Clusters play a critical role in the hydrodynamics of gas–solid flow. In this work, the probe method, the DBSCAN-based method, and the Voronoï-based method are used to identify clusters in gas–solid suspensions, and their structural and dynamic properties are then quantified. The structural properties obtained by the probe method, including cluster fraction, solid concentration inside cluster, and cluster size, are comparable to those obtained using the other two particle-based methods, but particle-based methods could offer more insights into the fractal dimension, shape, and topology of the clusters. However, the boundary particles in the DBSCAN algorithm may add ambiguity to the identification of the dense (or cluster) phase, which can lead to nonphysical results. Dynamic analysis using the Voronoï-based method reveals: (i) two characteristic lifetimes of clusters exist, one for particles coming together by chance and the other for the collective motion of particles; (ii) clusters in dilute gas−solid suspensions are relatively stable because the interaction between particles and clusters is quite weak; and (iii) the dynamic evolution of clusters is the combined effect of the continuous growth and shear detachment of single particles and the intermittent coalescence and breakage of clusters. Quantitative analysis of those processes could provide the critical kernels in the population balance modeling of cluster dynamics.

Spatiotemporal coherent structures are critical in quantifying the hydrodynamics of dense gas-solid flows. In this study, two data-driven methods, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD), are applied to identify and characterize the dominant spatiotemporal coherent structures in a bubbling fluidized bed. It is found that (i) with the same number of modes (or coherent structures), POD captures more defined energy than DMD; (ii) the main coherent structure of POD is symmetric and confirms the existence of bubble-emulsion two-phase structure; (iii) the coherent structures with a frequency of zero Hz in DMD analysis can construct the mean flow field more reasonably than POD; and (iv) POD reconstructs the transient flow fields more accurately with the same number of modes. The present study offers insights into the coherent structures in gas-solid systems.

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