On the relationship between the non-local clustering mechanism and preferential concentration

Bragg, Andrew D.; Ireland, Peter J.; Collins, Lance R.

doi:10.1017/jfm.2015.474

Cited by 45 publications

(45 citation statements)

References 38 publications

(38 reference statements)

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“…However, it was pointed out in [35] that unlike the regime St 1, in the regime St ≥ O(1) the mechanism generating the clustering is distinct from the preferential sweeping mechanism. Indeed, for St ≥ O(1) the clustering is generated by a non-local mechanism and not the preferential sampling of the local flow field [47,51]. As a result, while the results in figure 5 for St 1 can be directly explained in terms of the preferential sweeping mechanism, the same does not apply for St ≥ O(1).…”

Section: B Particle Settling Velocitiesmentioning

confidence: 90%

“…This dependence of the clustering on R λ is similar to that found in [17,23] where the RDF was used to analyze the clustering. Arguments in [17,23,47] suggest that this behavior arises because unless St is sufficiently large, particles in the dissipation range are not able to remember their interaction with the inerital-range turbulence along their pathhistory. In this case, their motion is dominated by the dissipate range dynamics of the flow, and their dissipation range motion is not affected by the changing size of the inertial range as R λ is increased.…”

Section: A Voronoï Volume Distributionsmentioning

confidence: 99%

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Local analysis of the clustering, velocities, and accelerations of particles settling in turbulence

Momenifar

Bragg

2020

Phys. Rev. Fluids

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Using 3D Voronoï analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using Direct Numerical Simulations (DNS). We independently vary the Taylor Reynolds number R λ ∈ [90, 398], Froude number F r ≡ a η /g ∈ [0.052, ∞] (where a η is the Kolmogorov acceleration, and g is the acceleration due to gravity), and Kolmogorov scale Stokes number St ≡ τ p /τ η ∈ [0, 3]. In agreement with previous results using global measures of particle clustering, such as the Radial Distribution Function (RDF), we find that for small Voronoï volumes (corresponding to the most clustered particles), the behavior is strongly dependent upon St and F r, but only weakly dependent upon R λ , unless St > 1. However, larger Voronoï volumes (void regions) exhibit a much stronger dependence on R λ , even when St ≤ 1, and we show that this, rather than the behavior at small volumes, is the cause of the sensitivity of the standard deviation of the Voronoï volumes that has been previously reported. We also show that the largest contribution to the particle settling velocities is associated with increasingly larger Voronoï volumes as the settling parameter Sv ≡ St/F r is increased.Our local analysis of the acceleration statistics of settling inertial particles shows that clustered particles experience a net acceleration in the direction of gravity, while particles in void regions experience the opposite. The particle acceleration variance, however, is a convex function of the Voronoï volumes, with or without gravity, which seems to indicate a non-trivial relationship between the Voronoï volumes and the sizes of the turbulent flow scales. Results for the variance of the fluid acceleration at the inertial particle positions are of the order of the square of the Kolmogorov acceleration and depend only weakly on Voronoï volumes. These results call into question the "sweep-stick" mechanism for particle clustering in turbulence which would lead one to expect that clustered particles reside in the special regions where the fluid acceleration is zero (or at least small).We then consider the properties of particles in clusters, which are regions of connected Voronoï cells whose volume is less than a certain threshold. The results show self-similarity of the clusters, and that the statistics of the cluster volumes depends only weakly on St, with a stronger dependance on F r and R λ . Finally, we compare the average settling velocities of all particles in the flow with those in clusters, and show that those in the clusters settle much faster, in agreement with previous work. However, we also find that this difference grows significantly with increasing R λ and exhibits a non-monotonic dependence on F r. The kinetic energy of the particles, however, are almost the

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Section: B Particle Settling Velocitiesmentioning

confidence: 90%

Section: A Voronoï Volume Distributionsmentioning

confidence: 99%

Local analysis of the clustering, velocities, and accelerations of particles settling in turbulence

Momenifar

Bragg

2020

Phys. Rev. Fluids

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“…Based upon a Lagrangian description of the relative motion between particle pairs Zaichik and Alipchenkov [64], Chun et al [8] and Zaichik and Alipchenkov [65] have derived models for the particles' radial distribution function. This type of approach is non-local, since the history of the fluid velocity field seen by the particles enters the description [5,25]. Note that the relevance of this non-local clustering mechanism for finite-size particles has not been verified to date.…”

Section: Introductionmentioning

confidence: 99%

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

Chouippe

Uhlmann

2018

Acta Mech

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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 interfaceresolved direct numerical simulation based on an immersed boundary method. The values of the particles' relative density (1.5) and of the Galileo number (180) are such that strong wakeinduced particle clustering would occur in the absence of turbulence [56]. 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 [55]. Here we detect a tendency to cluster with an intensity (quantified via the standard deviation of the distribution of Voronoï cell volumes) 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 (of the order of one percent) 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 (computed via local averaging over a particle-attached sphere) has on average a smaller magnitude (by 5-7%) than the ambient single-particle value.

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“…The early work emphasized the role of centrifugation of finite-inertia particles out of vortical structures in turbulence. More recent evidence that clustering arises even in random, irrotational flows suggests that, while vorticity still plays a role, the dominant role is played by socalled "history effects", in which inertial particle velocity dispersions at any location carry a memory of particle encounters with more remote flow regimes which have larger characteristic velocity differences [8][9][10]. These history effects lead to spatial gradients in particle random relative velocities, and these gradients in turn generate systematic flows or currents which can outweigh dispersive effects and produce zones of highly variable particle concentration [2][3][4]11].…”

Section: Background and Introductionmentioning

confidence: 99%

Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

2017

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Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into sub-volumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik & Alipchenkov [New Journal of Physics 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

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On the relationship between the non-local clustering mechanism and preferential concentration

Cited by 45 publications

References 38 publications

Local analysis of the clustering, velocities, and accelerations of particles settling in turbulence

Local analysis of the clustering, velocities, and accelerations of particles settling in turbulence

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

Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

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