Coarse-grid simulation of gas-particle flows in vertical risers

Continuum model equations for unsteady gas-particle flows in devices such as fluidized beds and circulating fluidized bed risers contain unstable modes whose length scale is of the order of 10 particle diameters. Yet, because of limited computational resources, these flows are routinely simulated by solving the discretized version of continuum models over coarse spatial grids. These simulations resolve the large-scale flow structures but not the finer scale structures. In most industrial applications involving large devices, it is impractical to resolve all the fine-scale structures, and therefore the effects of the unresolved structures must be addressed through suitable subgrid models. Using gas-particle flows in a wide and very tall vertical channel as an example, we have demonstrated in this study that the results obtained in coarse-grid integration of the microscopic equations for gas-particle flows change appreciably if subgrid corrections to account for the effects of unresolved structures are included. The addition of a simple time-averaged subgrid closure for the effective drag coefficient and particle phase viscosity and pressure led to a qualitative change in the simulation results. Our simulations also revealed a lack of separation of time scales between the resolved and unresolved structures. This led us to formulate a simple stochastic subgrid closure for the drag coefficient and investigate its consequence. The addition of a stochastic correction made quantitative, but not qualitative, changes to the simulation results.