Particle transport in turbulent square duct flows with a free surface

Direct numerical simulation combined with a one-way coupled Lagrangian particle tracking technique is employed to investigate dilute particle-laden turbulent flows in open square ducts with a free surface. The focus is on examining the influence of the mean cross-stream secondary flow on particle transport near the wall, free surface, and across the duct cross section. Based on the duct half-width and mean friction velocity, a shear Reynolds number of Re-tau = 300 is considered, with the corresponding particle Stokes numbers ranging from St(+) = 0.31 to 260. The results reveal that particle concentration near the sidewalls is lower than that near the bottom wall, and the minimum particle concentration is observed at the free surface. Along the bottom wall centerline orientated upward, particle concentration gradually decreases. An exception to this is in the vicinity of the free surface where a slight increase is observed for the heavier particles (St(+) >= 25), and the amplitude of this increase gradually declines as the Stokes number increases. In the streamwise direction near the free surface, heavier particles tend to preferentially concentrate in regions where the instantaneous transverse secondary flow velocity is negative. As the Stokes number increases, the position of the maximum streamwise velocity for heavier particles is closer to the free surface, and the rotation centers of inner and outer secondary particle motions gradually disappear. The streamwise root mean square velocity for the lightest St(+) = 0.31 particles is higher than that for particles with higher inertia in the middle region of the free surface.