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Experimental characterization of the agitation generated by bubbles rising at high Reynolds number

Published online by Cambridge University Press:  23 December 2009

GUILLAUME RIBOUX ,
FRÉDÉRIC RISSO  and
DOMINIQUE LEGENDRE
GUILLAUME RIBOUX
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
FRÉDÉRIC RISSO*
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
DOMINIQUE LEGENDRE
Affiliation:
Université de Toulouse; INPT, UPS; IMFT (Institut de Mécanique des Fluides de Toulouse); Allée Camille Soula, F-31400 Toulouse, France CNRS; IMFT; F-31400 Toulouse, France
*
†Email address for correspondence: risso@imft.fr
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Abstract

An experimental investigation of the flow generated by a homogeneous population of bubbles rising in water is reported for three different bubble diameters (d = 1.6, 2.1 and 2.5 mm) and moderate gas volume fractions (0.005 ≤ α ≤ 0.1). The Reynolds numbers, Re = V0d/ν, based on the rise velocity V0 of a single bubble range between 500 and 800. Velocity statistics of both the bubbles and the liquid phase are determined within the homogeneous bubble swarm by means of optical probes and laser Doppler anemometry. Also, the decaying agitation that takes place in the liquid just after the passage of the bubble swarm is investigated from high-speed particle image velocimetry measurements. Concerning the bubbles, the average velocity is found to evolve as V0α−0.1 whereas the velocity fluctuations are observed to be almost independent of α. Concerning the liquid fluctuations, the probability density functions adopt a self-similar behaviour when the gas volume fraction is varied, the characteristic velocity scaling as V0α0.4. The spectra of horizontal and vertical liquid velocity fluctuations are obtained with a resolution of 0.6 mm. The integral length scale Λ is found to be proportional to V02/g or equivalently to d/Cd0, where g is the gravity acceleration and Cd0 the drag coefficient of a single rising bubble. Normalized by using Λ, the spectra are independent on both the bubble diameter and the volume fraction. At large scales, the spectral energy density evolves as the power −3 of the wavenumber. This range starts approximately from Λ and is followed for scales smaller than Λ/4 by a classic −5/3 power law. Although the Kolmogorov microscale is smaller than the measurement resolution, the dissipation rate is however obtained from the decay of the kinetic energy after the passage of the bubbles. It is found to scale as α0.9V03/Λ. The major characteristics of the agitation are thus expressed as functions of the characteristics of a single rising bubble. Altogether, these results provide a rather complete description of the bubble-induced turbulence.

JFM classification

Drops and Bubbles: Bubble dynamics Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 509 - 539
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abbas, M. & Climent, E. 2006 Dynamics of bidisperse suspensions under stokes flows: linear shear flow and sedimentation. Phys. Fluids 18, 121504.CrossRefGoogle Scholar
Calfish, R. E. & Luke, H. C. 1985 Variance in the sedimentation speed of a suspension. Phys. Fluids 28, 759–760.Google Scholar
Cartellier, A. & Rivière, R. 2001 Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particle Reynolds numbers. Phys. Fluids 13, 2165–2181.Google Scholar
Cid, E. & Gardelle, F. 2005 Manuel d'utilisation du logiciel PIVis. Institut de Mécanique des Fluides de Toulouse.Google Scholar
Eames, I., Roig, V., Hunt, J. C. R. & Belcher, S. E. 2004 Vorticity annihilation and inviscid blocking in multibody flows. In NATO Advanced Study Institute: Flow and Transport Processes in Complex Obstructed Geometries: From Cities and Vegetative Canopies to Industrial Problems, Kiev, Ukraine.Google Scholar
Ellingsen, K. & Risso, F. 2001 On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity. J. Fluid Mech. 440, 235–268.Google Scholar
Garnier, C., Lance, M. & Marié, J. L. 2002 Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction. Exp. Therm. Fluid Sci. 26, 811–815.Google Scholar
Hunt, J. C. R. & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111–132.Google Scholar
Kiambi, S. L., Duquenne, A.-M., Dupont, J.-B., Colin, C., Risso, F. & Delmas, H. 2003 Measurements of bubble characteristics: comparison between double optical probe and imaging. Can. J. Ch. Engng 81.Google Scholar
Koch, D. L. 1993 Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers. Phys. Fluids A 5, 1141–1155.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly air–water flow. J. Fluid Mech. 222, 95–118.CrossRefGoogle Scholar
Larue de Tournemine, A. 2001 Etude expérimentale de l'effet du taux de vide en écoulement diphasique à bulles. PhD thesis, Institut National Polytechnique de Toulouse, France.Google Scholar
Manasseh, R., Riboux, G. & Risso, F. 2008 Sound generation on bubble coalescence following detachment. Intl J. Multiph. Flow 34, 938–949.CrossRefGoogle Scholar
Martinez-Mercado, J., Palacios-Morales, C. & Zenit, R. 2007 Measurement of pseudo-turbulence intensity in mono-dispersed bubbly liquids. Phys. Fluids 19, 103302.Google Scholar
Maxworthy, T., Gnann, C., Kurten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421–441.Google Scholar
Parthasarathy, R. N. & Faeth, G. M. 1990 Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech. 220, 485–514.Google Scholar
Rensen, J., Luther, S. & Lohse, A. 2005 The effect of bubbles on developed turbulence. J. Fluid Mech. 538, 153–187.Google Scholar
Risso, F. & Ellingsen, K. 2002 Velocity fluctuations in homogeneous dilute dispersion of high-Reynolds-number rising bubbles. J. Fluid Mech. 453, 395–410.Google Scholar
Risso, F., Roig, V., Amoura, Z., Riboux, G. & Billet, A.-M. 2008 Wake attenuation in large Reynolds number dispersed two-phase flows. Phil. Trans. R. Soc. A 366, 2177–2190.Google Scholar
Roig, V. & Larue de Tournemine, A. 2007 Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction. J. Fluid Mech. 572, 87–110.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.Google Scholar
Westerweel, J. & Scarano, F. 2005 Universal outlier detection for PIV data. Exp. Fluids 39, 1096–1100.Google Scholar
White, B. L. & Nepf, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 43–79.Google Scholar
Zenit, R., Koch, D. L. & Sangani, A. S. 2001 Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J. Fluid Mech. 429, 307–342.Google Scholar