We study the joint probability distributions of separation, $R$, and radial component of the relative velocity, $V_{\rm R}$, of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no gravity case. Distributions of $V_{\rm R}$ for fixed values of $R$ show a power-law dependence on $V_{\rm R}$ for a range of $V_{\rm R}$, exponent of the power-law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) moments of the distributions are anisotropic; the degree of anisotropy depends on particle's Stokes number, but does not depend on $R$ for small values of $R$. (b) mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.
Spatial clustering and intermittency in the relative velocity of heavy particles of the same size settling in turbulent flows can be strongly affected by gravity. We present a model for the timescale of the fluid velocity gradient seen by particle pairs and propose an effective Kubo number based on this timescale to explain the mechanism of gravity-enhanced clustering. We explore the mechanisms of the gravity-induced reduction or enhancement of the intermittency in the particle radial relative velocity (RRV) at different Stokes numbers based on backward-in-time relative dispersion and preferen…
We propose an experimental study on the gravitational settling velocity of dense, sub-Kolmogorov inertial particles under different background turbulent flows. We report Phase Doppler Particle Analyzer measurements in a low-speed wind tunnel uniformly seeded with micrometer scale water droplets. Turbulence is generated with three different grids (two consisting on different active-grid protocols while the third is a regular static grid), allowing us to cover a very wide range of turbulence conditions in terms of Taylor-scale based Reynolds numbers ($Re_λ\in [30-520]$), Rouse numbers ($Ro \in […
How non-spherical particles orient as they settle in a flow has important practical implications in a number of scientific and engineering problems. In a quiescent fluid, a slowly settling particle orients so that it settles with its broad side first. This is an effect of the torque due to convective inertia of the fluid set in motion by the settling particle, which maximises the drag experienced by the particle. Turbulent flows tend to randomise the particle orientation. Recently the settling of non-spherical particles in turbulence was analysed neglecting the effect of convective fluid inert…
Ice crystals settling through a turbulent cloud are rotated by turbulent velocity gradients. In the same way, turbulence affects the orientation of aggregates of organic matter settling in the ocean. In fact most solid particles encountered in Nature are not spherical, and their orientation affects their settling speed, as well as collision rates between particles. Therefore it is important to understand the distribution of orientations of non-spherical particles settling in turbulence. Here we study the angular dynamics of small prolate spheroids settling in homogeneous isotropic turbulence. …
One of the most enigmatic science question concerning inertial particle transport by a turbulent boundary layer flow is the value of the turbulent Schmidt number as the ratio of particle diffusivity and turbulent eddy viscosity. Using direct acoustic measurement of turbulent particle flux profile, and two-phase flow turbulence-resolving numerical simulation, it is demonstrated that turbulent dispersion of particles is reduced rather than enhanced when predicted with existing literature model. The explanation lies in the misleading assumption of settling velocity in quiescent water to estimate …
We present experimental and computational results for the orientation distributions of slender fibers and ramified particles settling in an isotropic turbulent flow. The rotational dynamics of the particles is modeled using a slender-body theory that includes the inertial torque due to sedimentation that tends to rotate the particles toward a broadside orientation. The particles are assumed to rotate due to viscous forces associated with the turbulent velocity gradients occurring on the particle length scale. In the simulations, the turbulence is obtained from a stochastic model of the velocit…
We explore the role of gravitational settling on inertial particle concentrations in a wall-bounded turbulent flow. While it may be thought that settling can be ignored when the settling parameter $Sv\equiv v_s/u_τ$ is small ($v_s$ - Stokes settling velocity, $u_τ$ - fluid friction velocity), we show that even in this regime the settling may make a leading order contribution to the concentration profiles. This is because the importance of settling is determined, not by the size of $v_s$ compared with $u_τ$ or any other fluid velocity scale, but by the size of $v_s$ relative to the other mechan…
We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane, and analyse the…
In a seminal article, \citet[J. Fluid Mech., 174:441-465]{maxey87} presented a theoretical analysis showing that enhanced particle settling speeds in turbulence occur through the preferential sweeping mechanism, which depends on the preferential sampling of the fluid velocity gradient field by the inertial particles. However, recent Direct Numerical Simulation (DNS) results in \citet[J. Fluid Mech., 796:659--711]{ireland16b} show that even in a portion of the parameter space where this preferential sampling is absent, the particles nevertheless exhibit enhanced settling velocities. Further, th…
The settling behaviour of small inertial particles in turbulent convection is a fundamental problem across several disciplines, from geophysics to metallurgy. In a geophysical context, the settling of dense crystals controls the mode of solidification of magma chambers and planetary-scale magma oceans, while rising of light bubbles of volatiles drives volcanic outgassing and the formation of primordial atmospheres. Motivated by these geophysical systems, we perform a systematic numerical study on the settling rate of particles in a rectangular two-dimensional Rayleigh-Benard system with Raylei…
We study the settling of finite-size rigid spheres in sustained homogeneous isotropic turbulence (HIT) by direct numerical simulations using an immersed boundary method to account for the dispersed solid phase. We study semi-dilute suspensions at different Galileo numbers, Ga. The Galileo number is the ratio between buoyancy and viscous forces, and is here varied via the solid-to-fluid density ratio. The focus is on particles that are slightly heavier than the fluid. We find that in HIT, the mean settling speed is less than that in quiescent fluid; in particular, it reduces by 6%-60% with resp…
The orientation of small anisotropic particles settling in a turbulent fluid determines some essential properties of the suspension. We show that the orientation distribution of small heavy spheroids settling through turbulence can be accurately predicted by a simple Gaussian statistical model that takes into account particle inertia and provides a quantitative understanding of the orientation distribution on the problem parameters when fluid inertia is negligible. Our results open the way to a parameterisation of the distribution of ice-crystals in clouds, and potentially leads to an improved…
We experimentally investigate the behaviour of instantaneous localised releases of heavy particles falling as turbulent clouds in quiescent water, both with and without background rotation. We present the results of 514 systematic experiments for no rotation and for three rotation rates $Ω= 5,10,20$rpm, and for the size of particles in the range $5μm$ to $1mm$, exploring four decades of the Rouse number $\mathcal{R} \in [6\times 10^{-4},4]$ which quantifies the inertia of particles. In the canonical framework of turbulent thermals described by Morton \textit{et al.}, [Proc. R. Soc. A: Math. Ph…
The Pi Chamber, located at Michigan Technological University, generates moist turbulent Rayleigh-Bénard flow in order to replicate steady-state cloud conditions. We take inspiration from this setup and consider a particle-laden, convectively-driven turbulent flow using direct numerical simulation (DNS). The aim of our study is to develop a simple stochastic model that can accurately describe the residence times of the particles in the flow, this time being determined by the complex competition between the gravitational settling of the particles, and the interaction of the particles with the tu…
Sedimentation of a dispersed solid phase is widely encountered in applications and environmental flows, yet little is known about the behavior of finite-size particles in homogeneous isotropic turbulence. To fill this gap, we perform Direct Numerical Simulations of sedimentation in quiescent and turbulent environments using an Immersed Boundary Method to account for the dispersed rigid spherical particles. The solid volume fractions considered are 0.5-1%, while the solid to fluid density ratio 1.02. The particle radius is chosen to be approximately 6 Komlogorov lengthscales. The results show t…
We investigate the gravitational settling of a long, model elastic filament in homogeneous isotropic turbulence. We show that the flow produces a strongly fluctuating settling velocity, whose mean is moderately enhanced over the still-fluid terminal velocity, and whose variance has a power-law dependence on the filament's weight but is surprisingly unaffected by its elasticity. In contrast, the tumbling of the filament is shown to be closely coupled to its stretching, and manifests as a Poisson process with a tumbling time that increases with the elastic relaxation time of the filament.
We suggest certain effects, caused by interaction between rotation and gravitation with turbulence structure, for the cooling/heating of dispersed phase of non-isothermal particles in rotating turbulent fluid flows. These effects are obtained through the derivation of kinetic or probability density function based macroscopic equations for the particles. In doing so, for one-way temperature coupling, we also show that homogeneous, isotropic non-isothermal fluid turbulence does not influence the mean temperature (though it influences mean velocity) of the dispersed phase of particles settling du…
We analyze the effect of the Basset history force on the sedimentation of nearly neutrally buoyant particles, exemplified by marine snow, in a three-dimensional turbulent flow. Particles are characterized by Stokes numbers much smaller than unity, and still water settling velocities, measured in units of the Kolmogorov velocity, of order one. The presence of the history force in the Maxey-Riley equation leads to individual trajectories which differ strongly from the dynamics of both inertial particles without this force, and ideal settling tracers. When considering, however, a large ensemble o…
Damping of the previously discovered resonant drag instability (RDI) of dust streaming in protoplanetary disc is studied using the local approach to dynamics of gas-dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other rev…
We use theory and Direct Numerical Simulations (DNS) to explore the average vertical velocities and spatial distributions of inertial particles settling in a wall-bounded turbulent flow. The theory is based on the exact phase-space equation for the Probability Density Function describing particle positions and velocities. This allowed us to identify the distinct physical mechanisms governing the particle transport. We then examined the asymptotic behavior of the particle motion near the wall, revealing the fundamental differences to the near wall behavior that is produced when incorporating gr…
For one-way coupled (1WC) flows, Tom & Bragg (J. Fluid Mech., 871, pp. 244-270, 2019) advanced the analysis of Maxey (J. Fluid Mech., 174, pp. 441-465, 1987), which applied to weakly inertial particles, to particles of arbitrary inertia, and the new theoretical result revealed the role that different scales play in the preferential sweeping mechanism that leads to enhanced particle settling in turbulent flows. Monchaux & Dejoan (Phys. Rev. Fluids, 2, 104302, 2017) showed using direct numerical simulations (DNS) that while for low particle loading the effect of two-way coupling (2WC) on the glo…
Using 3D Vorono\text{ï} analysis, we explore the local dynamics of small, settling, inertial particles in isotropic turbulence using Direct Numerical Simulations (DNS). We independently vary the Taylor Reynolds number $R_λ\in[90,398]$, Froude number $Fr\equiv a_η/g\in[0.052,\infty]$ (where $a_η$ is the Kolmogorov acceleration, and $g$ is the acceleration due to gravity), and Kolmogorov scale Stokes number $St\equivτ_p/τ_η\in[0,3]$. In agreement with previous results using global measures of particle clustering, such as the Radial Distribution Function (RDF), we find that for small Vorono\text{…
We study experimentally the spatial distribution, settling, and interaction of sub-Kolmogorov inertial particles with homogeneous turbulence. Utilizing a zero-mean-flow air turbulence chamber, we drop size-selected solid particles and study their dynamics with particle imaging and tracking velocimetry at multiple resolutions. The carrier flow is simultaneously measured by particle image velocimetry of suspended tracers, allowing the characterization of the interplay between both the dispersed and continuous phases. The turbulence Reynolds number based on the Taylor microscale ranges from $Re_λ…
The way particles interact with turbulent structures, particularly in regions of high vorticity and strain rate, has been investigated in simulations of homogeneous turbulence and in simple flows which have a periodic or persistent structure e.g. separating flows and mixing layers. The influence on both settling under gravity and diffusion has been reported and the divergence (compressibility) of the underlying particle velocity field along a particle trajectory has been recognized as an important quantity in quantifying these features. This paper shows how these features can be incorporated i…
It is known that ultrasound techniques yield non-intrusive measurements of hydrodynamic flows. For example, the study of the echoes produced by a large number of particle insonified by pulsed wavetrains has led to a now standard velocimetry technique. In this paper, we propose to extend the method to the continuous tracking of one single particle embedded in a complex flow. This gives a Lagrangian measurement of the fluid motion, which is of importance in mixing and turbulence studies. The method relies on the ability to resolve in time the Doppler shift of the sound scattered by the continuou…
The turbulence statistics of the intermittent region in a supersonic turbulent boundary layer are studied by direct numerical simulation. Recently, Kwon et al. (2016) have shown that this intermittent behavior, consisting of the coexistence of turbulent and non-turbulent flows separated by an interface, could result in perils when the traditional Reynolds decomposition is used to analyze data. Here, we extend the study of turbulent/non-turbulent interfaces to the supersonic regime and report turbulence statistics conditioned to the interface. We show that the mathematical artefact of the tradi…
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 in…
The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically.
Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to correctly describe the dynamics of particles over a wide range of sizes and densities. Our measurements show that acceleration statistics of particles dispersed in a turbulent flow do exhibit specific size and density effects but that they preserve an extremely robust turbulent signature with lognormal fluctuations, regardless of particles size and density. This…
We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero Lagrangian acceleration. However, the actual Lagrangian acceleration of the fluid elements where particles accumulate is not zero, and has a dependence on the Stokes number, the gravity acceleration, and the settling velocity of the particles.
Many plankton species undergo daily vertical migration to large depths in the turbulent ocean. To do this efficiently, the plankton can use a gyrotactic mechanism, aligning them with gravity to swim downwards, or against gravity to swim upwards. Many species show passive mechanisms for gyrotactic stability. For example, bottom-heavy plankton tend to align upwards. This is efficient for upward migration in quiescent flows, but it is often sensitive to turbulence which upsets the alignment. Here we suggest a simple, robust active mechanism for gyrotactic stability, which is only lightly affected…
We have performed spectral/spectral-element simulations of a single oblate spheroid with small geometrical aspect ratio settling in an unbounded ambient fluid, for a range of Galileo numbers covering the various regimes of motion (steady vertical, steady oblique, vertical periodic and chaotic). The high-fidelity data provided includes particle quantities (statistics in the chaotic case), as well as flow profiles and pressure maps. The reference data can be used as an additional benchmark for other numerical approaches, where a careful grid convergence study for a specific target parameter poin…
Considering turbulent clouds containing small inertial particles, we investigate the effect of particle collision, in particular collision-coagulation, on particle clustering and particle relative motion. We perform direct numerical simulation (DNS) of coagulating particles in isotropic turbulent flow in the regime of small Stokes number ($St=0.001-0.54$) and find that, due to collision-coagulation, the radial distribution functions (RDFs) fall-off dramatically at scales $r \sim d\,\,$ (where $d$ is the particle diameter) to small but finite values, while the mean radial-component of particle …
We investigate the statistics of phase fluctuations of an acoustic wave propagating through a turbulent flow in line of sight (LOS) configuration. Experiments are performed on a closed von Karman swirling flow whose boundaries are maintained at a constant temperature. In particular, we analyze the root mean square (RMS) and the power spectrum density (PSD) of phase fluctuations. A model is developed and analytical predictions obtained for these quantities using geometrical acoustics are shown to be in agreement with experimental observations.
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the fluid's statistics can be set up as a space-time path integral. Fluid space-time configuration sampling techniques naturally suggest a useful way, using an arbitrary initial statistics functional, to calculate averages.
This article presents direct numerical simulations of the growth of turbulent spots in the transitional regime of plane Couette flow. A quantitative description of the growth process and of the detail of the quadrupolar flow around the spot is given. Focus is put on formation of spanwise vorticity in the velocity streaks that resembles a secondary shear instability. The main features of the instability (coherence lengths, advection velocity) are studied in the context of the turbulent spot, below and above the threshold Reynolds number of appearance of the oblique turbulent bands of plane Coue…
We present a comparison of different particles' velocity and acceleration statistics in two paradigmatic turbulent swirling flows: the von Kármán flow in a laboratory experiment, and the Taylor-Green flow in direct numerical simulations. Tracers, as well as inertial particles, are considered. Results indicate that, in spite of the differences in boundary conditions and forcing mechanisms, scaling properties and statistical quantities reveal similarities between both flows, pointing to new methods to calibrate and compare models for particles dynamics in numerical simulations, as well as to cha…
We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average di…
We present Lagrangian one-particle statistics from the Risoe PTV experiment of a turbulent flow. We estimate the Lagrangian Kolmogorov constant $C_0$ and find that it is affected by the large scale inhomogeneities of the flow. The pdf of temporal velocity increments are highly non-Gaussian for small times which we interpret as a consequence of intermittency. Using Extended Self-Similarity we manage to quantify the intermittency and find that the deviations from Kolmogorov 1941 similarity scaling is larger in the Lagrangian framework than in the Eulerian. Through the multifractal model we calcu…
