We consider an equilibrium version of a common two-fluid model for pipe flow, containing one mixture mass equation and one mixture energy equation. This model can be derived from a five-equation model with instantaneous thermal equilibrium, to which additional phase relaxation terms are added. An original contribution of this paper is a quasilinear formulation of the instantaneous phase relaxation limit. From this, the mixture sound speed intrinsic to the model can be extracted. This allows us to directly prove some subcharacteristic conditions with respect to a previously established model hierarchy of different relaxation processes. These subcharacteristic conditions reveal the fundamental insight of this paper; in the hierarchy, thermodynamic versus velocity relaxation both reduce the mixture sound velocity with a factor that is independent of whether the other type of relaxation has been performed.
Accepté le :
DOI : 10.1051/m2an/2015074
Mots clés : Two-phase flows, relaxation, two-fluid model, subcharacteristic condition
@article{M2AN_2016__50_4_1167_0,
author = {Morin, Alexandre and Fl\r{a}tten, Tore},
title = {A two-fluid four-equation model with instantaneous thermodynamical equilibrium},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1167--1192},
publisher = {EDP-Sciences},
volume = {50},
number = {4},
year = {2016},
doi = {10.1051/m2an/2015074},
mrnumber = {3521716},
zbl = {1346.76196},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2015074/}
}
TY - JOUR AU - Morin, Alexandre AU - Flåtten, Tore TI - A two-fluid four-equation model with instantaneous thermodynamical equilibrium JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1167 EP - 1192 VL - 50 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2015074/ DO - 10.1051/m2an/2015074 LA - en ID - M2AN_2016__50_4_1167_0 ER -
%0 Journal Article %A Morin, Alexandre %A Flåtten, Tore %T A two-fluid four-equation model with instantaneous thermodynamical equilibrium %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1167-1192 %V 50 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2015074/ %R 10.1051/m2an/2015074 %G en %F M2AN_2016__50_4_1167_0
Morin, Alexandre; Flåtten, Tore. A two-fluid four-equation model with instantaneous thermodynamical equilibrium. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 4, pp. 1167-1192. doi : 10.1051/m2an/2015074. http://archive.numdam.org/articles/10.1051/m2an/2015074/
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