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

Published online by Cambridge University Press:  26 October 2011

Pedro José Martínez Ferrer ,
Tore Flåtten  and
Svend Tollak Munkejord
Pedro José Martínez Ferrer
Affiliation:
ENSMA, Teleport 2 - 1 avenue Clement Ader, 86961 Futuroscope Chasseneuil cedex, France. pedro.martinezferrer@ensma.fr ETSIA, Plaza de Cardenal Cisneros, 3, 28040 Madrid, Spain.
Tore Flåtten
Affiliation:
SINTEF Energy Research, P.O. Box 4761 Sluppen, 7465 Trondheim, Norway. Tore.Flatten@sintef.no; stm@pvv.org
Svend Tollak Munkejord
Affiliation:
SINTEF Energy Research, P.O. Box 4761 Sluppen, 7465 Trondheim, Norway. Tore.Flatten@sintef.no; stm@pvv.org
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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.

Keywords

Two-fluid modelrelaxation systemsubcharacteristic condition

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 2 , March 2012 , pp. 411 - 442
Copyright
© EDP Sciences, SMAI 2011

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