Coherent clusters of inertial particles in homogeneous turbulence

2017 ◽  
Vol 833 ◽  
pp. 364-398 ◽  
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.

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

2017 ◽  
Vol 814 ◽  
pp. 592-613 ◽  
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.

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

2005 ◽  
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.

scholarly journals Modelling of turbulence modulation in particle- or droplet-laden flows

2012 ◽  
Vol 706 ◽  
pp. 251-273 ◽  
Author(s):  
Daniel W. Meyer
Keyword(s):  
Isotropic Turbulence ◽  
Density Ratio ◽  
Joint Probability ◽  
Stokes Number ◽  
Navier Stokes ◽  
Grid Turbulence ◽  
Heavy Particles ◽  
Turbulence Modulation ◽  
Modelling Framework ◽  
Liquid Flows

AbstractAddition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1{\unicode{x2013}} 10)$, particle/fluid density ratio ${\rho }_{p} / \rho = 2000$, ${\Phi }_{v} = O(1{0}^{- 4} )$) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ($\mathit{St}= O(0. 1)$, ${\rho }_{p} / \rho \gtrsim 1$, ${\Phi }_{v} = O(1{0}^{- 3} )$) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible.

scholarly journals Experimental study of inertial particles clustering and settling in homogeneous turbulence

2019 ◽  
Vol 864 ◽  
pp. 925-970 ◽  
Author(s):  
Alec J. Petersen ◽  
Lucia Baker ◽  
Filippo Coletti
Keyword(s):  
Reynolds Number ◽  
Fluid Velocity ◽  
Stokes Number ◽  
Terminal Velocity ◽  
Solid Particles ◽  
Homogeneous Turbulence ◽  
Small Scale ◽  
Inertial Particles ◽  
Mean Flow ◽  
Integral Scale

We study experimentally the spatial distribution, settling and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_{\unicode[STIX]{x1D706}}\approx 200{-}500$, while the particle Stokes number based on the Kolmogorov scale varies between $St_{\unicode[STIX]{x1D702}}=O(1)$ and $O(10)$. Clustering is confirmed to be most intense for $St_{\unicode[STIX]{x1D702}}\approx 1$, but it extends over larger scales for heavier particles. Individual clusters form a hierarchy of self-similar, fractal-like objects, preferentially aligned with gravity and with sizes that can reach the integral scale of the turbulence. Remarkably, the settling velocity of $St_{\unicode[STIX]{x1D702}}\approx 1$ particles can be several times larger than the still-air terminal velocity, and the clusters can fall even faster. This is caused by downward fluid fluctuations preferentially sweeping the particles, and we propose that this mechanism is influenced by both large and small scales of the turbulence. The particle–fluid slip velocities show large variance, and both the instantaneous particle Reynolds number and drag coefficient can greatly differ from their nominal values. Finally, for sufficient loadings, the particles generally augment the small-scale fluid velocity fluctuations, which however may account for a limited fraction of the turbulent kinetic energy.

scholarly journals Intermittency in the relative separations of tracers and of heavy particles in turbulent flows

2014 ◽  
Vol 757 ◽  
pp. 550-572 ◽  
Author(s):  
L. Biferale ◽  
A. S. Lanotte ◽  
R. Scatamacchia ◽  
F. Toschi
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Isotropic Turbulence ◽  
Exit Time ◽  
Three Dimensional ◽  
Stokes Number ◽  
Inertial Range ◽  
Relative Dispersion ◽  
Heavy Particles ◽  
Self Similar

AbstractResults from direct numerical simulations (DNS) of particle relative dispersion in three-dimensional homogeneous and isotropic turbulence at Reynolds number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\mathit{Re}}_{\lambda } \sim 300$ are presented. We study point-like passive tracers and heavy particles, at Stokes number $\mathit{St}=0.6,1$ and 5. Particles are emitted from localised sources, in bunches of thousands, periodically in time, allowing an unprecedented statistical accuracy to be reached, with a total number of events for two-point observables of the order of ${10^{11}}$. The right tail of the probability density function (PDF) for tracers develops a clear deviation from Richardson’s self-similar prediction, pointing to the intermittent nature of the dispersion process. In our numerical experiment, such deviations are manifest once the probability to measure an event becomes of the order of – or rarer than – one part over one million, hence the crucial importance of a large dataset. The role of finite-Reynolds-number effects and the related fluctuations when pair separations cross the boundary between viscous and inertial range scales are discussed. An asymptotic prediction based on the multifractal theory for inertial range intermittency and valid for large Reynolds numbers is found to agree with the data better than the Richardson theory. The agreement is improved when considering heavy particles, whose inertia filters out viscous scale fluctuations. By using the exit-time statistics we also show that events associated with pairs experiencing unusually slow inertial range separations have a non-self-similar PDF.

Statistical properties of particle segregation in homogeneous isotropic turbulence

2011 ◽  
Vol 686 ◽  
pp. 338-351 ◽  
Author(s):  
Elena Meneguz ◽  
Michael W. Reeks
Keyword(s):  
Particle Concentration ◽  
Isotropic Turbulence ◽  
Concentration Field ◽  
Threshold Value ◽  
Stokes Number ◽  
Statistical Properties ◽  
Inertial Particles ◽  
Concentration Changes ◽  
Non Gaussian ◽  
Good Agreement

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).

scholarly journals The effect of turbulence on mass transfer rates between inertial polydisperse particles and fluid

2019 ◽  
Vol 874 ◽  
pp. 1147-1168 ◽  
Author(s):  
Ewa Karchniwy ◽  
Adam Klimanek ◽  
Nils Erland L. Haugen
Keyword(s):  
Mass Transfer ◽  
Time Scale ◽  
Transfer Rate ◽  
Particle System ◽  
Mass Transfer Rate ◽  
Stokes Number ◽  
Flow Time ◽  
Inertial Particles ◽  
Integral Scale ◽  
Order Of Magnitude

The current work investigates how turbulence affects the mass transfer rate between inertial particles and fluid in a dilute, polydisperse particle system. Direct numerical simulations are performed in which all scales of turbulence are fully resolved and particles are represented in a Lagrangian reference frame. The results show that, similarly to a monodisperse system, the mass transfer rate between particles and fluid decreases as a result of particle clustering. This occurs when the flow time scale (based on the turbulence integral scale) is long relative to the chemical time scale, and is strongest when the particle time scale is one order of magnitude smaller than the flow time scale (i.e. the Stokes number is around 0.1). It is also found that for larger solid mass fractions, the clustering of the heavier particles is enhanced by the effect of drag force from the particles on the fluid (momentum back-reactions or two-way coupling). In particular, when two-way coupling is accounted for, locations of particles of different sizes are much more correlated, which leads to a stronger effect of clustering, and thus a greater reduction of the particle–fluid mass transfer rate.

scholarly journals Hydrodynamic interactions and extreme particle clustering in turbulence

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.

scholarly journals Inertial-particle accelerations in turbulence: a Lagrangian closure

2016 ◽  
Vol 798 ◽  
pp. 187-200 ◽  
Author(s):  
S. Vajedi ◽  
K. Gustavsson ◽  
B. Mehlig ◽  
L. Biferale
Keyword(s):  
Numerical Simulations ◽  
Numerical Data ◽  
Direct Numerical Simulations ◽  
Inertial Particles ◽  
Inertial Particle ◽  
Order Unity ◽  
Heavy Particles ◽  
Preferential Sampling ◽  
Closure Scheme ◽  
Light Particles

The distribution of particle accelerations in turbulence is intermittent, with non-Gaussian tails that are quite different for light and heavy particles. In this article we analyse a closure scheme for the acceleration fluctuations of light and heavy inertial particles in turbulence, formulated in terms of Lagrangian correlation functions of fluid tracers. We compute the variance and the flatness of inertial-particle accelerations and we discuss their dependency on the Stokes number. The closure incorporates effects induced by the Lagrangian correlations along the trajectories of fluid tracers, and its predictions agree well with results of direct numerical simulations of inertial particles in turbulence, provided that the effects induced by inertial preferential sampling of heavy/light particles outside/inside vortices are negligible. In particular, the scheme predicts the correct functional behaviour of the acceleration variance, as a function of $St$, as well as the presence of a minimum/maximum for the flatness of the acceleration of heavy/light particles, in good qualitative agreement with numerical data. We also show that the closure works well when applied to the Lagrangian evolution of particles using a stochastic surrogate for the underlying Eulerian velocity field. Our results support the conclusion that there exist important contributions to the statistics of the acceleration of inertial particles independent of the preferential sampling. For heavy particles we observe deviations between the predictions of the closure scheme and direct numerical simulations, at Stokes numbers of order unity. For light particles the deviation occurs for larger Stokes numbers.

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