Instability of bounded gas-particle fluidized beds

Steady flows of gas and particles in unbounded-fluidized beds have been shown to lose stability to localized voidage disturbances. An insight is provided into the linear stability of bounded gas-particle flows using a kinetic theory approach. The stability analysis is carried out for two illustrative sets corresponding to fluidized systems having walls acting as sinks and sources of fluctuation energy. Instabilities are characterized by computing leading eigenvalue profiles and dominant eigenfunctiqn contour maps. Results show two types of dominant instability patterns (symmetric and antisymmetric) for flow in a vertical duct, both of which propagate through the bed in the form of traveling waves at speeds comparable to that of the solid phase. Moreover, model predictions show that increasing solids fraction and decreasing particle inelasticity will suppress the wavy disturbance. The physical mechanism of instability formation is further investigated using a term-by-term method of analysis. Results show that instability modes can be suppressed if solid phase inertia or inelastic particle collisions are eliminated from the momentum and pseudo-thermal energy balance equations. Finally, the symmetric instabilities were shown to develop into bubble-like structures while the antisymmetric instabilities develop into streamer-like structures.