A cascade model for neutrally buoyant dispersed two-phase homogeneous turbulence-I. Model formulation

This work proposes a cascade model approach to describe two-phase turbulent flows of neutrally buoyant liquid dispersions for high dispersed phase fractions. A continuum framework is selected for the representation of the mean flow momentum and continuity equations. The cascade model of Desnyansky & Novikov is extended to describe the energy spectrum and eddy intermittency in the presence of a dispersed phase. The Reynolds stress in the mean balance equation is related to the cascade variables by a spectral eddy viscosity model. A population balance is formulated for each eddy size. This approach permits the specification of the immediate environment of the drop processes modeled in the population balance. Specific drop-eddy events such as grazing collisions, drop entrapment and eddy shattering are suggested and their effects on the turbulent spectrum, eddy intermittencies and drop size distributions are examined. The energy, intermittency and population balance equations modified to include the effects of drop-eddy interactions form the proposed two-phase cascade model for homogeneous, neutrally buoyant, turbulent dispersions.