scholarly journals Towards Understanding the Structure of Subcritical and Transcritical Liquid–Gas Interfaces Using a Tabulated Real Fluid Modeling Approach

Energies ◽  
2021 ◽  
Vol 14 (18) ◽  
pp. 5621
Author(s):  
Sajad Jafari ◽  
Hesham Gaballa ◽  
Chaouki Habchi ◽  
Jean-Charles de Hemptinne
Keyword(s):  
Equations Of State ◽  
Fluid Model ◽  
Thermodynamic Characteristics ◽  
Diffuse Interface ◽  
Numerical Schemes ◽  
Two Phase ◽  
Jet Mixing ◽  
Fuel Atomization ◽  
Real Fluid ◽  
Rfm Model

A fundamental understanding and simulation of fuel atomization, phase transition, and mixing are among the topics researchers have struggled with for decades. One of the reasons for this is that the accurate, robust, and efficient simulation of fuel jets remains a challenge. In this paper, a tabulated multi-component real-fluid model (RFM) is proposed to overcome most of the limitations and to make real-fluid simulations affordable. Essentially, a fully compressible two-phase flow and a diffuse interface approach are used for the RFM model, which were implemented in the CONVERGE solver. PISO and SIMPLE numerical schemes were modified to account for a highly coupled real-fluid tabulation approach. These new RFM model and numerical schemes were applied to the simulation of different fundamental 1-D, 2-D, and 3-D test cases to better understand the structure of subcritical and transcritical liquid–gas interfaces and to reveal the hydro-thermodynamic characteristics of multicomponent jet mixing. The simulation of a classical cryogenic injection of liquid nitrogen coaxially with a hot hydrogen jet is performed using thermodynamic tables generated by two different equations of state: Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK). The numerical results are finally compared with available experimental data and published numerical studies with satisfactory agreement.

Numerical Computation of One-Dimensional Unsteady Two-Phase Flow Using HEM Model and IAPWS IF-97 Equations of State

2013 ◽  
Author(s):  
Nitin Khola ◽  
Manmohan Pandey
Keyword(s):  
Numerical Computation ◽  
Two Phase Flow ◽  
Equations Of State ◽  
Nuclear Reactors ◽  
Fluid Model ◽  
Equilibrium Mixture ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Momentum Integral

Numerical simulation of transients in two-phase flow is crucial to simulate accident-like and aberrant conditions of nuclear reactors for safety analysis. A considerable number of such problems can be treated as one-dimensional with significant reduction in complexity without much loss in applicability. Most commercial thermal hydraulic codes are based on the two-fluid model, which solves balance equations for each phase and also accounts for thermodynamic non-equilibrium between the phases. However, the homogenous equilibrium mixture (HEM) model of two-phase flow can be employed to develop simple and efficient codes for transient simulations, using which extensive parametric studies can be carried out. In the present work, a code for numerical computation of unsteady one-dimensional two-phase flow has been developed and reactor transients have been simulated. The governing equations were obtained by the HEM model and were decoupled and approximated using the sectionalized compressible flow (SC) model and the momentum integral (MI) model. The equations of state used in the code are based on IAPWS Industrial Formulation-97. Pressure and heat flux transients for PWR and BWR were simulated with the code and compared with those reported in the literature. Further numerical simulations with the code were carried out to predict the transient response of nuclear reactors to various perturbations.

scholarly journals Assessment of numerical schemes for complex two-phase flows with real equations of state

2020 ◽  
Vol 196 ◽  
pp. 104347
Author(s):  
Philippe Helluy ◽  
Olivier Hurisse ◽  
Lucie Quibel
Keyword(s):  
Equations Of State ◽  
Numerical Schemes ◽  
Two Phase Flows ◽  
Two Phase

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid

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.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

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

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.

A Physically Based, One-Dimensional Two-Fluid Model for Direct Contact Condensation of Steam Jets Submerged in Subcooled Water

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
David Heinze ◽  
Thomas Schulenberg ◽  
Lars Behnke
Keyword(s):  
Direct Contact ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Interfacial Area ◽  
Phase Flow ◽  
Two Phase ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Contact Condensation ◽  
Two Fluid

A simulation model for the direct contact condensation of steam in subcooled water is presented that allows determination of major parameters of the process, such as the jet penetration length. Entrainment of water by the steam jet is modeled based on the Kelvin–Helmholtz and Rayleigh–Taylor instability theories. Primary atomization due to acceleration of interfacial waves and secondary atomization due to aerodynamic forces account for the initial size of entrained droplets. The resulting steam-water two-phase flow is simulated based on a one-dimensional two-fluid model. An interfacial area transport equation is used to track changes of the interfacial area density due to droplet entrainment and steam condensation. Interfacial heat and mass transfer rates during condensation are calculated using the two-resistance model. The resulting two-phase flow equations constitute a system of ordinary differential equations, which is solved by means of the explicit Runge–Kutta–Fehlberg algorithm. The simulation results are in good qualitative agreement with published experimental data over a wide range of pool temperatures and mass flow rates.

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.

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