ANALYSIS OF TWOPHASE FLOW MODEL EQUATIONS

Abstract

Abstract. In this paper, we propose closures for multi-phase owmodels, which satisfy boundary conditions and conservation con-straints. The models governing the evolution of the uid mixing arederived by applying an ensemble averaging procedure to the micro-physical equations characterized by distinct phases. We considercompressible multi species multi-phase ow with surface tensionand transport. 1. IntroductionWe discuss compressible multi-phase ow equations obtained by av-eraging microphysical equations characterized by distinct phases. Themodels we consider have distinct phase pressures and lead to hyperbolicmodels, eliminating mathematical diculties of complex characteristicsassociated with single pressure ow models having distinct velocities.In this sense they are an outgrowth of earlier studies by Stewart andWendro [23], Ransom and Hicks [20], Chen et al. [4, 12], Saltz etal. [12] and Saurel et al. [22, 1, 8]. Multiphase ow has been studiedfor many decades, with the basic physics and equations developed inthe classical treateses of Wallis [24] and Drew [9]. The derivation ofaveraged equations leads to unde ned averages of nonlinear functions ofthe primitive variables. These quantities must be modeled to close thesystem of averaged equations.The main result, achieved in part here, is to identify a closure whichsatis es all the conservation and boundary constraints for the continuityand momentum equations. In a second paper, we will close the energy