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

We use Direct Numerical Simulations (DNS) and 3D Vorono\text{\"i} tessellation to analyze the local dynamics of small inertial particles in isotropic turbulence, considering the effect of Taylor Reynolds number ($R_\lambda$), Froude number ($Fr$), and Stokes number ($St$). In line with previous results using global measures of particle clustering, we find that for small Vorono\text{\"i} volumes, the behavior is strongly dependent upon $St$ and $Fr$, but only weakly dependent upon $R_\lambda$, unless $St>1$. However, larger Vorono\text{\"i} volumes (void regions) exhibit a much stronger dependence on $R_\lambda$, even when $St\leq 1$. This, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of Vorono\text{\"i} volumes to $R_\lambda$ that has been previously reported. Particle acceleration results indicate a non-trivial effect of gravity, while results for the fluid acceleration at the particle position call into question the sweep-stick mechanism for clustering. Comparing the local dynamics of particles in clusters to all particles in the flow reveals that while their kinetic energies are nearly the same, the clustered particles settle much faster on average, and this difference grows significantly with increasing $R_\lambda$.