Acceleration

Physics

Geology

Settling

Mechanics

Machine learning

Turbulence

Computer science

Cluster analysis

Environmental science

Classical mechanics

Thermodynamics

Physical Review Fluids

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 "..."

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