On the dynamics and breakup of a bubble immersed in a turbulent flow

Experimental investigations of the dynamics of a deformable bubble rising in a uniform turbulent flow are reported. The turbulence is characterized by fast PIV. Time-resolved evolutions of bubble translation, rotation and deformation are determined by three-dimensional shape recognition from three perpendicular camera views. The bubble dynamics involves three mechanisms fairly decoupled: (i) average shape is imposed by the mean motion of the bubble relative to liquid; (ii) wake instability generates almost periodic oscillations of velocity and orientation; (iii) turbulence causes random deformations that sometimes lead to breakup. The deformation dynamics is radically different from that observed in the absence of a significant sliding motion due to buoyancy. Large deformations that lead to breakup are not axisymmetric and correspond to elongations in the horizontal direction. The timescale of decay of shape oscillations is of the same order as their natural frequency f2, so that breakup always results from the interaction with a single turbulent eddy. This overdamping causes the statistics of large deformations and the statistics of breakup identical to the statistics of turbulence. The bubble response time f2 however controls the duration of individual breakup events

Agitation, Mixing, and Transfers Induced by Bubbles

Bubbly flows involve bubbles randomly distributed within a liquid. At large Reynolds number, they experience an agitation that can combine shear- induced turbulence (SIT), large-scale buoyancy-driven flows, and bubble- induced agitation (BIA). The properties of BIA strongly differ from those of SIT. They have been determined from studies of homogeneous swarms of rising bubbles. Regarding the bubbles, agitation is mainly caused by the wake-induced path instability. Regarding the liquid, two contributions must be distinguished. The first one corresponds to the anisotropic flow distur- bances generated near the bubbles, principally in the vertical direction. The second one is the almost isotropic turbulence induced by the flow instability through a population of bubbles, which turns out to be the main cause of horizontal fluctuations. Both contributions generate a k −3 spectral subrange and exponential probability density functions. The subsequent issue will be to understand how BIA interacts with SIT

Mécanisme de mélange par convection intermittente dans un nuage de bulles confinées

Ce travail s'intéresse au mélange d'un traceur passif peu diffusif dans un nuage homogène de bulles en ascension dans une cellule Hele-Shaw. Le nombre de Reynolds du mouvement relatif des bulles est élevé. L'écoulement peut être considéré comme bidimensionnel et possède une agitation du liquide très particulière, liée principalement aux sillages des bulles ([1], [2]). Nous avons réalisé des expériences de mélange en injectant un traceur fluorescent au sein du nuage de bulles pendant un temps fini. Une technique de mesure LIF originale et adaptée à cet écoulement à bulles a été développée. Elle consiste à éclairer avec un laser un volume de 0,5 mm³, à différentes distances de l'injecteur, et à observer avec une fibre optique la lumière de ce volume qui est transmise à un spectromètre permettant d'analyser la lumière fluorescée. Il est donc possible de remonter à la concentration locale à une fréquence de 250 Hz (résolution temporelle de la mesure). La figure 1.a montre une évolution typique de la concentration du colorant en un point situé à 150 mm au dessus de l'injection. Dans un premier temps, le traceur arrivant dans le volume de mesure, la concentration augmente, la diminution de concentration qui suit, se fait de manière exponentielle ce qui montre que le mélange en cellule Hele-Shaw n'est pas un processus diffusif de type Fickien [3]. De plus, nous observons à une échelle temporelle beaucoup plus courte des fluctuations de concentration très marquées. Cette intermittence est principalement due aux mécanismes intrinsèques au mélange en cellule de Hele-Shaw. Ce mélange se fait principalement par séquences de capture - transport - largage de colorant par les sillages des bulles (figure 1.b). Un modèle de mélange convectif intermittent a été développé et reproduit bien les expériences

Velocimetry of red blood cells in microvessels by the dual-slit method: Effect of velocity gradients

The dual-slit is a photometric technique used for the measurement of red blood cell (RBC) velocity in microvessels. Two photometric windows (slits) are positioned along the vessel. Because the light is modulated by the RBCs flowing through the microvessel, a time dependent signal is captured for each window. A time delay between the two signals is obtained by temporal cross correlation, and is used to deduce a velocity, knowing the distance between the two slits. Despite its wide use in the field of microvascular research, the velocity actually measured by this technique has not yet been unambiguously related to a relevant velocity scale of the flow (e.g. mean or maximal velocity) or to the blood flow rate. This is due to a lack of fundamental understanding of the measurement and also because such a relationship is crucially dependent on the non-uniform velocity distribution of RBCs in the direction parallel to the light beam, which is generally unknown. The aim of the present work is to clarify the physical significance of the velocity measured by the dual-slit technique. For that purpose, dual-slit measurements were performed on computer-generated image sequences of RBCs flowing in microvessels, which allowed all the parameters related to this technique to be precisely controlled. A parametric study determined the range of optimal parameters for the implementation of the dual-slit technique. In this range, it was shown that, whatever the parameters governing the flow, the measured velocity was the maximal RBC velocity found in the direction parallel to the light beam. This finding was then verified by working with image sequences of flowing RBCs acquired in PDMS micro-systems in vitro. Besides confirming the results and physical understanding gained from the study with computer generated images, this in vitro study showed that the profile of RBC maximal velocity across the channel was blunter than a parabolic profile, and exhibited a non-zero sliding velocity at the channel walls. Overall, the present work demonstrates the robustness and high accuracy of the optimized dual-slit technique in various flow conditions, especially at high hematocrit, and discusses its potential for applications in vivo

Modeling and simulation of inertial drop break-up in a turbulent pipe flow downstream of a restriction.

This work deals with the modeling of drop break-up in an inhomogeneous turbulent flow that develops downstream of a concentric restriction in a pipe. The proposed approach consists in coupling Euler–Lagrange simulations of the drop motion to an interface deformation model. First the turbulent flow downstream of the restriction is solved by means of direct numerical simulation. Single drop trajectories are then calculated from the instantaneous force balance acting on the drop within the turbulent field (one-way coupling). Concurrently, the interface deformation is computed assuming the drop to behave as a Rayleigh–Lamb type oscillator forced by the turbulent stress along its trajectory. Criterion for break-up is based upon a critical value of drop eformation. This model has been tested against experimental data. The flow conditions and fluids properties have been chosen to match those experimental investigations. Both turbulent flow statistics and break-up probability calculations are in good agreement with experimental data, strengthening the relevance of this approach for modeling break-up in complex unsteady flow

Dynamique d'un nuage de bulles homogène confiné

De nombreuses applications industrielles mettent en jeu des écoulements à bulles dans des échangeurs de masse et de chaleur ou des réacteurs. Les mouvements des bulles génèrent de l'agitation dans le liquide qui, en retour, influence la distribution spatiale des bulles et leur vitesse. La compréhension générique de ce problème de couplage inverse total est fondamentale mais délicate. Des travaux expérimentaux dédiés dans des configurations d'écoulements bien définies sont donc nécessaires pour atteindre cet objectif. Ce travail explore la dynamique d'un nuage de bulles en ascension à grand nombre de Reynolds dans une cellule de Hele-Shaw ([1]). Cette configuration apporte une contribution à une compréhension générale car elle permet d'étudier l'agitation générée par des bulles à grand nombre de Reynolds possédant des sillages instables tout en empêchant, par les effets de confinement, la production de turbulence. La comparaison avec la dynamique de nuages de bulles non confinés ([2]) est également éclairante. Par ailleurs, la détection des interfaces est considérablement facilitée par le confinement: une description complète et précise de la répartition spatiale et de la dynamique des bulles peut être ici obtenue directement par ombroscopie avec une seule caméra. De même, la mesure par PIV du champ de vitesse du liquide intégré dans l'épaisseur de la cellule permet de caractériser de manière pertinente la dynamique du liquide ([3]) (Fig.1-a). La dynamique des deux phases a ainsi été explorée pour des fractions volumiques de gaz α comprises entre 1% et 14% dans un régime où l'inertie est importante (Re≈500). Les bulles étudiées possèdent un sillage instable avec des lâchers tourbillonnaires réguliers et suivent une trajectoire ascendante oscillante tout en gardant une forme elliptique constante. Le frottement aux parois impose néanmoins une décroissance très forte des sillages ([4]). Les résultats montrent que l'on peut expliquer les statistiques associées au mouvement des bulles dans le nuage à partir de deux mécanismes élémentaires: (i) les oscillations induites par le sillage associées aux lâchers tourbillonnaires et (ii) la forte perturbation de vitesse localisée à l'arrière des bulles. Le mécanisme dominant dans la direction verticale est l'entrainement dans le sillage alors que celui qui régit la dynamique des bulles dans la direction horizontale est associé aux oscillations générées par les sillages dont l'intensité est indépendante de α (Fig.1-b). L'auto-dispersion des bulles a également été étudiée. Elle peut être caractérisée par des coefficients de dispersion qui évoluent linéairement avec α. En ce qui concerne l'agitation dans le liquide, comme en écoulement non confiné, les deux composantes des fluctuations de vitesse évoluent proportionnellement à αn avec ici αn=0.38 et 0.46 dans les directions horizontales et verticales respectivement. Le spectre spatial des fluctuations de vitesse évolue, sur une gamme de nombres d'ondes k bien définie, proportionnellement à k-³. Dans cette configuration où la turbulence ne peut se développer, cette évolution s'explique très clairement par la superposition linéaire de perturbations de vitesses aléatoires ([5]), il s'agit donc d'un effet statistique associé aux passages de perturbations convectées par les bulles

Dynamics of a high-Reynolds-number bubble rising within a thin gap

We report an experimental analysis of path and shape oscillations of an air bubble of diameter d rising in water at high Reynolds number in a vertical Hele-Shaw cell of width h. Liquid velocity perturbations induced by the relative movement have also been investigated to analyze the coupling between the bubble motion and the wake dynamics. The confinement ratio h/d is lower than unity so that the bubble is flattened in between the walls of the cell. As the bubble diameter is increased, the Archimedes and the Bond numbers increase within 10 6 Ar 6 104 and 6 × 10−3 6 Bo 6 140. Mean shapes become more and more elongated. They first evolve from in-plane circles to ellipses, then to complicated shapes without fore-aft symmetry and finally to semi-circular capped bubbles. The scaling law Re = 0.5Ar is however valid for a large range of Ar, indicating that the liquid films between the bubble and the walls do no contribute significantly to the drag force exerted on the bubble. The coupling between wake dynamics, bubble path and shape oscillations evolves and a succession of contrasted regimes of oscillations is observed. The rectilinear bubble motion becomes unstable from a critical value Ar1 through an Hopf bifurcation while the bubble shape is still circular. The amplitude of path oscillations first grows as Ar increases above Ar1 but then surprisingly decreases beyond a second Archimedes number Ar2. This phenomenon, observed for steady ellipsoidal shape with moderate eccentricity, can be explained by the rapid attenuation of bubble wakes caused by the confinement. Shape oscillations around a significantly elongated mean shape starts for Ar > Ar3. The wake structure progressively evolves due to changes in the bubble shape. After the break-up of the fore-aft symmetry, a fourth regime involving complicated shape oscillations is then observed for Ar > Ar4. Vortex shedding disappears and unsteady attached vortices coupled to shape oscillations trigger path oscillations of moderate amplitude. Path and shape oscillations finally decrease when Ar is further increased. For Ar > Ar5, capped bubbles followed by a steady wake rise on a straight path

Attenuation of the wake of a sphere in an intense incident turbulence with large length scales

We report an investigation of the wake of a sphere immersed in a uniform turbulent flow for sphere Reynolds numbers ranging from 100 to 1000. An original experimental setup has been designed to generate a uniform flow convecting an isotropic turbulence. At variance with previous works, the integral length scale of the turbulence is of the same order as the sphere diameter and the turbulence intensity is large. In consequence, the most intense turbulent eddies are capable of influencing the flow in the close vicinity of the sphere. Except in the attached region downstream of the sphere where the perturbation of the mean velocity is larger than the standard deviation of the incident turbulence, the flow is controlled by the incident turbulence. The distortion of the turbulence while the flow goes round the sphere leads to an increase in the longitudinal fluctuation and a decrease in the transversal one. The attenuation of the transversal fluctuations is still significant at 30 radii downstream of the sphere whereas the longitudinal fluctuations relax more rapidly toward the incident value. The more striking result however concerns the evolution of the mean velocity defect with the distance x from the sphere. It decays as x−2 and scales with the standard deviation of the incident turbulence instead of scaling with the mean incident velocity

Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 1: Bubble dynamics

The spatial distribution, the velocity statistics and the dispersion of the gas phase have been investigated experimentally in a homogeneous swarm of bubbles confined within a thin gap. In the considered flow regime, the bubbles rise on oscillatory paths while keeping a constant shape. They are followed by unstable wakes which are strongly attenuated due to wall friction. According to the direction that is considered, the physical mechanisms are totally different. In the vertical direction, the entrainment by the wake controls the bubble agitation, causing the velocity variance and the dispersion coefficient to increase almost linearly with the gas volume fraction. In the horizontal direction, path oscillations are the major cause of bubble agitation, leading to a constant velocity variance. The horizontal dispersion, which is lower than that in the vertical direction, is again observed to increase almost linearly with the gas volume fraction. It is however not directly due to regular path oscillations, which are unable to generate a neat deviation over a whole period, but results from bubble interactions which cause a loss of the bubble velocity time correlation

PIV with volume lighting in a narrow cell: An efficient method to measure large velocity fields of rapidly varying flows

In this work we test a methodology for PIV measurements when alargefield of view is required in planar confined geometries. Using a depth of fieldlarger than the channel width, we intend to measure the in-plane variations of the velocity of the fluid averaged through the width of the channel, and we examine in which operating conditions this becomes possible. Measurements of the flow through anarrow channel by PIV are challenging because of the strong velocity gradients that develop between the walls. In particular, all techniques that use small particles as tracers have to deal with the possible migration of the tracers in the direction perpendicular to the walls. Among the complex mechanisms for migration, we focus on the so called Segré–Silberberg effect which can lead to transverse migration of neutrally buoyant tracers of finite size. We report experimental PIV measurements in a Hele-Shaw cell of 1 mm gap, which have been carried out by using neutrally buoyant tracers of size around 10 μm. By considering steady flows, we have observed, in particular flow regimes, the effect of an accumulation of the tracers at a certain distance to the wall due to the so called Segré–Silberberg effect. The particle migration is expected to occur at any Reynolds numbers but the migration velocity depends on the Reynolds number. A significant migration therefore takes place each time the observation duration is large enough compared to the migration time. For a given observation duration, the tracers remain uniformly distributed at low Reynolds numbers whereas they all accumulate at the equilibrium position at large ones. When using volumelighting, the PIV algorithm provides the average velocity of the flow through the gap at low Reynolds number, while it leads to the velocity of the flow at the equilibrium position of the tracers at large Reynolds numbers. By considering unsteady flows, we have observed that the migration does not occur if the timescale of flow variation is short compared to the time required for the parabolic flow to develop across the gap. In this case, there is no transverse velocity gradient and the PIV algorithm provides the fluid velocity. Altogether, these results allow us to propose guidelines for the interpretation of PIV measurements in confined flow, which are based on the theoretical predictions of the tracer migration derived by Asmolov [1]