Coherent clusters of inertial particles in homogeneous turbulence

Abstract

Despite the widely acknowledged significance of turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of homogeneous isotropic turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoï diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.

Local analysis of the clustering, velocities, and accelerations of particles settling in turbulence

“…The results show that cluster sizes are distributed over a wide range of scales, from the dissipation up to integral range scales. In agreement with previous studies ( [20,27,30,32,52]), we find that the right hand side of the PDF is well described as a power law with exponent −2, which implies self-similarity of the clusters, in line with results in [20,55]. This slope was found to be ∼ −5/3 in the experimental study of [28].…”

“…They conjectured that this effect was due to interactions between the particles when they are sufficiently close. In our results we do not observe this crossover, and neither did the numerical studies of [24,30]. While this may be due to our neglect of the effect of particle interactions, we note that the crossover was also not observed in the recent experimental work of [25].…”

“…Figure 12 shows the same results in a log-lin plot to emphasize the behavior for larger clusters, and again we find a weak dependence on St, R λ and F r. One possible reason for the weak dependence is related to the fact that given that the average inter-particle distance is 7.9η, the clusters are quite large and so the effects of inertia are weaker than they would be for smaller clusters. Indeed, the study of [30] had a much smaller average inter-particle distance of ≈ 2.2η, and in their results the strongest effects of the particle inertia were found for the smallest clusters, as expected. To obtain clearer quantitative insight, the standard deviation (s.d.)…”

“…We refer the reader to [51] for a detailed discussion concerning theoretical issues with the sweep-stick mechanism. We now turn our attention to the results for clusters of particles, which are defined as connected Voronoï cells that have volumes ≤ ϑ C [30]. Figure 11 shows the PDF of cluster volumes normalized by the Kolmogorov scale.…”

“…In addition to analysis of the local particle concentration using Voronoï analysis, the DNS study of [30] explored the idea of coherent clusters of inertial particles, with F r = 0.1 in a low Reynolds number flow, R λ = 65. They defined a coherent cluster as a group of connected Voronoï cells whose volumes are smaller than a certain threshold.…”