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

Roig, Véronique; Roudet, Matthieu; Risso, Frédéric; Billet, Anne-Marie

doi:10.1017/jfm.2012.289

Cited by 79 publications

(137 citation statements)

References 22 publications

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“…At low gas volume fraction (↵ 6 1.2 %), bubble interactions have a weak influence and the average perturbation induced by a bubble inside the swarm is almost the same as that of an isolated bubble, which has been described in detail by Roig et al (2011). Above the bubble, the average flow perturbation is potential.…”

Section: Resultsmentioning

confidence: 93%

Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics

et al. 2014

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OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 15866 The agitation of the liquid phase has been investigated experimentally in a homogeneous swarm of bubbles rising at high Reynolds number within a thin gap. Owing to the wall friction, the bubble wakes are strongly attenuated. Consequently, liquid fluctuations result from disturbances localized near the bubbles and direct interactions between them. The signature of the average wake rapidly fades and the probability density function of the fluctuations becomes Gaussian as the gas volume fraction ↵ increases. The energy of the fluctuations scales differently with ↵ depending on the direction, indicating that hydrodynamic interactions are different in the horizontal and vertical directions. The spatial spectrum shows that the length scales of the fluctuations are independent of ↵ and exhibits a k 3 subrange, which results from localized random flow disturbances of various sizes. Comparisons with the dynamics of the gas phase show that liquid and bubble agitations are driven by the same mechanism in the vertical direction, whereas they turn out to be almost uncoupled in the horizontal direction. Comparisons with unconfined flows show that the generation of liquid fluctuations is very different. However, the cause of the k 3 spectral subrange is the same for confined flows as for the spatial fluctuation of unconfined flows.

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Section: Resultsmentioning

confidence: 93%

Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics

et al. 2014

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“…In the present study, we investigate the coupling between the motion of a bubble, the nature of its wake and its deformation in a configuration put forward in the detailed analysis of Roig et al (2012). This study considered high-Reynolds-number bubbles freely rising in liquid at rest confined in a thin-gap cell of width h = 1 mm (Hele-Shaw cell), for which the thin liquid films existing between the bubble and the walls do not contribute to the dynamics of the bubble.…”

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Oscillatory motion and wake of a bubble rising in a thin-gap cell

2015

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We investigate the characteristics of the oscillatory motion and wake of confined bubbles freely rising in a thin-gap cell (h = 3.1 mm width). Once the diameter d of the bubble in the plane of the cell is known, the mean vertical velocity of the bubble V b is proportional to the gravitational velocity (h/d) 1/6 √ gd, where g is the gravitational acceleration. This velocity is used to build the Reynolds number Re = V b d/ν that characterizes the flow induced by the bubble in the surrounding liquid (of kinematic viscosity ν), and which determines at leading order the mean deformation of the bubble given by the aspect ratio χ of the ellipse equivalent to the bubble contour. We then show that in the reference frame associated with the bubble (having a fixed origin and axes corresponding to the minor and major axes of the equivalent ellipse) the characteristics of its oscillatory motion in the plane of the cell display remarkable properties in the range 1200 < Re < 3000 and h/d < 0.4. In particular, the velocity of the bubble presents along its path an almost constant component along its minor axis (fluctuations in time of approximately 5 %), given by V a /V b 0.92 for all Re. The dimensionless amplitude of oscillation of the angular velocity is also constant for all Re,rd/V b 0.75, while that of the transverse velocity of the bubble (along its major axis) is given byṼ t /V b 0.32χ, reaching values comparable to those of the axial velocity V a for the most deformed bubbles (χ ≈ 3). Furthermore, the frequency f of oscillation scales with the inertial time scale based on the transverse velocity of the bubbleṼ t , corresponding to a constant Strouhal number St * = fd/Ṽ t 0.27. Using high-frequency particle image velocimetry, we investigate in detail the properties of the wake associated with the oscillatory motion of sufficiently confined bubbles. We observe that vortex shedding occurs for a maximal transverse velocity V t of the bubble, corresponding to a maximal drift angle of the bubble. Furthermore, the measured vorticity of the vortex at detachment corresponds to the estimation V b χ 3/2 /d of the vorticity produced at the bubble surface. Three stages then emerge concerning the evolution in time of the wake generated by the bubble. For one to two periods of oscillation T x following the release of a vortex, a rapid decay of the vorticity of the released vortex is observed. Meanwhile, the released vortex located initially at a distance of approximately one diameter from the bubble centre moves outwards from the bubblepath and expands. At intermediate times, the vortex † Email address for correspondence: roig@imft.fr Oscillatory motion and wake of a bubble rising in a thin-gap cell 61 street undergoes vortex pairing. When viscous effects become predominant at a time of the order of the viscous time scale τ ν = h 2 /(4ν), the vortex street becomes frozen and decays exponentially in place.

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“…In particular, the friction at the walls and the velocity gradient throughout the gap play a major role in the structure of the bubble wakes as shown by Roig et al (2012) , Bouche et al (2014) and Filella et al (2015) . Within a viscous time scale w 2 /(4 ν), the in-gap velocity profile generated by a bubble passage evolves from a plug flow profile to a Poiseuille flow profile with a maximum velocity decreasing exponentially with time.…”

Section: Experimental Set-upmentioning

confidence: 99%

Time-resolved measurement of concentration fluctuations in a confined bubbly flow by LIF

Alméras

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Roig

et al. 2016

International Journal of Multiphase Flow

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a b s t r a c tThe present work investigates the mixing of a low-diffusivity dye in a swarm of bubbles at high Reynolds number confined in a Hele-Shaw cell for gas volume fractions ranging from 1.4 to 5.4%. A patch of a fluorescent dye is injected within the swarm and, during its mixing, its concentration is measured at a given location in an observation volume of 4.5 mm 2 by means of Laser Induced Fluorescence at a frequency of 250 Hz. A spectrometer is used to analyse the light issued from the observation volume and to distinguish the fluoresced light from other light sources. Simultaneously, the bubble distribution around the observation volume is imaged with a high speed camera synchronised with the spectrometer in order to assess the LIF technique in bubbly flow. Thanks to the good time resolution, rapid and intense concentration fluctuations corresponding to dye patches passing through the observation volume are recorded and are superimposed to a slow global evolution. This slow global evolution shows first an increase of the concentration and then an exponential decrease due to the mixing by bubble-induced agitation. This exponential decay, which is incompatible with a diffusion process, is consistent with the transport by dye capture in bubbles wakes that are quickly dampened by the shear-stress at the walls. The one-point statistics of the concentration fluctuations (probability density function and spectrum) also point out that mixing in a confined bubbly flow is intermittent and convective.

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

Cited by 79 publications

References 22 publications

Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics

Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 2. Liquid dynamics

Oscillatory motion and wake of a bubble rising in a thin-gap cell

Time-resolved measurement of concentration fluctuations in a confined bubbly flow by LIF

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