Mechanisms of particle preferential concentration induced by secondary motions in a dilute turbulent square duct flow

Physics of Fluids, Volume 32, Issue 12, December 2020. Particle-laden turbulent square duct flows at Reτ = 300 (based on the duct half-width and the mean friction velocity) are investigated using direct numerical simulation with one-way coupled Lagrangian particle tracking. Four particle-to-fluid density ratios are considered with the corresponding shear Stokes number St+ = 0.31, 25, 125, and 260. Particle motion is governed by drag, lift, added-mass, and pressure gradient forces. The main purpose of this work is to examine the effect of the turbulence-driven secondary flows on particle preferential accumulation and their dependence on the Stokes number. Results obtained indicate that the cross-stream secondary motions encourage inertial particles to accumulate preferentially in the duct corners, where the maximum of the cross-sectional particle concentration occurs. The extent of accumulation here is strongly dependent on the Stokes number, with the greatest accumulation found at St+ = 25. Interestingly, the maximum of the intensity of the secondary particle velocity along the corner bisector is also achieved at St+ = 25, whereas in the region adjacent to the wall, it is found to decrease with a particle Stokes number. Additionally, it is observed that the higher inertia particles are more easily trapped in the stagnation zone of secondary flows with low turbulence intensity in the corner region. In the near-wall region, the heavier particles (St+ ≥ 25) are prone to reside and form elongated clusters along the low-speed streamwise velocity streaks, with this trend less pronounced with the increasing Stokes number. Along the wall, away from the corner where the secondary motion is attenuated, particle accumulation is dominated by the near-wall coherent vortices. This phenomenon is further discussed using a region-based correlation analysis between the particle spatial distribution and local flow topology. An in-depth particle dynamic analysis determines that the average cross-sectional drag force resulting from the secondary flow is mainly responsible for the particle motion throughout the duct cross section, which tends to push particles away from the walls in the near-wall region but shows the exact opposite trend in the bulk flow region. Moreover, the pressure gradient force also plays an important role for low-inertia particles. As the Stokes number is increased, the lift force becomes progressively dominant in the viscous sublayer, acting to pull particles toward the corners and walls of the duct.