Connections between density waves in fluidized beds and compressible flows

Abstract

Abstract Under certain simplifying assumptions, model equations of motion and continuity for the particles in a fluidized bed can be related to those of a compressible fluid acted on by a density dependent force. A linear stability analysis shows that the base state of the compressible flow equations can lose stability in the form of plane density waves. The plane waves emerge through a Hopf bifurcation and propagate through the bed as traveling waves. Through a bifurcation analysis coupled with parameter continuation, the solution structure of the fully‐developed plane waves was computed. As the amplitudes of the plane waves increase, they lose stability in the lateral direction. A comparison of these results with previous work on gas‐fluidized beds shows that salient features of the instability of a gas‐fluidized bed are captured by the basic physics of compressible flows.