Conservation of mass

momentum and fluctuation energy equations for solid and gas phases are used to compute the hydrodynamics of flow in a vertical riser. The present two phase flow model is derived starting from the Boltzman equation for velocity distribution of particles. The model is generated from the Navier Stokes equation

except that the solids viscosity and stresses are computed by simultaneously solving a fluctuating energy equation for the particulate phase. The turbulence of the gas phase is treated using a SGS turbulence closure model. A no slip boundary condition for the gas phase and slip boundary condition for the particulate phase are used. The model predicted the core annular flow structure in a riser

similar to that found experimentally in a dense gas solid flow. The predicted time averaged particle concentration

velocity and viscosity of particles are compared with the experimental data of Miller and Gidaspow and reasonable agreement is observed in a circulating fluidized bed. It is shown that the flow behavior is strongly affected by the plastic fluctuation energy

and the momentum and energy transfer between the particulate and the fluid constituents.