The role of meso-scale structures in rapid gas-solid flows

Meso-scale structures that take the form of clusters and streamers are comm only observed in dilute gas-particle flows, such as those encountered in ri sers. Continuum equations for gas-particle flows, coupled with constitutive equations for particle-phase stress deduced from kinetic theory of granula r materials, can capture the formation of such meso-scale structures. These structures arise as a result of an inertial instability associated with th e relative motion between the gas and particle phases, and an instability d ue to damping of the fluctuating motion of particles by the interstitial fl uid and inelastic collisions between particles. It is demonstrated that the mesoscale structures are too small, and hence too expensive, to be resolve d completely in simulation of gas-particle flows in large process vessels. At the same time, failure to resolve completely the meso-scale structures i n a simulation leads to grossly inaccurate estimates of inter-phase drag, p roduction/dissipation of pseudo-thermal energy associated with particle flu ctuations, the effective particle-phase pressure and the effective viscosit ies. It is established that coarse-grid simulation of gas-particle flows mu st include sub-grid models, to account for the effects of the unresolved me soscale structures. An approach to developing a plausible sub-grid model is proposed.