Spatial clustering of polydisperse inertial particles in turbulence: I. Comparing simulation with theory

Saw, Ewe-Wei; Salazar, Juan P. L. C.; Collins, Lance R.; Shaw, Raymond A.

doi:10.1088/1367-2630/14/10/105030

Cited by 52 publications

(80 citation statements)

References 45 publications

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“…When the droplet size distribution is broad, it is necessary to understand the influence of different Stokes number on droplet dispersion. However, only few studies have considered polydispersed droplets, for instance, see Lazaro & Lasheras (1992), Kiger & Lasheras (1995), Aliseda et al (2002), Ferrand et al (2003), Saw et al (2008Saw et al ( , 2012a. (ii) As pointed out by Fessler et al (1994), it is not only important to know what particle size is most preferentially concentrated but also at what scale the concentration occurs.…”

Section: Motivationmentioning

confidence: 99%

Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion

2016

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The effect of entrained air turbulence on dispersion of droplets (with Stokes number based on the Kolmogorov time scale, St η , of the order of 1) in a polydispersed spray is experimentally studied through simultaneous and planar measurements of droplet size, velocity and gas flow velocity (Hardalupas et al., Exp. Fluids, vol. 49, 2010, pp. 417-434). The preferential accumulation of droplets at various measurement locations in the spray was examined by two independent methods viz. counting droplets on images by dividing the image in to boxes of different sizes, and by estimating the radial distribution function (RDF). The dimension of droplet clusters (obtained by both approaches) was of the order of Kolmogorov's length scale of the fluid flow, implying the significant influence of viscous scales of the fluid flow on cluster formation. The RDF of different size classes indicated an increase in cluster dimension for larger droplets (higher St η ). The length scales of droplet clusters increased towards the outer spray regions, where the gravitational influence on droplets is stronger compared to the central spray locations. The correlation between fluctuations of droplet concentration and droplet and gas velocities were estimated and found to be negative near the spray edge, while it was close to zero at other locations. The probability density function of slip between fluctuating droplet velocity and gas velocity 'seen' by the droplets signified presence of considerable instantaneous slip velocity, which is crucial for droplet-gas momentum exchange. In order to investigate different mechanisms of turbulence modulation of the carrier phase, the three correlation terms in the turbulent kinetic energy equation for particle-laden flows (Chen & Wood, Can. J. Chem. Engng, vol. 65, 1985, pp. 349-360) are evaluated conditional on droplet size classes. Based on the comparison of the correlation terms, it is recognized that although the interphase energy transfer due to fluctuations of droplet concentration is low compared to the energy exchange only due to droplet drag (the magnitude of which is controlled by average droplet mass loading), the former cannot be considered negligible, and should be accounted in two phase flow modelling.

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Section: Motivationmentioning

confidence: 99%

Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion

2016

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“…At first glance, these numbers appear rather small compared to what has been observed in various studies of inertial particle clustering (e.g. [12,72,73]). However, comparing the diffusiophoretic velocity to the Kolmogorov velocity v η helps to classify these results properly.…”

Section: Resultsmentioning

confidence: 66%

“…Defining a Stokes number Stk for inertial particles as Stk = τ p /λ −1 , we similarly divide the maximum diffusiophoretic velocity by v η , which results in a non-dimensional number that is 3 × 10 −2 . According to Saw et al [72], inertial particles with Stk similar to 3 × 10 −2 have clustering exponents of order 10 −2 . This agrees well with the clustering exponents found in our study.…”

Section: Resultsmentioning

confidence: 99%

Clustering of particles in turbulence due to phoresis

et al. 2016

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We demonstrate that diffusiophoretic, thermophoretic and chemotactic phenomena in turbulence lead to clustering of particles on multi-fractal sets that can be described using one single framework, valid when the particle size is much smaller than the smallest length scale of turbulence l0. To quantify the clustering, we derive positive pair correlations and fractal dimensions that hold for scales smaller than l0. For scales larger than l0 the pair correlation function is predicted to show a stretched exponential decay towards 1. In the case of inhomogeneous turbulence we find that the fractal dimension depends on the direction of inhomogeneity. By performing experiments with particles in a turbulent gravity current we demonstrate clustering induced by salinity gradients in conformity to the theory. The particle size in the experiment is comparable to l0, outside the strict validity region of the theory, suggesting that the theoretical predictions transfer to this practically relevant regime. This clustering mechanism may provide the key to the understanding of a multitude of processes such as formation of marine snow in the ocean and population dynamics of chemotactic bacteria.

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“…Consequently, the magnitude of cloud droplet clustering in situ and in the laboratory has been a subject of intense interest for the last 25 years (see, e.g., Baker, 1992;Baumgardner et al, 1993;Brenguier, 1993;Borrmann et al, 1993;Shaw et al, 1998;Uhlig et al, 1998;Davis et al, 1999;Kostinski and Jameson, 2000;Chaumat and Brenguier, 2001;Kostinski and Shaw, 2001;Pinsky and Khain, 2001;Shaw et al, 2002;Shaw, 2003;Marshak et al, 2005;Larsen, 2006;Lehmann et al, 2007;Salazar et al, 2008;Saw et al, 2008;Small and Chuang, 2008;Baker and Lawson, 2010;Siebert et al, 2010;Bateson and Aliseda, 2012;Larsen, 2012;Saw et al, 2012b;Beals et al, 2015;Siebert et al, 2015;O'Shea et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

“…Although arguments can be made for any number of these tools, this study focuses on the radial distribution function (rdf or g(r)) because (i) it is a direct scale-localized measure of deviation from perfect spatial randomness, (ii) it is directly related to variances and means through the correlation-fluctuation theorem, (iii) many numerical and theoretical discussions about particle clustering are explicitly presented in terms of the radial distribution function (see, e.g., Balkovsky et al, 2001;Holtzer and Collins, 2002;Collins and Keswani, 2004;Chun et al, 2005;Salazar et al, 2008;Saw et al, 2008;Zaichik and Alipchenkov, 2009;Monchaux et al, 2012;Saw et al, 2012a;Larsen et al, 2014), and (iv) most other common methods of characterizing cloud droplet clustering can be derived from or quantitatively related to a measurement of the radial distribution function (Landau and Lifshitz, 1980;Kostinski and Jameson, 2000;Shaw et al, 2002;Larsen, 2006Larsen, , 2012.…”

Section: Introductionmentioning

confidence: 99%

A method for computing the three-dimensional radial distribution function of cloud particles from holographic images

Larsen

Shaw

2018

Atmos. Meas. Tech.

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Abstract. Reliable measurements of the three-dimensional radial distribution function for cloud droplets are desired to help characterize microphysical processes that depend on local drop environment. Existing numerical techniques to estimate this three-dimensional radial distribution function are not well suited to in situ or laboratory data gathered from a finite experimental domain. This paper introduces and tests a new method designed to reliably estimate the three-dimensional radial distribution function in contexts in which (i) physical considerations prohibit the use of periodic boundary conditions and (ii) particle positions are measured inside a convex volume that may have a large aspect ratio. The method is then utilized to measure the three-dimensional radial distribution function from laboratory data taken in a cloud chamber from the Holographic Detector for Clouds (HOLODEC).

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Spatial clustering of polydisperse inertial particles in turbulence: I. Comparing simulation with theory

Cited by 52 publications

References 45 publications

Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion

Droplet–turbulence interaction in a confined polydispersed spray: effect of turbulence on droplet dispersion

Clustering of particles in turbulence due to phoresis

A method for computing the three-dimensional radial distribution function of cloud particles from holographic images

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