Inertial Particle Cluster Dynamics in the Core Region of a Turbulent Duct Flow

Abstract

The spatial and temporal characteristics of clusters of small and heavy particles in fully developed turbulence are studied in the central region of a vertical duct flow. A series of time-resolved three-dimensional particle positions from direct numerical simulations is used as dataset. New methods are presented to define and track cluster structures that reduce the processing time of large datasets with large number of particles. Clusters are identified using a density-based clustering algorithm, and only a reduced set of all particles is used to correlate clusters in consecutive time instances exploiting morphological information. This approach eliminates the need for particle tracking when individual particle dynamics are not sought or known a priori. A hierarchy of clusters is evidenced with size and time of presence probability distributions exhibiting power-law behaviors. Clusters across all sizes are seen to predominantly evolve breaking up into smaller parts and merging to form larger structures, with a significant number of structures also losing particles until disintegrating. The time clusters persist positively correlates on average with their size. The instantaneous volume rate of change of clusters scales with the turnover time of equivalent size eddies in the inertial range, supporting that clustering is driven by multi-scale turbulent eddies for Stη>O(1). Clusters shrink on average at a faster pace than they grow, which is related to positive average particle velocity divergence within clusters, which increases with increasing local particle concentration.

Keywords: particle clustering, DBSCAN, cluster dynamics, lifetime, particle velocity divergence