Two statistical models for predicting collision rates of inertial particles in homogeneous isotropic turbulence

Abstract

The objective of the paper is to present and compare two models for the collision rate of inertial particles immersed in homogeneous isotropic turbulence. The merits and demerits of several known collision models are discussed. One of the models proposed in the paper is based on the assumption that the velocities of the fluid and a particle obey a correlated Gaussian distribution. The other model stems from a kinetic equation for the probability density function of the relative velocity distribution of two particles. The predictions obtained by means of these two models are compared with numerical simulations published in the literature.

The role of air turbulence in warm rain initiation

“…Of significance is the fact that the above parameterizations for both w r and g 12 consider the effects of flow Reynolds number which cannot be fully represented by the hybrid simulations. For example, the parameterization for w r makes use of velocity correlations that are valid for both the dissipation subrange and the energy-containing subrange of turbulence (Zaichik et al, 2003). The intermittency of small-scale turbulent fluctuations can be incorporated into the model for RDF (Chun et al, 2005).…”

Clustering and collisions of heavy particles in random smooth flows

“…In their approach they separate, in a somehow artificial way (as argued in Ref. 14), two contributions. The first named shear mechanism corresponds to the carrier fluid velocity shear, that is very similar to the SaffmanTurner result.…”

“…This was indeed demonstrated by means of DNS and theoretical analysis. 3, 14,16,21,32 Thus most of the efforts focused in predicting the net effect of clustering. 35 This is surely crucial for (close to) monodisperse suspensions of particles with very small sizes, but this approach cannot catch collisions between particles with different sizes.…”

“…In the last few years, much effort has been devoted both from a theoretical 10,11,12,13,14 and numerical 15,16,17,18 point of view to understand and quantify the enhancement of collision rates induced by inertia. Two mechanisms have been identified: preferential concentration increases the probability for two particles to be at a colliding distance, 3,16 detachment from fluid trajectories may enhance the relative velocity between two approaching particles.…”

Acceleration statistics of heavy particles in turbulence

“…In parallel with experimental effort, theoretical analysis (Balkovsky, Falkovich & Fouxon 2001, Falkovich & Pumir 2004, Bec, Gawedzki & Horvai 2004, Zaichik, Simonin & Alipchenkov 2003 and numerical simulations (Boivin, Simonin & Squires 1998, Reade & Collins 2000, Zhou, Wexler & Wang 2001, Chun et al 2005 are paving the way to a thorough understanding of inertial particle dynamics in turbulent flows. Recently, the presence of strong inhomogeneities characterised by fractal and multifractal properties have been predicted, and found in theoretical and numerical studies of stochastic laminar flows (Balkovsky, Falkovich & Fouxon 2001, Bec, Gawedzki & Horvai 2004, Bec 2005, in two dimensional turbulent flows (Boffetta, De Lillo & Gamba 2004) and in three dimensional turbulent flows at moderate Reynolds numbers in the limit of vanishing inertia (Falkovich & Pumir 2004).…”