The cross-sectional distributions of a neutrally buoyant spherical particle suspended in square duct flow

Neutrally buoyant spherical particles suspended in duct flow are known to cross main flow due to the inertial lift force and eventually to focus on certain points in the duct cross section. Many studies have shown that the particles in square duct flow focus near the centers of sides of the cross section. In this study, we have numerically estimated the distributions of suspended particles passing through duct cross-sections with various travelled distances from the inlet and have discussed the translational velocity of a suspended particle in motion. We conducted the numerical simulations for the lift force exerted on a spherical particle suspended in square duct flow, and for the translational velocity of the particle when the net force vanishes. To estimate the evolution of the particle distributions, we calculated the particle trajectories by the inertial lift and Stokes drag, and by the translational velocity. The distributions obtained numerically are compared with corresponding experimental results. We have found that the evolution of particle distributions estimated from the lift force and Stokes drag are faster than those observed in experiments, whereas the distributions calculated from the translational velocity explain the experimental observations.