Gravity-Driven Enhancement of Heavy Particle Clustering in Turbulent Flow

Abstract

Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles. These two competing effects can either increase or decrease the geometrical collision rates between same-size particles and are crucial for realistic modeling of coalescing particles.Many industrial, atmospheric, and astrophysical phenomena ranging from the microphysics of cloud formation, to planet formation in a dusty circumstellar disk of gas, involves the modeling of the interactions between small solid particles suspended in a turbulent carrier flow. Two main effects are typically at play: a viscous drag that particles experience with the agitated fluid and an external force, such as gravity, that acts because of their density contrast with the fluid. While drag is predominant for small particles, gravity takes over the dynamics of large particles and most studies treat these two asymptotics independently. However it is usually at this critical transition that standard modeling fails, as is evident when estimating for instance the rate at which rain is triggered in warm clouds [1,2]. Most models are unable to circumvent a bottleneck in the droplet growth for diameters around 20-40µm. A key improvement might be to combine turbulent and gravitational effects.In this Letter we understand the intriguing interplay between turbulence, gravity, and particle sizes. This question is of fundamental importance in fluid dynamics, in particular, and in non-equilibrium statistical physics, in general, as it is central to modeling coalescences in natural or laboratory droplet suspensions. The most noticeable effect of turbulence on the settling of heavy particles is the increase of their terminal velocity induced by a preferential sweeping along the downward fluid flow [3][4][5]. This phenomenon is mostly understood on qualitative grounds and has been quantified only in model flows [6]. Furthermore very little is known on the effect of gravitational settling on two-particle statistics. Fundamental theoretical and numerical studies of the clustering of particle pairs [7,8] and of the enhancement of collisions due to inertia [9, 10] usually neglect gravity. We present here, by combining state-of-the-art direct numerical simulations with theoretical results based on our asymptotic analysis, a systematic study of the dynamical and statistical properties of particles as a function of (i) the level of turbulence of the carrier flow (Reynolds number), (ii) the inertia of the particles (Stokes number), and (iii) the ratio between the turbulent accelerations and gravity (Froude numb...

Inhomogeneous distribution of water droplets in cloud turbulence

“…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].…”

“…The latters' motion is influenced by gravity most significantly: the typical value of the ratio F r of acceleration of air parcels to g is small [3]. Indeed, recent simulations indicate that in this case gravity plays dominant role in the formation of particles' density [24]. Inclusion of gravity into the theory is thus necessary to describe rain.…”

“…When F r 1, this decoherence is so significant that the impact of one vortex on particle's motion is negligible -the sedimenting particle leaves the vortex before that catches it to produce the sling, cf. [24,34]. It is only smooth accumulated averaged action of many vortices that has finite effect.…”

Microbubbles and Microparticles are Not Faithful Tracers of Turbulent Acceleration

“…Their findings were instrumental in highlighting the role of gravity on the clustering and the enhancement of settling velocities of heavy particles in a flow. More recently, inertial effects on settling particles were analysed using direct numerical simulations of fully developed homogeneous isotropic turbulence [17,18,[34][35][36]. These revealed that gravity can lead to major modifications of particle clustering, relative velocity and pair statistics, which could be characterized as a function of St and the ratio of turbulent to gravitational acceleration: a η /g.…”

Turbulent thermal convection driven by heated inertial particles

“…In presence of gravity (Wang & Maxey 1993) identified a preferential sweeping effect that increases the settling velocity. Recently, Dejoan & Monchaux (2013) and Bec, Homann & Ray (2014b) further discussed the influence of the Stokes number on the particle clustering in this situation.…”