrium, in agreement with entropy growth criterion.

scholarly journals A relaxation scheme for a hyperbolic multiphase flow model

2019 ◽  
Vol 53 (5) ◽  
pp. 1763-1795 ◽  
Author(s):  
Khaled Saleh
Keyword(s):  
Multiphase Flow ◽  
Flow Model ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Energy Inequality ◽  
Approximation Error ◽  
Finite Volume Scheme ◽  
Phase Flow ◽  
Two Phase ◽  
Relaxation Scheme

This article is the first of two in which we develop a relaxation finite volume scheme for the convective part of the multiphase flow models introduced in the series of papers (Hérard, C.R. Math. 354 (2016) 954–959; Hérard, Math. Comput. Modell. 45 (2007) 732–755; Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). In the present article we focus on barotropic flows where in each phase the pressure is a given function of the density. The case of general equations of state will be the purpose of the second article. We show how it is possible to extend the relaxation scheme designed in Coquel et al. (ESAIM: M2AN 48 (2013) 165–206) for the barotropic Baer–Nunziato two phase flow model to the multiphase flow model with N – where N is arbitrarily large – phases. The obtained scheme inherits the main properties of the relaxation scheme designed for the Baer–Nunziato two phase flow model. It applies to general barotropic equations of state. It is able to cope with arbitrarily small values of the statistical phase fractions. The approximated phase fractions and phase densities are proven to remain positive and a fully discrete energy inequality is also proven under a classical CFL condition. For N = 3, the relaxation scheme is compared with Rusanov’s scheme, which is the only numerical scheme presently available for the three phase flow model (see Boukili and Hérard, ESAIM: M2AN 53 (2019) 1031–1059). For the same level of refinement, the relaxation scheme is shown to be much more accurate than Rusanov’s scheme, and for a given level of approximation error, the relaxation scheme is shown to perform much better in terms of computational cost than Rusanov’s scheme. Moreover, contrary to Rusanov’s scheme which develops strong oscillations when approximating vanishing phase solutions, the numerical results show that the relaxation scheme remains stable in such regimes.

scholarly journals Maximum Flow Rate of a Single Component, Two-Phase Mixture

1965 ◽  
Vol 87 (1) ◽  
pp. 134-141 ◽  
Author(s):  
F. J. Moody
Keyword(s):  
Flow Rate ◽  
Static Pressure ◽  
Maximum Flow ◽  
Single Component ◽  
Maximum Flow Rate ◽  
Vapor Flow ◽  
Two Phase ◽  
Slip Ratio ◽  
Phase Mixture ◽  
Local Slip

A theoretical model is developed for predicting the maximum flow rate of a single component, two-phase mixture. It is based upon annular flow, uniform linear velocities of each phase, and equilibrium between liquid and vapor. Flow rate is maximized with respect to local slip ratio and static pressure for known stagnation conditions. Graphs are presented giving maximum steam/water flow rates for: local static pressures between 25 and 3,000 psia, with local qualities from 0.01 to 1.00; local stagnation pressures and enthalpies which cover the range of saturation states.

Microstructure of Polycrystalline MgO Penetrated by a Silicate Liquid

1996 ◽  
Vol 2 (3) ◽  
pp. 113-128 ◽  
Author(s):  
Sundar Ramamurthy ◽  
Michael P. Mallamaci ◽  
Catherine M. Zimmerman ◽  
C. Barry Carter ◽  
Peter R. Duncombe ◽  
...  
Keyword(s):  
Grain Boundaries ◽  
Grain Growth ◽  
Glassy Phase ◽  
Silicate Liquid ◽  
Two Phase ◽  
The Matrix ◽  
Devitrification Process ◽  
Phase Mixture

Dense, polycrystalline MgO was infiltrated with monticellite (CaMgSiO4) liquid to study the penetration of liquid along the grain boundaries of MgO. Grain growth was found to be restricted with increasing amounts of liquid. The inter-granular regions were generally found to be comprised of a two-phase mixture: crystalline monticellite and a glassy phase rich in the impurities present in the starting MgO material. MgO grains act as seeding agents for the crystallization of monticellite. The location and composition of the glassy phase with respect to the MgO grains emphasizes the role of intergranular liquid during the devitrification process in “snowplowing” impurities present in the matrix.

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