Particle Flow Instabilities

Previous work has indicated that inelastic grains undergoing homogeneous cooling may be unstable, giving rise to the formation of velocity vortices and particle clusters for sufficiently large systems. Such instabilities are observed in industrial coal and biomass gasifiers and are known to influence gas-solid contact area, mixing dynamics, and heat/mass transfer rates. However, the driving mechanisms that lead to vortices and clusters are not well understood. Discrete-particle simulations provide a well-established method for understanding such mechanisms but are not a feasible technique for predicting the behavior of large-scale systems. Kinetic-theory-based hydrodynamic (continuum) models offer an effective means of describing such flows, and instabilities present a stringent test of such models due to the transient, three- dimensional nature of instabilities and the large range of time and length scales over which these mechanisms occur. This work begins with the study, via a combination of hydrodynamic (continuum) models and discrete-particle simulations, of a relatively simple flow and includes additional complexities in a stepwise manner to assess various driving mechanisms. Comparisons with discrete-particle simulations, which offer detailed, well-established (but computationally limited) descriptions of particle flows, indicate the ability of hydrodynamic (continuum) models to accurately incorporate each mechanism. Specifically, the critical length scale for velocity vortices and/or particle clusters are studied in systems of moderate dissipation and particle concentration, extreme dissipation, frictional particles, high gradients, polydisperse particles, and gas-solid flows. This effort begins with a granular flow of monodisperse, frictionless spheres. The results indicate the validity of the hydrodynamic model, derived from the revised Enskog equation, in predicting the onset of instabilities for moderately dense and dissipative flows. Granular flows of extreme dissipation are then studied to determine the accuracy of the standard Sonine polynomial approximation. Discrepancies are observed for extreme levels of dissipation. A Sonine approximation with a modified zeroth-order contribution is shown to remedy this disagreement. Frictional particle interactions introduce a new mechanism for the dissipation of granular energy that is not relevant for frictionless interactions. Counterintuitive findings, which stem from the interplay of rotation and translation, for the influence of friction on instabilities are presented. While monodisperse particles flows allow for a straightforward choice of the hydrodynamic quantities present in the balance equations, polydispersity allows for separate species energy balances or a single mixture-temperature-based energy balance. The results indicate that a mixture-temperature-based energy balance is successful. Granular flows containing high gradients are studied. These flows introduce an important challenge to hydrodynamic descriptions because the constitutive quantities depend on first-order closures. The results indicate the ability of Navier-Stokes-order theories beyond the expected range of applicability. The introduction of a fluid phase leads to a new source of instability: fluid-solid drag. A model that incorporates the fluid force into the starting kinetic equation is assessed via comparison with direct numerical simulation. Additionally, we compare the relative importance of the drag force in such systems, and find that this mechanism is relevant in such flows