TURBULENT GAS-SOLID FLOWS, PART II: EXPLICIT ALGEBRAIC MODELS

Abstract

Algebraic closures are derived for the Reynolds stresses and the fluxes of the void fraction in the Reynolds-averaged transport equations of gas-solid turbulent flows with low volume fraction and high density ratio. These closures are obtained from the hierarchy of secondorder moment closures and are favored over conventional models based on the Boussinesq-type (linear gradient diffusion) approximations. With a liberal use of the Cayley-Hamilton theorem, "explicit" solutions of the algebraic equations are obtained for the Reynolds stresses of both the carrier and the dispersed phases, and the turbulent fluxes of the void fraction. The predictions of the model for the Reynolds stresses are shown to compare well with direct numerical simulation (DNS) data of particle-laden homogeneous turbulent shear flows.