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Article Dans Une Revue Physical Review Letters Année : 2020

Preferential Concentration of Free-Falling Heavy Particles in Turbulence

Résumé

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. In spite of its apparent simplicity, the problem of spherical particles settling in a fluid hides a whole hierarchy of rich intricate phenomena, some of which are still shrouded in mystery, and which impacts numerous real situations. Atmospheric pollutants, cloud droplets, dust in proto-planetary accretion disks, sprays in engines are just examples pertaining to the broad class of turbulent flows laden with particles, which occur in many industrial and natural systems [1, 2]. In the context of pandemics, a current example of the importance of particle transport is given by the role of pollutants and aerosols as vectors of transmission and long range propagation of viruses [3]. In these situations, the flow carrying the particles is turbulent. Unveiling the fundamental mechanisms driving the dynamics of transport and settling is therefore a crucial issue to improve our capacity to model and predict particle dispersion and deposition. As surprising as this may seem, our modelling capacity is so weak that we are still unable to give quantitative answers to questions as simple as: Do small (point-like) spherical particles in a turbulent environment settle slower, faster, or at the same speed as in a quiescent fluid? What is, statistically, the spatial distribution of particles in a turbulent flow? And how is the distribution modified by gravity? The reasons are certainly related to the complexity of turbulence, one of the best known examples of out-of-equilibrium statistical systems, and to the difficulty added to the problem when the multi-scale and random dynamics of the flow is coupled to the particles' dynamics [4, 5]. One of the most striking examples of this complexity is given by the phenomenon of preferential concentration: whereas turbulence is generally considered as a mixing enhancer, inertial particles in turbulence tend on the contrary to get unmixed, and to concentrate in certain regions forming clusters. This effect impacts a whole range of the particles' dynamical features, as it changes their effective mean free path, impacting on cloud formation, particle aggregation, phase transitions, and predictions of local hazard thresholds [6, 7]. In this letter we address the question of the mechanism driving preferential concentration of inertial particles in turbulence focusing on the interplay between clustering and settling. It has been observed in direct numerical simulations (DNSs) and experiments that preferential concentration is stronger when the Stokes number St (the ratio of the particle relaxation time to the Kol-mogorov time) is close to unity [8, 9]. The reason why turbulence affects the spatial distribution of particles is not completely clear, although an explanation is based on the centrifugal expulsion of heavy particles from turbulent eddies, that would result in the accumulation of particles in low-vorticity regions of the carrier flow [10]. A more recent scenario, the so-called sweep-stick mechanism , was proposed in which particles cluster instead in regions of null Lagrangian acceleration [11]. There has been growing evidence that for particles with St < 1 there is a prevalence of centrifugal effects and particles cluster in low vorticity regions, whereas for St > 1 the sweep-stick mechanism is more prominent and particles cluster in low Lagrangian acceleration points [8, 12]. Nevertheless, these accumulation mechanisms do not take into account the effect of gravity, which is important when particles are heavy and can settle or precipitate. Gustavsson and coworkers [7] have shown that clustering properties may be significantly affected by gravity, pointing to the strong link between preferential concentration and settling. In the same context, an extension of the sweep-stick mechanism has been proposed, suggesting that settling particles concentrate in regions where the Lagrangian acceleration of the carrier flow equals that of the gravity [13], although to our knowledge no experimental or numerical studies have explored this mechanism yet. More generally, the settling of inertial particles has been studied focusing on the possible enhancement or hindering by turbulence of the particles' terminal velocity (see, e.g., [14, 15] for recent results), but except for a few recent studies [16-21] the interplay between preferential concentration and gravity for inertial particles has generally been neglected, either because it was not considered in simulations, or because it was negligible in the range of parameters considered in experiments. This is the case we focus on in our study. By studying
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Dates et versions

hal-02964657 , version 1 (12-10-2020)

Identifiants

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Florencia Flakinhoff, Martin Obligado, Mickaël Bourgoin, Pablo Mininni. Preferential Concentration of Free-Falling Heavy Particles in Turbulence. Physical Review Letters, 2020, 125 (6), ⟨10.1103/PhysRevLett.125.064504⟩. ⟨hal-02964657⟩
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