Meso-scale structures that take the form of clusters and streamers are commonly
observed in dilute gas–particle flows, such as those encountered in risers. Continuum
equations for gas–particle flows, coupled with constitutive equations for particle-phase
stress deduced from kinetic theory of granular materials, can capture the formation of
such meso-scale structures. These structures arise as a result of an inertial instability
associated with the relative motion between the gas and particle phases, and an
instability due to damping of the fluctuating motion of particles by the interstitial
fluid and inelastic collisions between particles. It is demonstrated that the meso-scale
structures are too small, and hence too expensive, to be resolved completely in
simulation of gas–particle flows in large process vessels. At the same time, failure
to resolve completely the meso-scale structures in a simulation leads to grossly
inaccurate estimates of inter-phase drag, production/dissipation of pseudo-thermal
energy associated with particle fluctuations, the effective particle-phase pressure and
the effective viscosities. It is established that coarse-grid simulation of gas–particle
flows must include sub-grid models, to account for the effects of the unresolved meso-scale
structures. An approach to developing a plausible sub-grid model is proposed.