Modelling of two-phase flow with second-order accurate scheme
type: Item
instance of: scholarly article
title: Modelling of two-phase flow with second-order accurate scheme
zbMATH Open document ID: 0918.76050
author: Iztok Tiselj
author: Stojan Petelin
published in: Journal of Computational Physics
publication date: 1999-08-19T00:00:00Z
review text: The authors simulate numerically two-phase flows of liquid and vapor by using a second-order accurate computational scheme. They derive six differential equations from basic principles of continuity, momentum and energy for each phase, in a simplified one-dimensional formulation, but with proper attention to the mutual interactions between the phases. Two additional equations of state for each phase are needed to close the system of equations. Since mutual interactions between the phases cannot be precisely described, they rely on an extensive modeling with the best available knowledge. Furthermore, the Jacobian matrix of these equations possesses complex eigenvalues. The authors modify extensively the virtual-mass term, so that the equations become hyperbolic. As applications, the authors examine the Toumi's two-phase shock tube problem, the Riemann problem for the two-fluid-model, and Edwards transient pipe flow problem. In the two-phase shock tube problem, the authors illustrate the effects of the stiff source term, and show that the total energy profiles obtained from the first-order and second-order schemes are essentially the same. In the transient pipe flow problem, some comparisons of the obtained results on pressure variation against time at a certain location are made with the experimental data. There is practically no difference between the first-order and second-order calculations. However, both the first-order and second-order results on void-fraction at 1.5 m from the end of the pipe cannot follow the fast variation from the experimental data. The authors recognize significant uncertainties in the modeling of the general two-phase flows, although they claim the importance of the second-order schemes for fast transient events. The reviewer is torn between the inexactness of many approximations introduced in the study with higher-order computations, and the importance of simulating events when accident occurs in nuclear reactors.
Mathematics Subject Classification ID: 76M20
Mathematics Subject Classification ID: 76T99
zbMATH DE Number: 1084045
zbMATH Keywords: vapor-liquid flows
zbMATH Keywords: interactions between phases
zbMATH Keywords: effects of stiff source
zbMATH Keywords: Jacobian matrix
zbMATH Keywords: complex eigenvalues
zbMATH Keywords: virtual-mass term
zbMATH Keywords: Toumi's two-phase shock tube problem
zbMATH Keywords: Riemann problem
zbMATH Keywords: Edwards transient pipe flow problem
zbMATH Keywords: total energy
zbMATH Keywords: pressure variation
describes a project that uses: CLAWPACK
describes a project that uses: EISPACK
describes a project that uses: CATHARE
MaRDI profile type: Publication
full work available at URL: jcph.1997.5778
OpenAlex ID: W2034976201
cites work: How to prevent pressure oscillations in multicomponent flow calculations: A quasi conservative approach
cites work: An assessment of multiphase flow models using the second law of thermodynamics
cites work: The analysis of virtual mass effects in two-phase flow
cites work: Q4891309
cites work: Q3994335
cites work: Q4090062
cites work: Multicomponent flow calculations by a consistent primitive algorithm
cites work: Q4889859
cites work: A study of numerical methods for hyperbolic conservation laws with stiff source terms
cites work: Numerical Methods for Hyperbolic Conservation Laws With Stiff Relaxation I. Spurious Solutions
cites work: The Growth of Vapor Bubbles in Superheated Liquids
cites work: Approximate Riemann solvers, parameter vectors, and difference schemes
cites work: On the effect of term in multiphase mechanics
cites work: Matrix eigensystem routines - EISPACK guide. 2nd ed
cites work: Q4295149
cites work: A weak formulation of Roe's approximate Riemann solver
cites work: An approximate linearized Riemann solver for a two-fluid model
cites work: A choked-flow calculation criterion for nonhomogeneous, nonequilibrium, two-phase flows
cites work: A nearly-implicit hydrodynamic numerical scheme for two-phase flows
DOI: 10.1006/JCPH.1997.5778
description: scientific article; zbMATH DE number 1084045