Attached eddy-like particle clustering in a turbulent boundary layer under net sedimentation conditions

Abstract

Abstract Characteristics of particle clustering in a particle-laden turbulent boundary layer at a moderate frictional Reynolds number ($Re_\\tau =5500$) are experimentally investigated based on Voronoï analysis. High-inertia sand grains with a large viscous-time-based Stokes number, i.e. $St_p=10^2 - 10^3$, are used as the dispersed phase. The bulk particle volume fraction is $\\varPhi _V\\sim O(10^{-5})$. Two-dimensional velocity fields of the fluid and particle phases in the streamwise–wall-normal plane are simultaneously measured via particle image/tracking velocimetry. Under the net sedimentation condition, a self-similarity of the geometries of particle clusters is clearly seen in the log layer. This can be characterized by the $-5/3$ power law of the probability density functions of the particle cluster areas and the $y$-scaling of their first- and second-order moments. Considering the self-similarity of wall-attached structures in the attached eddy hypothesis, we propose a conceptual model in which a large proportion of particle clusters prefer to reside on the back ridges of low-momentum attached $u$-structures due to the high-strain effect caused by converging sweep–ejection events. Such a scenario can be partly evidenced by the conditional streamwise spectra of the streamwise and wall-normal fluid-phase velocity components being conditioned inside cluster-occupied regions, which present a distinct $y$-scaling in the log layer. Furthermore, the fluid-phase sweep and ejection events inside particle clusters are observed to be weaker than the cases outside cluster-occupied regions, and the local rate of strain inside cluster-occupied regions is relatively higher than in all unconditional statistics. Finally, conditional statistics reveal that those sand grains with relatively small slip velocities are prone to be captured by low-momentum turbulent motions to form particle clusters.