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

Using three-dimensional Voronoi analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using direct numerical simulations. We independently vary the Taylor Reynolds number Reλ[90,398], Froude number Fraη/g[0.052,∞] (where aη is the Kolmogorov acceleration, and g is the acceleration due to gravity), and Kolmogorov scale Stokes number Stτp/τη[0,3]. In agreement with previous results using global measures of particle clustering, such as the radial distribution function, we find that for small Voronoi volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon St and Fr, but only weakly dependent upon Reλ, unless St>1. However, larger Voronoi volumes (void regions) exhibit a much stronger dependence on Reλ, even when St≤1, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Voronoi volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Voronoi volumes as the settling parameter SvSt/Fr is increased. Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Voronoi volumes, with or without gravity, which seems to indicate a nontrivial relationship between the Voronoi volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle positions are of the order of the square of the Kolmogorov acceleration and depend only weakly on Voronoi volumes. These results call into question the "sweep-stick" mechanism for particle clustering in turbulence which would lead one to expect that clustered particles reside in the special regions where the fluid acceleration is zero (or at least small). We then consider the properties of particles in clusters, which are regions of connected Voronoi cells whose volume is less than a certain threshold. The results show self-similarity of the clusters, and that the statistics of the cluster volumes depends only weakly on St, with a stronger dependence on Fr and Reλ. Finally, we compare the average settling velocities of all particles in the flow with those in clusters, and show that those in the clusters settle much faster, in agreement with previous work. However, we also find that this difference grows significantly with increasing Reλ and exhibits a nonmonotonic dependence on Fr. The kinetic energy of the particles, however, is almost the same for particles whether or not they are in clusters.

Duke Scholars

Author Andrew Bragg Civil and Environmental Engineering