Skip to main content
×
Home

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

  • MURALI R. CHOLEMARI (a1) and JAYWANT H. ARAKERI (a2)
Abstract

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter=9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 108. Under these conditions the convection is turbulent, and the time-averaged velocity at any point is ‘zero’. The Reynolds number based on the Taylor microscale, Reλ, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6–7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as Ra1/2Sc1/2, and the Reynolds number would scale as Ra1/2Sc−1/2. The velocity and the flux measurements appear to be consistent with the Ra1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are much higher compared to what would be obtained in Rayleigh–Bénard (R–B) convection for similar density differences.

Copyright
Corresponding author
Email address for correspondence: jaywant@mecheng.iisc.ernet.in
References
Hide All
Amati G., Koal K., Massaioli F., Sreenivasan K. R. & Verzicco R. 2005 Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number. Phys. Fluids 17 (121701), 14.
Arakeri J. H., Avila F. E., Dada J. M. & Tovar R. O. 2000 Convection in a long vertical tube due to unstable stratification-a new type of turbulent flow? Curr. Sci. 79 (6), 859866.
Arakeri J. H. & Cholemari M. R. 2002 Fully developed buoyancy driven turbulence in a tube. In Proc. Ninth Asian Cong. Fluid Mech. (ed. Shirani E. & Pishevar A. R.). Isfahan University of Technology, Iran.
Aronson D. Johansson A. V. & Löfdahl L. 1997 Shear free turbulence near a wall. J. Fluid Mech. 338, 363385.
Batchelor G. K., Canuto V. M. & Chasnov J. R. 1991 Homogeneous buoyancy-generated turbulence. J. Fluid Mech. 235, 349378.
Calzavarini E., Lohse D., Toschi F. & Tripiccione R. 2005 Rayleigh and prandtl number scaling in the bulk of rayleigh-bnard turbulence. Phys. Fluids 17 (055107), 17.
Chandrasekhar S. 1981 Hydrodynamic and Hydromagnetic Stability. Dover Publications.
Cholemari M. R. 2004 Buoyancy driven turbulence in a vertical pipe. PhD thesis. Department of mechanical engineering, Indian Institute of Science, Bangalore, Karnataka, India.
Cholemari M. R. 2007 Modelling and correction of peak-locking in digital PIV. Exp. Fluids 42 (6), 913922.
Cholemari M. R. & Arakeri J. H. 2005 Experiments and a model of turbulent exchange flow in a vertical pipe. Int. J. Heat Mass Transfer 48, 44674473.
Cholemari M. R. & Arakeri J. H. 2006 A model relating eulerian spatial and temporal velocity correlations. J. Fluid Mech. 551, 1929.
Christensen K. T. 2004 On the influence of peaklocking errors on turbulence statistics compared from PIV ensembles. Exp. Fluids 36 (3), 484497.
Constantin P. & Doering C. R. 1999 Infinite prandtl number convection. J. Stat. Phys. 94 (1–2), 159172.
Debacq M., Fanguet V., Hulin J.-P., Salin D. & Perrin B. 2001 Self-similar concentration profiles in buoyant mixing of miscible fluids in a vertical tube. Phys. Fluids 13, 3097.
Debacq M., Hulin J.-P. & Salin D. 2003 Buoyant mixing of miscible fluids of varying viscosities in vertical tubes. Phys. Fluids 15 (12), 38463855.
Doering C. R., Otto F. & Reznikoff M. G. 2006 Bounds on vertical heat transport for infinite-Prandtl-number Rayleigh–Benard convection. J. Fluid Mech. 560, 229241.
Epstein M. 1988 Buoyancy driven exchange flow through small openings in horizontal partitions. J. Heat Transfer 110, 885893.
Fitzjarrald D. E. 1976 An experimental study of turbulent convection in air. J. Fluid Mech. 73 (pt. 4), 693719.
Gardener G. C. 1977 Motion of miscible and immiscible fluids in closed horizontal and vertical ducts. Int. J. Multiphase Flow 3, 305318.
Gibert M., Pabiou H., Chilla F. & Castaing B. 2006 High-Rayleigh-number convection in a vertical channel. Phys. Rev. Lett. 96, 084501-1084501-4.
Grossmann S. & Lohse D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.
Hunt J. C. R. & Graham J. M. R. 1978 Free stream turbulence near plane boundaries. J. Fluid Mech. 84, 209235.
Hyun B. S., Balachander R., Yu K. & Patel V. C. 2003 Assessment of PIV to measure mean velocity and turbulence in open channel flow. Exp. Fluids 35, 262267.
Keane R. D. & Adrian R. J. 1992 Theory of cross-correlation analysis of PIV images. Appl. Sci. Res. 49, 191215.
Kim J. Moin P. & Moser R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kraichnan R. H. 1962 Turbulent thermal convection at arbitrary prandtl number. Phys. Fluids 5 (11), 13741389.
Lecordier B., Demare D., Vervisch L. M. J., Réveillon J. & Trinité M. 2001 Estimation of the accuracy of PIV treatments for turbulent flow studies by direct numerical simulation of multi-phase flow. Meas. Sci. Technol. 12 (13821391).
Lohse D. & Toschi F. 2003 Ultimate state of thermal convection. Phys. Rev. Lett. 90 (3), 034502.
Monin A. S. & Yaglom A. M. 1971 Statistical Fluid Mechanics: Mechanics of Turbulence (vol. 1). The MIT press.
Niemela J. J., Skrbek L., Sreenivasan K. R. & Donnelly R. J. 2000 Turbulent convection at high Rayleigh numbers. Nature 404, 837841.
Niemela J. J., Skrbek L., Sreenivasan K. R. & Donnelly R. J. 2001 The wind in confined thermal convection. J. Fluid Mech. 449, 169178.
Niemela J. J. & Sreenivasan K. R. 2003 Confined turbulent convection. J. Fluid Mech. 481, 355384.
Niemela J. J. & Sreenivasan K. R. 2006 Turbulent convection at high Rayleigh numbers and aspect ratio 4. J. Fluid Mech. 557, 411422.
Nikolaenko A., Brown E., Funfschilling D. & Ahlers G. 2005 Heat transport by turbulent Rayleigh-Bénard convection in cylindrical cells with aspect ratio one and less. J. Fluid Mech. 523, 251260.
Noullez A., Wallace G., Lempert W., Miles R. B. & Frisch U. 1997 Transverse velocity increments in turbulent flow using the relief technique. J. Fluid Mech. 339, 287307.
Perot B. & Moin P. 1995 Shear free turbulent boundary layers. Part 1. Physical insights to near wall turbulence. J. Fluid Mech. 295, 199227.
Pope Stephen B. 2000 Turbulent Flows. Cambridge University Press.
Prasad A. K. 2000 Particle image velocimetry. Curr. Sci. 79, 5160.
Raffel M., Willert C. E. & Kompenhans J. 1998 Particle Image Velocimetry. Springer.
Roche P.-E., Castaing B., Chabaud B. & Hébral B. 2001 Observation of the 1/2 power law in Rayleigh–Bénard convection. Phys. Rev. E 63, 045303.
Saarenrinne P. & Piirto M. 2000 Turbulent kinetic energy dissipation rate estimation from PIV velocity vector fields. Exp. Fluids (suppl.) 29 (7), S300S307.
Saarenrinne P., Piirto M. & Eloranta H. 2001 Experiences of turbulence measurement with PIV. Meas. Sci. Technol. 12, 19041910.
Siggia E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137168.
Stringano G. & Verzicco R. 2006 Mean flow structure in thermal convection in a cylindrical cell of aspect ratio one half. J. Fluid Mech. 548, 116.
Tennekes H. & Lumley J. L. 1972 A First Course in Turbulence. The MIT press.
Theerthan S. A. & Arakeri J. H. 1998 A model for near-wall dynamics in turbulent Rayleigh–Bénard convection. J. Fluid Mech. 373, 221254.
Theerthan S. A. & Arakeri J. H. 2000 Planform structure and heat transfer in turbulent free convection over horizontal surfaces. Phys. Fluids 12 (4), 884894.
Thomas N. H. & Hancock P. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82, 481496.
Uzkan T. & Reynolds W. C. 1967 A shear-free turbulent boundary layer. J. Fluid Mech. 28, 803821.
Verzicco R. & Sreenivasan K. R. 2008 Confined thermal convection in a ‘cigar box’ cylindrical cell. Private communication.
Westerweel J. 1997 Fundamentals of digital particle image velocimetry. Meas. Sci. Technol. 8, 13791392.
Westerweel J., Dabiri D. & Gharib M. 1997 the effect of a descrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Exp. Fluids 23, 2028.
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: 47 *
Loading metrics...

Abstract views

Total abstract views: 169 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 22nd November 2017. This data will be updated every 24 hours.