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Direct numerical simulations of two- and three-dimensional turbulent natural convection flows in a differentially heated cavity of aspect ratio 4

Published online by Cambridge University Press:  14 August 2007

F. X. TRIAS ,
M. SORIA ,
A. OLIVA  and
C. D. PÉREZ-SEGARRA
F. X. TRIAS
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC) Universitat Poitécnica de Catalunya (UPC), c/Colom 11, 08222 Terrassa, Spain
M. SORIA
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC) Universitat Poitécnica de Catalunya (UPC), c/Colom 11, 08222 Terrassa, Spain
A. OLIVA
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC) Universitat Poitécnica de Catalunya (UPC), c/Colom 11, 08222 Terrassa, Spain
C. D. PÉREZ-SEGARRA
Affiliation:
Centre Tecnològic de Transferència de Calor (CTTC) Universitat Poitécnica de Catalunya (UPC), c/Colom 11, 08222 Terrassa, Spain
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Abstract

A set of complete two- and three-dimensional direct numerical simulations (DNS) in a differentially heated air-filled cavity of aspect ratio 4 with adiabatic horizontal walls is presented in this paper. Although the physical phenomenon is three-dimensional, owing to its prohibitive computational costs the majority of the previous DNS of turbulent and transition natural convection flows in enclosed cavities assumed a two-dimensional behaviour. The configurations selected here (Rayleigh number based on the cavity height 6.4 × 108, 2 × 109 and 1010, Pr = 0.71) are an extension to three dimensions of previous two-dimensional problems.

An overview of the numerical algorithm and the methodology used to verify the code and the simulations is presented. The main features of the flow, including the time-averaged flow structure, the power spectra and probability density distributions of a set of selected monitoring points, the turbulent statistics, the global kinetic energy balances and the internal waves motion phenomenon are described and discussed.

As expected, significant differences are observed between two- and three-dimensional results. For two-dimensional simulations the oscillations at the downstream part of the vertical boundary layer are clearly stronger, ejecting large eddies to the cavity core. In the three-dimensional simulations these large eddies do not persist and their energy is rapidly passed down to smaller scales of motion. It yields on a reduction of the large-scale mixing effect at the hot upper and cold lower regions and consequently the cavity core still remains almost motionless even for the highest Rayleigh number. The boundary layers remain laminar in their upstream parts up to the point where these eddies are ejected. The point where this phenomenon occurs clearly moves upstream for the three-dimensional simulations. It is also shown that, even for the three-dimensional simulations, these eddies are large enough to permanently excite an internal wave motion in the stratified core region. All these differences become more marked for the highest Rayleigh number.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 586 , 10 September 2007 , pp. 259 - 293
Copyright
Copyright © Cambridge University Press 2007

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References

Betts, P. L. & Bokhtari, I. H. 2000 Experiments on turbulent natural convection in an enclosed tall cavity. Intl J. Heat Fluid Flow 21, 675–683.CrossRefGoogle Scholar
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. J. Comput. Phys. 22, 745–762.Google Scholar
Chorin, A. J. 1993 A Mathematical Introduction to Fluid Mechanics. Springer.Google Scholar
Christon, M. A., Gresho, P. M. & Sutton, S. B. 2002 Computational predictability of time-dependent natural convection flows in enclosures (including a benchmark solution). Intl J. Numer. Meth. Fluids 201, 953–980.Google Scholar
Farhangnia, M., Biringen, S. & Peltiery, L. 1996 Numerical simulation of two-dimensional bouyancy-driven turbulence in a tall rectangular cavity. Intl J. Numer. Meth. Fluids 23, 1311–1326.3.0.CO;2-8>CrossRefGoogle Scholar
Fusegi, F., Farouk, B., Hyun, J. M. & Kuwahara, K. 1990 A direct numerical simulation of periodic natural convection in differentially heated cubical enclosure. In Proc. Intl Symp. on Engineering Turbulence Modeling and Measurements, pp. 261–268.Google Scholar
Fusegi, T., Hyun, J., Kuwahara, K. & Farouk, B. 1991 A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure. Intl J. Heat Mass Transfer 34, 1543–1557.Google Scholar
Fusegi, T., Hyun, J. M. & Kuwahara, K. 1992 Three-dimensional numerical simulation of periodic natural convection in differentially heated cubical enclosure. Appl. Sci. Res. 49, 271–282.CrossRefGoogle Scholar
Henkes, R. 1995 Natural-convection boundary layers. PhD thesis, Faculty of Applied Physics, Delft University of Technology.Google Scholar
Henkes, R. A. W. M. & Le Quéré, P. 1996 Three-dimensional transition of natural-convection flows. J. Fluid Mech. 319, 281–303.CrossRefGoogle Scholar
Hortmann, M., Peric, M. & Scheuerer, G. 1990 Finite volume multigrid prediction of laminar natural convection: bench-mark solutions. Intl J. Numer. Meth. Fluids 11, 189–207.CrossRefGoogle Scholar
Jansen, R. J. A. & Henkes, R. A. W. M. 1996 Instabilities in three-dimensional differentially-heated cavities with adiabatic horizontal walls. Phys. Fluids 8 (1), 62–74.CrossRefGoogle Scholar
Jansen, R. J. A., Henkes, R. A. W. M. & Hoogendoorn, C. J. 1993 Transition to time-periodicity of a natural-convection flow in a 3-D differentially heated cavity. Intl J. Heat Mass Transfer 36 (11), 2927–2940.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Inertial-ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423.CrossRefGoogle Scholar
Labrosse, G., Tric, E., Khallouf, H. & Betrouni, M. 1997 A direct (pseudo-spectral) solver of the 2-D/3-D Stokes problem: transition to unsteadiness of natural-convection flow in a differentially heated cubical cavity. Numer. Heat Transfer B 31, 261–276.Google Scholar
Lartigue, B., Lorente, S. & Bourret, B. 2000 Multicellular natural convection in a high aspect ratio cavity: experimental and numerical results. Intl J. Heat Mass Transfer 43, 3157–3170.Google Scholar
Le Quéré, P. 1990 A note on multiple and unsteady solutions in two-dimensional convection in a tall cavity. J. Heat Transfer 112, 965–974.Google Scholar
Le Quéré, P. 1991 Accurate solutions to the square thermally driven cavity at high rayleigh number. Computers Fluids 20, 29–41.CrossRefGoogle Scholar
Le Quéré, P. 1994 Transition to unsteadiness routes to chaos and simulation of turbulent flows in cavities heated from the side: a review of present status. In Heat Transfer: Proceedings of the 10th Intl Heat Transfer Conf., vol. 1, pp. 281–296. Hewitt GF.CrossRefGoogle Scholar
Le Quéré, P. & Behnia, M. 1998 From onset of unsteadiness to chaos in a differentially heated square cavity. J. Fluid Mech. 359, 81–107.CrossRefGoogle Scholar
Lighthill, J. 2002 Waves in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Paolucci, S. 1990 Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity. J. Fluid Mech. 215, 229–262.CrossRefGoogle Scholar
Paolucci, S. & Chenoweth, D. R. 1989 Transition to chaos in a differentially heated vertical cavity. J. Fluid Mech. 201, 379–410.CrossRefGoogle Scholar
Penot, F., N'Dame, A. & Le Quéré, P. 1990 Investigation of the route to turbulence in a differentially heated cavity. In 9th Intl Heat Transfer Conference, pp. 417–422. Jerusalem.CrossRefGoogle Scholar
Ravi, M., Henkes, R. & Hoogendoorn, C. 1994 On the high-Rayleigh-number structure of steady laminar natural-convection flow in a square enclosure. J. Fluid Mech. 262, 325–351.CrossRefGoogle Scholar
Roache, P. J. 2002 Code verification by the method of manufactured solutions. Trans. ASME I: J. Fluids Engng 124, 4–10.Google Scholar
Salat, J., Xin, S., Joubert, P., Sergent, A., Penot, F. & Le Quéré, P. 2004 Experimental and numerical investigation of turbulent natural convection in large air-filled cavity. Intl J. Heat Fluid Flow 25, 824–832.CrossRefGoogle Scholar
Schweiger, H., Oliva, A., Costa, M. & Pérez-Segarra, C. D. 1995 Numerical experiments on laminar natural convection in rectangular cavities with and without honeycomb structures. Intl J. Numer. Meth. Heat Fluid Flow 5, 243–443.CrossRefGoogle Scholar
Soria, M., Pérez-Segarra, C. D. & Oliva, A. 2002 A direct parallel algorithm for the efficient solution of the pressure-correction equation of incompressible flow problems using loosely coupled computers. Numer. Heat Transfer B 41, 117–138.CrossRefGoogle Scholar
Soria, M., Pérez-Segarra, C. D. & Oliva, A. 2003 A direct Schur–Fourier decomposition for the solution of the three-dimensional poisson equation of incompressible flow problems using loosely parallel computers Numer. Heat Transfer B 43, 467–488.CrossRefGoogle Scholar
Soria, M., Trias, F. X., Pérez-Segarra, C. D. & Oliva, A. 2004 Direct numerical simulation of a three-dimensional natural-convection flow in a differentially heated cavity of aspect ratio 4 Numer. Heat Transfer A 45, 649–673.Google Scholar
Tian, Y. S. & Karayiannis, T. G. 2000 a Low turbulence natural convection in an air filled square cavity. Part I: the thermal and fluid flow fields Intl J. Heat Mass Transfer 43, 849–866.CrossRefGoogle Scholar
Tian, Y. S. & Karayiannis, T. G. 2000 b Low turbulence natural convection in an air filled square cavity. Part II: the turbulence quantities Intl J. Heat Mass Transfer 43, 867–884.CrossRefGoogle Scholar
Trias, F. X., Soria, M., Oliva, A. & Verstappen, R. 2006 a Regularization models for the simulation of turbulence in a differentially heated cavity. In Proc. European Comput. Fluid Dynamics Conference (ECCOMAS CFD 2006). Egmond aan Zee, The Netherlands.Google Scholar
Trias, F. X., Soria, M., Pérez-Segarra, C. D. & Oliva, A. 2006 b A direct Schur–Fourier decomposition for the efficient solution of high-order poisson equations on loosely coupled parallel computers Numerical Linear Algebra with Applications 13, 303–326.Google Scholar
Tric, E., Labrosse, G. & Betrouni, M. 2000 A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity. Intl J. Heat Mass Transfer 43, 4043–4056.Google Scholar
de Vahl Davis, G. & Jones, I. P. 1983 Natural convection in a square cavity: a comparison exercise. Intl J. Numer. Meth. FLuids 3, 227–248.CrossRefGoogle Scholar
Verstappen, R. 2007 On restraining the production of small scales of motion in a turbulent channel flow. Computers Fluids (to appear).CrossRefGoogle Scholar
Verstappen, R. & Veldman, A. 1997 Direct numerical simulation of turbulence at lower costs. J. Engng Maths 32, 143–159.CrossRefGoogle Scholar
Verstappen, R. W. C. P. & Veldman, A. E. P. 1998 Spectro-consistent discretization of Navier–Stokes: a challenge to RANS and LES. J. Engng Maths 34, 163–179.Google Scholar
Verstappen, R. W. C. P. & Veldman, A. E. P. 2003 Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187, 343–368.CrossRefGoogle Scholar
Wan, D., Patnaik, B. & Wei, G. 2001 A new benchmark quality solution for the buoyancy-driven cavity by discrete singular convolution Numer. Heat Transfer B 40, 199–228.Google Scholar
Winters, K. H. 1987 Hopf bifurcation in the double-glazing problem with conducting boundaries. J. Heat Transfer 109, 894–898.CrossRefGoogle Scholar
Xin, S. & Le Quéré, P. 1995 Direct numerical simulations of two-dimensional chaotic natural convection in a differentially heated cavity of aspect ratio 4. J. Fluid Mech. 304, 87–118.CrossRefGoogle Scholar
Xin, S. & Le Quéré, P. 2002 An extended chebyshev pseudo-spectral benchmark for the 8:1 differentially heated cavity. Intl J. Numer. Meth. Fluids 8, 2182–2189.Google Scholar
Yanenko, N. N. 1971 The Method of Fractional Steps. Springer.CrossRefGoogle Scholar