Spatial clustering of polydisperse inertial particles in turbulence: II. Comparing simulation with experiment

Abstract

Particles that are heavy compared to the fluid in which they are embedded (inertial particles) tend to cluster in turbulent flow, with the degree of clustering depending on the particle Stokes number. The phenomenon is relevant to a variety of multiphase flows, including atmospheric clouds; in most realistic systems, particles have a continuous distribution of sizes and therefore the clustering of 'polydisperse' particle populations is of special relevance. In this part of the study, measurements of spatial correlations of particles in high-Reynolds-number turbulence are compared with the results of a direct numerical simulation of particle-laden turbulence. The experimentally derived radial distribution functions (RDFs) exhibit a pronounced scale break at approximately 10-30 times the Kolmogorov scale, with large-scale clustering arising from 5 International Collaboration for Turbulence Research. 6 2 'scalar mixing' of the droplet field, and smaller-scale clustering depending on the particle Stokes numbers. A procedure is outlined for isolating the RDF due to inertial clustering from that resulting from large-scale mixing. Reasonable agreement between the experiment and the direct numerical simulations (DNS) is obtained for St 0.3 when particle Stokes number distributions in the DNS match those existing in the experiments. The experimental RDFs are consistent with the flattening or saturation scale appearing for bidisperse particles, but as in the companion paper, also support the 'saturation' effect in the asymmetric response of the power-law slope. The evidence for a universal scale break, as observed in both the DNS and the experiments, suggests that the pre-factor in the theoretical expression for the RDF is inherently tied to the power-law exponent, and an empirical form for this is given. Finally, no strong influence of the turbulence Reynolds number was observed for the clustering phenomenon. The consistency between the carefully analyzed DNS and experiments, in terms of St dependence, dissipation-range scale break and saturation of clustering for polydisperse particles, provides an indirect confirmation of the diffusion-drift theory of Chun et al (2005 J. Fluid Mech. 536 219-51).

Collision rates of small ellipsoids settling in turbulence

“…Additionally, the values of Γ Within the dissipation range the dependence of the RRV and the RDF on the particle separation distance is known to follow a power-law behaviour for inertial and motile spheres (Bec et al 2010;Saw et al 2012;Durham et al 2013). Hence, a similar spread is expected for the values obtained at the distances 2r min , 2r mean , and 2r max .…”

“…However, in turbulence the collision likelihood is different (figure 1c). For particle relaxation time scales in the range of the turbulent time scales, the particles are driven out of turbulent eddies and cluster outside (Squires & Eaton 1991;Wang & Maxey 1993;Sundaram & Collins 1997;Saw et al 2012). This increases the number of possible collision partners but due to the spatial correlation the relative velocity of the collision partners is rather small.…”

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

“…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.…”

Clustering of particles in turbulence due to phoresis

“…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.…”

“…It is obtained experimentally by counting the number of particles in a circle with radius 2η, according to the definition of Eq. (73). This size of the circle is chosen in order to find a sufficient number of particles (> 1) inside the circle.…”