Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence

Zaichik, L. I.; Alipchenkov, V. M.

doi:10.1063/1.2813044

Cited by 49 publications

(55 citation statements)

References 55 publications

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“…This remarkable agreement suggests that the outer flow information coming from the inertial subrange and beyond has very little to do with the power-law scaling of the RDF within the dissipation range over the entire range of Stokes numbers considered in this study. This important result supports theories like those by Chun et al (2005) and Zaichik & Alipchenkov (2007) that are based on a similar local assumption. According to the model shown in (3.4), the satellite particles drift inwards towards the primary particle with a velocity proportional to their separation, which is counteracted by a random diffusion term that is assumed to be given by the fluid velocity at the satellite particle position.…”

Section: Dns Versus Sps: Unfiltered Turbulencesupporting

confidence: 80%

Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

Ray

Collins

2013

J. Fluid Mech.

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Clustering (or preferential concentration) of weakly inertial particles suspended in a homogeneous isotropic turbulent flow is driven primarily by the smallest eddies at the so-called Kolmogorov scale. In particle-laden large-eddy simulations (LES), these small scales are not resolved by the grid and hence their effect on both the resolved flow scales and the particle motion have to be modelled. In order to predict clustering in a particle-laden LES, it is crucial that the subgrid model for the particles captures the mechanism by which the subgrid scales affect the particle motion (Ray & Collins, J. Fluid Mech., vol. 680, 2011, pp. 488-510). In this paper, we describe novel satellite particle simulations (SPS), in which we study the clustering and relative velocity statistics of inertial particles at separation distances well below the Kolmogorov length scale. SPS is designed to isolate pairwise interactions of particles, and is therefore well suited for developing two-particle models. We show that the power-law dependence of the radial distribution function (RDF), a statistical measure of clustering, is predicted by the SPS in excellent agreement with direct numerical simulations (DNS) for Stokes numbers up to 3, implying that no explicit information from the inertial range is required to accurately describe particle clustering. This result further explains our successful prediction of the RDF power using the drift-diffusion model of Chun et al. (J. Fluid Mech., vol. 536, 2005, pp. 219-251) for St 0.4. We also consider the second-order longitudinal relative velocity structure function for the particles; we show that the SPS is able to capture its power-law exponent for St 0.5 and attribute the disagreement at larger St to the effect of the larger scales of motion not captured by the SPS. Further, the SPS is able to capture the 'caustic activation' of the structure function at zero separation and predict the critical St and rate of activation in agreement with the DNS (Salazar & Collins, J. Fluid. Mech., vol. 696, 2012, pp. 45-66). We show comparisons between filtered DNS and equivalently filtered SPS, and the findings are similar to the unfiltered case. Overall, SPS is an efficient and accurate computational tool for investigating particle pair dynamics at small separations, as well as an interesting platform for developing LES subgrid models designed to accurately reproduce particle clustering.

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Section: Dns Versus Sps: Unfiltered Turbulencesupporting

confidence: 80%

Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

Ray

Collins

2013

J. Fluid Mech.

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“…Equation (2.3) is exact, but unclosed, due to the term ∆u(r p (t), t) r which describes the average of ∆u experienced by particle pairs at the separation r p (t) = r. Even though ∆u(r, t) = 0 for isotropic flows, ∆u(r p (t), t) r = 0 for finite St because the inertial particles preferentially sample the underlying field ∆u(x, r, t). In the ZT, this term is closed by approximating ∆u(x, r, t) as a spatio-temporally correlated Gaussian field and using the Furutsu-Novikov closure method (Zaichik & Alipchenkov 2007;. However, for the purposes of this analysis, it is not necessary to introduce any such closure approximations.…”

Section: Theoretical Analysismentioning

confidence: 99%

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

2015

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'Preferential concentration ' (Phys. Fluids A3:1169-78, 1991 refers to the clustering of inertial particles in the high-strain, low-rotation regions of turbulence. The 'centrifuge mechanism' of Maxey (J. Fluid Mech. 174:441-65, 1987) appears to explain this phenomenon. In a recent paper, Bragg & Collins (New J. Phys. 16:055013, 2014) showed that the centrifuge mechanism is dominant only in the regime St 1, where St is the Stokes number based on the Kolmogorov time scale. Outside this regime, the centrifuge mechanism gives way to a non-local, path-history symmetry breaking mechanism. However, despite the change in the clustering mechanism, the instantaneous particle positions continue to correlate with high-strain, low-rotation regions of the turbulence. In this paper, we analyze the exact equation governing the radial distribution function and show how the non-local clustering mechanism is influenced by, but not dependent upon, the preferential sampling of the fluid velocity gradient tensor along the particle path-histories in such a way as to generate a bias for clustering in high-strain regions of the turbulence. We also show how the non-local mechanism still generates clustering, but without preferential concentration, in the limit where the timescales of the fluid velocity gradient tensor measured along the inertial particle trajectories approaches zero (such as whitenoise flows or for particles in turbulence settling under strong gravity). Finally, we use data from a direct numerical simulation of inertial particles suspended in Navier-Stokes turbulence to validate the arguments presented in this study.

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“…2,6,7 The singular or near-singular behavior of the rdf near zero separation means that inertial particles tend to cluster in turbulence. Evidences for the power-law behavior of the rdf were also provided by Zaichik and Alipchenkov 8,9 and Chun et al 10 based on theoretical models. Theoretical and numerical analyses by Balkovsky et al, 11 Falkovich et al, 12 and Falkovich and Pumir 13 have indicated that the moments of the coarse-grained particle concentration exhibit the power-law behavior, which give an explanation of preferential concentration from a different perspective.…”

Section: Introductionmentioning

confidence: 93%

“…8,9 However, there are some subtle but important differences. The transport equation for the pdf given by Chun et al 10 did not explicitly contain the derivatives with respect to the relative particle velocity.…”

Section: Introductionmentioning

confidence: 95%

“…An unknown correlation between the particle velocity increment and the pdf fluctuation appeared in the ensemble-averaged transport equation for the averaged pair distribution function. Unlike Zaichik and Alipchenkov, 8,9 without assuming the Gaussian properties of the relative particle velocity field, Chun et al 10 used a formal solution for the pdf fluctuation to calculate the correlation. This led to an integral-differential equation for the averaged pair distribution function.…”

Section: Introductionmentioning

confidence: 99%

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Probability density function of small separation between two inertial particles in homogenous isotropic turbulence

Liu

2010

Physics of Fluids

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Refinement of the probability density function model for preferential concentration of aerosol particles in isotropic turbulence

Cited by 49 publications

References 55 publications

Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

Investigation of sub-Kolmogorov inertial particle pair dynamics in turbulence using novel satellite particle simulations

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

Probability density function of small separation between two inertial particles in homogenous isotropic turbulence

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