Particle radial distribution function and relative velocity measurement in turbulence at small particle-pair separations

Hammond, Adam; Meng, Hui

doi:10.1017/jfm.2021.486

Cited by 11 publications

(53 citation statements)

References 43 publications

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“…At large separation distances, the p.d.f.s of relative velocity are slightly negatively skewed, which is a natural consequence of vortex stretching in turbulence (Tavoularis, Bennett & Corrsin 1978). For smaller separations (figure 3c), the p.d.f.s become symmetric, which is in line with the relative velocity p.d.f.s of Saw et al (2014), who did not observe significant skewness in their relative velocity p.d.f.s at r/η ≈ 1 for inertialess particles; the tails of our relative velocity p.d.f.s are somewhat higher but much lower than reported in Hammond & Meng (2021) for inertial particles. The essentially straight tails for r/D = 3.5 hint at a decrease of the particles' relative motion, contrary to finite-Stokes-number particles where the tails of the p.d.f.s are wide.…”

Section: Resultssupporting

confidence: 92%

“…Dynamic conditional concentration kernels are based on the measurement of inter-particle distances using analogous but larger particles centred on the real particles. Further experimental work, such as the recent study by Hammond & Meng (2021), needs to focus on finite-size inertial particles, since analogous inertial particles would behave differently than real host particles near contact. Recent DNS by Ababaei et al (2021) show that finite-size effects should remain an important factor when inertial particles come into contact and largely contribute to accurately estimating collision kernels.…”

Section: Discussionmentioning

confidence: 99%

“…However, the only way to isolate geometric from ghost conditional concentration is to consider long-enough particle tracks in order to analyse the temporal history of particle pairs. This is one of the novel aspects in the present study compared to the recent experimental work of Hammond & Meng (2021). Different kernels have been introduced in the present study:…”

Section: Introductionmentioning

confidence: 98%

“…The 3-D PTV and four-frame PTV techniques provide comparable accuracy of particle relative velocity measurement; the four-frame PTV is a 2-D technique whose out-of-plane component of particle velocity is lost when projected onto an imaging plane (Dou et al 2018b). This problem was very recently addressed by Hammond & Meng (2021) who performed four-pulse particle image velocimetry (PIV) and measured simultaneously the RDF and the RV in a homogeneous and isotropic flow for inertial particles for separation distances of the order of the particle size. In this paper, we explore similar properties for inertialess particles and report the effect of the turbulent Reynolds number and finite particle size.…”

Section: Introductionmentioning

confidence: 99%

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Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

2022

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We report experimental measurements of kinematic and dynamic particle concentration kernels conditioned by the separation distances of solid inertialess particles in isotropic turbulence by three-dimensional particle tracking velocimetry with particle diameters smaller than the Kolmogorov length scale. Particle radial relative velocity statistics are measured from the dissipation to the integral length-scale range. The radial scaling of particle and fluid relative velocity variance $\langle w_r(r)^{2} \rangle \sim r^{2/3}$ in the inertial subrange, consistent with Kolmogorov's theory, is reported, while a new scaling is found for small distances due to finite-size effects between particles. The measured concentration kernels at small separation distances therefore deviate from those in the theory of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) at small inter-particle distances due to hydrodynamic interactions. A real kernel taking into account the history of the particle tracks and excluding multiple events is also calculated, while the normalised particle concentration kernels are found to be essentially insensitive to the flow Reynolds number.

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Section: Resultssupporting

confidence: 92%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

2022

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“…[21][22][23], or the relative positions and velocities (only) of droplet pairs separated by tens of diameters or larger [e.g. 8,9,24,25]. Here we evaluated these quantities and furthermore calculate the relative acceleration down to surface-to-surface separations as small as one-tenth the droplets' diameters as described below.…”

mentioning

confidence: 99%

Relative accelerations characterize the hydrodynamic interaction of cloud droplets

Kearney¹,

Bewley²

2022

Preprint

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Water droplets coalesce into larger ones in atmospheric clouds to form rain. But droplets on collision courses do not always coalesce due to the cushioning effects of the air between them. The extent to which these so-called hydrodynamic interactions reduce coalescence rates is embodied in the collision efficiency, which is often small and is not generally known. In order to characterize the mechanisms that determine the collision efficiency, we exploited new time-resolved three-dimensional droplet tracking techniques to measure the positions of cloud droplet pairs settling through quiescent air. We did so with an unprecedented precision that enabled us to calculate the relative positions, velocities, and accelerations of the droplets at droplet surface-to-surface separations as small as about one-tenth of a droplet diameter. We show that relative accelerations clearly distinguish coalescing from non-coalescing droplet trajectories, the former being associated with relative accelerations that exceeded a threshold value. We outline how relative accelerations relate to hydrodynamic interactions, and present scaling arguments that predict the threshold relative acceleration. We speculate that the relative acceleration distribution of droplets in turbulent clouds can parameterize the collision efficiency, and that this distribution together with the well-known relative position and velocity distributions can generate a physical description of both the collision and coalescence rates of cloud droplets. I. INTRODUCTIONIn warm atmospheric clouds, liquid water droplets are set onto collision courses by mechanisms that include differential sedimentation and turbulence [1][2][3]. The rate at which this happens can be explained by the way turbulence generates droplet relative position and velocity distributions [4,5]. In order for droplets on collision courses to coalescence into one larger droplet, however, they need to squeeze out the air between them, a process that couples the motions of droplets relative to one another through hydrodynamic interaction (HI) [e.g. 6, 7]. These interactions cause droplets to decelerate, which modifies the probability distributions of droplet relative positions and velocities in a way as yet unknown [e.g. 8-10]. The effect is most pronounced precisely where these distributions need to be evaluated, which is at the moment of contact between two droplets.Theoretical and empirical descriptions of the relative velocity distributions [e.g. 11-13] and radial distribution functions [e.g. 14-16] exist for droplets that are separated widely enough that they do not

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Hydrodynamic interactions and extreme particle clustering in turbulence

et al. 2021

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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.

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Particle radial distribution function and relative velocity measurement in turbulence at small particle-pair separations

Abstract: Abstract

Cited by 11 publications

References 43 publications

Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

Relative accelerations characterize the hydrodynamic interaction of cloud droplets

Hydrodynamic interactions and extreme particle clustering in turbulence

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