Skip to main content
×
Home

On bubble clustering and energy spectra in pseudo-turbulence

  • JULIÁN MARTÍNEZ MERCADO (a1), DANIEL CHEHATA GÓMEZ (a1), DENNIS VAN GILS (a1), CHAO SUN (a1) and DETLEF LOHSE (a1)...
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.

Copyright
Corresponding author
Email address for correspondence: j.martinezmercado@tnw.utwente.nl
References
Hide All
Ahlers G., Grossmann S. & Lohse D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503537.
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.
Batchelor G. K. 1967 An Introduction of Fluid Dynamics. Cambridge University Press.
Batchelor G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245268.
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, 349358.
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.
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.
van den Berg T. H. 2006 The effect of bubbles on developed turbulence. PhD Thesis, University of Twente, The Netherlands.
Bourgoin M., Ouellette N. T., Xu H., Berg T. & Bodenschatz E. 2006 The role of pair dispersion in turbulent flow. Science 311, 835838.
Brenner M. P. 1999 Screening mechanisms in sedimentation. Phys. Fluids 11, 754772.
Bruun H. H. 1995 Hot Wire Anemometry: Principles and Signal Analysis. Oxford University Press.
Bunner B. & Tryggvason G. 2002 a Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech. 466, 1752.
Bunner B. & Tryggvason G. 2002 b Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech. 466, 5384.
Bunner B. & Tryggvason G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77118.
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.
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, 1324.
Cartellier A. & Barrau E. 2001 Monofiber optical probes for gas detection and gas velocity measurements: conical probes. Intl J. Multiphase Flows 24, 12651294.
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.
Climent E. & Magnaudet J. 1999 Large-scale simulations of bubble-induced convection in a liquid layer. Phys. Rev. Lett. 82 (24), 48274830.
Cui Z. & Fan L. S. 2004 Turbulence energy distributions in bubbling gas–liquid and gas–liquid–solid flow systems. Chem. Engng Sci. 59, 17551766.
Daya Z. A. & Ecke R. E. 2001 Does turbulent convection feel the shape of the container? Phys. Rev. Lett. 87, 184501.
Deckwer B. D. 1992 Bubble Column Reactors, 1st edn. Wiley.
Ervin E. A. & Tryggvason G. 1997 The rise of bubbles in a vertical shear flow. J. Fluids Engng 119, 443449.
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.
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, 339359.
Hoyer K., Holzner M., Luethi B., Guala M., Liberzon A. & Kinzelbach W. 2005 three-dimensional scanning particle tracking velocimetry. Exps. Fluids 39, 923934.
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.
Kok J. B. W. 1993 Dynamics of a pair of bubbles moving through liquid. Part 1. Theory. Eur. J. Mech. B 12, 515540.
Lance M. & Bataille J. 1991 Turbulence in the liquid phase of a uniform bubbly water–air flow. J. Fluid Mech. 222, 95118.
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.
Mazzitelli I. M. & Lohse D. 2009 Evolution of energy in flow driven by rising bubbles. Phys. Rev. E 79 (6), 066317.
Mazzitelli I. M., Lohse D. & Toschi F. 2003 The effect of microbubbles on developed turbulence. Phys. Fluids 15, L5L8.
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.
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), 144.
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, 42174224.
Qiu X. L. & Tong P. 2001 Large-scale velocity structures in turbulent thermal convection. Phys. Rev. E 64, 036304.
Rensen J., Luther S. & Lohse D. 2005 The effects of bubbles on developed turbulence. J. Fluid Mech. 538, 153187.
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).
Risso F. & Ellingsen K. 2002 Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles. J. Fluid Mech. 453, 395410.
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, 21772190.
Roig V. & de Tournemine L. 2007 Measurement of interstitial velocity of homogeneous bubbly flows at low to moderate void fraction. J. Fluid Mech. 572, 87110.
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, 245256.
Sangani A. S. & Didwana A. K. 1993 Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 250, 307337.
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.
Smereka A. S. 1993 On the motion of bubbles in a peridic box. J. Fluid Mech. 254, 79112.
Sugiyama K., Takagi S. & Matsumoto Y. 2001 Multi-scale analysis of bubbly flows. Comput. Methods Appl. Mech. Engng 191 (6–7), 689704.
Sun C. & Xia K. Q. 2005 Scaling of the Reynolds number in turbulent thermal convection. Phys. Rev. E 72, 067302.
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), 21172129.
Tomiyama A., Tamai H., Zun I. & Hosokawa S. 2002 Transverse migration of single bubbles in simple shear flows. Chem. Engng Sci. 57 (11), 18491858.
Toschi F. & Bodenschatz E. 2009 Lagrangian properties of particles in turbulence. Annu. Rev. Fluid Mech. 41, 375404.
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), 20842089.
van Wijngaarden L. 1993 The mean rise velocity of pairwise-interacting bubbles in liquid. J. Fluid Mech. 251, 5578.
van Wijngaarden L. 2005 Bubble velocities induced by trailing vortices behind neighbours. J. Fluid Mech. 541, 203229.
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.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 125 *
Loading metrics...

Abstract views

Total abstract views: 172 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd November 2017. This data will be updated every 24 hours.