On the influence of forced homogeneous-isotropic turbulence on the settling and clustering of finite-size particles

TL;DR

This study uses interface-resolved DNS with an Immersed Boundary Method to examine heavy finite-size particles settling under gravity in forced homogeneous-isotropic turbulence at density ratio $\rho_p/\rho_f=1.5$ and $Ga\approx180$. By comparing cases with two turbulent Reynolds numbers ($Re_\lambda^{SP}=95$ and $140$) and gravity versus no-gravity references, it shows that the mean settling velocity remains close to that of a single particle in ambient flow, with small turbulence-dependent deviations. Clustering is found to be intermediate between wake-induced clustering in ambient settling and turbulence-only clustering, and it behaves non-monotonically with relative turbulence intensity, suggesting competing wake- and turbulence-driven mechanisms. The analysis highlights the role of crossing-trajectory effects and eddy-scale resonance in gravity-influenced clustering, and it reveals that forced turbulence both disrupts small-scale wake-induced clusters and enables preferential concentration via large-scale structures, with implications for sedimentation and pollutant transport in geophysical and engineering settings.

Abstract

We investigate the motion of heavy particles with a diameter of several multiples of the Kolmogorov length scale in the presence of forced turbulence and gravity, resorting to interface-resolved DNS based on an IBM. The values of the particles' relative density (1.5) and of the Galileo number (180) are such that strong wake-induced particle clustering would occur in the absence of turbulence. The forced turbulence in the two present cases (with Taylor-scale Reynolds number 95 and 140) would lead to mild levels of clustering in the absence of gravity. Here we detect a tendency to cluster with an intensity which is intermediate between these two limiting cases, meaning that forced background turbulence decreases the level of clustering otherwise observed under ambient settling. However, the clustering strength does not monotonously decay with the relative turbulence intensity. Various mechanisms by which coherent structures can affect particle motion are discussed. It is argued that the reduced interaction time due to particle settling through the surrounding eddy (crossing trajectories) has the effect of shifting upwards the range of eddies with a time scale matching the characteristic time scale of the particle. In the present cases this shift might bring the particles into resonance with the energetic eddies of the turbulent spectrum. Concerning the average particle settling velocity we find very small deviations from the value obtained for an isolated particle in ambient fluid when defining the relative velocity as an apparent slip velocity (i.e. as the difference between the averages computed separately for the velocities of each phase). This is consistent with simple estimates of the non-linear drag effect. However, the relative velocity based upon the fluid velocity seen by each particle has on average a smaller magnitude (by 5-7%) than the ambient single-particle value.

Figures (15)

• Figure 1: Visualization of particle positions for both types of initial state used in the current study: (a-c) columns (corresponding to the final state of the case G178) used in G178-R95, (d-f) Randomly distributed particles used in G180-R140.
• Figure 2: Time evolution of the different terms in the budget of the volume averaged kinetic energy: $0=-\hbox{d}\left< E_k \right > _{\Omega}/\hbox{d}t-\varepsilon_\Omega+\Psi^{(t)}+\Psi^{(p)}$ scaled by the dissipation of the corresponding single phase simulation for case G178-R95 (a) and G180-R140 (b). Linestyle: $$$(-\hbox{d}\left<E_k\right>_{\Omega}/\hbox{d}t)$, $\color{red}{}$$(-\varepsilon_\Omega)$, $\color{blue}{}$$\Psi^{(t)}$, $\color{magenta}{}$$\Psi^{(p)}$
• Figure 3: (a) Longitudinal two-point correlation function in the z-coordinate direction, $\mathcal{R}_{ww}(r_z)$. Linestyle: $\color{red}{}$ G178-R95, $\color{blue}{}$ G180-R140, ${}$ G178, $$$$$$ R95
• Figure 4: P.d.f. of the second invariant of the velocity gradient tensor, $Q$, hunt:88 for the unfiltered field (solid lines) and the filtered field (dashed lines). The field has been filtered with a box-filter of width $\Delta_{filt}=89\Delta x$ for the particle-laden cases (corresponding to $\Delta_{filt}=3.7D$ for the settling cases and $\Delta_{filt}=5.6D$ for G0-R120) and $\Delta_{filt}=45\Delta x$ for the single phase case such as to keep the same ratio $\Delta_{filt}/\eta^{SP}$ as G178-R95. The dashed-dotted lines correspond to the values of $Q$ sampled on the spheres $\mathcal{S}_{(i)}$ centered on the particles. Linestyle: $\color{blue}{}$ G180-R140, $\color{red}{}$ G178-R95, ${}$ G178, $\color{cyan}{}$ R95. The table lists the standard deviation of $Q$ computed for the unfiltered field ($Q$) and the filtered field ($Q^{filt}$).
• Figure 5: Isocontour of $Q$ for the unfiltered field (blue) and the filtered field (yellow) for the single phase case R95 (a), the case G0-R120 (b) and the case G178 (d). The filter width is equal to $\Delta_{filt}=89\Delta x$ for both cases G0-R114 and G178, and to $\Delta_{filt}=45\Delta x$ for R95. For the unfiltered field the isocontour corresponds to $Q=1.5 \sigma(Q)$ in the absence of gravity and $Q=0.5 \sigma(Q)$ for M178, while the filtered field corresponds to $Q_{filt}=1.5 \sigma(Q_{filt})$. For the three figures the visualizations represent one eighth of the domain in the depth (into the page) and the total domain in the other two directions.