A FOUR-EQUATION MODEL FOR PREDICTION OF GAS-SOLID TURBULENT FLOWS

Abstract

A four-equation model is proposed for prediction of dilute turbulent gas-solid flows where the ratio of the particle and the gas densities is large. The model is based on explicit algebraic relations for Reynolds stresses and turbulent fluxes of the void fraction, which were derived in an earlier work within the context of Reynolds-averaged Navier-Stokes (RANS) methodology. These relations are manipulated here to derive nonlinear eddy-viscosity-type models for thin-shear flows. Further, new models are proposed for third-order correlations which are also simplified for thin-shear flows. These models are used to propose four transport equations for the turbulence kinetic energy of the carrier phase and its rate of dissipation, the turbulence kinetic energy of the dispersed phase, and the velocity covariance of the two phases. The final four-equation model is implemented for prediction of a particle-laden turbulent jet, and encouraging agreements with available laboratory data are observed.