Resolving particle dynamics in turbulent wall-bounded flow

Abstract

Wall-bounded flows in the atmosphere, rivers and oceans are turbulent in nature and mixed with discrete particles. The particle length scale including the wake, can be important because it will affect whether a particle slides, rolls, lifts off or collides with the wall or bounding surface. To understand the transport of discrete particles due to particle-wall and particle-turbulence interactions, spheres extending into the logarithmic region with $d^+=56$ and 116 (when $Re_\tau=670$ and 1300 respectively) were considered. The mean fluid velocity statistics surrounding a fixed sphere on the wall with $Re_p=730$ and 1730 respectively were first investigated across the streamwise-wall-normal and wall-parallel planes. Then, spheres with specific gravities ranging from 1.006 (P1) to 1.152 (P3) were released individually from rest and allowed to propagate with the incoming fluid. Both sphere and fluid motions were tracked simultaneously via 3D particle tracking and stereoscopic particle image velocimetry over the streamwise-spanwise plane at multiple locations, respectively. The perturbations induced by a fixed sphere on the wall extend over a significant distance in both the streamwise ($x/\delta>1.6$; $x/d>17$) and spanwise ($|z|/\delta\sim0.3$; $|z|/d\sim3.3$) directions. When $Re_\tau$ increases, at $y/d=0.7$ ($y^+=40$ and 80 respectively), the vortex shedding increases the magnitude of the negative mean wall-normal velocity in the wake more significantly than the mean spanwise fluid velocity. By contrast, the streamwise velocity deficit downstream of the sphere recovers more rapidly when $Re_\tau$ increases. The presence of the sphere also leads to an increase in fluid velocity both upstream of and above the sphere. Hence, the particle length scale is important as it modulates the turbulence and the surrounding flow field. With sufficient mean shear, sphere P1 lifted off of the wall upon release before descending back towards the wall at both $Re_\tau$. These descents were prompted by a decrease in shear lift due to the surrounding slow-moving zone, downwash, and possibly upward tilting wake. While descending, the sphere either ascended again without returning to the wall or else contacted the wall and then slid before lifting off again. These subsequent lift-offs were prompted by upwash and/or instantaneous shear lift due to a passing high momentum region with large relative velocity. By contrast, the denser sphere P3 did not lift off upon release and mainly slid along the wall. At $Re_{{\tau}}=670$, the initial acceleration of the dense sphere P3 was significantly retarded by the opposing friction force, in contrast to the other spheres that accelerated steeply over a streamwise distance of $\delta$. Strong wake signatures were always observed downstream of this sphere, with loop-like vortices shedding off of the sphere. The streamwise velocities of both lifting and wall-interacting spheres correlated strongly with the fast- and slow-moving zones that approach and move over them. For the lifting sphere, the sphere streamwise velocity fluctuation within each run was also correlated with the sphere wall-normal positions. Meanwhile, the streamwise velocity fluctuation of the denser sphere was well correlated with the vortex shedding. As the denser sphere slid unsteadily downstream, it began to roll forward due to fluid torque induced by the wall-normal fluid motion as well as the shearing effect due to an approaching high momentum region. The sphere also accelerated to greater translational velocity due to an increase in angular velocity and/or the surrounding fast-moving zone. The forward rolling also induced small, repeated lift-off events due to Magnus lift. In all cases, the spheres migrated significantly in the spanwise direction, up to 12\% of the streamwise distance traveled. The sphere spanwise motion was prompted by the localized spanwise fluid motion, Magnus side-lift, and/or meandering of the coherent structures. Side force induced by spanwise gradients of streamwise velocity could be important especially when the relative velocity was large, as upon release. The spheres did not appear to migrate preferentially into the slow-moving zones. Instead, they traveled with either fast- and/or slow-moving zones throughout the observed trajectories based on the relative velocity and the spanwise forces.