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

## TL;DR

This study uses 3D Voronoï analysis and DNS to investigate how small inertial particles settle in turbulence, revealing how local clustering, velocities, and accelerations depend on turbulence intensity, particle inertia, and gravity effects.

## Contribution

It introduces a local Voronoï-based analysis of particle clustering, velocities, and accelerations in turbulent flows, highlighting the dependence on Reynolds, Froude, and Stokes numbers, and clarifying the role of void regions.

## Key findings

- Small Voronoï volumes are strongly influenced by St and Fr, weakly by Rλ unless St>1.
- Void regions show a strong Rλ dependence, affecting clustering variability.
- Largest settling velocities correlate with larger Voronoï volumes as Sv increases.

## Abstract

Using 3D Vorono\text{\"i} 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{\"i} 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{\"i} volumes (void regions) exhibit a much stronger dependence on $R_\lambda$, even when $St\leq 1$, 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{\"i} 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{\"i} 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{\"i} volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Vorono\text{\"i} volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle "..."