Dynamics and wall collision of inertial particles in a solid–liquid turbulent channel flow

Abstract

The dynamics and wall collision of inertial particles were investigated in non-isotropic turbulence of a horizontal liquid channel flow. The inertial particles were $125~\unicode[STIX]{x03BC}\text{m}$ glass beads at a volumetric concentration of 0.03 %. The bead-laden flow and the unladen base case had the same volumetric flow rates, with a shear Reynolds number, $Re_{\unicode[STIX]{x1D70F}}$, of the unladen flow equal to 410 based on the half-channel height and friction velocity. Lagrangian measurements of three-dimensional trajectories of both fluid tracers and glass beads were obtained using time-resolved particle tracking velocimetry based on the shake-the-box algorithm of Schanz et al. (Exp. Fluids, vol. 57, no. 5, 2016, pp. 1–27). The analysis showed that on average the near-wall glass beads decelerate in the streamwise direction, while farther away from the wall, the streamwise acceleration of the glass beads became positive. The ejection motions provided a local maximum streamwise acceleration above the buffer layer by transporting glass beads to high velocity layers and exposing them to a high drag force in the streamwise direction. Conversely, the sweep motion made the maximum contribution to the average streamwise deceleration of glass beads in the near-wall region. The wall-normal acceleration of the beads was positive in the vicinity of the wall, and it became negative farther from the wall. The investigation showed that the glass beads with sweeping motion had the maximum momentum, streamwise deceleration, and wall-normal acceleration among all the beads close to the wall and these values increased with increasing their trajectory angle. The investigation of the beads that collided with the wall showed that those with shallow impact angles (less than $1.5^{\circ }$) typically slide along the wall. The sliding beads had a small streamwise momentum exchange of ${\sim}5\,\%$ during these events. The duration of their sliding motion could be as much as five times the inner time scale of the unladen flow. The wall-normal velocity of these beads after sliding was greater than their wall-normal velocity before sliding, and was associated with the rotation induced lift force. Beads with impact angles greater than $1.5^{\circ }$ had shorter interaction times with the wall and smaller streamwise and wall-normal restitution ratios.

Particle–fluid–wall interaction of inertial spherical particles in a turbulent boundary layer

“…The mean acceleration profiles are in close agreement with the recent experiments of Ebrahimian et al. (2019), who considered particles with and in a channel flow at . The mean acceleration is negligible in the free stream, as expected in a fully developed flow.…”

“…(1995 a ), Righetti & Romano (2004) and Ebrahimian et al. (2019). The present PIV resolution does not allow reliable measurements at such small heights, but the canonical shape of the boundary-layer profile suggests that the lag is vanishing approaching the wall.…”

“…(2011) and Ebrahimian et al. (2019). The wall-normal component instead reaches a peak 30 %–60 % larger than in those studies, being comparable to the streamwise component.…”

“…(2008) and Ebrahimian et al. (2019): particles that fall vertically find themselves surrounded by slower fluid, which decelerates them; and vice versa for particles moving vertically upward. The mean vertical acceleration is instead unaffected by conditioning on ascending/descending particles.…”

“…2017; Ebrahimian et al. 2019). The optimal width of the kernel is determined from the variance of the particle acceleration magnitude in the data set: the latter is calculated for a range of kernel widths, and the smallest value for which the variance start decaying exponentially is adopted (figure 6).…”