Clustering and preferential concentration of finite-size particles in forced homogeneous-isotropic turbulence

Abstract

We have performed interface-resolved direct numerical simulations of forced homogeneous-isotropic turbulence in a dilute suspension of spherical particles in the Reynolds number range $Re_{\unicode[STIX]{x1D706}}=115{-}140$. The solid–fluid density ratio was set to $1.5$, gravity was set to zero and two particle diameters were investigated corresponding to approximately $5$ and $11$ Kolmogorov lengths. Note that these particle sizes are clearly outside the range of validity of the point-particle approximation, as has been shown by Homann & Bec (J. Fluid Mech., vol. 651, 2010, pp. 81–91). At the present parameter points the global effect of the particles upon the fluid flow is weak. We observe that the dispersed phase exhibits clustering with moderate intensity. The tendency to cluster, which was quantified in terms of the standard deviation of Voronoï cell volumes, decreases with the particle diameter. We have analysed the relation between particle locations and the location of intense vortical flow structures. The results do not reveal any significant statistical correlation. Contrarily, we have detected a small but statistically significant preferential location of particles with respect to the ‘sticky points’ proposed by Goto & Vassilicos (Phys. Rev. Lett., vol. 100 (5), 2008, 054503), i.e. points where the fluid acceleration field is acting such as to increase the local particle concentration in one-way coupled point-particle models under Stokes drag. The presently found statistical correlation between the ‘sticky points’ and the particle locations further increases when focusing on regions with high local concentration. Our results suggest that small finite-size particles can be brought together along the expansive directions of the fluid acceleration field, as previously observed only for the simplest model for sub-Kolmogorov particles. We further discuss the effect of density ratio and collective particle motion upon the basic Eulerian and Lagrangian statistics.