The role of mesoscale structures in rapid granular and gas-solid flows

Meso-scale structures form readily in many types of multiphase flows. In granular and dilute gas-solid flows these structures take the form of clusters and filaments, and in the case of dense suspensions, bubbles. The presence of these structures leads to persistent fluctuations, which in turn significantly affects the flow behavior at the macro-scale, especially by modifying the effective stresses, interphase drag, as well the effective rates of heat and mass transfer. Unfortunately, since the characteristic size of these structures is much smaller than the size of the process vessel in which the macroscopic flow occurs, they cannot be resolved in simulations of reactor vessels of practically relevant dimensions. Because such coarse-grid simulations do not adequately capture the meso-scale fluctuations, they perform rather poorly in terms of predicting the overall flow behavior.; We present an approach to developing a sub-grid model for the hydrodynamics of rapid-gas solid flows. The intent of the sub-grid model is to help us simulate the macro-scale structures correctly without having to resolve the meso-scale structures. Before carrying out the requisite simulations to develop the sub-grid model, we examine meso-scale structures in freely evolving and rapidly sheared granular materials using the kinetic theory of granular materials. Our analysis shows that the kinetic theory of granular materials provides a sound framework with sufficient predictive capabilities and that it can be adapted to model rapid gas-solid flows.; We next present numerous simulations of gas-solid flow in small domains and extract the fluctuation statistics. We are able to deduce forms for the effective interphase drag and effective stresses in the two phases. These are drastically different from the drag and stress expressions appearing in the continuum equations of motion. We use these effective quantities to build a sub-grid model and demonstrate its simple scaling behavior. Finally we discuss ways in which the sub-grid model can be further developed at the hydrodynamic level, and how it can be extended to include heat and mass transfer effects.