Particle dispersion over side-by-side square cylinders: Proximity interference effects

Abstract

This paper investigates the dispersion of tiny inertial particles in the two-dimensional laminar wake from a pair of square cylinders placed side-by-side to each other. The flow Reynolds number (defined based on the cylinder size $h$ and uniform inflow velocity $U_c$) in our study is fixed at 75. The wake pattern resulting from the interaction between vortices shed from individual cylinders depends on the cross-stream spacing between the cylinders, i.e. spacing ratio $s/h$. We examine the effect of varying the cross-stream spacing between the cylinders on the body impaction and dispersion of particles in the wake flow over a range of their responses. Three different spacing ratios, $s/h$ = 0.3, 2, and 4 are considered. We find that the impaction efficiency of Stokes number $St$ = 0.1 particles is not sensitive to the spacing ratio. However, the impaction efficiency of $St$ = 1 and 10 particles is dependent on the spacing ratio and increases with the latter. We illustrate how the distribution and clustering of representative inertial particles (i.e., with Stokes number unity) evolve over a vortex shedding cycle uniquely due to the wake flow in each spacing ratio configuration and explain the physical mechanism of particle clustering using backward tracking. The non-uniform clustering of particles with different responses to the wake flow in each spacing ratio configuration is analyzed using the Voronoï diagrams. The spacing ratio effects on the dispersion of particles are quantified in terms of mean statistical quantities such as mean local concentration, clustering intensity, and velocity statistics. The local concentration of $St$ = 1 and 10 particles at streamwise positions away from cylinders is significantly influenced by the wake flow behavior governed by the choice of the spacing ratio. Further, the combined effect of gravity and hydrodynamic drag forces on the impaction and clustering behavior of particles is reported, where the Froude number $Fr=0.32$. In all the cases, particles exhibit ballistic behavior, showing a significantly reduced tendency to form clusters and a drastic increase in the impaction efficiency.