Application of a Two-Fluid Model to Simulate the Heating of Two-Phase Flows

International audienceThis paper is dedicated to the simulation of two-phase flows on the basis of a two-fluid model that allows to account for the disequilibrium of velocities, pressures , temperatures and chemical potentials (mass transfer). The numerical simulations are performed using a fractional step method treating separately the convective part of the model and the source terms. The scheme dealing with the convective part of the model follows a Finite Volume approach and is based on a relaxation scheme. In the sequel, a special focus is put on the discretization of the terms that rule the mass transfer. The scheme proposed is a first order implicit scheme and can be verified using an analytical solution. Eventually, a test case of the heating of a mixture of steam and water is presented, which is representative of a steam generator device

Phase appearance or disappearance in two-phase flows

This paper is devoted to the treatment of specific numerical problems which appear when phase appearance or disappearance occurs in models of two-phase flows. Such models have crucial importance in many industrial areas such as nuclear power plant safety studies. In this paper, two outstanding problems are identified: first, the loss of hyperbolicity of the system when a phase appears or disappears and second, the lack of positivity of standard shock capturing schemes such as the Roe scheme. After an asymptotic study of the model, this paper proposes accurate and robust numerical methods adapted to the simulation of phase appearance or disappearance. Polynomial solvers are developed to avoid the use of eigenvectors which are needed in usual shock capturing schemes, and a method based on an adaptive numerical diffusion is designed to treat the positivity problems. An alternate method, based on the use of the hyperbolic tangent function instead of a polynomial, is also considered. Numerical results are presented which demonstrate the efficiency of the proposed solutions

Large time-step positivity-preserving method for multiphase flows

Summary. Using a relaxation strategy in a Lagrangian-Eulerian formulation, we propose a scheme in local conservation form for approximating weak solutions of complex compressible flows involving wave speeds of different orders of magnitude. Explicit time integration is performed on slow transport waves for the sake of accuracy while fast acoustic waves are dealt with implicitly to enable large time stepping. A CFL condition based on the slow waves is derived ensuring positivity properties on the density and the mass fraction. Numerical benchmarks validate the method. 1 Statement of the problem The present work treats the numerical approximation of the discontinuous solutions of the following PDE syste

Time varying grids for gas dynamics

Summary. In the context of offshore oil production, we are interested in accurate and fast computation of two-phase flows in pipelines. A one dimensional model of hyperbolic equations is solved numerically by an explicit Lagrange- Euler projection method. This paper shows that adaptive multiresolution techniques can speed up the computation significantly. Even more so when local time stepping enhancement is used. 1 Modeling of the physical problem In this short paper we restrict ourselves to a homogeneous model for two-phase flows. The density ρ, velocity u and the gas mass fraction Y of the mixture of oil and gas are related through a PDE system ⎨∂t(ρ

A Simple Finite-Volume Method for Compressible Isothermal Two-Phase Flows Simulation

International audienceWe present a simple method for simulating isothermal compressible two-phase flows with mass transfer. The convective part of the model is compatible with the Least Action Principle and the system is endowed with an entropy inequality which accounts for phase change terms and phasic pressure unbalance. A study of the system as a relaxed model of two equilibrium models is performed. This study allows the design of two-step relaxation-convection Finite-Volume discretization scheme which complies with the entropy balance of the model which drives the mass transfer phase-change process. Numerical results involving dynamical phase-change are presented

DOI: 10.1142/S0218202512500145 Relaxation of fluid systems

International audienceWe propose a relaxation framework for general fluid models which can be understood as a natural ex- tension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The numerical method is particularly simple in the case of a fully degenerate relaxation system for which the solution of the Riemann problem is explicit. Indeed, the Godunov solver for the homogeneous relaxation system results in an HLLC-type solver for the equilibirum model. Discrete entropy inequalities are established under a natural Gibbs principle

Phase Change Simulation for Isothermal Compressible Two-Phase Flows

International audienceWe present a numerical scheme based on a two-step convection-relaxation strategy for the simulation of compressible two-phase flows with phase change. The core system used here is a simple isothermal model where stiff source terms account for mass transfer

A splitting method for the isentropic Baer-Nunziato two-phase flow model

In the present work, we propose a fractional step method for computing approximate solutions of the isentropic Baer-Nunziato two-phase flow model. The scheme relies on an operator splitting method corresponding to a separate treatment of fast propagation phenomena due to the acoustic waves on the one hand and slow propagation phenomena due to the fluid motion on the other. The scheme is proved to preserve positive values of the statistical fractions and densities. We also provide two test-cases that assess the convergence of the method. <br> Nous proposons ici une méthode à pas fractionnaires pour le calcul de solutions approchées pour la version isentropique du modèle diphasique de Baer-Nunziato. Le schéma s’appuie sur un splitting de l’opérateur temporel correspondant à la prise en compte différenciée des phéno-mènes de propagation rapide dus aux ondes acoustiques et des phénomènes de propagation lente dus aux ondes matérielles. On prouve que le schéma permet de préserver des valeurs positives pour les taux statistiques de présence des phases ainsi que pour les densités. Deux cas tests numériques permettent d’illustrer la convergence de la méthode

Convergence of time-space adaptive algorithms for nonlinear conservation laws

International audienceA family of explicit adaptive algorithms is designed to solve nonlinear scalar one-dimensional conservation laws. Based on the Godunov scheme on a uniform grid, a first strategy uses the multiresolution analysis of the solution to design an adaptive grid that evolves in time according to the time-dependent local smoothness. The method is furthermore enhanced by a local time-stepping strategy. Both numerical schemes are shown to converge towards the unique entropy solution