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

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

Received: 10 February 2011
Revised: 23 May 2011

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.