Experimental investigation of three-dimensional flow around particles in a turbulent channel flow

The interaction between particles and turbulent flow is investigated by simultaneous measurement of the time-resolved three-dimensional (3D) velocity of particles and the carrier liquid phase. The investigation is conducted in a horizontal channel flow at a Reynolds number, Re, of 20 000, based on the average velocity and full channel height. The particle-laden suspension is produced by nearly neutrally buoyant beads with a density of $1.05\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$ and a mean diameter of 370 μm at a volumetric concentration of $0.1\%$. The liquid phase is seeded with 2 μm tracers, the images of which are digitally separated from the larger beads using a medina filter, and processed using time-resolved 3D particle tracking velocimetry. Conditional sampling of the beads and their surrounding fluid, based on the beads’ wall-normal motion, showed that ascending beads were mostly located within ejection motions of the fluid. However, the descending beads did not indicate any correlation with the streamwise fluid velocity; the beads were surrounded by wallward fluid motions with both positive and negative streamwise velocity fluctuations. For both ascending and descending beads, the surrounding fluid motion had a strong spanwise velocity component. Inspection of the 3D beads’ pathlines showed a spiral motion of beads around a streamwise axis. At $y/h<0.2$, the descending beads showed a stronger correlation with their surrounding fluid, while ascending beads demonstrated a stronger correlation with their surrounding flow farther away from the wall. Conditional sampling of the beads and their surrounding flow was also performed based on the streamwise acceleration of the beads. The results showed that, in the near-wall region of $y/h<0.2$, slip velocity and the resultant drag force were not in the same direction as the bead acceleration. Therefore, for this near-wall region, the drag force is not sufficient to model the dynamics of the large nearly buoyant beads.

Figure 1

Schematic of the flow loop demonstrating its main components. The inset shows the test section and the streamwise ($x$), wall-normal ($y$), and spanwise ($z$) directions. The origin of the coordinate system is on the bottom wall of the channel.

Figure 2

Schematic of the four cameras and the laser sheet with respect to the channel and the coordinate system.

Figure 3

Profiles of the normalized (a) mean streamwise velocity and (b) Reynolds stresses for the unladen flow at $\mathrm{R}{\mathrm{e}}_{\tau }=1090$. The results are compared with the channel flow DNS results of Lee and Moser [40] at $\mathrm{R}{\mathrm{e}}_{\tau }=1087$.

Figure 4

Profiles of the normalized (a) mean streamwise velocity and (b) Reynolds stresses for the beads and carrier fluid phase at $\mathrm{R}{\mathrm{e}}_{\tau }=1090$ and ${\phi }_v=0.1\%$ measured by 4D-PTV. The error bars show the estimated uncertainty based on Appendix pp1. Only three locations are chosen to show the error bars for clarity.

Figure 5

Conditional average of (a) streamwise, (b) wall-normal, and (c) absolute spanwise velocity of the beads and their surrounding fluid based on the wall-normal direction of the beads.

Figure 6

The correlation coefficients of ascending and descending beads with their surrounding fluid in (a) streamwise, (b) wall-normal, and (c) spanwise directions.

Figure 7

The fraction of the fluid surrounding the (a) ascending and (b) descending beads based on the four quadrants of velocity fluctuations.

Figure 8

JPDF of (a) streamwise $(u_f,u_b)$, (b) wall-normal $(v_f,v_b)$, and (c) spanwise $(w_f,w_b)$ velocity of beads and surrounding fluid for $0<y/h<0.26$. The blue dashed contours show the results related to the ascending beads, and red dotted contours represent JPDF of descending beads. The JPDF percentages vary from $1.0\%$ to $8.0\%$ in steps of $2.3\%$ for the most inner to the most outer contour, respectively.

Figure 9

Conditional average of fluid velocity fluctuation, ${\langle u_f\rangle }_c$ and ${\langle v_f\rangle }_c$, surrounding (a) ascending and (b) descending beads in the $XY$ plane. The red arrow shows the reference vector size.

Figure 10

Conditional average of fluid velocity fluctuation, ${\langle u_f\rangle }_c$ and ${\langle |w_f|\rangle }_c$, around (a) ascending and (b) descending beads in the $XZ$ plane. The vectors are scaled relative to the reference vector shown in Fig. 9.

Figure 11

Conditional average of fluid velocity relative to the beads, ${\langle {\mathit{U}}_r\rangle }_c={\langle {\mathit{U}}_f-{\mathit{U}}_b\rangle }_c$, in the $XY$ plane for (a) ascending and (b) descending beads. The red arrow shows the reference vector size.

Figure 12

Conditional average of fluid velocity in the $XZ$ plane relative to the (a) ascending and (b) descending beads. For the spanwise component, the absolute value of relative velocity, i.e., ${\langle |W_f-W_b|\rangle }_c$, is used. The vectors are scaled similar to Fig. 11.

Figure 13

Conditional average of (a) streamwise, (b) wall-normal, and (c) absolute spanwise velocity of the beads and their surrounding fluid sampled based on $a_b$ sign.

Figure 14

Conditional average of relative fluid velocity, ${\langle {\mathit{U}}_r\rangle }_c={\langle {\mathit{U}}_f-{\mathit{U}}_b\rangle }_c$, in the $XY$ plane surrounding (a) accelerating $(a_b>0)$ and (b) decelerating beads $(a_b<0)$. The red arrow shows the reference vector size.

Figure 15

Conditional average of relative velocity field, ${\langle {\mathit{U}}_r\rangle }_c={\langle {\mathit{U}}_f-{\mathit{U}}_b\rangle }_c$, in the $XZ$ plane surrounding (a) accelerating beads $(a_b>0)$ and (b) decelerating beads $(a_b<0)$. The red arrow shows the reference vector size.

Figure 16

Sample 3D trajectories of beads (shown in black) and their projection on $xy, yz$, and $xz$ planes. The spiral of the pathlines (3) and (4) about the $x$ direction can be recognized as they move forward. For better representation, $y$ and $z$ axes are magnified by a factor of 3.5 with respect to the $x$ axis.

Figure 17

(a) The PDF of the number of local maxima $\left(y_{max}\right)$ and minima $\left(y_{min}\right)$ in the wall-normal position of the beads, and the number of local extrema in the spanwise position of the beads $\left(z_{\mathrm{ext}}\right)$. (b) Normalized number density profile of the beads across the bottom-half channel.

Figure 18

Statistical convergence of (a) the mean velocity and (b) Reynold stresses of the beads at $y^{+}=500 (y/h=0.46)$. The maximum and minimum values for $n/N$ of 0.8 to 1 are used to estimate the random error.