Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays

Frédérique Laurent

ESAIM: Mathematical Modelling and Numerical Analysis (2006)

  • Volume: 40, Issue: 3, page 431-468
  • ISSN: 0764-583X

Abstract

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The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in a discretization of the droplet size variable into cells called sections. This analysis provides a justification of the “right” choice for this discretization to obtain a first order accurate and monotone scheme, with no restrictive CFL condition. This result leads to the development of a class of methods of arbitrary high order accuracy through the use of moments on the droplet surface in each section and a Godunov type method. Moreover, an extension of the two moments method is proposed which preserves the positivity and limits the total variation. Numerical results of the multi-fluid methods are compared to examine their capability to accurately describe the mass density in the spray with a small number of variables. This is shown to be a key point for the use of such methods in realistic flow configurations.

How to cite

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Laurent, Frédérique. "Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays." ESAIM: Mathematical Modelling and Numerical Analysis 40.3 (2006): 431-468. <http://eudml.org/doc/249729>.

@article{Laurent2006,
abstract = { The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in a discretization of the droplet size variable into cells called sections. This analysis provides a justification of the “right” choice for this discretization to obtain a first order accurate and monotone scheme, with no restrictive CFL condition. This result leads to the development of a class of methods of arbitrary high order accuracy through the use of moments on the droplet surface in each section and a Godunov type method. Moreover, an extension of the two moments method is proposed which preserves the positivity and limits the total variation. Numerical results of the multi-fluid methods are compared to examine their capability to accurately describe the mass density in the spray with a small number of variables. This is shown to be a key point for the use of such methods in realistic flow configurations. },
author = {Laurent, Frédérique},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Spray; evaporation; multi-fluid method; kinetic schemes.; spray; kinetic schemes},
language = {eng},
month = {7},
number = {3},
pages = {431-468},
publisher = {EDP Sciences},
title = {Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays},
url = {http://eudml.org/doc/249729},
volume = {40},
year = {2006},
}

TY - JOUR
AU - Laurent, Frédérique
TI - Numerical analysis of Eulerian multi-fluid models in the context of kinetic formulations for dilute evaporating sprays
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2006/7//
PB - EDP Sciences
VL - 40
IS - 3
SP - 431
EP - 468
AB - The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in a discretization of the droplet size variable into cells called sections. This analysis provides a justification of the “right” choice for this discretization to obtain a first order accurate and monotone scheme, with no restrictive CFL condition. This result leads to the development of a class of methods of arbitrary high order accuracy through the use of moments on the droplet surface in each section and a Godunov type method. Moreover, an extension of the two moments method is proposed which preserves the positivity and limits the total variation. Numerical results of the multi-fluid methods are compared to examine their capability to accurately describe the mass density in the spray with a small number of variables. This is shown to be a key point for the use of such methods in realistic flow configurations.
LA - eng
KW - Spray; evaporation; multi-fluid method; kinetic schemes.; spray; kinetic schemes
UR - http://eudml.org/doc/249729
ER -

References

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