The models of bubble dynamic wave velocity (BDWV) has been derived as a theoretical description of the bubbling characteristics of fluidized bed systems. In this work, the expressions of the BDWV in an unsteady state was developed by considering the effect of acceleration. A bubble-based energy minimization multi-scale (EMMS) model was applied to obtain key parameters of the BDWV in the bubbling fluidized bed. The bubble fractions predicted by the model were in good agreement with the experimental results in gas-solid fluidized bed. Both of the model-calculated and experimentally-measured bubble fractions gradually increased with the increase in superficial velocity. The variation trend of BDW energy with superficial velocity was similar to that of meso-scale pressure fluctuation energy in a classical air-solid fluidized bed, which was obtained by decomposing the measured pressure fluctuations. The BDW energy was proved as a common parameter to characterize the meso-scale fluid dynamic of the bubbling fluidization. (C) 2017 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.