Local instant formulation of two-phase flow

Abstract

The local instant formulation of mass, momentum and energy conservations of two-phase flow has been developed. Distribution, an extended notion of a function, has been introduced for this purpose because physical parameters of two-phase flow media change discontinuously at the interface and the Lebesgue measure of an interface is zero. Using a characteristic function of each phase, the physical parameters of two-phase flow have been defined as field quantities. In addition to this, the source terms at the interface are defined in terms of the local instant interfacial area concentration. Based on these field quantities, the local instant field equations of mass, momentum and total energy conservations of two-phase flow have been derived. Modification of these field equations gives the single field representation of the local instant field equations of two-phase flow. Neglecting the interfacial force and energy, this formulation coincides with the field equations of single-phase flow, except in the definition of differentiation. The local instant two-fluid formulation of two-phase flow has also been derived. This formulation consists of six local instant field equations of mass, momentum and total energy conservations of both phases. Interfacial mass, momentum and energy transfer terms appear in these equations, which are expressed in terms of the local instant interfacial area concentration.