CHAPMAN-ENSKOG CLOSURE APPROXIMATION IN THE KINETIC-THEORY OF DILUTE TURBULENT GAS-PARTICULATE SUSPENSIONS

The Chapman-Enskog approach is applied to a generalised Fokker-Planck equation for the ensemble-averaged phase-space number density of parti cles to find a closure approximation for the third-order fluctuating v elocity correlations in the particle phase of a turbulent dilute gas-p articulate suspension. The resulting closed set of continuum equations is shown to be free of empirical parameters, provided the particles a re sufficiently large and the turbulence in the both phases is locally isotropic. Special attention is paid to the case where the particle p hase is near equilibrium state. In this case the transport equations f or diagonal components of the particle Reynolds stresses reduce to a c onservation equation for the turbulent kinetic energy. The effective e nergy transfer coefficient is calculated and the boundary conditions a t the rigid wall are formulated. The resulting system of continuum equ ations and boundary conditions is analysed for fully developed flow be tween the vertical plane walls of a dilute but densely loaded gas-part iculate suspension. Such a flow models a number of practical applicati ons, e.g. the flow in the riser section of fast (circulating) fluidise d bed. Copyright (C) 1998 Elsevier Science B.V. All rights reserved.