Study on preferential concentration of inertial particles in homogeneous isotropic turbulence via big-data techniques

We present an experimental study of the preferential concentration of sub-Kolmogorov inertial particles in active-grid-generated homogeneous and isotropic turbulence, characterized via Voronoi tessellations. We show that the detection and quantification of clusters and voids are influenced by the intensity of the laser and high values of particles volume fraction ${\varphi }_v$. Different biases on the statistics of Voronoi cells are analyzed to improve the reliability of the detection and the robustness in the characterization of clusters and voids. We do this by adapting big-data techniques that allow us to process the particle images up to 10 times faster than standard algorithms. Finally, as preferential concentration is known to depend on multiple parameters, we perform experiments where one parameter is varied and all others are kept constant (${\varphi }_v$, the Reynolds number based on the Taylor length scale ${\text{Re}}_{\lambda }$, and residence time of the particles interacting with the turbulence). Our results confirm, in agreement with published work, that clustering increases with both ${\varphi }_v$ and ${\text{Re}}_{\lambda }$. On the other hand, we find evidence that the mean size of clusters increases with ${\text{Re}}_{\lambda }$ but decreases with ${\varphi }_v$ and that the cluster settling velocity is strongly affected by ${\text{Re}}_{\lambda }$ up to the maximum value studied here, ${\text{Re}}_{\lambda }=250$.

Figure 1

Typical histogram of particle centers detected on the measuring window (a). Processing time for 4500 images as a function of the mean number of particles detected per image (b).

Figure 2

(a) Number of detected particles and their standard deviation vs laser intensity. Red symbols corresponds to laser A and blue ones to laser B. (b) PDFs of normalized Voronoi cells areas $\mathcal{V}$. (c) Standard deviation of $\mathcal{V}$ as a function of laser intensity. All data have been obtained for a volume fraction of ${\varphi }_v=2.47\times {10}^{-5}$ and a freestream velocity $U_{\infty }=2.1\mathrm{m}/\mathrm{s}$.

Figure 3

(a) PDF of cluster size normalized with its mean value. (b) Same as in (a) but for voids. (c) Cluster area and (d) void area as a function of laser intensity.

Figure 4

(a) Total number of particles detected and (b) their standard deviation at constant pulse energy and different flow conditions. Also shown are the corresponding PDFs of (c) $\mathcal{V}$ and (d) ${\sigma }_{\mathcal{V}}$. In (d) red circles mark the events that are outliers of the straight line from (a).

Figure 5

(a) Plot of ${\sigma }_{\mathcal{V}}$ as a function of the volume concentration of droplets ${\varphi }_v$. (b) Evolution with the same parameter of the mean area of clusters $A_{\text{clusters}}$ normalized with $\eta$ ($b$).

Figure 6

(a) Value of the mean concentration on clusters $C_{\text{clusters}}$ normalized with the global concentration $C_0$ ($C_0=\langle N\rangle /\langle A\rangle$). (b) Same parameter as in (a) but for voids. (c) Cluster settling velocity $V_{\text{cl}}$ as a function of the same parameter. Here $V_{\text{cl}}$ is defined, following the analysis from [17], as $V_{\text{cl}}=\frac{1}{60}\frac{{\rho }_p}{{\rho }_{\text{air}}}\frac{g}{{\nu }_{\text{air}}}\langle C_{\text{cl}}\rangle \langle A_{\text{cl}}\rangle$, with $C_{\text{cl}}$ the cluster mean volume concentration. In addition, ${\rho }_p$ and ${\rho }_{\text{air}}$ are, respectively, the particle and fluid density. The Stokes velocity is defined as $V_{\text{St}}=\sqrt{\frac{4}{3}g\frac{D_{\text{max}}}{C_D}\frac{{\rho }_p-{\rho }_f}{{\rho }_f}}$, where the drag coefficient $C_D$ has been estimated via the Schiller-Neumann relation [27]. As the value of $D_{\text{max}}$ is constant, we find $V_{\text{St}}=4.56\mathrm{cm}/\mathrm{s}$ for all cases. The ratios of $V_{\text{cl}}/V_{\text{St}}$ as a function of the volume fraction between the random and open modes are 9, 3.5, and 1.25.