On Two-Phase Pressure and Temperature Equilibration with Mie-Grüneisen Equations of State

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.

Download Full-text

Two-Phase Flows in Mini-/Micro-Gas Flow Channels of PEM Fuel Cells

Volume 6B: Energy ◽

10.1115/imece2013-66070 ◽

2013 ◽

Author(s):

Sung Chan Cho ◽

Yun Wang

Keyword(s):

Pressure Drop ◽

Gas Flow ◽

Fluid Model ◽

Pem Fuel Cells ◽

Two Phase ◽

Micro Gas Flow ◽

Two Fluid Model ◽

The Impact ◽

Two Fluid ◽

Phase Pressure

In this paper, two-phase flow dynamics in a micro channel with various wall conditions are both experimentally and theoretically investigated. Annulus, wavy and slug flow patterns are observed and location of liquid phase on different wall condition is visualized. The impact of flow structure on two-phase pressure drop is explained. Two-phase pressure drop is compared to a two-fluid model with relative permeability correlation. Optimization of correlation is conducted for each experimental case and theoretical solution for the flows in a circular channel is developed for annulus flow pattern showing a good match with experimental data in homogeneous channel case.

Download Full-text

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

International Journal of Modern Physics C ◽

10.1142/s0129183117501200 ◽

2017 ◽

Vol 28 (09) ◽

pp. 1750120 ◽

Cited By ~ 5

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.

Download Full-text

Discussion: “Prediction of Two-Phase Pressure Drop and Density Distribution From Mixing Length Theory” (Levy, S., 1963, ASME J. Heat Transfer, 85, pp. 137–150)

Journal of Heat Transfer ◽

10.1115/1.3686034 ◽

1963 ◽

Vol 85 (2) ◽

pp. 150-150

Author(s):

P. Lottes

Keyword(s):

Heat Transfer ◽

Pressure Drop ◽

Density Distribution ◽

Mixing Length ◽

Two Phase ◽

Mixing Length Theory ◽

Phase Pressure

Download Full-text

An Experimentally Validated Model for Two-Phase Sudden Contraction Pressure Drop in Microchannel Tube Headers

1st International Conference on Microchannels and Minichannels ◽

10.1115/icmm2003-1026 ◽

2003 ◽

Author(s):

John Wesley Coleman

Keyword(s):

Pressure Loss ◽

Accurate Determination ◽

Time Data ◽

Two Phase ◽

Pressure Transducers ◽

Pressure Losses ◽

Mass Fluxes ◽

Data Points ◽

Minor Losses ◽

Phase Pressure

This paper presents the results of an experimental investigation of two-phase pressure loss of R134a in microchannel headers using various end-cut techniques. Novel experimental techniques and test sections were developed to enable the accurate determination of the minor losses without obfuscating the problem with a lengthwise pressure gradient. This technique represents a departure from approaches used by other investigators that have extrapolated minor losses from air-water experiments and the combined effects of expansion, contraction, deceleration, and lengthwise pressure gradients. Pressure losses were recorded over the entire range of qualities from 100% vapor to 100% liquid. In addition, the tests were conducted for five different refrigerant mass fluxes between 185 kg/m2-s and 785 kg/m2-s using two differnt end-cut techniques. More than 790 data points were recorded to obtain a comprehensive understanding of the effects of mass flux and quality on minor pressure losses. High accuracy instrumentation such as coriolis mass flowmeters, RTDs, pressure transducers, and real-time data analyses were used to ensure accuracy in the results. The results show that many of the commonly used correlations for estimating two-phase pressure losses significantly underpredict the pressure losses found in compact microchannel tube headers. Furthermore, the results show that the end-cut technique can substantially affect the pressure losses in microchannel headers. A new model for estimating the pressure loss in microchannel headers is presented and a comparison of the end-cut techniques on the minor losses is reported.

Download Full-text