Modelling evaporation fronts with reactive Riemann solvers
type: Item
instance of: scholarly article
title: Modelling evaporation fronts with reactive Riemann solvers
zbMATH Open document ID: 1088.76051
published in: Journal of Computational Physics
publication date: 2005-06-13T00:00:00Z
review text: This work deals with the modelling of permeable fronts and the building of a numerical method describing a multi-dimensional propagation of such fronts. Particular attention is paid to evaporation waves which appear in cavitating systems. Such systems leave their metastable liquid state with temperature above the saturated temperature (caused by rarefaction wave excitation) and produce a liquid-vapor mixture at thermodynamic equilibrium, which flows with high velocity (e.g.\ of about 100 m/s). During such transformations, occuring at finite rate, a subsonic phase transition front propagates through the superheated liquid (with velocity of e.g.\ 1 m/s). The fronts are considered as discontinuities separating the liquid phase from the liquid-vapor mixture. In the present paper, no structure of the discontinuity is taken into account. In order to determine the kinetics, the evaporation front is assumed to propagate at maximum admissible speed corresponding to the Chapman-Jouguet deflagration point [\textit{J. R. Simões-Moreira, J. E. Shepherd}, J. Fluid. Mech. 382, 63--86 (1999; Zbl 0953.76508)]. The Rankine-Hugoniot relations for the equations of state of the liquid and the liquid-vapor mixture are derived to express the mass, momentum and energy conservation across the front. Then the liquid-vapor phase transition is described. Therefore the associated reactive Riemann problem has to be solved. But, in the case of multi-dimensional propagation of permeable fronts which are subsonic, the conventional averaging scheme (such as the Godunov scheme) is inappropriate. To overcome this difficulty, the reactive Riemann problem solution is embedded into the discrete equations method (DEM) [\textit{R. Abgrall, R. Saurel}, J. Comput. Phys. 186, No. 2, 361--396 (2003; Zbl 1072.76594); \textit{R. Saurel, S. Gavrilyuk, F. Renaud}, J. Fluid Mech. 495, 283--321 (2003; Zbl 1080.76062)]. Thus, the DEM method is here extended to interfaces and multiphase mixtures and then applied to se…
reviewed by: Claudia-Veronika Meister
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76V05
Mathematics Subject Classification ID: 76T10
Mathematics Subject Classification ID: 80A32
zbMATH DE Number: 2175583
zbMATH Keywords: cavitation
zbMATH Keywords: detonation
zbMATH Keywords: Chapman-Jouguet deflagration point
zbMATH Keywords: discrete equation method
author: O. Le Métayer
author: Jacques Massoni
author: R. Saurel
describes a project that uses: HE-E1GODF
MaRDI profile type: Publication
full work available at URL: j.jcp.2004.11.021
OpenAlex ID: W2142745686
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DOI: 10.1016/J.JCP.2004.11.021
description: scientific article; zbMATH DE number 2175583