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Bubbling reduces intermittency in turbulent thermal convection

Published online by Cambridge University Press:  17 March 2014

Rajaram Lakkaraju*
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands Department of Mechanical Engineering, Birla Institute of Technology and Science-Pilani, K. K. Birla Goa Campus, NH 17B, Zuari Nagar, Goa-403726, India
Federico Toschi
Affiliation:
Department of Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy
Detlef Lohse
Affiliation:
Physics of Fluids Group, Faculty of Science and Technology, J.M. Burgers Center for Fluid Dynamics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
*
Email address for correspondence: rajaram.lv@gmail.com

Abstract

Intermittency effects are numerically studied in turbulent bubbling Rayleigh–Bénard (RB) flow and compared to the standard RB case. The vapour bubbles are modelled with a Euler–Lagrangian scheme and are two-way coupled to the flow and temperature fields, both mechanically and thermally. To quantify the degree of intermittency we use probability density functions, structure functions, extended self-similarity (ESS) and generalized extended self-similarity (GESS) for both temperature and velocity differences. For the standard RB case we reproduce scaling very close to the Obukhov–Corrsin values common for a passive scalar and the corresponding relatively strong intermittency for the temperature fluctuations, which are known to originate from sharp temperature fronts. These sharp fronts are smoothed by the vapour bubbles owing to their heat capacity, leading to much less intermittency in the temperature but also in the velocity field in bubbling thermal convection.

Type
Papers
Copyright
© 2014 Cambridge University Press 

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References

Ahlers, G., Brown, E., Araujo, F. F., Funfschilling, D., Grossmann, S. & Lohse, D. 2006 Non-Oberbeck–Boussinesq effects in strongly turbulent Rayleigh–Bénard convection. J. Fluid Mech. 569, 409.Google Scholar
Ahlers, G., Grossmann, S. & Lohse, D. 2009 Heat transfer and large scale dynamics in turbulent Rayleigh–Bénard convection. Rev. Mod. Phys. 81, 503.Google Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63.Google Scholar
Babiano, A., Dubrulle, B. & Frick, P. 1995 Scaling properties of numerical two-dimensional turbulence. Phys. Rev. 52, 3719.Google Scholar
Belin, F., Tabeling, P. & Willaime, H. 1996 Exponents of the structure functions in a low temperature helium experiment. Physica D 93, 52.Google Scholar
Benzi, R., Biferale, L., Ciliberto, S., Struglia, M. V. & Tripiccione, R. 1996 Generalized scaling in fully developed turbulence. Physica D 96, 162.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Trippiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E (R) 48, 29.Google Scholar
Biferale, L., Perlekar, P., Sbragaglia, M. & Toschi, F. 2012 Convection in multiphase fluid flows using Lattice-Boltzmann methods. Phys. Rev. Lett. 108, 104502.Google Scholar
Bolgiano, R. 1959 Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res. 64, 2226.Google Scholar
Briscolini, M., Santangelo, P., Succi, S. & Benzi, R. 1994 Extended self-similarity in the numerical simulation of three-dimensional homogeneous flows. Phys. Rev. E (R) 50, 1745.Google Scholar
Burnishev, Y. & Steinberg, V. 2012 Statistics and scaling properties of temperature field in symmetrical non-Oberbeck–Boussinesq turbulent convection. Phys. Fluids 24, 045102.Google Scholar
Calzavarini, E., Toschi, F. & Tripiccione, R. 2002 Evidences of Bolgiano–Obukhov scaling in three-dimensional Rayleigh–Bénard convection. Phys. Rev. E 66, 016304.Google Scholar
Castaing, B., Gunaratne, G., Heslot, F., Kadanoff, L., Libchaber, A., Thomae, S., Wu, X.-Z., Zaleski, S. & Zanetti, G. 1989 Scaling of hard thermal turbulence in Rayleigh–Bénard convection. J. Fluid Mech. 204, 1.Google Scholar
Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. 2000 Universality and saturation of intermittency in passive scalar turbulence. Phys. Rev. Lett. 84, 2385.CrossRefGoogle ScholarPubMed
Chen, S. & Kraichnan, R. H. 1998 Simulations of a randomly advected passive scalar field. Phys. Fluids 10, 2867.CrossRefGoogle Scholar
Ching, E. S. C. 2000 Intermittency of temperature field in turbulent convection. Phys. Rev. E (R) 61, 33.Google Scholar
Ching, E. S. C., Cohen, Y., Gilbert, T. & Procaccia, I. 2003 Active and passive fields in turbulent transport: the role of statistically preserved structures. Phys. Rev. E 67, 016304.Google Scholar
Corrsin, S. 1951 On the spectrum of isotropic temperature fluctuations in isotropic turbulence. J. Appl. Phys. 22, 469.Google Scholar
Daya, Z. A. & Ecke, R. E. 2001 Does turbulent convection feel the shape of the container?. Phys. Rev. Lett. 87, 184501.Google Scholar
Dhir, V. K. 1998 Boiling heat transfer. Annu. Rev. Fluid Mech. 30, 365.Google Scholar
Frisch, U. 1995 Turbulence, The Legacy of A. N. Kolmogorov. Cambridge University Press.Google Scholar
Gollub, J. P., Clarke, J., Gharib, M., Lane, B. & Mesquita, O. N. 1991 Fluctuations and transport in a stirred fluid with a mean gradient. Phys. Rev. Lett. 67, 3507.Google Scholar
Gotoh, T., Fukayama, D. & Nakano, T. 2002 Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation. Phys. Fluids 14, 1065.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Reeh, A. 1997a Application of extended self-similarity in turbulence. Phys. Rev. E 56, 5473.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Reeh, A. 1997b Different intermittency for longitudinal and transversal turbulent fluctuations. Phys. Fluids 9, 3817.CrossRefGoogle Scholar
Holzer, M. & Pumir, A. 1993 Simple models of non-Gaussian statistics for a turbulently advected passive scalar. Phys. Rev. E 47, 202.Google Scholar
Holzer, M. & Siggia, E. D. 1994 Turbulent mixing of a passive scalar. Phys. Fluids 6, 1820.CrossRefGoogle Scholar
Kunnen, R. P. J., Clercx, H. J. H., Geurts, B. J., van Bokhoven, L. J. A., Akkermans, R. A. D. & Verzicco, R. 2008 Numerical and experimental investigation of structure-function scaling in turbulent Rayleigh–Bénard convection. Phys. Rev. E 77, 016302.CrossRefGoogle ScholarPubMed
Lakkaraju, R., Schmidt, L. E., Oresta, P., Toschi, F., Verzicco, R., Lohse, D. & Prosperetti, A. 2011 Effect of vapor bubbles on velocity fluctuations and dissipation rates in bubbly Rayleigh–Bénard convection. Phys. Rev. E 84, 036312.Google Scholar
Lakkaraju, R., Stevens, R. J. A. M., Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2013 Heat transport in bubbling turbulent convection. Proc. Natl Acad. Sci. USA 110 (23), 9237.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Lohse, D. & Xia, K. Q. 2010 Small scale properties of turbulent Rayleigh–Bénard convection. Annu. Rev. Fluid Mech. 42, 335.Google Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883.Google Scholar
Moisy, F., Willaime, H., Anderson, J. & Tabeling, P. 2001 Passive scalar intermittency in low temperature helium flows. Phys. Rev. Lett. 86, 4827.Google Scholar
Mydlarski, L., Pumir, A., Shraiman, B. I., Siggia, E. D. & Warhaft, Z. 1998 Structures and multipoint correlaters for turbulent advection: Predictions and experiments. Phys. Rev. Lett. 81, 4373.Google Scholar
Obukhov, A. M. 1949 Structures of temperature field in a turbulent flow. Izv. Akad. Nauk SSSR Geogr. Geofiz 13, 58.Google Scholar
Obukhov, A. M. 1959 Effect of Archimedean forces on the structure of the temperature field in a turbulent flow. Dokl. Akad. Nauk SSSR 125, 1246.Google Scholar
Oresta, P., Verzicco, R., Lohse, D. & Prosperetti, A. 2009 Heat transfer mechanisms in bubbly Rayleigh–Bénard convection. Phys. Rev. E 80, 026304.Google Scholar
Prosperetti, A. & Tryggvason, G.(Eds.) 2007 Computational Methods For Multiphase Flow. Cambridge University Press.Google Scholar
Pumir, A. 1994 A numerical study of the mixing of a passive scalar in three dimensions in the presence of a mean gradient. Phys. Fluids 6, 2118.Google Scholar
Pumir, A. 1998 Structure of the three-point correlation function of a passive scalar in the presence of a mean gradient. Phys. Rev. E 57, 2914.Google Scholar
Pumir, A., Shraiman, B. & Siggia, E. D. 1991 Exponential tails and random advection. Phys. Rev. Lett. 66, 2984.Google Scholar
Ruiz-Chavarria, G., Baudet, C. & Ciliberto, S. 1996 Scaling laws and dissipation scale of a passive scalar in fully developed turbulence. Physica D 99, 369.Google Scholar
Schmidt, L. E., Oresta, P., Toschi, F., Verzicco, R., Lohse, D. & Prosperetti, A. 2011 Modification of turbulence in Rayleigh–Bénard convection by phase change. New J. Phys. 13, 025002.Google Scholar
She, Z. S. & Leveque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336.Google Scholar
Shraiman, B. I. & Siggia, E. D. 1990 Transport in high Rayleigh number convection. Phys. Rev. A 42, 3650.Google Scholar
Shraiman, B. I. & Siggia, E. D. 2000 Scalar turbulence. Nature 405, 639.Google Scholar
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137.Google Scholar
Sreenivasan, K. R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434, 165.Google Scholar
Sreenivasan, K. R. & Antonia, R. A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29, 435.Google Scholar
Staicu, A. & van de Water, W. 2003 Small scale velocity jumps in shear turbulence. Phys. Rev. Lett. 90, 094501.Google Scholar
Sun, C., Zhou, Q. & Xia, K. Q. 2006 Cascades of velocity and temperature fluctuations in buoyancy-driven thermal turbulence. Phys. Rev. Lett. 97, 144504.Google Scholar
Verzicco, R. & Camussi, R. 2003 Numerical experiments on strongly turbulent thermal convection in a slender cylindrical cell. J. Fluid Mech. 477, 19.CrossRefGoogle Scholar
Warhaft, Z. 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203.Google Scholar
Watanabe, T. & Gotoh, T. 2004 Statistics of a passive scalar in homogeneous turbulence. New J. Phys. 6, 40.Google Scholar