The evolution of a two-dimensional small-amplitude voidage disturbance in a uniformly fluidized bed

Summary

The evolution of a small-amplitude localized voidage disturbance through a two-dimensional fluidized bed is considered. A solution of the full initial-value problem reveals that the stability condition for the uniform state is found to be in agreement with that given by Needham and Merkin [1] for narrow beds. Further, it is shown that for a given flow rate for which the uniform state is unstable, more and more cross-channel modes become instable with increasing bed width, in accordance with the observations of Didwania and Homsy [3]. Finally a solution is obtained forF ≪ 1, whereF is the Froude number. The resulting Fourier series is summed numerically, which enables the evolution of the initial disturbance to be followed by plotting contours of constant voidage with increasing time. This shows that in narrow beds the motion is primarily one-dimensional, confirming the supposition of [1], with cross-stream variations becoming more dominant as the bed width increases.