# On the effect of temperature and velocity relaxation in two-phase flow models

Pedro José Martínez Ferrer; Tore Flåtten; Svend Tollak Munkejord

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 46, Issue: 2, page 411-442
- ISSN: 0764-583X

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topMartínez Ferrer, Pedro José, Flåtten, Tore, and Munkejord, Svend Tollak. "On the effect of temperature and velocity relaxation in two-phase flow models." ESAIM: Mathematical Modelling and Numerical Analysis 46.2 (2011): 411-442. <http://eudml.org/doc/222124>.

@article{MartínezFerrer2011,

abstract = {
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This allows us to directly prove a subcharacteristic condition; each level of equilibrium assumption imposed reduces the propagation velocity of pressure waves. Furthermore, we show that each relaxation procedure reduces the mixture sound velocity with a factor that is independent of whether the other relaxation procedure has already been performed.
Numerical simulations indicate that thermal relaxation in the two-fluid model has negligible impact on mass transport dynamics. However, the velocity difference of sonic propagation in the thermally relaxed and unrelaxed two-fluid models may significantly affect practical simulations.
},

author = {Martínez Ferrer, Pedro José, Flåtten, Tore, Munkejord, Svend Tollak},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Two-fluid model; relaxation system; subcharacteristic condition; two-fluid model},

language = {eng},

month = {10},

number = {2},

pages = {411-442},

publisher = {EDP Sciences},

title = {On the effect of temperature and velocity relaxation in two-phase flow models},

url = {http://eudml.org/doc/222124},

volume = {46},

year = {2011},

}

TY - JOUR

AU - Martínez Ferrer, Pedro José

AU - Flåtten, Tore

AU - Munkejord, Svend Tollak

TI - On the effect of temperature and velocity relaxation in two-phase flow models

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/10//

PB - EDP Sciences

VL - 46

IS - 2

SP - 411

EP - 442

AB -
We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This allows us to directly prove a subcharacteristic condition; each level of equilibrium assumption imposed reduces the propagation velocity of pressure waves. Furthermore, we show that each relaxation procedure reduces the mixture sound velocity with a factor that is independent of whether the other relaxation procedure has already been performed.
Numerical simulations indicate that thermal relaxation in the two-fluid model has negligible impact on mass transport dynamics. However, the velocity difference of sonic propagation in the thermally relaxed and unrelaxed two-fluid models may significantly affect practical simulations.

LA - eng

KW - Two-fluid model; relaxation system; subcharacteristic condition; two-fluid model

UR - http://eudml.org/doc/222124

ER -

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