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Register a new userPreferential concentration of free-falling heavy particles in turbulence
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Added by
Florencia Falkinhoff Ms
Publication date
2020
fields
Physics
and research's language is
English
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We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero Lagrangian acceleration. However, the actual Lagrangian acceleration of the fluid elements where particles accumulate is not zero, and has a dependence on the Stokes number, the gravity acceleration, and the settling velocity of the particles.
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In a seminal article, citet[J. Fluid Mech., 174:441-465]{maxey87} presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent Direct Numerical Simulation (DNS) results in citet[J. Fluid Mech., 796:659--711]{ireland16b} show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, there are several outstanding questions concerning the role of different turbulent flow scales on the enhanced settling, and the role of the Taylor Reynolds number $R_lambda$. The analysis of Maxey does not explain these issues, partly since it was restricted to particle Stokes numbers $Stll1$. To address these issues, we have developed a new theoretical result, valid for arbitrary $St$, that reveals the multiscale nature of the mechanism generating the enhanced settling speeds. In particular, it shows how the range of scales at which the preferential sweeping mechanism operates depends on $St$. This analysis is complemented by results from DNS where we examine the role of different flow scales on the particle settling speeds by coarse-graining the underlying flow. The results show how the flow scales that contribute to the enhanced settling depend on $St$, and that contrary to previous claims, there can be no single turbulent velocity scale that characterizes the enhanced settling speed. The results explain the dependence of the particle settling speeds on $R_lambda$, and show how the saturation of this dependence at sufficiently large $R_lambda$ depends upon $St$. The results also show ...
Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high concentration regions, i.e. clusters, and low concentration regions, i.e. voids, due to the interaction with the turbulence. In this work, we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters have been varied over significant ranges: $Re_{lambda} in [170 - 450]$, $Stin [0.1 - 5]$ and volume fraction $phi_vin [2times 10^{-6} - 2times 10^{-5}]$. The scaling of clustering characteristics, such as the distribution of Voronoi areas and the dimensions of cluster and void regions, with the three parameters are discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasi-linearly) by $Re_{lambda}$ and noticeably (with a square-root dependency) with $phi_v$, while the cluster and void sizes, scaled with the Kolmogorov lengthscale $eta$, are driven primarily by $Re_{lambda}$. Cluster length $sqrt{langle A_c rangle}$ scales up to $approx 100 {eta}$, measured at the highest $Re_{lambda}$, while void length $sqrt{langle A_v rangle}$ scaled also with $eta$ is typically two times larger ($approx 200 {eta}$). The lack of sensitivity of the above characteristics to the Stokes number lends support to the sweep-stick particle accumulation scenario. The non-negligible influence of the volume fraction, however, is not considered by that model and can be connected with collective effects.
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust description of the small scale properties of the system exploiting the convergence of the statistics with respect to the regularisation parameter. It is shown that sub-Kolmogorov particles/droplets modify the energy spectrum leading to a scaling law, $E(k)propto k^{-4}$, that emerges at small scales where the particle forcing balances the viscous dissipation. This regime is confirmed by Direct Numerical Simulation data of a particle-laden statistically steady homogeneous shear flow, demonstrating the ability of the regularised model to capture the relevant small-scale physics. The energy budget in spectral space, extended to account for the inter-phase momentum exchange, highlights how the particle provide an energy sink in the production range that turns into a source at small scales. Overall, the dissipative fluid-particle interaction is found to stall the energy cascade processes typical of Newtonian turbulent flows. In terms of particle statistics, clustering at small scale is depleted, with potential consequences for collision models.
In this video, we present the dynamics of an array of falling particles at intermediate Reynolds numbers. The film shows the vorticity plots of 3, 4, 7, 16 falling particles at $Re = 200$. We highlight the effect of parity on the falling configuration of the array. In steady state, an initially uniformly spaced array forms a convex shape when $n=3$, i.e the middle particle leads, but forms a concave shape when $n = 4$. For larger odd numbers of particles, the final state consists of a mixture of concave and convex shapes. For larger even numbers of particles, the steady state remains a concave shape. Below a threshold of initial particle spacing, particles cluster in groups of 2 to 3.
We present a field study of snow settling dynamics based on simultaneous measurements of the atmospheric flow field and snow particle trajectories. Specifically, a super-large-scale particle image velocimetry (SLPIV) system using natural snow particles as tracers is deployed to quantify the velocity field and identify vortex structures in a 22 m $times$ 39 m field of view centered 18 m above the ground. Simultaneously, we track individual snow particles in a 3 m $times$ 5 m sample area within the SLPIV using particle tracking velocimetry (PTV). The results reveal the direct linkage among vortex structures in atmospheric turbulence, the spatial distribution of snow particle concentration, and their settling dynamics. In particular, with snow turbulence interaction at near-critical Stokes number, the settling velocity enhancement of snow particles is multifold, and larger than what has been observed in previous field studies. SLPIV measurements show higher concentration of snow particles preferentially located on the downward side of the vortices identified in the atmospheric flow field. PTV, performed on high resolution images around the reconstructed vortices, confirms the latter trend and provides statistical evidence of the acceleration of snow particles, as they move toward the downward side of vortices. Overall, the simultaneous multi-scale particle imaging presented here enables us to directly quantify the salient features of preferential sweeping, supporting it as an underlying mechanism of snow settling enhancement in the atmospheric surface layer.
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