Local and global recurrences in dynamic gas-solid flows

We investigate recurrent patterns in a lab-scale fluidized bed consisting of Np ≈ 57 000 glass particles by the means of computational fluid dynamics and the discrete element method (CFD-DEM). We generalize single-point measures for recurrence quantification analysis (RQA) to spatially extended particle density fields and compare the embedding dimensions necessary to unambiguously identify similar states. In accordance with many previous studies, we find locally very low-dimensional behavior (Dloc ≈ 5). Globally, the correlation dimension, i.e. the number of effective degrees of freedom, increases to Dglobal ≈ 18, which is still several orders of magnitude smaller than the 6Np microscopic translational degrees of freedom and explains the observed, characteristic structures. Distance plots reveal a combination of fast, recurrent motion interrupted by rare events like large eruptions. The temporal evolution of the average nearest-neighbor distance shows a rapid initial drop and follows a power law related to the correlation dimension for longer times. Given a sufficient tolerance, most states reappear after a few seconds, which indicates why in recent, small-scale recurrence CFD (rCFD) simulations, the complicated long-term bed motion could be approximated with information from short-term studies within the scope of current computation techniques. From the perspective of numerical efficiency, the presented analysis allows to determine the shortest time series from which a significant amount of information on the underlying system may be obtained.