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

Abstract

Using 3D Vorono\text{ï} analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using Direct Numerical Simulations (DNS). We independently vary the Taylor Reynolds number $R_{\lambda }\in [90,398]$, Froude number $Fr\equiv a_{\eta }/g\in [0.052,\infty ]$ (where $a_{\eta }$ is the Kolmogorov acceleration, and $g$ is the acceleration due to gravity), and Kolmogorov scale Stokes number $St\equiv {\tau }_p/{\tau }_{\eta }\in [0,3]$. In agreement with previous results using global measures of particle clustering, such as the Radial Distribution Function (RDF), we find that for small Vorono\text{ï} volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon $St$ and $Fr$, but only weakly dependent upon $R_{\lambda }$, unless $St>1$. However, larger Vorono\text{ï} volumes (void regions) exhibit a much stronger dependence on $R_{\lambda }$, even when $St\le 1$, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Vorono\text{ï} volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Vorono\text{ï} volumes as the settling parameter $Sv\equiv St/Fr$ 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 Vorono\text{ï} volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Vorono\text{ï} volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle "..."