Constant-fractional-lag model for axisymmetric two-phase flow

Abstract

The suitability of the constant-fractional-lag model for axisymmetric two-phase flow with small particle loading is examined for an inviscid incompressible counter flow. A counterflow is a low-order approximation for the flow within a solid-rocket motor with a long bore of constant radius. In the model, each component of the particle-phase velocity is expressed as a certain constant multiple of the corresponding component of the gasphase velocity. A different lag constant is required for the radial and the axial components of the particlevelocity field. For light particle loading, the constant-fractional-lag model yields mathematically accurate solutions (of the formulation) for both small and finite values of the interphase-velocity-slip parameter. Comparisons with results from the Lagrangian-particle-tracking method show excellent agreement at sites outside the Stokes layer holding in that portion of the two-phase flow immediately contiguous to the gas-grain interface; i.e., the agreement holds independently of the initial particle velocity at the solid-gas interface. The constantfractional-lag model is easier to apply than the Lagrangian-particle-tracking method, and results are conveniently obtained in Eulerian form. Since the validity of the model here is proven only for an inviscid incompressible counterflow, it is recommended that further study be undertaken to delineate the validity of the approximation for more general categories of axisymmetric flow.