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Anisotropic particle clustering in the viscous sublayer of wall-bounded turbulent flows

DOI: 10.1615/THMT-18.1230
pages 1073-1084

Dmitrii Ph. Sikovsky
Institute of Thermophysics, Siberian Branch of the Russian Academy of Sciences, Acad. Lavrentyev ave. 1, 630090 Novosibirsk; Novosibirsk State University, Pirogova Street 2, 630090, Novosibirsk, Russian Federation

Abstract

We study the clustering of inertial particles in the viscous sublayer of wall-bounded turbulent flows, where the instantaneous fluid velocity is governed by the wall shear. We derive the kinetic equation for the probability density function (PDF) of particle pair relative velocity and position, which is exact in the limit of zero wall distance. In this limit, we obtain the diffusion equation for the pair correlation function of particles and show that at small separations the solution has a self-similar form with the singular power-law dependence from the particle relative position. The exponent dependence upon the Stokes number is determined from the eigenvalue problem for the angular dependent part of pair correlation function. The negative exponent in the power law is also related to the correlation dimension of particle clusters, which is shown to decrease from 2.0 to 0.205 as the Stokes number increases from zero to infinity. We show that the pair correlation function of particles in the spanwise cross-section have the self-similar rhomboidal form highly flattened in the wall-normal direction.

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