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Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction

Published online by Cambridge University Press:  23 January 2007

V. ROIG
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR 5502 CNRS-INP-UPS, Allée C. Soula, 31400 Toulouse, France
A. LARUE DE TOURNEMINE
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR 5502 CNRS-INP-UPS, Allée C. Soula, 31400 Toulouse, France

Abstract

We develop a new methodology to examine the conditional and unconditional vertical velocity induced by high-Reynolds-number bubbles rising in a uniform flow, at low to moderate void fraction α (up to 15%). These statistics provide a local description of the perturbation of the liquid velocity around a test bubble in the swarm. In particular, the attenuation of the length of the wakes with increasing void fraction is measured for a large range of void fraction. The strong attenuation of the wakes is related to wake intermingling mechanisms. The methodology also enables a definition of the interstitial liquid flow. The velocity of the fluid averaged over all the interstitial volume far away from the bubbles is introduced. It is a useful concept, in particular to define the relative velocity, or for drift models. Our experimental results allow a discussion of the predictions of irrotational drift models. For low void fraction (α≤2%), potential flow models provide practical estimates of the interstitial velocity field. At higher void fractions, the effect of vorticity is important. A simple phenomenological model is proposed to include the effect of the flow generated by the bubble wakes.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G. K. 1972 Sedimentation in dilute dispersions of spheres. J. Fluid Mech. 52, 245268.CrossRefGoogle Scholar
Betz, A. 1927 Ein Verfahren zur direkten Ermittlund des Profilwiderstandes. Z. Flugtech. Motorluftschiffahrt 16, 42.Google Scholar
Biesheuvel, A. & van Wijngaarden, L. 1984 Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J. Fluid Mech. 148, 301318.CrossRefGoogle Scholar
Bruun, H. H. 1995 Hot-wire anemometry, Principles and signal analysis. Oxford University Press.CrossRefGoogle Scholar
Bush, J. W. M. & Eames, I. 1998 Fluid displacement by high Reynolds number bubble motion in a thin gap. Intl J. Multiphase Flow 24, 411430.CrossRefGoogle Scholar
Cartellier, A. & Riviere, N. 2001 Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particule Reynolds numbers. Phys. Fluids 13, 21652181.CrossRefGoogle Scholar
Clark, N. N. & Turton, R. 1988 Chord length distributions related to bubble size distributions in multiphase flows. Intl J. Multiphase Flow 14, 413424.CrossRefGoogle Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubbles, Drops and Particles. Academic Press.Google Scholar
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325332.CrossRefGoogle Scholar
Drew, D. A. 1983 Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261291.CrossRefGoogle Scholar
Eames, I., Belcher, S. E. & Hunt, J. C. R. 1994 Drift, partial drift and Darwin's proposition. J. Fluid Mech. 275, 201223.CrossRefGoogle Scholar
Eames, I., Hunt, J. C. R. & Belcher, S. E. 2004 Inviscid mean flow through and around groups of bodies. J. Fluid Mech. 515, 371389.CrossRefGoogle Scholar
Eames, I., Roig, V., Hunt, J. C. R. & Belcher, S. E. 2004 Vorticity annihilation and inviscid blocking in multibody flows. NATO meeting, Ukraine, May 2004.Google Scholar
Ellingsen, K. 1998 Hydrodynamique des écoulements pilotés par l‘ascension de bulles d'air virevoltantes. PhD Dissertation, Institut National Polytechnique de Toulouse.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, 235268.CrossRefGoogle Scholar
Ellingsen, K., Risso, F., Roig, V. & Suzanne, C. 1997 Improvements of velocity measurements in bubbly flows by comparison of simultaneous hot-film and laser-Doppler anemometry signals. Proc. ASME Fluid Engng Div. Summer Meeting, Vancouver, Canada, paper 97-3529.Google Scholar
Esmaeeli, A. & Tryggvason, G. 1998 Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays. J. Fluid Mech. 377, 313345.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 1999 Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays. J. Fluid Mech. 385, 325358.CrossRefGoogle Scholar
Farrar, B., Samways, A. L., Ali, J. & Bruun, H. H. 1995 A computer based technique for two-phase flow measurements. Meas. Sci. Technol. 6, 15281537.CrossRefGoogle 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, 811815.CrossRefGoogle Scholar
Hinze, J.O. 1987 Turbulence. McGraw-Hill.Google Scholar
Hunt, J. C. R. & Eames, I. 2002 The disappearance of laminar and turbulent wakes in complex flows. J. Fluid Mech. 457, 111132.CrossRefGoogle Scholar
Kamp, A. 1996 Ecoulements turbulents à bulles dans une conduite en micropesanteur. PhD Dissertation, Institut National Polytechnique de Toulouse.Google Scholar
Koch, D. L. 1993 Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers. Phys. Fluids 5, 11411155.CrossRefGoogle Scholar
Koch, D. L. & Brady, J. 1985 Dispersion in fixed beds. J. Fluid Mech. 154, 399427.CrossRefGoogle Scholar
Kowe, R., Hunt, J. C. R., Hunt, A. & Couet, B. 1988 The effects of bubbles on the volume fluxes and the pressure gradients in unsteady and non-uniform flow of liquids. Intl J. Multiphase Flow 14, 587606.CrossRefGoogle Scholar
Lamb, H. 1932 Hydrodynamics. Dover.Google Scholar
Larue de Tournemine, A. 2001 Etude expérimentale de l'effet du taux de vide en écoulements diphasiques à bulles. PhD Dissertation, Institut National Polytechnique de Toulouse.Google Scholar
Legendre, D., Magnaudet, J. & Mougin, G. 2003 Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech. 497, 133166.CrossRefGoogle Scholar
Risso, F. & Ellingsen, K. 2002 Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles. J. Fluid Mech. 453, 395410.CrossRefGoogle Scholar
Risso, F. & Legendre, D. 2003 Velocity fluctuations induced by high-Reynolds-number rising bubbles : experiments and numerical simulations. ERCOFTAC Bulletin, March.Google Scholar
Roig, V. 1993 Zones de mélange d'écoulements diphasiques à bulles. PhD Dissertation, Institut National Polytechnique de ToulouseGoogle Scholar
Serizawa, A., Kataoka, I. & Michiyoshi, I. 1975 Turbulence structure of air-water bubbly flow. Intl J. Multiphase Flow 2, 221259.CrossRefGoogle Scholar
Serizawa, A., Tsuda, K. & Michiyoshi, I. 1983 Real-time measurements of two-phase flow turbulence using a dual-sensor anemometry. Proc. Sympo. on Measuring Techniques in Gas-Liquid Two-Phase Flows, Nancy, France, pp. 495–523.Google Scholar
Spelt, P. & Sangani, A. 1998 Properties and averaged equations for flows of bubbly liquids. Appl. Sci. Res. 58, 337386.CrossRefGoogle Scholar
Taylor, G. I. 1928 The energy of a body moving in an infinite fluid with applications to airships. Proc. R. Soc. Lond. A 70, 1321.Google Scholar
White, B. L. & Nepf, H. M. 2003 Scalar transport in random cylinder arrays at moderate Reynolds number. J. Fluid Mech. 487, 4379.CrossRefGoogle Scholar
van Wijngaarden, L. & Kapteyn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111137.CrossRefGoogle 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, 307342.CrossRefGoogle Scholar