Statistical properties of particle segregation in homogeneous isotropic turbulence

AbstractA full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent flow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the flow. Qualitative good agreement is observed with previous kinematic simulations (KS) (IJzermans, Meneguz & Reeks, J. Fluid Mech., vol. 653, 2010, pp. 99–136): in particular, the existence of singularities in the particle concentration field and a threshold value for the particle Stokes number $\mathit{St}$ above which the net compressibility of the particle concentration changes sign (from compression to dilation). A further KS analysis is carried out by examining the distribution in time of the compression of an elemental volume of particles, which shows that it is close to Gaussian as far as the third and fourth moments but non-Gaussian (within the uncertainties of the measurements) for higher-order moments when the contribution of singularities in the tails of the distribution increasingly dominates the statistics. Measurements of the rate of occurrence of singularities show that it reaches a maximum at $\mathit{St}\ensuremath{\sim} 1$, with the distribution of times between singularities following a Poisson process. Following the approach used by Fevrier, Simonin & Squires (J. Fluid Mech., vol. 553, 2005, pp. 1–46), we also measured the random uncorrelated motion (RUM) and mesoscopic components of the compression for $\mathit{St}= 1$ and show that the non-Gaussian highly intermittent part of the distribution of the compression is associated with the RUM component and ultimately with the occurrence of singularities. This result is consistent with the formation of caustics (Wilkinson et al. Phys. Fluids, vol. 19, 2007, p. 113303), where the activation of singularities precedes the crossing of trajectories (RUM).

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Snowflakes in the atmospheric surface layer: observation of particle–turbulence dynamics

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.13 ◽

2017 ◽

Vol 814 ◽

pp. 592-613 ◽

Cited By ~ 15

Author(s):

Andras Nemes ◽

Teja Dasari ◽

Jiarong Hong ◽

Michele Guala ◽

Filippo Coletti

Keyword(s):

Large Scale ◽

Isotropic Turbulence ◽

Volume Fraction ◽

Response Times ◽

Field Measurements ◽

Stokes Number ◽

Inertial Particles ◽

Natural Setting ◽

Scale Particle ◽

Particle Imaging

We report on optical field measurements of snow settling in atmospheric turbulence at $Re_{\unicode[STIX]{x1D706}}=940$. It is found that the snowflakes exhibit hallmark features of inertial particles in turbulence. The snow motion is analysed in both Eulerian and Lagrangian frameworks by large-scale particle imaging, while sonic anemometry is used to characterize the flow field. Additionally, the snowflake size and morphology are assessed by digital in-line holography. The low volume fraction and mass loading imply a one-way interaction with the turbulent air. Acceleration probability density functions show wide exponential tails consistent with laboratory and numerical studies of homogeneous isotropic turbulence. Invoking the assumption that the particle acceleration has a stronger dependence on the Stokes number than on the specific features of the turbulence (e.g. precise Reynolds number and large-scale anisotropy), we make inferences on the snowflakes’ aerodynamic response time. In particular, we observe that their acceleration distribution is consistent with that of particles of Stokes number in the range $St=0.1{-}0.4$ based on the Kolmogorov time scale. The still-air terminal velocities estimated for the resulting range of aerodynamic response times are significantly smaller than the measured snow particle fall speed. This is interpreted as a manifestation of settling enhancement by turbulence, which is observed here for the first time in a natural setting.

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An Investigation of Crossing Trajectory Effects in Turbulent Shear Flow (Keynote)

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2005-77303 ◽

2005 ◽

Cited By ~ 2

Author(s):

Lionel Thomas ◽

Benoiˆt Oesterle´

Keyword(s):

Shear Flow ◽

Isotropic Turbulence ◽

Fluid Velocity ◽

Stokes Number ◽

Turbulent Shear ◽

Inertial Particles ◽

Turbulent Shear Flow ◽

Velocity Magnitude ◽

Dispersed Particles ◽

Lagrangian Tracking

The dispersion of small inertial particles moving in a homogeneous, hypothetically stationary, shear flow is investigated using both theoretical analysis and numerical simulation, under one-way coupling approximation. In the theoretical approach, the previous studies are extended to the case of homogeneous shear flow with a corresponding anisotropic spectrum. As it is impossible to obtain a closed theoretical solution without some drastic simplifications, the motion of dispersed particles is also investigated using kinematic simulation where random Fourier modes are generated according to a prescribed anisotropic spectrum with a superimposed linear mean fluid velocity profile. The combined effects of particle Stokes number and dimensionless drift velocity (magnitude and direction) are investigated by computing the statistics from Lagrangian tracking of a large number of particles in many flow field realizations, and comparison is made between the observed effects in shear flow and in isotropic turbulence.

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Eddy diffusivities of inertial particles under gravity

Journal of Fluid Mechanics ◽

10.1017/jfm.2011.562 ◽

2012 ◽

Vol 694 ◽

pp. 426-463 ◽

Cited By ~ 13

Author(s):

Marco Martins Afonso ◽

Andrea Mazzino ◽

Paolo Muratore-Ginanneschi

Keyword(s):

Particle Velocity ◽

Large Scale ◽

Particle Concentration ◽

Mass Density ◽

Concentration Field ◽

Eddy Diffusivity ◽

Inertial Particles ◽

Differential Problem ◽

Carrier Flow ◽

Eddy Diffusivities

AbstractThe large-scale/long-time transport of inertial particles of arbitrary mass density under gravity is investigated by means of a formal multiple-scale perturbative expansion in the scale-separation parameter between the carrier flow and the particle concentration field. The resulting large-scale equation for the particle concentration is determined, and is found to be diffusive with a positive definite eddy diffusivity. The calculation of the latter tensor is reduced to the resolution of an auxiliary differential problem, consisting of a coupled set of two differential equations in a $(6+ 1)$-dimensional coordinate system (three space coordinates plus three velocity coordinates plus time). Although expensive, numerical methods can be exploited to obtain the eddy diffusivity, for any desirable non-perturbative limit (e.g. arbitrary Stokes and Froude numbers). The aforementioned large-scale equation is then specialized to deal with two different relevant perturbative limits: (i) vanishing of both Stokes time and sedimenting particle velocity; (ii) vanishing Stokes time and finite sedimenting particle velocity. Both asymptotics lead to a greatly simplified auxiliary differential problem, now involving only space coordinates and thus easily tackled by standard numerical techniques. Explicit, exact expressions for the eddy diffusivities have been calculated, for both asymptotics, for the class of parallel flows, both static and time-dependent. This allows us to investigate analytically the role of gravity and inertia on the diffusion process by varying relevant features of the carrier flow, such as the form of its temporal correlation function. Our results exclude a universal role played by gravity and inertia on the diffusive behaviour: regimes of both enhanced and reduced diffusion may exist, depending on the detailed structure of the carrier flow.

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Coherent clusters of inertial particles in homogeneous turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.700 ◽

2017 ◽

Vol 833 ◽

pp. 364-398 ◽

Cited By ~ 23

Author(s):

Lucia Baker ◽

Ari Frankel ◽

Ali Mani ◽

Filippo Coletti

Keyword(s):

Isotropic Turbulence ◽

Stokes Number ◽

Inertial Particles ◽

Gravitational Acceleration ◽

Self Similarity ◽

Integral Scale ◽

Heavy Particles ◽

Diagram Method ◽

Vorticity Vector ◽

Definition Of

Despite the widely acknowledged significance of turbulence-driven clustering, a clear topological definition of particle cluster in turbulent dispersed multiphase flows has been lacking. Here we introduce a definition of coherent cluster based on self-similarity, and apply it to distributions of heavy particles in direct numerical simulations of homogeneous isotropic turbulence, with and without gravitational acceleration. Clusters show self-similarity already at length scales larger than twice the Kolmogorov length, as indicated by the fractal nature of their surface and by the power-law decay of their size distribution. The size of the identified clusters extends to the integral scale, with average concentrations that depend on the Stokes number but not on the cluster dimension. Compared to non-clustered particles, coherent clusters show a stronger tendency to sample regions of high strain and low vorticity. Moreover, we find that the clusters align themselves with the local vorticity vector. In the presence of gravity, they tend to align themselves vertically and their fall speed is significantly different from the average settling velocity: for moderate fall speeds they experience stronger settling enhancement than non-clustered particles, while for large fall speeds they exhibit weakly reduced settling. The proposed approach for cluster identification leverages the Voronoï diagram method, but is also compatible with other tessellation techniques such as the classic box-counting method.

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In Search of Random Uncorrelated Particle Motion (RUM) in a Simple Random Flow Field

Volume 1: Symposia, Parts A and B ◽

10.1115/fedsm2006-98383 ◽

2006 ◽

Cited By ~ 2

Author(s):

Michael W. Reeks ◽

Luca Fabbro ◽

Alfredo Soldati

Keyword(s):

Flow Field ◽

Particle Velocity ◽

Particle Motion ◽

Particle Concentration ◽

Concentration Field ◽

Spatial Separation ◽

Stokes Number ◽

Velocity Correlation ◽

Pair Separation ◽

Random Flow

DNS studies of dispersed particle motion in isotropic homogeneous turbulence [1] have revealed the existence of a component of random uncorrelated motion (RUM) dependent on the particle inertia τp (normalised particle response time or Stoke number). This paper reports the presence of RUM in a simple linear random smoothly varying flow field of counter rotating vortices where the two-particle velocity correlation was measured as a function of spatial separation. Values of the correlation less than one for zero separation indicated the presence of RUM. In terms of Stokes number, the motion of the particles in one direction corresponds to either a heavily damped (τp < 0.25) or lightly damped (τp > 0.25) harmonic oscillator. In the lightly damped case the particles overshoot the stagnation lines of the flow and are projected from one vortex to another (the so-called sling-shot effect). It is shown that RUM occurs only when τp > 0.25, increasing monotonically with increasing Stokes number. Calculations of the particle pair separation distribution function show that equilibrium of the particle concentration field is never reached, the concentration at zero separation increasing monotonically with time. This is consistent with the calculated negative values of the average Liapounov exponent (finite compressibility) of the particle velocity field.

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How turbulence enhances coalescence of settling particles with applications to rain in clouds

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2005.1490 ◽

2005 ◽

Vol 461 (2062) ◽

pp. 3059-3088 ◽

Cited By ~ 34

Author(s):

S Ghosh ◽

J Dávila ◽

J.C.R Hunt ◽

A Srdic ◽

H.J.S Fernando ◽

...

Keyword(s):

Particle Concentration ◽

Critical Radius ◽

Experimental Studies ◽

Turbulent Energy ◽

Inertial Particles ◽

Gravitational Acceleration ◽

Cloud Droplets ◽

Size Spectra ◽

Developed Turbulence ◽

Good Agreement

From theoretical, numerical and experimental studies of small inertial particles with density equal to β (>1) times that of the fluid, it is shown that such particles are ‘centrifuged’ out of vortices and eddies in turbulence. Thus, in the presence of gravitational acceleration g , their average sedimentation velocity V T in a size range just below a critical radius a cr is increased significantly by up to about 80%. We show that in fully developed turbulence, a cr is determined by the circulation Γ k of the smallest Kolmogorov micro-scale eddies, but is approximately independent of the rate of turbulent energy dissipation ϵ , because Γ k is about equal to the kinematic viscosity ν . It is shown that a cr varies approximately like and is about 20 μm (±2 μm) for water droplets in most types of cloud. New calculations are presented to show how this phenomena causes higher collision rates between these ‘large’ droplets and those that are smaller than a cr , leading to rapid growth rates of droplets above this critical radius. Calculations of the resulting droplet size spectra in cloud turbulence are in good agreement with experimental data. The analysis, which explains why cloud droplets can grow rapidly from 20 to 80 μm irrespective of the level of cloud turbulence is also applicable where a cr ∼1 mm for typical sand/mud particles. This mechanism, associated with unequal droplet/particle sizes is not dependant on higher particle concentration around vortices and the results differ quantitatively and physically from theories based on this hypothesis.

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Hydrodynamic interactions and extreme particle clustering in turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.1099 ◽

2021 ◽

Vol 933 ◽

Author(s):

Andrew D. Bragg ◽

Adam L. Hammond ◽

Rohit Dhariwal ◽

Hui Meng

Keyword(s):

Experimental Data ◽

Distribution Function ◽

Radial Distribution Function ◽

Radial Distribution ◽

Isotropic Turbulence ◽

Stokes Number ◽

Particle Radius ◽

Hydrodynamic Interactions ◽

Inertial Particles ◽

Physical Mechanisms

Expanding recent observations by Hammond & Meng (J. Fluid Mech., vol. 921, 2021, A16), we present a range of detailed experimental data of the radial distribution function (r.d.f.) of inertial particles in isotropic turbulence for different Stokes number, $St$ , showing that the r.d.f. grows explosively with decreasing separation r, exhibiting $r^{-6}$ scaling as the collision radius is approached, regardless of $St$ or particle radius $a$ . To understand such explosive clustering, we correct a number of errors in the theory by Yavuz et al. (Phys. Rev. Lett., vol. 120, 2018, 244504) based on hydrodynamic interactions between pairs of small, weakly inertial particles. A comparison between the corrected theory and the experiment shows that the theory by Yavuz et al. underpredicts the r.d.f. by orders of magnitude. To explain this discrepancy, we explore several alternative mechanisms for this discrepancy that were not included in the theory and show that none of them are likely the explanation. This suggests new, yet-to-be-identified physical mechanisms are at play, requiring further investigation and new theories.

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