Computations of Compressible Two-Phase Flow Models

Abstract

Computations of Compressible Two-Phase Flow Models Two-phase flow is generally understood as being a simultaneous flow of two different im- miscible phases separated by an infinitesimal thin interface. Phases are identified as ho- mogeneous parts of the fluid for which unique local state and transport properties can be defined. In most cases, phases are simply referred to as the state of matter, e.g. gas/vapor, liquid, or solid. Typical examples are the flow of liquid carrying vapor or gas bubbles, or the flow of gas carrying liquid droplets or solid particles. However, more complex flow pro- cesses may exist where the phase distribution is less well defined. This work is concerned with the numerical approximation of homogenized two-phase flow models. The models are obtained by averaging the balance laws for single phases and are non-strictly hyperbolic and non-conservative, i.e. they are not expressible in divergence form. The seven-equation two-phase models are regarded as well-established and can be applied to study various two- phase flow phenomena. However, physical and numerical difficulties are associated with these models. In most situations, the general physics of the models is not needed, thus, more compact models may be enough. For that reason, the reduced five- and six-equation models, deduced from the seven-equation models, are investigated in this dissertation. The five-equation model is obtained under the asymptotic limit of stiff velocity and pressure re- laxations, while the six-equation model assumes stiff velocity relaxation only. Our primary objective is to develop a deeper understanding of these models containing non-conservative derivatives and to numerically approximate them. The high order kinetic flux-vector split- ting (KFVS) scheme, the space-time conservation element and solution element (CESE) method, the high resolution central schemes, and the HLLC-type Riemann solvers are ap- plied to solve these models. Several test problems are carried out for all considered models and the numerical results of suggested schemes are compared with each other and with those available in the literature.