Lagrangian velocity and acceleration correlations of large inertial particles in a closed turbulent flow

We investigate the response of large inertial particle to turbulent fluctuations in a inhomogeneous and anisotropic flow. We conduct a Lagrangian study using particles both heavier and lighter than the surrounding fluid, and whose diameters are comparable to the flow integral scale. Both velocity and acceleration correlation functions are analyzed to compute the Lagrangian integral time and the acceleration time scale of such particles. The knowledge of how size and density affect these time scales is crucial in understanding partical dynamics and may permit stochastic process modelization using two-time models (for instance Saw-ford's). As particles are tracked over long times in the quasi totality of a closed flow, the mean flow influences their behaviour and also biases the velocity time statistics, in particular the velocity correlation functions. By using a method that allows for the computation of turbulent velocity trajectories, we can obtain unbiased Lagrangian integral time. This is particularly useful in accessing the scale separation for such particles and to comparing it to the case of fluid particles in a similar configuration

Two-dimensionalization of the flow driven by a slowly rotating impeller in a rapidly rotating fluid

We characterize the two-dimensionalization process in the turbulent flow produced by an impeller rotating at a rate $\omega$ in a fluid rotating at a rate $\Omega$ around the same axis for Rossby number $Ro=\omega/\Omega$ down to $10^{-2}$. The flow can be described as the superposition of a large-scale vertically invariant global rotation and small-scale shear layers detached from the impeller blades. As $Ro$ decreases, the large-scale flow is subjected to azimuthal modulations. In this regime, the shear layers can be described in terms of wakes of inertial waves traveling with the blades, originating from the velocity difference between the non-axisymmetric large-scale flow and the blade rotation. The wakes are well defined and stable at low Rossby number, but they become disordered at $Ro$ of order of 1. This experiment provides insight into the route towards pure two-dimensionalization induced by a background rotation for flows driven by a non-axisymmetric rotating forcing.Comment: Accepted for publication in Physical Review Fluid

Influence of the multipole order of the source on the decay of an inertial wave beam in a rotating fluid

We analyze theoretically and experimentally the far-field viscous decay of a two-dimensional inertial wave beam emitted by a harmonic line source in a rotating fluid. By identifying the relevant conserved quantities along the wave beam, we show how the beam structure and decay exponent are governed by the multipole order of the source. Two wavemakers are considered experimentally, a pulsating and an oscillating cylinder, aiming to produce a monopole and a dipole source, respectively. The relevant conserved quantity which discriminates between these two sources is the instantaneous flowrate along the wave beam, which is non-zero for the monopole and zero for the dipole. For each source the beam structure and decay exponent, measured using particle image velocimetry, are in good agreement with the predictions

Turbulent drag in a rotating frame

What is the turbulent drag force experienced by an object moving in a rotating fluid? This open and fundamental question can be addressed by measuring the torque needed to drive an impeller at constant angular velocity $\omega$ in a water tank mounted on a platform rotating at a rate $\Omega$. We report a dramatic reduction in drag as $\Omega$ increases, down to values as low as $12$\% of the non-rotating drag. At small Rossby number $Ro = \omega/\Omega$, the decrease in drag coefficient $K$ follows the approximate scaling law $K \sim Ro$, which is predicted in the framework of nonlinear inertial wave interactions and weak-turbulence theory. However, stereoscopic particle image velocimetry measurements indicate that this drag reduction rather originates from a weakening of the turbulence intensity in line with the two-dimensionalization of the large-scale flow.Comment: To appear in Journal of Fluid Mechanics Rapid

An experimental study on the settling velocity of inertial particles in different homogeneous isotropic turbulent flows

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 ($Re_\lambda \in [30-520]$), Rouse numbers ($Ro \in [0-5]$) and volume fractions ($\phi_v \in[0.5\times10^{-5} - 2.0\times10^{-5}]$). We find, in agreement with previous works, that enhancement of the settling velocity occurs at low Rouse number, while hindering of the settling occurs at higher Rouse number for decreasing turbulence energy levels. The wide range of flow parameters explored allowed us to observe that enhancement decreases significantly with the Taylor Reynolds number and is significantly affected by the volume fraction $\phi_v$. We also studied the effect of large-scale forcing on settling velocity modification. The possibility of changing the inflow conditions by using different grids allowed us to test cases with fixed $Re_\lambda$ and turbulent intensity but different integral length scale. Finally, we assess the existence of secondary flows in the wind tunnel and their role on particle settling. This is achieved by characterising the settling velocity at two different positions, the centreline and close to the wall, with the same streamwise coordinate.Comment: 21 pages, 11 figures, submitted to the Journal of Fluid Mechanic

Changement de phase de grosses particules dans un écoulement turbulent

Le changement de phase d’une particule solide advectée dans un écoulement turbulent est un problème complexe car le transfert thermique entre le fluide et la particule dépend du glissement fluide-particule. Si, dans le cas d'une particule fixe dans un écoulement laminaire, le flux de chaleur dépend de la racine carré du nombre de Reynolds, le cas de grosses particules librement transportées est un problème ouvert du fait des interactions non linéaires entre l’écoulement et la particule. Nous étudions la fusion de billes de glace dans un écoulement de von Kármán en eau, pleinement turbulent, dont la température est maintenue fixe. Différentes vitesses de rotation des disques forçant l’écoulement permettent d’atteindre des nombres de Reynolds basés sur l’échelle de Taylor allant de 300 à 600. Un montage ombroscopique avec un faisceau parallèle illumine la quasi-totalité du dispositif, permettant un suivi des billes de glace, sans biais de mesure de taille. L’écoulement à 1 ou 2 disques et le cas de glaçons fixes ou librement advectées ont été étudiées, ainsi que des glaçons de différentes tailles, dans une gamme de l’ordre de grandeur de l’échelle intégrale de l’écoulement turbulent. Toutes les expériences se situent dans des gammes de vitesses suffisamment grandes, où les transferts thermiques par diffusion et convection naturelle sont négligeables. Ainsi, les mesures de la taille des glaçons au cours du temps suffisent à obtenir le flux de chaleur dans les différentes configurations. Dans le cas des glaçons fixes, le comportement est similaire au cas laminaire, mais avec un exposant plus proche de 4/5, cohérents avec des résultats obtenus pour des goutes s'évaporant dans l'air. Le cas des glaçons librement advectés est très différents : le transfert thermique est uniquement proportionnel à la vitesse du fluide et donc indépendant de la taille des billes de glace

Wake of inertial waves of a horizontal cylinder in horizontal translation

We analyze theoretically and experimentally the wake behind a horizontal cylinder of diameter $d$ horizontally translated at constant velocity $U$ in a fluid rotating about the vertical axis at a rate $\Omega$. Using particle image velocimetry measurements in the rotating frame, we show that the wake is stabilized by rotation for Reynolds number ${\rm Re}=Ud/\nu$ much larger than in a non-rotating fluid. Over the explored range of parameters, the limit of stability is ${\rm Re} \simeq (275 \pm 25) / {\rm Ro}$, with ${\rm Ro}=U/2\Omega d$ the Rossby number, indicating that the stabilizing process is governed by the Ekman pumping in the boundary layer. At low Rossby number, the wake takes the form of a stationary pattern of inertial waves, similar to the wake of surface gravity waves behind a ship. We compare this steady wake pattern to a model, originally developed by [Johnson, J. Fluid Mech. 120, 359 (1982)], assuming a free-slip boundary condition and a weak streamwise perturbation. Our measurements show a quantitative agreement with this model for ${\rm Ro}\lesssim 0.3$. At larger Rossby number, the phase pattern of the wake is close to the prediction for an infinitely small line object. However, the wake amplitude and phase origin are not correctly described by the weak-streamwise-perturbation model, calling for an alternative model for the boundary condition at moderate rotation rate.Comment: Accepted for publication in Physical Review Fluid

Signature of salt-indiced diffusion of particules in a turbulent water jet

International audienceWe study particles dispersion in a turbulent water jet. We focus especially on salt-induced particle transport (diffusiophore-sis). A coarse graining operation is used on scalar fields to quantify mixing scale evolution. Preliminary results show changes in the particle transport, characterized by an enhanced (or reduced) diffusion coefficient

Migration de particules par gradients salins

Le transport et le mélange de molécules ou de particules jouent un rôle significatif dans de nombreux processus. À très petites échelles, le transport et le mélange constituent une composante importante du développement de laboratoires sur puce ; en effet, les dimensions réduites interdisent tout processus de mélange turbulent. Seule la diffusion moléculaire, peu efficace, intervient. Une voie prometteuse pour l’amélioration du mélange dans des micro-systèmes s’appuie sur la génération d’advection chaotique laminaire (Stroock et al. 2002, Raynal et al. 2007). Le mélange est alors assuré par une succession d’étirements et de repliements du fluide (transformation du boulanger). À plus grandes échelles, le mélange turbulent génère de façon similaire des étirements et des repliements du fluide à différentes échelles. Toutefois, que ce soit en advection chaotique ou en mélange turbulent, c’est la diffusion moléculaire qui joue le rôle final d’homogénéisation du mélange. Abécassis et al. (2008) ont montré que la présence de gradients salins pouvait considérablement modifier le comportement diffusif de grosses molécules et ainsi améliorer le mélange ou, au contraire, s’y opposer : ce phénomène est nommé diffusiophorèse. Nous caractérisons expérimentalement le comportement de grosses particules (colloïdes ≈ 250 nm) en présence de gradients salins. Deux configurations sont étudiées : - une cellule de Hele-Shaw où le mode de mélange privilégié est l’advection chaotique laminaire. - un jet turbulent dans l’eau. Dans les deux configurations, nous nous intéressons aux cas suivants : - injection de particules dans un milieu salé (hyperdiffusion). - injection de particules et de sel dans l’eau (tout se déroule alors comme si nous étions en présence d’une diffusion négative !). Des techniques de PLIF (Planar Laser-Induced Fluorescence) et de PIV sont utilisées afin de caractériser l’écoulement et le mélange dans les deux configurations

Fragmentation mechanisms in coaxial two-fluid atomization

The destabilization and subsequent fragmentation of a liquid phase by a turbulent gas phase is at the core of many applications that aim at producing high-quality sprays. Certain underlying physical mechanisms of spray formation remain unresolved, hindering process efficiency and control. I will present a multiscale characterization of these mechanisms in a two-fluid atomizer, where a round liquid jet is fragmented by a turbulent annular gas jet. The interfacial instabilities, and resulting large-scale dynamics, are experimentally characterized using two high-speed imaging methods, back-lit optical imaging and synchrotron X-ray radiography. A spatial characterization of the flapping dynamics of the liquid jet indicates that the flapping dimensionality is related to the change between shear break-up to bag break-up. At higher gas velocities, the scaling laws of the transport of the interfacial instabilities highlight the change to fiber-type atomization. Similarly, studying statistics and temporal dynamics of the length of the liquid jet in a broad parameter space poses a framework to quantitively describe changes in fragmentation mechanisms. In addition, I will show how introducing angular momentum (swirl) in the gas jet dramatically changes the topology and dynamics of the atomized liquid jet, resulting in drastic changes in the spray