A Parameter-Based Approach for Two-Phase-Equilibrium Prediction With Cubic Equations of State

1996 ◽  
Vol 11 (04) ◽  
pp. 273-279 ◽  
Author(s):  
Pradeep Kaul ◽  
R.L. Thrasher
Keyword(s):  
Phase Equilibrium ◽  
Equations Of State ◽  
Two Phase

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.

Phase Equilibrium of Mg-Nd-Zn System near Mg-Nd Side at 400°C

2016 ◽  
Vol 873 ◽  
pp. 18-22
Author(s):  
Ming Li Huang ◽  
Xue Shen ◽  
Hong Xiao Li
Keyword(s):  
Solid Solution ◽  
Phase Equilibrium ◽  
Ternary Isothermal Section ◽  
Phase Region ◽  
X Ray Diffraction ◽  
Maximum Solubility ◽  
Two Phase ◽  
Solubility Range ◽  
Three Phase ◽  
Equilibrium Alloys

The equilibrium alloys closed to Mg-Nd side in the Mg-rich corner of the Mg-Zn-Nd system at 400°C have been investigated by scanning electron microscopy, electron probe microanalysis and X-ray diffraction. The binary solid solutions Mg12Nd and Mg3Nd with the solubility of Zn have been identified. The maximum solubility of Zn in Mg12Nd is 4.8at%, and Mg12Nd phase can be in equilibrium with Mg solid solution. However, only when the solubility range of Zn in 26at%~32.2at%, Mg3Nd can be in two-phase equilibrium with Mg solid solution. As the results, two two-phase regions as Mg+Mg12Nd and Mg+Mg3Nd and a three-phase region as Mg+Mg12Nd+Mg3Nd in Mg-Nd-Zn ternary isothermal section at 400°C have been identified.

Study on C–S and P–R EOS in pseudo-potential lattice Boltzmann model for two-phase flows

2017 ◽  
Vol 28 (09) ◽  
pp. 1750120 ◽  
Author(s):  
Yong Peng ◽  
Yun Fei Mao ◽  
Bo Wang ◽  
Bo Xie
Keyword(s):  
Surface Tension ◽  
Lattice Boltzmann ◽  
Equations Of State ◽  
Density Ratio ◽  
Maximum Density ◽  
Lattice Boltzmann Model ◽  
Two Phase Flows ◽  
Two Phase ◽  
Spurious Currents ◽  
Pseudo Potential

Equations of State (EOS) is crucial in simulating multiphase flows by the pseudo-potential lattice Boltzmann method (LBM). In the present study, the Peng and Robinson (P–R) and Carnahan and Starling (C–S) EOS in the pseudo-potential LBM with Exact Difference Method (EDM) scheme for two-phase flows have been compared. Both of P–R and C–S EOS have been used to study the two-phase separation, surface tension, the maximum two-phase density ratio and spurious currents. The study shows that both of P–R and C–S EOS agree with the analytical solutions although P–R EOS may perform better. The prediction of liquid phase by P–R EOS is more accurate than that of air phase and the contrary is true for C–S EOS. Predictions by both of EOS conform with the Laplace’s law. Besides, adjustment of surface tension is achieved by adjusting [Formula: see text]. The P–R EOS can achieve larger maximum density ratio than C–S EOS under the same [Formula: see text]. Besides, no matter the C–S EOS or the P–R EOS, if [Formula: see text] tends to 0.5, the computation is prone to numerical instability. The maximum spurious current for P–R is larger than that of C–S. The multiple-relaxation-time LBM still can improve obviously the numerical stability and can achieve larger maximum density ratio.

scholarly journals Two-phase equilibrium in binary and ternary systems II. The system methane-ethylene III. The system methane-ethane-ethylene

1940 ◽  
Vol 176 (964) ◽  
pp. 140-152 ◽  
Keyword(s):  
Phase Equilibrium ◽  
Ternary System ◽  
Binary Systems ◽  
Ternary Systems ◽  
Two Phase ◽  
Composition Diagram ◽  
Wide Range ◽  
Binary And Ternary Systems

The liquid-vapour equilibrium of the system methane-ethylene has been determined at 0, -42 , -78, -88 and -104° C over a wide range of pressures and the results are shown on a pressure-composition-temperature diagram and by a series of pressure-composition curves. The liquid-vapour equilibrium of the ternary system methane-ethane-ethylene has been determined at -104, -78 and 0° C. Values for the two binary systems methane-ethane and methane-ethylene and for the ternary system methane-ethane-ethylene are shown on a composite pressure-composition diagram.

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