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On bubble clustering and energy spectra in pseudo-turbulence

Published online by Cambridge University Press:  24 March 2010

JULIÁN MARTÍNEZ MERCADO ,
DANIEL CHEHATA GÓMEZ ,
DENNIS VAN GILS ,
CHAO SUN  and
DETLEF LOHSE
JULIÁN MARTÍNEZ MERCADO*
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
DANIEL CHEHATA GÓMEZ
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
DENNIS VAN GILS
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
CHAO SUN
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
DETLEF LOHSE
Affiliation:
Physics of Fluids Group, Department of Science and Technology, J.M. Burgers Centre for Fluid Dynamics and IMPACT Institute, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
†Email address for correspondence: j.martinezmercado@tnw.utwente.nl
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Abstract

Three-dimensional particle tracking velocimetry (PTV) and phase-sensitive constant temperature anemometry in pseudo-turbulence – i.e. flow solely driven by rising bubbles – were performed to investigate bubble clustering and to obtain the mean bubble rise velocity, distributions of bubble velocities and energy spectra at dilute gas concentrations (α ≤ 2.2 %). To characterize the clustering the pair correlation function G(r, θ) was calculated. The deformable bubbles with equivalent bubble diameter db = 4–5 mm were found to cluster within a radial distance of a few bubble radii with a preferred vertical orientation. This vertical alignment was present at both small and large scales. For small distances also some horizontal clustering was found. The large number of data points and the non-intrusiveness of PTV allowed well-converged probability density functions (PDFs) of the bubble velocity to be obtained. The PDFs had a non-Gaussian form for all velocity components and intermittency effects could be observed. The energy spectrum of the liquid velocity fluctuations decayed with a power law of −3.2, different from the ≈ −5/3 found for homogeneous isotropic turbulence, but close to the prediction −3 by Lance & Bataille (J. Fluid Mech., vol. 222, 1991, p. 95) for pseudo-turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 650 , 10 May 2010 , pp. 287 - 306
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503–537.CrossRefGoogle Scholar
Ayyalasomayajula, S., Gylfason, A., Collins, L. R., Bodenschatz, E. & Warhaft, Z. 2006 Lagrangian measurements of inertial particle accelerations in grid generated wind tunnel turbulence. Phys. Rev. Lett. 97, 144507.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1967 An Introduction of Fluid Dynamics. Cambridge University Press.Google Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245–268.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Celani, A., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 a Accelerations statistics of heavy particles in turbulence. J. Fluid Mech. 550, 349–358.CrossRefGoogle Scholar
Bec, J., Biferale, L., Boffetta, G., Cencini, M., Musacchio, S. & Toschi, F. 2006 b Lyapunov exponents of heavy particles in turbulence. Phys. Fluids 18, 091702.CrossRefGoogle Scholar
Berg, J., Lüthi, B., Mann, J. & Ott, S. 2006 Backwards and forwards relative dispersion in turbulent flow: an experimental investigation. Phys. Rev. E 74, 016304.CrossRefGoogle ScholarPubMed
van den Berg, T. H. 2006 The effect of bubbles on developed turbulence. PhD Thesis, University of Twente, The Netherlands.Google Scholar
Bourgoin, M., Ouellette, N. T., Xu, H., Berg, T. & Bodenschatz, E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835–838.CrossRefGoogle ScholarPubMed
Brenner, M. P. 1999 Screening mechanisms in sedimentation. Phys. Fluids 11, 754–772.CrossRefGoogle Scholar
Bruun, H. H. 1995 Hot Wire Anemometry: Principles and Signal Analysis. Oxford University Press.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002 a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 17–52.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2002 b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 53–84.CrossRefGoogle Scholar
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77–118.CrossRefGoogle Scholar
Calzavarini, E., van der Berg, T. H., Toschi, F. & Lohse, D. 2008 a Quantifying microbubble clustering in turbulent flow from single-point measurements. Phys. Fluids 20, 040702.CrossRefGoogle Scholar
Calzavarini, E., Kerscher, M., Lohse, D. & Toschi, F. 2008 b Dimensionality and morphology of particle and bubble clusters in turbulent flow. J. Fluid Mech. 607, 13–24.CrossRefGoogle Scholar
Cartellier, A. & Barrau, E. 2001 Monofiber optical probes for gas detection and gas velocity measurements: conical probes. Intl J. Multiphase Flows 24, 1265–1294.CrossRefGoogle Scholar
Cartellier, A. & Rivière, N. 2001 Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particle Reynolds number. Phys. Fluids 13, 8.CrossRefGoogle Scholar
Climent, E. & Magnaudet, J. 1999 Large-scale simulations of bubble-induced convection in a liquid layer. Phys. Rev. Lett. 82 (24), 4827–4830.CrossRefGoogle Scholar
Cui, Z. & Fan, L. S. 2004 Turbulence energy distributions in bubbling gas–liquid and gas–liquid–solid flow systems. Chem. Engng Sci. 59, 1755–1766.CrossRefGoogle Scholar
Daya, Z. A. & Ecke, R. E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87, 184501.CrossRefGoogle Scholar
Deckwer, B. D. 1992 Bubble Column Reactors, 1st edn. Wiley.Google Scholar
Ervin, E. A. & Tryggvason, G. 1997 The rise of bubbles in a vertical shear flow. J. Fluids Engng 119, 443–449.CrossRefGoogle Scholar
Esmaeeli, A. & Tryggvason, G. 2005 A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number. Phys. Fluids 17, 093303.CrossRefGoogle Scholar
Guala, M., Liberzon, A., Lüthi, B., Tsinober, A. & Kinzelbach, W. 2005 On the evolution of material lines and vorticity in homogeneous turbulence. Phys. Rev. E 533, 339–359.Google Scholar
Hoyer, K., Holzner, M., Luethi, B., Guala, M., Liberzon, A. & Kinzelbach, W. 2005 three-dimensional scanning particle tracking velocimetry. Exps. Fluids 39, 923–934.CrossRefGoogle Scholar
Juliá, J. E., Harteveld, W. K., Mudde, R. F. & van der Akker, H. E. A. 2005 On the accuracy of the void fraction measurements using optical probes in bubbly flows. Rev. Sci. Instrum. 76, 035103.CrossRefGoogle Scholar
Kok, J. B. W. 1993 Dynamics of a pair of bubbles moving through liquid. Part 1. Theory. Eur. J. Mech. B 12, 515–540.Google Scholar
Lance, M. & Bataille, J. 1991 Turbulence in the liquid phase of a uniform bubbly water–air flow. J. Fluid Mech. 222, 95–118.CrossRefGoogle Scholar
Luther, S., Rensen, J., van den Berg, T. H. & Lohse, D. 2005 Data analysis for hot-film anemometry in turbulent bubbly flow. Exp. Therm. Fluid Sci. 29, 821.CrossRefGoogle Scholar
Mazzitelli, I. M. & Lohse, D. 2009 Evolution of energy in flow driven by rising bubbles. Phys. Rev. E 79 (6), 066317.CrossRefGoogle ScholarPubMed
Mazzitelli, I. M., Lohse, D. & Toschi, F. 2003 The effect of microbubbles on developed turbulence. Phys. Fluids 15, L5–L8.CrossRefGoogle Scholar
Martínez-Mercado, J., Palacios-Morales, C. & Zenit, R. 2007 Measurements of pseudoturbulence intensity in monodispersed bubbly liquids for 10 < Re < 500. Phys. Fluids 19, 103302.CrossRefGoogle Scholar
Mordant, N., Leveque, E. & Pinton, J. F. 2004 Experimental and numerical study of the Lagrangian dynamics of high Reynolds turbulence. New J. Phys. 6 (116), 1–44.CrossRefGoogle Scholar
Mudde, R. F., Groen, J. S. & van der Akker, H. E. A. 1997 Liquid velocity field in a bubble column: LDA experiments. Chem. Engng Sci. 52, 4217–4224.CrossRefGoogle Scholar
Qiu, X. L. & Tong, P. 2001 Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304.CrossRefGoogle ScholarPubMed
Rensen, J., Luther, S. & Lohse, D. 2005 The effects of bubbles on developed turbulence. J. Fluid Mech. 538, 153–187.CrossRefGoogle Scholar
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. (in press).CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
Roig, V. & de Tournemine, L. 2007 Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction. J. Fluid Mech. 572, 87–110.CrossRefGoogle Scholar
Salazar, J. P. L. C., de Jong, J., Cao, L., Woodward, S. H., Meng, H. & Collins, L. R. 2008 Experimental and numerical investigation of inertial particle clustering in isotropic turbulence. J. Fluid Mech. 600, 245–256.CrossRefGoogle Scholar
Sangani, A. S. & Didwana, A. K. 1993 Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 250, 307–337.CrossRefGoogle Scholar
Saw, E. W., Shaw, R. A., Ayyalasomayajula, S., Chuang, P. Y. & Gylfason, A. 2008 Inertial clustering of particles in high-Reynolds-number turbulence. Phys. Rev. Lett. 100, 214501.CrossRefGoogle ScholarPubMed
Smereka, A. S. 1993 On the motion of bubbles in a peridic box. J. Fluid Mech. 254, 79–112.CrossRefGoogle Scholar
Sugiyama, K., Takagi, S. & Matsumoto, Y. 2001 Multi-scale analysis of bubbly flows. Comput. Methods Appl. Mech. Engng 191 (6–7), 689–704.CrossRefGoogle Scholar
Sun, C. & Xia, K. Q. 2005 Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E 72, 067302.CrossRefGoogle ScholarPubMed
Takagi, S., Ogasawara, T. & Matsumoto, Y. 2008 The effects of surfactant on the multiscale structure of bubbly flows. Phil. Trans. R. Soc. Lond. A 366 (1873), 2117–2129.Google ScholarPubMed
Tomiyama, A., Tamai, H., Zun, I. & Hosokawa, S. 2002 Transverse migration of single bubbles in simple shear flows. Chem. Engng Sci. 57 (11), 1849–1858.CrossRefGoogle Scholar
Toschi, F. & Bodenschatz, E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375–404.CrossRefGoogle Scholar
Volk, R., Calzavarini, E., Verhille, G., Lohse, D., Mordant, N., Pinton, J. F. & Toschi, F. 2008 Acceleration of heavy and light particles in turbulence: comparison between experiments and direct numerical simulations. Physica D 237 (14–17), 2084–2089.CrossRefGoogle Scholar
van Wijngaarden, L. 1993 The mean rise velocity of pairwise-interacting bubbles in liquid. J. Fluid Mech. 251, 55–78.CrossRefGoogle Scholar
van Wijngaarden, L. 2005 Bubble velocities induced by trailing vortices behind neighbours. J. Fluid Mech. 541, 203–229.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, 307–342.CrossRefGoogle Scholar