On the Wave Structure of Two-Phase Flow Models

We explore the relationship between two common two-phase flow models, usually denoted as the two-fluid and drift-flux models. They differ in their mathematical description of momentum transfer between the phases. In this paper we provide a framework in which these two model formulations are unified. The drift-flux model employs a mixture momentum equation and treats interphasic momentum exchange indirectly through the slip relation, which gives the relative velocity between the phases as a function of the flow parameters. This closure law is in general highly complex, which makes it difficult to analyse the model algebraically. To facilitate the analysis, we express the quasilinear formulation of the drift-flux model as a function of three parameters; the derivatives of the slip with respect to the vector of unknown variables. The wave structure of this model is investigated using a perturbation technique. Then we rewrite the drift-flux model with a general slip relation such that it is expressed in terms of the canonical two-fluid form. That is, we replace the mixture momentum equation and the slip relation with equivalent evolution equations for the momentums of each phase. We obtain a mathematically equivalent formulation in terms of a two-fluid model and by this bridge some of the gap between the drift-flux model and the two-fluid model. Finally, the effect of the various exchange terms on the wave structure of the two-fluid model is investigated. subject classification. 15A90, 35L65, 35P15, 76T10 key words. hyperbolic system of conservation laws, two phase flow, drift-flux model, two-fluid model, perturbation method, eigenvalues, interface friction