A two-fluid four-equation model with instantaneous thermodynamical equilibrium

¹ Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Kolbjørn Hejes vei 1B, NO-7491 Trondheim, Norway.
² SINTEF Materials and Chemistry, P. O. Box 4760 Sluppen, NO-7465 Trondheim, Norway.
alexandre.morin@sintef.no; Tore.Flatten@sintef.no

Received: 28 March 2015
Revised: 7 August 2015
Accepted: 18 September 2015

Abstract

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.