Extraction of coherent clusters and grid adaptation in particle-laden turbulence using wavelet filters

Abstract

In this study, a wavelet-based method for extraction of clusters of inertial particles in turbulent flows is presented that is based on decomposing Eulerian particle-number-density fields into the sum of coherent (organized) and incoherent (disorganized) components. The coherent component is associated with the clusters and is extracted by filtering the wavelet-transformed particle-number-density field based on an energy threshold. The method is applied to direct numerical simulations of homogeneous-isotropic turbulence laden with small Lagrangian particles. The analysis shows that in regimes where the preferential concentration is important, the coherent component representing the clusters can be described by just 1.6% of the total number ofwavelet coefficients, thereby illustrating the sparsity of the particle-number-density field. On the other hand, the incoherent portion is visually structureless and much less correlated than the coherent one. An application of the method, motivated by particle-laden radiative-heat-transfer simulations, is illustrated in the form of a grid-adaptation algorithm that results in nonuniform meshes with fine and coarse elements near and away from particle clusters, respectively. In regimes where preferential concentration in clusters is important, the grid adaptation leads to a significant reduction of the number of control volumes by one to two orders of magnitude.