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Direct numerical simulation of laminar and turbulent Bénard convection

Published online by Cambridge University Press:  20 April 2006

Günther Grötzbach
Günther Grötzbach
Affiliation:
Institut für Reaktorentwicklung, Kernforschungszentrum Karlsruhe, Postfach 3640, D-7500 Karlsruhe, Federal Republic of Germany
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Abstract

The TURBIT-3 computer code has been used for the direct numerical simulation of Bénard convection in an infinite plane channel filled with air. The method is based on the three-dimensional non-steady-state equations for the conservation of mass, momentum and enthalpy. Subgrid-scale models of turbulence are not required, as calculations with different grids show that the spatial resolution of grids with about 322 × 16 nodes provides sufficient accuracy for Rayleigh numbers up to Ra = 3·8 × 105. Hence this simulation model contains no tuning parameters.

The simulations start from nearly random initial conditions. This has been found to be essential for calculating flow patterns and statistical data insensitive to grid parameters and agreeing with experimental experience. The numerical results show the theoretically predicted ‘skewed varicose’ instability at Ra = 4000. Warm and cold ‘blobs’ are identified as causing temperature-gradient reversals for all the high Rayleigh numbers under consideration. The calculated wavelengths and the corresponding flow regimes observed in the transition range confirm the stability maps determined theoretically. In the turbulent range the wavelengths agree qualitatively with low-aspect-ratio experiments. Accordingly, the Nusselt numbers lie at the upper end of the scatter band of experimental data, as these also depend on the aspect ratio. Appropriately normalized, the velocity and temperature fluctuation peaks are independent of the Rayleigh number. The vertical profiles agree largely with experimental data and, especially in case of temperature statistics, exhibit comparable or less scatter.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 119 , June 1982 , pp. 27 - 53
Copyright
© 1982 Cambridge University Press

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References

Adrian, R. J. 1975 Turbulent convection in water over ice. J. Fluid Mech. 69, 753–781.Google Scholar
Brown, W. 1973 Heat-flux transitions at low Rayleigh number. J. Fluid Mech. 60, 539–559.Google Scholar
Busse, F. H. & Clever, R. M. 1979 Instabilities of convection rolls in a fluid of moderate Prandtl number. J. Fluid Mech. 91, 319–335.Google Scholar
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Prandtl number convection. J. Fluid Mech. 66, 67–79.Google Scholar
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141–159.Google Scholar
Clever, R. M. & Busse, F. H. 1978 Large wavelength convection rolls in low Prandtl number fluids. Z. angew. Math. Phys. 29, 711–714.Google Scholar
Daly, B. J. 1974 A numerical study of turbulence transitions in convective flow. J. Fluid Mech. 64, 129–165.Google Scholar
Deardorff, J. W. & Willis, G. E. 1965 The effect of two-dimensionality on the suppression of thermal turbulence. J. Fluid Mech. 23, 337–353.Google Scholar
Deardoff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675–704.Google Scholar
Denton, R. A. & Wood, I. R. 1979 Turbulent convection between two horizontal plates. Int. J. Heat Mass Transfer 22, 1339–1346.Google Scholar
Dubois, M. & Bergé, P. 1978 Experimental study of the velocity field in Rayleigh-Bénard convection. J. Fluid Mech. 85, 641–653.Google Scholar
Fitzjarrald, D. E. 1976 An experimental study of turbulent convection in air. J. Fluid Mech. 73, 693–719.Google Scholar
Gille, J. 1967 Interferometric measurement of temperature gradient reversal in a layer of convecting air. J. Fluid Mech. 30, 371–384.Google Scholar
Goldstein, R. J. & Chu, T. Y. 1969 Thermal convection in a horizontal layer of air. Prog. Heat Mass Transfer 2, 55–75.Google Scholar
Grötzbach, G. 1977 Direkte numerische Simulation turbulenter Geschwindigkeits-, Druck- und Temperaturfelder bei Kanalströmungen. KfK 2426, Thesis, Universität Karlsruhe. (English translation in DOE-tr-61.)
Grötzbach, G. 1979 Numerical investigation of radial mixing capabilities in strongly buoyancyinfluenced vertical, turbulent channel flows. Nucl. Engng & Design 54, 49–66.Google Scholar
Grötzbach, G. 1980 Über das räumliche Auflsungsvermögen numerischer Simulationen von turbulenter Bénard-Konvektion. KfK 2981 B.
Grötzbach, G. & Schumann, U. 1979 Direct numerical simulation of turbulent velocity-, pressure- and temperature-fields in channel flows. In Turbulent Shear Flows I (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 370–385. Springer.
Hollands, K. G. T., Raithby, G. D. & Konicek, L. 1975 Correlation equations for free convection heat transfer in horizontal layers of air and water. Int. J. Heat. Mass Transfer 18, 879–884.Google Scholar
Koschmieder, E. L. & Pallas, S. G. 1974 Heat transfer through a shallow, horizontal convecting fluid layer. Int. J. Heat Mass Transfer 17, 991–1002.Google Scholar
Krishnamurti, R. 1970 On the transition to turbulent convection. Part 1. The transition from two- to three-dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285–303.Google Scholar
Lipps, F. B. 1976 Numerical simulation of three-dimensional Benard convection in air. J. Fluid Mech. 75, 113–148.Google Scholar
Lipps, F. B. & Somerville, C. J. 1971 Dynamics of variable wavelength in finite-amplitude Benard convection. Phys. Fluids 14, 759–765.Google Scholar
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection. Proc. R. Soc. Lond. A 225, 185–195.
Ozoe, H., Yamamoto, K., Churchill, S. W. & Sayama, H. 1976 Three-dimensional, numerical analysis of laminar natural convection in a confined fluid heated from below. J. Heat Transfer 98, 202–207.Google Scholar
Schumann, U. 1973 Ein Verfahren zur direkten numerischen Simulation turbulenter Strömungen in Flatten- und Ringspaltkanalen und über seine Anwendung zur Untersuchung von Turbulenzmodellen. KfK 1854, Thesis, Universität Karlsruhe.
Schumann, U. 1975a Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Phys. 18, 376–404.Google Scholar
Schumann, U. 1975b Linear stability of finite difference equations for three-dimensional flow problems. J. Comp. Phys. 18, 465–470.Google Scholar
Silveston, P. L. 1958 Wärmedurchgang in waagerechten Flüssigkeitsschichten. Forsch. Ing.- Wes. 24, 29–32, 59–69.Google Scholar
Thomas, D. B. & Townsend, A. A. 1957 Turbulent convection over a heated horizontal surface. J. Fluid Mech. 2, 473–492.Google Scholar
Threlfall, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 17–28.Google Scholar
Willis, G. E. & Deardorff, J. W. 1965 Measurements on the development of thermal turbulence in air between horizontal plates. Phys. Fluids 8, 2225–2229.Google Scholar
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux. J. Fluid Mech. 54, 351–367.Google Scholar