Volume Averaged Pressure Interactions for Dispersed Droplet Phase Modeling of Multiphase Flow
This study addresses cross-phase interactions and momentum exchange between dispersed (droplet) and carrier (air) phases of multiphase flow. Alternative formulations are developed for the volume averaged interfacial pressure and apparent mass forces. Algebraic source terms in the momentum equation can accommodate the interfacial shear stresses. Multiphase turbulent stresses in the carrier phase are modeled with a Boussinesq assumption. New interfacial pressure modeling in an Eulerian formulation with volume averaging is developed. Nomenclature ai = surface of the phase interface akw = surface of phase k in contact with the wall surface C D = drag coefficient Dd = droplet diameter g = gravity I = identity tensor jk = flux of the general scalar quantity ˙ mk = mass flux for the particular phase nk, n1, n2 = normal vector for the particular phase nkw = normal vector for the particular phase at the wall surface p = pressure pk = local pressure of phase k � pk� =v olume-averaged pressure of phase k � pki� =v olume-averaged interfacial pressure of phase k Rer = relative (droplet-air) Reynolds number S = surface ˆ S = source term V =v olume v = phase velocity [v, dispersed phase; va,