On the suitability of first-order differential models for two-phase flow prediction

The stability features of a general class of one-dimensional two-phase flow models are examined. This class of models is characterized by the presence of first-order derivatives and algebraic functions of the flow variables, higher-order differential terms being absent, and can accommodate a variety of physical effects such as added mass and unequal phase pressures in some formulations. By taking a general standpoint, a number of results are obtained applicable to the entire class of models considered. In particular, it is found that, despite the presence of algebraic terms in the equations (describing, e.g. drag effects) the stability criteria are independent of the wavenumber of the perturbation. As a consequence, reality of characteristics is necessary, althoug not sufficient, for stability. To illustrate the theory, three specific models are considered in detail