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Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction

Published online by Cambridge University Press:  16 December 2014

Damien Colombet ,
Dominique Legendre ,
Frédéric Risso ,
Arnaud Cockx  and
Pascal Guiraud
Damien Colombet
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS and Université de Toulouse, Allée Camille Soula, 31400 Toulouse, France Université de Toulouse; INSA, UPS, INP; LISBP, 135 Avenue de Rangueil, F-31077 Toulouse, France INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France CNRS, UMR5504, F-31400 Toulouse, France SOLVAY R&I – Rhodia, 85 Avenue des Frères Perret, BP 62, 69192 Saint Fons, France
Dominique Legendre*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS and Université de Toulouse, Allée Camille Soula, 31400 Toulouse, France
Frédéric Risso
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS and Université de Toulouse, Allée Camille Soula, 31400 Toulouse, France
Arnaud Cockx
Affiliation:
Université de Toulouse; INSA, UPS, INP; LISBP, 135 Avenue de Rangueil, F-31077 Toulouse, France INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France CNRS, UMR5504, F-31400 Toulouse, France
Pascal Guiraud
Affiliation:
Université de Toulouse; INSA, UPS, INP; LISBP, 135 Avenue de Rangueil, F-31077 Toulouse, France INRA, UMR792 Ingénierie des Systèmes Biologiques et des Procédés, F-31400 Toulouse, France CNRS, UMR5504, F-31400 Toulouse, France
*
†Email address for correspondence: legendre@imft.fr
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Abstract

The present work focuses on the collective effect on both bubble dynamics and mass transfer in a dense homogeneous bubble swarm for gas volume fractions ${\it\alpha}$ up to 30 %. The experimental investigation is carried out with air bubbles rising in a square column filled with water. Bubble size and shape are determined by means of a high-speed camera equipped with a telecentric lens. Gas volume fraction and bubble velocity are measured by using a dual-tip optical probe. The combination of these two techniques allows us to determine the interfacial area between the gas and the liquid. The transfer of oxygen from the bubbles to the water is measured from the time evolution of the concentration of oxygen dissolved in water, which is obtained by means of the gassing-out method. Concerning the bubble dynamics, the average vertical velocity is observed to decrease with ${\it\alpha}$ in agreement with previous experimental and numerical investigations, while the bubble agitation turns out to be weakly dependent on ${\it\alpha}$. Concerning mass transfer, the Sherwood number is found to be very close to that of a single bubble rising at the same Reynolds number, provided the latter is based on the average vertical bubble velocity, which accounts for the effect of the gas volume fraction on the bubble rise velocity. This conclusion is valid for situations where the diffusion coefficient of the gas in the liquid is very low (high Péclet number) and the dissolved gas is well mixed at the scale of the bubble. It is understood by considering that the transfer occurs at the front part of the bubbles through a diffusion layer which is very thin compared with all flow length scales and where the flow remains similar to that of a single rising bubble.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 254 - 285
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Copyright
© 2014 Cambridge University Press 

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Footnotes

‡

Present address: LEGI, Energetic Team, Joseph Fourier University, Grenoble, France.

References

Aguilar Corona, A.2008 Agitation des particules dans un lit fluidisé liquide: Etude expérimentale. PhD thesis, Toulouse University, France.Google Scholar
Aguilar Corona, A., Zenit, R. & Masbernat, O. 2011 Collisions in a liquid fluidized bed. Intl J. Multiphase Flow 37 (7), 695–705.Google Scholar
Alves, S., Vasconcelos, J. & Orvalho, S. P. 2006 Mass transfer to clean bubbles at low turbulent energy dissipation. Chem. Engng Sci. 61, 1334–1337.Google Scholar
Ayed, H., Chahed, J. & Roig, V. 2007 Hydrodynamics and mass transfer in a turbulent buoyant bubbly shear layer. AIChE J. 53, 2742–2753.CrossRefGoogle Scholar
Beyer, W. H. 1987 Standard Mathematical Tables, 28th edn. CRC Press.Google Scholar
Bouche, E., Roig, V., Risso, F. & Billet, A. M. 2012 Homogeneous swarm of high-Reynolds-number bubbles rising within a thin gap. Part 1. Bubble dynamics. J. Fluid Mech. 794, 211–231.Google Scholar
Boussinesq, J. 1905 Calcul du pouvoir refroidissant des courants fluides. J. Math. Pures Appl. 6, 285–332.Google Scholar
Bridge, A., Lapidus, L. & Elgin, J. 1964 The mechanics of vertical gas–liquid fluidized system I: countercurrent flow. AIChE J. 10 (6), 819–826.Google Scholar
Buffo, A., Vanni, M. & Marchisio, D. L. 2012 Multidimensional population balance model for the simulation of turbulent gas–liquid systems in stirred tank reactors. Chem. Engng Sci. 70, 31–44.Google Scholar
Bunner, B. & Tryggvason, G. 2002a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 17–52.Google Scholar
Bunner, B. & Tryggvason, G. 2002b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 53–84.Google Scholar
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77–118.Google Scholar
Clift, R., Grace, J. R. & Weber, M. E. 1978 Bubles, Drops and Particules. Academic.Google Scholar
Cockx, A., Do-Quang, Z., Liné, A. & Roustan, M. 1999 Use of computational fluid dynamics for simulating hydrodynamics and mass transfer in industrial ozonation towers. Chem. Engng Sci. 54, 5085–5090.CrossRefGoogle Scholar
Colombet, D.2012 Modélisation de réacteurs gaz-liquide de type colonne à bulles en conditions industrielles. PhD thesis, Toulouse University.Google Scholar
Colombet, D., Legendre, D., Cockx, A. & Guiraud, P. 2013 Mass or heat transfer inside a spherical gas bubble at low to moderate Reynolds number. Intl J. Heat Mass Transfer 67, 1096–1105.CrossRefGoogle Scholar
Colombet, D., Legendre, D., Cockx, A., Guiraud, P., Risso, F., Daniel, C. & Galinat, S. 2011 Experimental study of mass transfer in a dense bubble swarm. Chem. Engng Sci. 66, 3432–3440.Google Scholar
Comolet, R. 1979 Sur le mouvement d’une bulle de gaz dans un liquide. La Houille Blanche 1, 31–42.Google Scholar
Darmana, D., Deen, N. G. & Kuipers, J. A. M. 2005 Detailed modeling of hydrodynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model. Chem. Engng Sci. 60, 3383–3404.Google Scholar
Deen, N. G., Kriebitzsch, S. H. L., van der Hoef, M. A. & Kuipers, J. A. M. 2012 Direct numerical simulation of flow and heat transfer in dense fluid–particle systems. Chem. Engng Sci. 81, 329–344.CrossRefGoogle Scholar
Dijkhuizen, W., Roghair, I., Van Sint Annaland, M. & Kuipers, J. A. M. 2010 DNS of gas bubbles behaviour using an improved 3D front tracking model—drag force on isolated bubbles and comparison with experiments. Chem. Engng Sci. 65 (4), 1415–1426.Google Scholar
Duhar, G. & Colin, C. 2006 Dynamics of bubble growth and detachment in a viscous shear flow. Phys. Fluids 18, 077101.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.CrossRefGoogle Scholar
Fayolle, Y., Cockx, A., Gillot, S., Roustan, M. & Heduit, A. 2007 Oxygen transfer prediction in aeration tanks using CFD. Chem. Engng Sci. 62, 7163–7171.CrossRefGoogle Scholar
Figueroa, B. & Legendre, D. 2010 Mass or heat transfer from spheroidal gas bubbles rising through a stationary liquid. Chem. Engng Sci. 65, 6296–6309.Google Scholar
Gaddis, E. S. & Vogelpohl, A. 1986 Bubble formation in quiescent liquids under constant flow conditions. Chem. Engng Sci. 41, 97–105.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, 811–815.CrossRefGoogle Scholar
Gunn, D. J. 1978 Transfer of heat or mass to particles in fixed and fluidized beds. Intl J. Heat Mass Transfer 21, 467–476.Google Scholar
Gunn, D. J. & Souza, J. F. C. 1974 Heat transfer and axial dispersion in packed beds. Chem. Engng Sci. 29, 1363–1371.Google Scholar
Hallez, Y. & Legendre, D. 2011 Interaction between two spherical bubbles rising in a viscous liquid. J. Fluid Mech. 673, 406–431.Google Scholar
Harper, J. F. 1997 Bubbles rising in line: why is the first approximation so bad? J. Fluid Mech. 351, 289–300.Google Scholar
Higbie, R. 1935 The rate of absorption of a pure gas into a still liquid during short periods of exposure. Trans. Am. Inst. Chem. Eng. 31, 365–389.Google Scholar
Ishii, M. & Chawla, T. C.1979 Local drag laws in dispersed two-phase flow. Tech. Rep. Argonne National Lab, IL, USA.Google Scholar
Ishii, M. & Zuber, N. 1979 Drag coefficient and relative velocity in bubbly, droplet or particulate flow. AIChE J. 25 (5), 843–855.CrossRefGoogle Scholar
Kawase, Y., Halard, B. & Moo-Young, M. 1987 Theoretical prediction of volumetric mass transfer coefficients in bubble columns for Newtonian and non-Newtonian fluids. Chem. Engng Sci. 42, 1609–1617.Google Scholar
Kiambi, S. L., Duquenne, A. M., Bascoul, A. & Delmas, H. 2001 Measurements of local interfacial area: application of bi-optical fibre technique. Chem. Engng Sci. 56, 6447–6453.Google Scholar
Kishore, N., Chhabra, R. P. & Eswaran, V. 2008 Bubble swarms in power-law liquids at moderate Reynolds numbers: drag and mass transfer. Chem. Engng Res. Des. 86 (1), 39–53.CrossRefGoogle Scholar
Koynov, A. & Khinast, J. G. 2005 Mass transfer and chemical reactions in bubble swarms with dynamic interfaces. AIChE J. 51 (10), 2786–2800.Google Scholar
Lamont, J. C. & Scott, D. S. 1970 An eddy cell model of mass transfer into the surface of a turbulent liquid. AIChE J. 16, 513–519.Google Scholar
Legendre, D. 2007 On the relation between the drag and the vorticity produced on a clean bubble. Phys. Fluids 19, 018102.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, 133–166.Google Scholar
Legendre, D., Zenit, R. & Velez-Cordero, J. R. 2012 On the deformation of gas bubbles in liquids. Phys. Fluids 24, 043303.Google Scholar
Letzel, H. M., Schouten, J. C., Krishna, R. & van den Bleek, C. M. 1999 Gas holdup and mass transfer in bubble column reactors operated at elevated pressure. Chem. Engng Sci. 54, 2237–2246.Google Scholar
Linek, V., Kordac, M., Fujasova, M. & Moucha, T. 2004 Gas liquid mass transfer coefficient in stirred tanks interpreted through models of idealized eddy structure of turbulence in the bubble vicinity. Chem. Engng Process. 43, 1511–1517.Google Scholar
Littman, H. & Silva, D. E.1970 Gas-particle heat-transfer coefficients in packed beds at low Reynolds numbers. In Fourth International Heat Transfer Conference, Paris-Versailles, France.Google Scholar
Lochiel, A. C. & Calderbank, P. H. 1964 Mass transfer in the continuous phase around axisymmetric bodies of revolution. Chem. Engng Sci. 19, 471–484.CrossRefGoogle Scholar
Magnaudet, J. & Calmet, I. 2006 Turbulent mass transfer through a flat shear-free surface. J. Fluid Mech. 553, 115–185.CrossRefGoogle Scholar
Manasseh, R., Riboux, G. & Risso, F. 2008 Sound generation on bubble coalescence following detachment. Intl J. Multiphase Flow 34, 938–949.CrossRefGoogle Scholar
Martin, M., Montes, F. J. & Galan, M. A. 2007 Bubble coalescence at sieve plates: II. Effect of coalescence on mass transfer. Superficial area versus bubble oscillations. Chem. Engng Sci. 62, 1741–1752.Google Scholar
Martínez-Mercado, J., Palacios-Morales, C. A. & Zenit, R. 2007 Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for $10<\mathit{Re}<500$ . Phys. Fluids 19, 1–13.Google Scholar
Massol, A.2004 Simulations numériques d’écoulements au travers des réseaux fixes de sphères monodisperses et bidisperses, pour des nombres de Reynolds modérés. PhD thesis, INP Toulouse, France.Google Scholar
Mendelson, H. D. 1967 The prediction of bubble terminal velocities from wave theory. AIChE J. I3, 250–253.Google Scholar
Mersmann, A. 1977 Auselegung und massstrabsvergrosserung von blasen und tropfensaulen. Chem. Ing. Tech. 49, 679–691.Google Scholar
Michaelides, E. E. 2006 Particles, Bubbles and Drops: Their Motion, Heat and Mass Transfer. World Scientific.Google Scholar
Miyauchi, T., Kataoka, H. & Kikuchi, T. 1976 Gas film coefficient of mass transfer in low Peclet number region for sphere packed beds. Chem. Engng Sci. 31, 9–13.Google Scholar
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161–176.Google Scholar
Moore, D. W. 1965 The velocity rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749–766.CrossRefGoogle Scholar
Nedeltchev, S., Jordan, U. & Schumpe, A. 2006 Correction of the penetration theory applied to the prediction of kLa in a bubble column with organic liquids. Chem. Engng Technol. 29, 1113–1117.Google Scholar
Nedeltchev, S., Jordan, U. & Schumpe, A. 2007 Correction of the penetration theory based on mass-transfer data from bubble columns operated in the homogeneous regime under high pressure. Chem. Engng Sci. 62, 6263–6273.Google Scholar
Petitti, M., Vanni, M., Marchisio, D. L., Buffo, A. & Podenzani, F. 2013 Simulation of coalescence, break-up and mass transfer in a gas–liquid stirred tank with CQMOM. Chem. Engng J. 228, 1182–1194.CrossRefGoogle Scholar
Ranz, W. E. & Marshall, W. R. 1952 Evaporation from drops. Chem. Engng Prog. 48 (4), 173–180.Google Scholar
Riboux, G.2007 Hydrodynamique d’un essaim de bulles en ascension. PhD thesis, INP Toulouse, France.Google Scholar
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509–539.Google Scholar
Risso, F. & Ellingsen, K. 2002 Velocity fluctuations in a 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. Lond. A 366, 2177–2190.Google ScholarPubMed
Roghair, I.2012 Direct numerical simulations of hydrodynamics and mass transfer in dense bubbly flows. PhD thesis, Eindhoven University of Technology.Google Scholar
Roghair, I., Lau, Y. M., Deen, N. G., Slagter, H. M., Baltussen, M. W., Van Sint Annaland, M. & Kuipers, J. A. M. 2011 On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers. Chem. Engng Sci. 66 (14), 3204–3211.Google Scholar
Roig, V. & Larue de Tounemine, A. 2007 Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction. J. Fluid Mech. 572, 87–110.CrossRefGoogle Scholar
Rowe, P. N. & Claxton, K. T. 1965 Heat and mass transfer from a single sphere to fluid flowing through an array. Trans. Inst. Chem. Engrs-Lond. 43, 321–331.Google Scholar
Rusche, H. & Issa, R. I.2000 The effect of voidage on the drag force on particules, droplets and bubbles in dispersed two-phase flow. Tech. Rep. BRITE-EURAM III program.Google Scholar
Ruzicka, M. C. 2000 On bubbles rising in line. Intl J. Multiphase Flow 26, 1141–1181.Google Scholar
Shimada, N., Tomiyama, A. & Ozaki, T.2007 Numerical prediction of bubbly flow in a bubble column with chemisorption. In ICMF, Leipzig, Germany.Google Scholar
Takemura, F. & Yabe, A. 1998 Gas dissolution process of spherical rising bubbles. Chem. Engng Sci. 53, 2691–2699.Google Scholar
Tomiyama, A., Kataoka, I., Zun, I. & Sakaguchi, T. 1998 Drag coefficients of single bubbles under normal and micro gravity conditions. JSME Intl J. B 41 (2), 472–479.Google Scholar
Turner, G. A. & Otten, L. 1973 Values of thermal (and other) parameters in packed beds. Ind. Eng. Chem. Proc. D. D. 12 (4), 417–424.CrossRefGoogle Scholar
Vejrazka, J., Sechet, P., Vecer, M., Orvalho, S., Ruzicka, M. & Cartellier, A. 2010 Measurement accuracy of a mono-fiber optical probe in a bubbly flow. Intl J. Multiphase Flow 36 (7), 533–548.Google Scholar
Wallis, G. B.1961 Some hydrodynamic aspects of two-phase flow and boiling. In Int. Heat Transfer Conference, Boulder, Colorado USA, Vol. 2, pp. 319–325.Google Scholar
Wallis, G. B. 1969 One Dimensional Two-Phase Flow. McGraw-Hill.Google Scholar
Wijngaarden, L. v. & Kapteijn, C. 1990 Concentration waves in dilute bubble/liquid mixtures. J. Fluid Mech. 212, 111–137.Google Scholar
Winnikow, S. 1967 Letters to the editor. Chem. Engng Sci. 22, 22–477.Google Scholar
Yuan, H. & Prosperetti, A. 1994 On the in-line motion of two spherical bubbles in a viscous fluid. J. Fluid Mech. 278, 325–349.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