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

Abstract

Using 3D Voronoï 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 λ ∈ [90, 398], Froude number F r ≡ a η /g ∈ [0.052, ∞] (where a η is the Kolmogorov acceleration, and g is the acceleration due to gravity), and Kolmogorov scale Stokes number St ≡ τ p /τ η ∈ [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 Voronoï volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon St and F r, but only weakly dependent upon R λ , unless St > 1. However, larger Voronoï volumes (void regions) exhibit a much stronger dependence on R λ , 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 Voronoï volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Voronoï volumes as the settling parameter Sv ≡ St/F r 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 Voronoï volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Voronoï 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 Voronoï 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 Voronoï 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 dependance on F r and R λ . 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 R λ and exhibits a non-monotonic dependence on F r. The kinetic energy of the particles, however, are almost the

Settling and clustering of snow particles in atmospheric turbulence

“…We characterize such spatial clustering in the next section. Here we stress that the more turbulent cases display stronger clustering, and that the latter is typically concurrent with settling enhancement by preferential sweeping (Aliseda et al 2002;Baker et al 2017;Petersen et al 2019;Momenifar & Bragg 2020). Direct evidence of preferential sweeping in the more turbulent datasets is provided by the correlation between the local concentration and the simultaneous vertical velocity.…”

Life and death of inertial particle clusters in turbulence

“…2017; Monchaux & Dejoan 2017; Petersen et al. 2019; Momenifar & Bragg 2020, among others), strongly suggestive of a self-similar process; while the latter follows an approximately exponential distribution, indicating a dominant time scale. Therefore, the relation between both quantities is non-trivial and its mathematical modelling requires further investigation.…”

“…This translates to a minimum threshold on the cluster size (calculated as the cubic root of the cluster volume) between and (where is the Kolmogorov length scale), the precise value of which does not affect the conclusions of the study. The average inter-particle distance is around 6, for which qualitative biases in the characterization of the clusters are not expected (Momenifar & Bragg 2020).…”

“…This feature was used by Baker et al (2017) to show that clusters of heavy particles in homogeneous turbulence are self-similar objects with a broad range of sizes, and that they have significantly different fall speeds compared to non-clustered particles. The approach has been used to characterize individual clusters, including their shape, orientation, velocity and acceleration, in homogeneous turbulence (Petersen, Baker & Coletti 2019;Momenifar & Bragg 2020) and in wall-bounded flows (Fong, Amili & Coletti 2019).…”

Divergence and convergence of inertial particles in high-Reynolds-number turbulence

“…The influence of Stokes and Reynolds numbers has been analysed in Sumbekova et al (2017). Recently, local cluster analysis of small, settling, inertial particles in isotropic turbulence was performed in Momenifar & Bragg (2020) using 3-D Voronoi tessellation.…”