Laminar dispersed two-phase flows at low concentration II. Disturbance Equations

Abstract

In a preceding paper (Part I), a generalised system of equations was proposed to represent multi-D flows of particle-fluid mixtures. It was based on a coupling of two sets of equations, one for each phase: the Lundgren hierarchy for the continuous phase and an adaptation of the well-known B.B.G.K.Y. hierarchy for the dispersed phase. It happens that at any order, many of the equations obtained remain intricate: several important terms are difficult either to interpret or to compute effectively such as the averaged extra-deformation tensors, the interfacial force density and finally the pseudo-turbulent tensors in the momentum equations for both phases, arising from inclusion motions alone. That can be remedied by introducing the concept of an "averaged disturbance field" based on differences between two successive conditionally averaged variables. All the equations of both hierarchies are transformed in terms of these fields, which play a central role in our theory, except for the first-order equations of both hierarchies; these correspond to conservation equations of standard two-fluid models.