Gravity-driven clustering of inertial particles in turbulence

Park, Yongnam; Lee, Chang‐Hoon

doi:10.1103/physreve.89.061004

Cited by 26 publications

(37 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For St = 2.0, the settling influence is intermediate: the spectrum becomes lower around the peak, whereas it becomes higher for the lager wavenumbers, where the slope becomes gentler. Similar enhancement of turbulent clustering was reported by some research groups [20,23,24]. They focused on the scales smaller than l η but, in Fig.…”

Section: Stokes Number Dependence Of Turbulent Clusteringsupporting

confidence: 75%

“…For large S v , droplet clusters are extended in vertical direction; i.e., the vertical scales of void scales become larger compared with the horizontal scales as S v increases. This vertically-extended clustering is corresponding to the nearly-two-dimensional "curtain shape" clustering, which was observed by Woittiez [24] and some other authors [20,23]. Figure 2 shows the power spectra of droplet number density fluctuations, E np (k), for the case of Re204St1g-L.…”

Section: Radar Reflectivity Factormentioning

confidence: 53%

See 1 more Smart Citation

Influence of Gravitational Settling on Turbulent Droplet Clustering and Radar Reflectivity Factor

Matsuda

Onishi

Takahashi

2016

Flow Turbulence Combust

View full text Add to dashboard Cite

This study investigates the influence of gravitational settling of droplets on turbulent clustering and the radar reflectivity factor. A three-dimensional direct numerical simulation (DNS) of particle-laden isotropic turbulence is performed to obtain turbulent droplet clustering data. The turbulent clustering data are then used to calculate the power spectrum of droplet number density fluctuations. The results show that the gravitational settling modulates the power spectrum more significantly as the settling becomes larger. The gravitational settling weakens the intensity of clustering at large wavenumbers for St ≤ 1, whereas it significantly enlarges the intensity for St > 1. The dependence on the Taylor-microscale-based Reynolds number is also investigated to discuss the contribution of large-scale eddies to the settling influence. The results show that large-scale eddies modulate the small scale clustering structure of large St droplets. The increment of radar reflectivity factor due to turbulent clustering is estimated from the power spectrum for the case of St = 1.0. The result shows that the influence of gravitational settling on the radar reflectivity factor can be significant for the case of large settling velocity droplets.

show abstract

Section: Stokes Number Dependence Of Turbulent Clusteringsupporting

confidence: 75%

Section: Radar Reflectivity Factormentioning

confidence: 53%

Influence of Gravitational Settling on Turbulent Droplet Clustering and Radar Reflectivity Factor

Matsuda

Onishi

Takahashi

2016

Flow Turbulence Combust

View full text Add to dashboard Cite

show abstract

“…For some applications, this limits the applicability of the model. Under the effect of gravity, particles can form curtainlike manifolds, which profoundly affect both the spatial distribution and the relative velocity of the particles [12,[34][35][36][37][38][39][40]). Gravity reduces the formation of caustics [35] and the power-law prediction is expected to fail.…”

Section: Stmentioning

confidence: 99%

Relative velocity distribution of inertial particles in turbulence: A numerical study

Perrin

Jonker

2015

Phys. Rev. E

View full text Add to dashboard Cite

The distribution of relative velocities between particles provides invaluable information on the rates and characteristics of particle collisions. We show that the theoretical model of Gustavsson and Mehlig [K. Gustavsson and B. Mehlig, J. Turbul. 15, 34 (2014)], within its anticipated limits of validity, can predict the joint probability density function of relative velocities and separations of identical inertial particles in isotropic turbulent flows with remarkable accuracy. We also quantify the validity range of the model. The model matches two limits (or two types) of relative motion between particles: one where pair diffusion dominates (i.e., large coherence between particle motion) and one where caustics dominate (i.e., large velocity differences between particles at small separations). By using direct numerical simulation combined with Lagrangian particle tracking, we assess the model prediction in homogeneous and isotropic turbulence. We demonstrate that, when sufficient caustics are present at a given separation and the particle response time is significantly smaller than the integral time scales of the flow, the distribution exhibits the same universal power-law form dictated by the correlation dimension as predicted by the model of Gustavsson and Mehlig. In agreement with the model, no strong dependency on the Taylor-based Reynolds number is observed.

show abstract

“…The asymptotic independence of a fractal dimension on St was found in numerical simulations in [24] (see statement of independent work below), see also [34]. When gravity is strong, a new pattern of vertical clustering of sedimenting particles was recently observed [35]. However, no theoretical predictions comparable in detail to Eqs.…”

mentioning

confidence: 95%

“…This is likely to produce a difference in the structure of the fractal in horizontal and vertical directions in accord with [35]. The resulting fractal geometry is the topic of the study in progress [49].…”

mentioning

confidence: 99%

Inhomogeneous distribution of water droplets in cloud turbulence

et al. 2015

Self Cite

View full text Add to dashboard Cite

We solve the problem of spatial distribution of inertial particles that sediment in turbulent flow with small ratio of acceleration of fluid particles to acceleration of gravity g. The particles are driven by linear drag and have arbitrary inertia. The pair-correlation function of concentration obeys a power-law in distance with negative exponent. Divergence at zero signifies singular distribution of particles in space. Independently of particle size the exponent is ratio of integral of energy spectrum of turbulence times the wavenumber to g times numerical factor. We find Lyapunov exponents and confirm predictions by direct numerical simulations of Navier-Stokes turbulence. The predictions include typical case of water droplets in clouds. This significant progress in the study of turbulent transport is possible because strong gravity makes the particle's velocity at a given point unique.PACS numbers: 47.10. Fg, 05.45.Df, 47.53.+n Inhomogeneity of distribution of water droplets in clouds, caused by air turbulence, is significant factor in the formation of rain [1][2][3]. Due to inhomogeneity droplets collide and coalesce more often speeding up the formation of larger drops. It rains when the drops get so large as to reach the ground without evaporating on the way.Turbulence-induced inhomogeneities of transported quantities could seem contradicting to the well-known mixing of turbulence producing uniform distribution [4]. Indeed mixing dominates on larger scales. On smaller scales turbulence produces highly irregular spatial structures. Similarly to ordinary centrifuges the rotating turbulent vortices push the inertial droplets out [5] causing very strong non-uniformities in droplets distribution to accumulate with time. Those occur at the typical scale of the vortices (the Kolmogorov scale) which is much smaller than the typical scale of the flow. Thus formation of inhomogeneities of particles by turbulence is small-scale phenomenon, often disregarded due to finite resolution of instruments. Since it is at those scales that droplets collide then the study of the inhomogeneities is necessary to predict rain formation.Much progress was obtained in the study of nonuniform distributions of inertial particles in the flow when gravity is negligible [1][2][3][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. In the regime where the inertia is not too large, which is where turbulence is most relevant in the rain formation process [3], the paircorrelation function of concentration was demonstrated to obey a power-law with negative exponent signifying singular (fractal) structure formed by particles in space. Furthermore the leading order term for the exponent at small inertia was obtained for Navier-Stokes turbulence without model-dependent assumptions on the statistics * Electronic address: itzhak8@gmail.com † Electronic address: clee@yonsei.ac.kr of turbulence [1,6]. It depends on statistics of turbulence via the ratio of time integral of correlation function of laplacian of pressure divided by...

show abstract

Gravity-driven clustering of inertial particles in turbulence

Cited by 26 publications

References 30 publications

Influence of Gravitational Settling on Turbulent Droplet Clustering and Radar Reflectivity Factor

Influence of Gravitational Settling on Turbulent Droplet Clustering and Radar Reflectivity Factor

Relative velocity distribution of inertial particles in turbulence: A numerical study

Inhomogeneous distribution of water droplets in cloud turbulence

Contact Info

Product

Resources

About