Statistical properties of particle segregation in homogeneous isotropic turbulence

Abstract

A full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent flow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the flow. Qualitative good agreement is observed with previous kinematic simulations (KS) (IJzermans, Meneguz & Reeks, J. Fluid Mech., vol. 653, 2010, pp. 99–136): in particular, the existence of singularities in the particle concentration field and a threshold value for the particle Stokes number $\mathit{St}$ above which the net compressibility of the particle concentration changes sign (from compression to dilation). A further KS analysis is carried out by examining the distribution in time of the compression of an elemental volume of particles, which shows that it is close to Gaussian as far as the third and fourth moments but non-Gaussian (within the uncertainties of the measurements) for higher-order moments when the contribution of singularities in the tails of the distribution increasingly dominates the statistics. Measurements of the rate of occurrence of singularities show that it reaches a maximum at $\mathit{St}\ensuremath{\sim} 1$, with the distribution of times between singularities following a Poisson process. Following the approach used by Fevrier, Simonin & Squires (J. Fluid Mech., vol. 553, 2005, pp. 1–46), we also measured the random uncorrelated motion (RUM) and mesoscopic components of the compression for $\mathit{St}= 1$ and show that the non-Gaussian highly intermittent part of the distribution of the compression is associated with the RUM component and ultimately with the occurrence of singularities. This result is consistent with the formation of caustics (Wilkinson et al. Phys. Fluids, vol. 19, 2007, p. 113303), where the activation of singularities precedes the crossing of trajectories (RUM).

On the nature, formation and diversity of particulate coherent structures in microgravity conditions and their relevance to materials science and problems of astrophysical interest

“…As the particles cluster onto a network of caustic lines (analogous to the networks of optical caustics that can be seen on the bottom of a swimming pool) this process can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce Mehlig 2005, Wilkinson et al 2007). This model of particle segregation in homogeneous isotropic turbulence was confirmed by Meneguz and Reeks (2011), who amongst other things identified an interesting threshold value for the particle Stokes number above which the net compressibility of the particle concentration changes sign (from compression to dilation). All these processes are important influences on particle agglomeration and play a crucial role in (terrestrial) atmospheric phenomena such as droplet formation in turbulent clouds , Devenish et al 2012).…”

Inertial-particle dynamics in turbulent flows: caustics, concentration fluctuations and random uncorrelated motion

“…We show that as det J approaches zero, Tr Z → −∞. We briefly comment on the statistical properties of the singularities (Meneguz and Reeks 2011).…”

“…The modes are chosen in such a way that the associated energy spectrum approximates a prescribed form, namely that originally used by Kraichnan (1970). The model is identical to that used by IJzermans et al (2010) and Meneguz and Reeks (2011). For convenience, we briefly summarize its relevant features below.…”

“…The small volume may vanish at isolated singular points in time, giving rise to instantaneous singularities in the particleconcentration field. Using this approach, the statistical properties of these singularities were analysed by Meneguz and Reeks (2011).…”

Mitigation of preferential concentration of small inertial particles in stationary isotropic turbulence using electrical and gravitational body forces

“…Dynamical systems theory has been applied to the motion of particles, first by Sommerer and Ott 15 and in turbulent flows by Bec 16 and Wilkinson et al 17 who showed that periods in time exist where particle trajectories may cross leading to particle collisions. Relaxing an assumption of Wilkinson et al, 17 that the typical correlation time of the carrier flow is small, Reeks and co-workers have deployed the full Lagrangian method (FLM) of Ostiptsov 18 first in synthetic flows 19 and recently in isotropic turbulence 20 to quantify non-uniformities and singularities in the spatial distribution of particles more generally. The advantage of FLM being that the analysis takes place on infinitesimally small scales and does not rely on defining a box size for counting purposes and that a small Stokes number limit is not implicit in the method.…”