Anisotropic clustering of inertial particles in homogeneous shear flow

Abstract

Recently, clustering of inertial particles in turbulence has been thoroughly analysed for statistically homogeneous isotropic flows. Phenomenologically, spatial homogeneity of particle configurations is broken by the advection of a range of eddies determined by the Stokes relaxation time of the particles. This in turn results in a multi-scale distribution of local particle concentration and voids. Much less is known concerning anisotropic flows. Here, by addressing direct numerical simulations (DNS) of a statistically steady particle-laden homogeneous shear flow, we provide evidence that the mean shear preferentially orients particle patterns. By imprinting anisotropy on large-scale velocity fluctuations, the shear indirectly affects the geometry of the clusters. Quantitative evaluation is provided by a purposely designed tool, the angular distribution function (ADF) of particle pairs, which allows to address the anisotropy content of particle aggregates on a scale-by-scale basis. The data provide evidence that, depending on the Stokes relaxation time of the particles, anisotropic clustering may occur even in the range of scales in which the carrier phase velocity field is already recovering isotropy. The strength of the singularity in the anisotropic component of the ADF quantifies the level of fine-scale anisotropy, which may even reach values of more than 30% direction-dependent variation in the probability to find two closeby particles at viscous-scale separation.