Filtered models for gas-particle flow hydrodynamics

Continuum model equations for unsteady gas-particle flows in devices such as fluidized beds contain unstable modes whose length scale is of the order of ten particle diameters. Yet, because of limited computational resources, these flows are routinely simulated by solving discretized continuum models over coarse spatial grids. These simulations resolve the large-scale flow structures, but not the finer scale structures which affect macroscopic flow. In most industrial applications involving large devices, it is impractical to resolve all the fine-scale structures in numerical simulations. We address this problem by constructing a filtered model for coarse grid simulation of gas-particle flows. In this approach, simulations resolve the coarse details of the flow, and the influence of small-scale flow details are modeled and incorporated through computationally-derived constitutive relationships.; Using gas-particle flows in a wide and very tall vertical channel as an example, we demonstrate that the results obtained in coarse-grid numerical simulation of the microscopic equations for gas-particle flows are substantially different than those obtained in simulation of the filtered model. We continue by developing a systematic filtering approach to construct closure relationships for the drag coefficient and the effective stresses in the gas and particle phases that are appropriate for the coarse-grid simulations gas-particle flows. We then examine the validity of the filtered equations in this context by comparing the predictions of the filtered model equations with highly resolved simulations of the microscopic two fluid model equations. The filtered model results suggest this approach is valid.; This thesis contains three supplementary studies. We address the issues involved in formulating a steady state model to predict the time-averaged gas-particle flow characteristics and show that the filtered models developed in this thesis can prove useful in this effort. We investigate the possibility of dynamic contributions to the inter-phase interaction force in filtered gas-particle flow models and conclude that dynamic contributions may exist, but do not exhibit significant influence in fluidization. Finally, we evaluate several spatial discretization schemes for the numerical solution of our filtered model equations and conclude that common flux-limiting schemes provide the accuracy and stability required.