Suspension of large inertial particles in a turbulent swirling flow

We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high-speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank, whatever their size or density. At high rotation rate, particles are loosely confined: small particles become nearly homogeneously distributed while very large objects are preferentially found near the top, as if gravity was reversed. We discuss these observations in light of a minimal model of random walk accounting for particle inertia and show that large particles have a stronger probability to remain in the upper part of the flow because they are too large to reach descending flow regions. As a consequence, particles exhibit random horizontal motions near the top, until they reach the central region where the mean flow vanishes or until a turbulent fluctuation gets them down.

Figure 1

Experimental setup. (a) Geometry of the von Kármán flow with only one disk rotating at the top, and optical setup to perform particle tracking velocimetry. (b) Sketch of the mean flow topology composed of a strong azimuthal motion and a poloidal recirculation.

Figure 2

(a) Cylindrical polar grid used to compute mean flow properties for PM3 particles. The two dashed lines mark the two vertical planes at $\theta \approx \pi /16$ and $\theta \approx 5\pi /16$ corresponding to (e) and (f), respectively. Mean flow components normalized by the disk velocity $2\pi \mathrm{\Omega }R$ for three different heights: (b) $z\approx 0.7\mathrm{cm}$, (c) $z\approx 10.5\mathrm{cm}$, and (d) $z\approx 20.3\mathrm{cm}$. Arrows represent a quiver plot of horizontal components ($\langle u_x\rangle ,\langle u_y\rangle$); colors: vertical component $\langle u_z\rangle$. (e),(f) Mean flow components in two vertical planes at $\theta \approx \pi /16$ and $\theta \approx 5\pi /16$, respectively. Dashed lines indicate the half width of the tank, $L/2$. (g),(h) Fluctuation magnitude $\sqrt{\langle u^{\prime 2}\rangle }/2\pi R\mathrm{\Omega }$ in the same vertical planes, with $u^{\prime 2}={\left(u_r^{\prime }\right)}^2+{\left(u_{\theta }^{\prime }\right)}^2+{\left(u_z^{\prime }\right)}^2$ and $u_k^{\prime }=u_k-\langle u_k\rangle$ ($k=r,\theta ,z$).

Figure 3

Axisymmetric PDFs of position for PM3 (first line) and PM6 (second line) particles plotted with the same color bar. From left to right, rotation frequencies are $\mathrm{\Omega }=2.0$, 3.0, 4.0, 5.0 and $6.0\mathrm{Hz}$. Dashed lines correspond to the bulk limit accessible to the particles: $r=L/2-d_p/2$.

Figure 4

Axisymmetric PDFs of the position for PM10 (first line) and PM18 (second line) particles plotted with the same color bar. From left to right, rotation frequencies are $\mathrm{\Omega }=2.0$, 3.0, 4.0, 5.0 and $6.0\mathrm{Hz}$. Dashed lines correspond to the bulk limit accessible to the particles: $r=L/2-d_p/2$. No data are available in the case $\mathrm{\Omega }=6\mathrm{Hz}$ and $d_p=10\mathrm{mm}$, as the particle was trapped in the spacing between the disk and one corner of the vessel, whose width almost exactly fits the particle size.

Figure 5

1D PDFs of position, ${\langle P\rangle }_{x,y}\left(z\right)$, for PM3 (left) and PM18 (right) particles and different rotation rates.

Figure 6

Mean normalized altitude $\overline{z}/H$ (left) and mean normalized radial position $\overline{r}/(L/2)$ (right) of PM and PC particles plotted against the rotation rate $\mathrm{\Omega }$. PM3: ($▾$); PM6: ($•$); PM10: ($⧫$); PM15: ($\blacksquare$); and PM18: ($▴$). PC2: ($▿$); PC6: ($\circ$); PC10: ($◊$); and PC18: ($▵$). Inset of left figure: normalized rms altitude $z_{\mathrm{rms}}/H$ against the rotation rate $\mathrm{\Omega }$ for the same cases. In all cases, the error on the estimation of the mean altitude is smaller than $E=2\mathrm{mm}$ ($E/H<0.01$).

Figure 7

Mean normalized altitude $\overline{z}/H$ of PM and PC particles plotted against the inverse of the turbulent Péclet number $1/{\mathrm{Pe}}_{\mathrm{turb}}=R^2\mathrm{\Omega }/H{v}_s$. PM3: ($▾$); PM6: ($•$); PM10: ($⧫$); PM15: ($\blacksquare$); and PM18: ($▴$). PC2: ($▿$); PC6: ($\circ$); PC10: ($◊$); and PC18: ($▵$).

Figure 8

Normalized axisymmetric vertical probability current ${\langle P\rangle }_{\theta }(r,z){\langle v_{p,z}\rangle }_{\theta }(r,z)/(P_0·2\pi R\mathrm{\Omega })$, with $P_0={\langle P\rangle }_{r,\theta ,z}$, for PolyaMid particles and a rotation rate $\mathrm{\Omega }=5\mathrm{Hz}$. From left to right: PM3, PM6, PM10, PM15, and PM18 particles. The domain corresponds to the volume actually accessible to each particle. Dashed lines correspond to the bulk limit accessible to the particles: $r=L/2-d_p/2$.