Clustering of inertial spheres in evolving Taylor-Green vortex flow

Clustering of inertial spheres in a statistically unsteady flow field is believed to be different from particle clustering observed in statistically steady flows. The continuously evolving three-dimensional Taylor-Green vortex (TGV) flow exhibits time-varying length and time scales, which are likely to alter the resonance of a given particle with the evolving flow structures. The tendency of homogeneously introduced spherical point-particles to cluster preferentially in the TGV flow is observed to depend on the particle inertia, parameterized in terms of the particle response time tau(p). The degree of the inhomogeneity of the particle distribution is measured by the variance sigma(2) of Voronoi volumes. The time evolution of the particle-laden TGV flow is characterized by a viscous dissipation time scale tau(d) and the effective Stokes number St(eff) = tau(p)/tau(d). Particles with low/little inertia do not cluster in the early stage when the TGV flow only consists of large-scale and almost inviscid structures and St(eff) < 1. Later, when the large structures have been broken down into smaller vortices, the least inertial particles exhibit a stronger preferential concentration than the more inertial spheres. At this stage, when the viscous energy dissipation has reached its maximum level, the effective Stokes number of these particles has reached the order of one. Particles are generally seen to cluster preferentially at strain-rate dominated locations, i.e., where the second invariant Q of the velocity gradient tensor is negative. However, a memory effect can be observed in the course of the flow evolution where high sigma(2) values do not always correlate with Q < 0.