). An appropriate level of approximation subsignal was systematically specified as a threshold for cluster identification, based on multiresolution analysis (MRA) of wavelet transformation. By the established threshold, the dynamic properties of clusters including the appearance time fraction of clusters F cl , average cluster duration time s cl , cluster frequency f cl , and local average solids holdup in clusters e sc , at different radial and axial positions were determined under the turbulent, transition and fast fluidization flow regimes. The results also describe the dynamic properties of clusters and flow patterns in the splash zone along with the dense bottom region of the circulating fluidized beds.

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