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Thermal cellular convection in rotating rectangular boxes

Published online by Cambridge University Press:  20 April 2006

K. Bühler  and
H. Oertel
K. Bühler
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität (TH) Karlsruhe, Germany
H. Oertel
Affiliation:
Institut für Strömungslehre und Strömungsmaschinen, Universität (TH) Karlsruhe, Germany
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Abstract

The thermal cellular convection in rotating rectangular boxes has been investigated both theoretically and experimentally. In the theoretical analysis, a linear stability theory is used to calculate the stability behaviour and the configuration of the three-dimensional convection flow. The numerical results show that the rolls change their orientation for a Taylor number greater than a critical value. In the experimental investigation, the flow patterns were visualized by a special differential interferometer. The experimental results are presented in stability diagrams and interferogram series which demonstrate the influence of rotation as well as initial and boundary conditions on the convective flow. We found that the effects of the Coriolis force and those of centrifugal forces could be studied separately by the choice of different test fluids, e.g. nitrogen is good for the Coriolis-force effect while silicone oil is good for the centrifugal-force effect.

When compared with experimental results, our theoretical model is shown to be good for fluids of small Prandtl number such as nitrogen gas. We also compare our results with the well-known asymptotic behaviour of the critical Rayleigh number and wavenumber.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 261 - 282
Copyright
© 1972 Cambridge University Press

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References

Abell, S. & Hudson, J. L. 1975 An experimental study of centrifugal driven free convection in a rectangular cavity. Int. J. Heat Mass Transfer 18, 1415–1423.Google Scholar
Bühler, K. 1979 Zellularkonvektion in rotierenden Behältern. Dissertation Karlsruhe, Fortschritt-Berichte VDI-Z., Reihe 7, Nr. 54.
Bühler, K., Kirchartz, K. R. & Oertel, H. 1979 Steady convection in a horizontal fluid layer. Acta Mech. 31, 155–171.Google Scholar
Busse, F. H. & Heikes, K. E. 1980 Convection in a rotating layer: a simple case of turbulence. Science 208, 173–175.CrossRefGoogle Scholar
Catton, I. 1970 Convection in a closed rectangular region: the onset of motion. J. Heat Transfer 92, 186–188.Google Scholar
Chandrasekhar, R. S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Clever, R. M. & Busse, F. H. 1979 Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis. J. Fluid Mech. 94, 609–627.Google Scholar
Davis, S. H. 1967 Convection in a box: linear theory. J. Fluid Mech. 30, 465–478.Google Scholar
Davies-Jones, R. P. & Gilman, P. A. 1971 Convection in a rotating annulus uniformly heated from below. J. Fluid Mech. 46, 65–81.Google Scholar
Finlayson, B. A. 1968 The Galerkin method applied to convective instability problems. J. Fluid Mech. 33, 201–208.Google Scholar
Frick, H. & Clever, R. M. 1980 Einfluß der Seitenwände auf das Einsetzen der Konvektion in einer horizontalen Flüssigkeitsschicht. Z. angew. Math. Phys. 31, 502–513.Google Scholar
Gershuni, G. Z. & Zukhovitskii, E. M. 1976 Convective Instability of Incompressible Fluids. Jerusalem: Keter.
Gilman, P. A. 1973 Convection in a rotating annulus uniformly heated from below. Part 2. Nonlinear results. J. Fluid Mech. 57, 381–400.Google Scholar
Gray, D. D. & Giorgini, A. 1976 The validity of the Boussinesq approximation. Int. J. Heat Mass Transfer 19, 545–551.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Harris, D. L. & Reid, W. H. 1958 On orthogonal functions which satisfy four boundary conditions. Astrophys. J. Suppl. Series 3, 429–453.Google Scholar
Homsy, G. M. & Hudson, J. L. 1971a The asymptotic stability of a bounded rotating fluid heated from below: conductive basic state. J. Fluid Mech. 45, 353–373.Google Scholar
Homsy, G. M. & Hudson, J. L. 1971b Centrifugal convection and its effect on the asymptotic stability of a bounded rotating fluid heated from below. J. Fluid Mech. 48, 605–624.Google Scholar
Homsy, G. M. & Hudson, J. L. 1972 Stability of a radially bounded rotating fluid heated from below. Appl. Sci. Res. 26, 33–66.Google Scholar
Hopfinger, E. J., Atten, P. & Busse, F. H. 1979 Instability and convection in fluid layers: A report on Euromech 106. J. Fluid Mech. 92, 217–240.Google Scholar
Hudson, J. L. 1979 Experiments on centrifugally driven, thermal convection in a rotating cylinder. J. Fluid Mech. 86, 147–159.Google Scholar
Hunter, C. & Riahi, N. 1975 Nonlinear convection in a rotating fluid. J. Fluid Mech. 72, 433–454.Google Scholar
Koschmieder, E. L. 1967 On convection on a uniformly heated rotating plane. Beitr. z. Phys. Atmos. 40, 216–225.Google Scholar
Küppers, G. 1970 The stability of steady finite amplitude convection in a rotating fluid layer. Phys. Letters A, 32, 7–8.Google Scholar
Küppers, G. & Lortz, D. 1969 Transition from laminar convection to thermal turbulence in a rotating fluid layer. J. Fluid Mech. 35, 609–620.Google Scholar
Niiler, P. P. & Bisshop, F. E. 1965 On the influence of Coriolis force on onset of thermal convection. J. Fluid Mech. 22, 753–761.Google Scholar
Oertel, H. 1978 Einfluß der Rotation auf die stationäre Zellularkonvektion. Z. angew. Math. Mech. 59, 248–252.Google Scholar
Oertel, H. 1979 Thermische Zellularkonvektion. Habilitationsschrift Universität Karlsruhe (TH).
Oertel, H. 1980 Three-dimensional convection within rectangular boxes. The 19th National Heat Transfer Conf., Orlando, Florida, HTD, vol. 8.
Oertel, H. 1981 J. Fluid Mech. (submitted).
Oertel, H. & Bühler, K. 1978 A special differential interferometer used for heat convection investigations. Int. J. Heat Mass Transfer 21, 1111–1115.Google Scholar
Oertel, H., Bühler, K., Kirchartz, K. R. & Srulijes, J. 1978 Experimentelle und theoretische Untersuchung der Zellularkonvektion. Mitteilungen des Instituts für Strömungslehre und Strömungsmaschinen, Universität (TH) Karlsruhe Nr. 24, pp. 40–72.
Oertel, H. & Kirchartz, K. R. 1979 Influence on initial and boundary conditions on Bénard convection. Recent Developments in Theoretical and Experimental Fluid Mechanics. Springer.
Ostrach, S. 1972 Natural convection in enclosures. Adv. Heat Transfer 8, 161–227.Google Scholar
Rossby, H. T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309–335.Google Scholar
Smith, B. T., Boyle, J. M., Dongarra, J. J., Garbow, B. S., Ikebe, Y., Klema, V. C. & Moler, C. B. 1976 Matrix Eigensystem Routines — EISPACK Guide, Lecture Notes in Computer Science, vol. 6. Springer.
Sommerville, R. C. & Lipps, F. B. 1973 A numerical study in three space dimensions of Bénard convection in a rotating fluid. J. Atmospheric Sci. 30, 590–596.Google Scholar
Stork, K. & Müller, U. 1972 Convection in boxes: experiments. J. Fluid Mech. 54, 599–611.Google Scholar
Spiegel, E. A. & Veronis, G. 1960 On the Boussinesq approximation for a compressible fluid. Astrophys. J. 131, 442–447.Google Scholar
Torrest, M. A. & Hudson, L. 1974 The effect of centrifugal convection on the stability of a rotating fluid heated from below. Appl. Sci. Res. 29, 273–289.Google Scholar
Veronis, G. 1968 Large-amplitude Bénard convection in a rotating fluid. J. Fluid Mech. 31, 113–139.Google Scholar