A bifurcation approach to understanding instabilities in gas-fluidized beds using a single phase compressible flow model

It has been shown that the equations of motion and continuity for the particles in a fluidized bed can be related to those of a compressible fluid acted upon by a density-dependent force. In the previous work on the compressible flow equations, the solution structure of fully developed plane (one-dimensional) waves was computed. It was shown that the plane waves can lose stability in the lateral direction. In this work we study the two-dimensional solutions which reveal that bubble-like solutions can evolve both from the plane waves as well as from the uniform state. A representative value of the lateral wavenumber is chosen and the global bifurcation diagram is explored, which consists of a number of distinct one- and two-dimensional branches. The existence of mixed mode and double humped solutions is demonstrated and transient simulations are used to examine the mechanism of density wave development and coalescence.