Note on a wave-hierarchy interpretation of fluidized bed instabilities

Abstract

The technological importance of fluidized beds is well known. Experi­mental observations indicate that a uniformly fluidized bed is unstable to small planar voidage disturbances that grow exponentially upwards along the bed and, under certain circumstances, attain saturation at finite amplitudes. The linearized theory is recast into a form that shares mathe­matical similarities and interpretations with ‘wave hierarchies’. In wave hierarchies, the higher-order waves, which correspond to higher-frequency waves nearer the distributor, have wave speeds that are lower than those of the lower-order waves, and the stability condition is thus violated. The lower-order waves correspond to these lower-frequency waves further along the fluidized bed. Thus voidage signals grow exponentially along the higher-order waves. Such waves will eventually be left behind and sur­passed by the faster lower-order waves along which voidage perturbations will be ‘focused’ owing to an effective negative diffusion coefficient. The peculiar double peaks in voidage perturbation waves observed by El-Kaissy and Homsy appear to be explicable by the present wave-hierarchy inter­pretation of the linearized theory.