Time–frequency investigation of different modes of bubble flow in a gas–solid fluidized bed

Three modes of bubble flow in fluidized beds, identified and explained in a previous work (S. Sasic, F. Johnsson, B. Leckner, Interaction between a fluidized bed and its air-supply system: some observations, Ind. Eng. Chem. Res. 43 (2004) 5730–5737), are studied here by linear methods (wavelet analysis) in the time–frequency plane. The modes are: (1) single bubble regime characterized by the presence of one bubble at a time in the bed; (2) a regime where single bubbles still dominate the flow field, but another type of structure (so-called exploding bubbles) becomes significant at a different frequency; (3) a regime in which exploding bubbles, conceived as gaseous structures stretching from the air distributor to the surface of the bed, clearly dominate the flow field, but pressure waves, originating from single bubbles in the bed, are still observed. The signals representing single bubbles, exploding bubbles and pressure waves are extracted from the original pressure signals by discrete wavelet analysis. These phenomena are identified as distinct local maxima in the distribution of energy over wavelet scales in a wavelet energy spectrum (obtained by statistical analysis of wavelet coefficients). Also, a model, treating the data recorded as an organized event (e.g. bubbles) and an accompanying white noise process, is used for calculation of the time scales of phenomena present in the bed in a certain fluidization situation. It is shown how these phenomena are localized in time.