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An experimental study of turbulent convection in air

Published online by Cambridge University Press:  29 March 2006

Daniel E. Fitzjarrald
Affiliation:
Institute of Geophysics and Planetary Physics, Los Angeles, California 90024 Present address: Wave Propagation Laboratory NOAA, Boulder, Colorado.

Abstract

An experiment was performed in a 3·5 by 3·5 m variable-height, closed convection box, with conditions ranging from a Rayleigh number of 4 × 104 up to 7 × 109, using air as the working fluid. Heat-flux measurements made at Rayleigh numbers up to 7 × 109 yielded a Nusselt number Nu = 0·13Ra0·30. Velocities and temperatures were measured up to Ra = 1·7 × 107, and Fourier spectra calculated to find the predominant horizontal scales of the motion midway between the boundaries. The predominant scale at Ra ∼ 105 was approximately four times the distance between plates, changing to six as Ra increased to 106. With side walls introduced so that the transverse aspect ratio was equal to five, Fourier spectra indicated considerable smaller scale motions, approximately equal to the layer depth. These motions decreased in size as Ra was increased. The results are discussed in relation to previous experimental and theoretical work.

Type
Research Article
Copyright
© 1976 Cambridge University Press

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References

Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer Phys. Fluids, 15, 15451554.Google Scholar
Browand, F. K. & Winant, C. D. 1973 Laboratory observations of shear-layer instability in a stratified fluid Boundary-Layer Met. 5, 6778.Google Scholar
Brown, W. S. 1973 Heat-flux transitions at low Rayleigh number J. Fluid Mech. 60, 539559.Google Scholar
Busse, F. H. 1967 On the stability of two-dimensional convection in a layer heated from below J. Math. & Phys. 46, 140179.Google Scholar
Busse, F. H. 1969 On Howard's upper bound for heat transport by turbulent convection J. Fluid Mech. 37, 457477.Google Scholar
Busse, F. H. & Whitehead, J. A. 1974 Oscillatory and collective instabilities in large Rayleigh number convection J. Fluid Mech. 66, 6779.Google Scholar
Carroll, J. J. 1971 The structure of turbulent convection. Ph.D. dissertation, Department of Meteorology, U.C.L.A.
Chen, M. M. & Whitehead, J. A. 1968 Evolution of two-dimensional periodic Rayleigh convection cells of arbitrary wavenumbers J. Fluid Mech. 31, 115.Google Scholar
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water J. Fluid Mech. 60, 141159.Google Scholar
Deardorff, J. W. 1970 Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection J. Atmos. Sci. 27, 12111213.Google Scholar
Deardorff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates J. Fluid Mech. 28, 675704.Google Scholar
Goldstein, R. J. & Chu, T. Y. 1969 Thermal convection in a horizontal layer of air. Prog. Heat and Mass. Trans. vol. 2, pp. 5575. Pergamon.
Howard, L. N. 1963 Heat transport by turbulent convection J. Fluid Mech. 17, 405432.Google Scholar
Jakob, M. 1949 Heat Transfer, vol. 1. Wiley.
Jakob, M. 1957 Heat Transfer, vol. 2. Wiley.
Kraichnan, R. H. 1962 Turbulent thermal convection at arbitrary Prandtl number Phys. Fluids, 5, 13741389.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, 295307.Google Scholar
Malkus, W. V. R. 1954a Discrete transitions in turbulent convection. Proc. Roy. Soc A 225, 185195.Google Scholar
Malkus, W. V. R. 1954b Heat transport and spectrum of thermal turbulence. Proc. Roy. Soc A 225, 196212.Google Scholar
Schlichting, H. 1960 Boundary-layer Theory, 4th edn. McGraw-Hill.
Thomas, D. B. & Townsend, A. A. 1957 Turbulent convection over a heated horizontal surface J. Fluid Mech. 2, 473492.Google Scholar
Willis, G. E. & Deardorff, J. W. 1967 Confirmation and renumbering of the discrete heat-flux transitions Malkus Phys. Fluids, 10, 18611866.Google Scholar
Willis, G. E. & Deardorff, J. W. 1974 A laboratory model of the unstable planetary boundary layer J. Atmos. Sci. 31, 12971307.Google Scholar
Willis, G. E. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon the heat flux J. Fluid Mech. 54, 351367.Google Scholar