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


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.

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G. Amati , K. Koal , F. Massaioli , K. R. Sreenivasan & R. Verzicco 2005 Turbulent thermal convection at high Rayleigh numbers for a Boussinesq fluid of constant Prandtl number. Phys. Fluids 17 (121701), 14.

E. Calzavarini , D. Lohse , F. Toschi & R. Tripiccione 2005 Rayleigh and prandtl number scaling in the bulk of rayleigh-bnard turbulence. Phys. Fluids 17 (055107), 17.

M. R. Cholemari 2007 Modelling and correction of peak-locking in digital PIV. Exp. Fluids 42 (6), 913922.

M. R. Cholemari & J. H. Arakeri 2005 Experiments and a model of turbulent exchange flow in a vertical pipe. Int. J. Heat Mass Transfer 48, 44674473.

K. T. Christensen 2004 On the influence of peaklocking errors on turbulence statistics compared from PIV ensembles. Exp. Fluids 36 (3), 484497.

P. Constantin & C. R. Doering 1999 Infinite prandtl number convection. J. Stat. Phys. 94 (1–2), 159172.

M. Debacq , V. Fanguet , J.-P. Hulin , D. Salin & B. Perrin 2001 Self-similar concentration profiles in buoyant mixing of miscible fluids in a vertical tube. Phys. Fluids 13, 3097.

M. Debacq , J.-P. Hulin & D. Salin 2003 Buoyant mixing of miscible fluids of varying viscosities in vertical tubes. Phys. Fluids 15 (12), 38463855.

M. Epstein 1988 Buoyancy driven exchange flow through small openings in horizontal partitions. J. Heat Transfer 110, 885893.

G. C. Gardener 1977 Motion of miscible and immiscible fluids in closed horizontal and vertical ducts. Int. J. Multiphase Flow 3, 305318.

M. Gibert , H. Pabiou , F. Chilla & B. Castaing 2006 High-Rayleigh-number convection in a vertical channel. Phys. Rev. Lett. 96, 084501-1084501-4.

B. S. Hyun , R. Balachander , K. Yu & V. C. Patel 2003 Assessment of PIV to measure mean velocity and turbulence in open channel flow. Exp. Fluids 35, 262267.

R. D. Keane & R. J. Adrian 1992 Theory of cross-correlation analysis of PIV images. Appl. Sci. Res. 49, 191215.

R. H. Kraichnan 1962 Turbulent thermal convection at arbitrary prandtl number. Phys. Fluids 5 (11), 13741389.

B. Lecordier , D. Demare , L. M. J. Vervisch , J. Réveillon & M. Trinité 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).

D. Lohse & F. Toschi 2003 Ultimate state of thermal convection. Phys. Rev. Lett. 90 (3), 034502.

J. J. Niemela , L. Skrbek , K. R. Sreenivasan & R. J. Donnelly 2000 Turbulent convection at high Rayleigh numbers. Nature 404, 837841.

M. Raffel , C. E. Willert & J. Kompenhans 1998 Particle Image Velocimetry. Springer.

P. Saarenrinne & M. Piirto 2000 Turbulent kinetic energy dissipation rate estimation from PIV velocity vector fields. Exp. Fluids (suppl.) 29 (7), S300S307.

P. Saarenrinne , M. Piirto & H. Eloranta 2001 Experiences of turbulence measurement with PIV. Meas. Sci. Technol. 12, 19041910.

E. D. Siggia 1994 High Rayleigh number convection. Annu. Rev. Fluid Mech. 26, 137168.

S. A. Theerthan & J. H. Arakeri 2000 Planform structure and heat transfer in turbulent free convection over horizontal surfaces. Phys. Fluids 12 (4), 884894.

J. Westerweel 1997 Fundamentals of digital particle image velocimetry. Meas. Sci. Technol. 8, 13791392.

J. Westerweel , D. Dabiri & M. Gharib 1997 the effect of a descrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Exp. Fluids 23, 2028.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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