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An experimental determination of transition limits in a vertical natural convection flow adjacent to a surface

Published online by Cambridge University Press:  19 April 2006

R. L. Mahajan  and
B. Gebhart
R. L. Mahajan
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo Present address: Western Electric Company, Inc., Engineering Research Center, P.O. Box 900, Princeton, New Jersey 08540.
B. Gebhart
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo
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Abstract

This paper reports the results of an experimental investigation to determine transition mechanisms and limits in gases at high pressure levels. We sought also to refine further the parameters for transition, in particular the role of kinematic viscosity. In flow adjacent to a vertical uniform-flux surface in nitrogen, pressures to 16 atm were used. Both mean and disturbance quantities for the temperature and velocity fields were measured for various values of the heat flux, downstream location and ambient pressure level. Hot-wire and fine thermocouple probes were used. We found that the velocity and thermal fields remain closely coupled. Velocity, or fluid-dynamic, transition is immediately followed by thermal transition. Each was detected as a decrease in the rate of increase of both the maximum velocity and the overall temperature difference, respectively, from the laminar downstream trends. Also, the ends of transition for the velocity and the thermal fields, respectively, signalled by no further appreciable change in the intermittency distributions, were simultaneous. These results re-affirm the finding that the events of transition are not correlated by the Grashof number alone. An additional dependence on both downstream location and pressure level arises. A fixed value of the parameter $Q_{BT} = qB^{\frac{2}{15}}= 290$ characterizes the beginning of transition, where q is the fifth root of the local non-dimensional wall heat flux and B is the unit Grashof number. The end of transition, on the other hand, is best correlated by $Q_{ET} = QB^{\frac{1}{30}} = 11.4$, where Q is the fifth root of the local non-dimensional total heat convected in the boundary region. A re-examination of other transition studies, in both gases and liquids, supports these correlations, although many such data were not determined with fast response to local sensors. There remains a small level of uncertainty in establishing exact limits for transition, since the apparently proper standards for determining them are very difficult to apply precisely in experiments. However, such limits are very important in separating regimes of different transport mechanisms.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 1 , 9 March 1979 , pp. 131 - 154
Copyright
© 1979 Cambridge University Press

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References

Audunson, T. & Gebhart, B. 1976 Secondary mean motions arising in a buoyancy induced flow. Int. J. Heat Mass Transfer 19, 337–350.Google Scholar
Bill, R. G. & Gebhart, B. 1975 The transition of plane plumes. Int. J. Heat Mass Transfer 18, 513.Google Scholar
Bill, R. G. & Gebhart, B. 1978 Development of turbulent transport in vertical natural convection boundary layer. To be published.
Cheesewright, R. 1968 Turbulent natural convection from a vertical plane surface. J. Heat Transfer 90, 1–8.Google Scholar
Colak-Antic, P. 1964 Hitzdraht messungen des laminar-turbulenten Umschlagas bei freier Konvektion. Jahrbuch der WGLR pp. 1972–1976.Google Scholar
Dring, R. P. & Gebhart, B. 1968 A theoretical investigation of disturbance amplification in external laminar natural convection. J. Fluid Mech. 34, 551–564.Google Scholar
Eckert, E. R. G., Hartnett, J. P. & Irvine, T. F. 1960 Flow visualization studies of transition in turbulence in free convection. A.S.M.E. Paper no. 60-WA-250.Google Scholar
Eckert, E. R. G. & Soehngen, E. 1951 Interferometric studies on the stability and transition to turbulence of a free-convection boundary layer. Proc. Gen. Disc. Heat Transfer, London, pp. 321–323.Google Scholar
Gebhart, B. 1962 Effects of viscous dissipation in natural convection. J. Fluid Mech. 14, 225.Google Scholar
Gebhart, B. 1969 Natural convection flow, instability and transition. J. Heat Transfer 91, 293–309.Google Scholar
Gebhart, B. 1971 Heat Transfer, 2nd edn. McGraw-Hill.
Gebhart, B. 1973 Instability transition and turbulence in buoyancy-induced flows. Ann. Rev. Fluid Mech. 5, 213–246.Google Scholar
Gebhart, B. & Mahajan, R. L. 1975 Characteristic disturbance frequency in vertical natural convection flow. Int. J. Heat Mass Transfer 18, 1143–1148.Google Scholar
Godaux, R. & Gebhart, B. 1974 An experimental study of the transition of natural convection flow adjacent to a vertical surface. Int. J. Heat Mass Transfer 17, 93–107.Google Scholar
Hauptmann, E. G. 1968 The influence of temperature dependent viscosity on laminar boundary layer stability. Int. J. Heat Mass Transfer 11, 1049–1052.Google Scholar
Hieber, C. A. & Gebhart, B. 1971 Stability of vertical natural convection boundary layers: some numerical solutions. J. Fluid Mech. 48, 625–646.Google Scholar
Hugot, G., Jannot, M. & Pirovano, A. 1971 Compte-redu de Fin de Contrat DGST no. 69$01-773.
Jaluria, Y. & Gebhart, B. 1973 An experimental study of nonlinear disturbance behaviour in natural convection. J. Fluid Mech. 61, 337.Google Scholar
Jaluria, Y. & Gebhart, B. 1974 On transition mechanisms in vertical natural convection flow. J. Fluid Mech. 66, 309–337.Google Scholar
Klebanoff, P. S. 1954 Characteristics of turbulence in a boundary layer with zero pressure gradient. N.A.C.A. Tech. Note no. 3178.Google Scholar
Lock, G. S. H. & Trotter, F. J. de B. 1968 Observations on the structure of a turbulent free convection boundary layer. Int. J. Heat Mass Transfer 11, 1225–1232.Google Scholar
Mahajan, R. L. 1977 Higher order effects, stability and transition in vertical natural convection flows. Ph.D. thesis, Cornell University.
Mahajan, R. L. & Gebhart, B. 1978 Hot-wire anemometer calibration for measurements in free, mixed and forced convection in pressurized nitrogen. J. Heat Transfer. To be published.Google Scholar
Qureshi, Z. & Gebhart, B. 1978 Transition and transport in a buoyancy driven flow in water adjacent to a vertical uniform flux surface. Int. J. Heat Mass Transfer. To be published.Google Scholar
Regnier, G. M. & Kaplan, C. 1963 Visualization of natural convection on a plane wall and in a vertical gap by differential interferometry. Transitional and turbulent regimes. Proc. 1963 Heat Transfer Fluid Mech. Inst. pp. 94–110. Stanford University Press.
Schubauer, G. B. & Klebanoff, P. S. 1956 Contributions on the mechanics of boundary layer transition. N.A.C.A. Rep. no. 1289.Google Scholar
Szewczyk, A. A. 1962 Stability and transition of the free convection layer along a vertical flat plate. Int. J. Heat Mass Transfer 5, 903–914.Google Scholar
Vliet, G. C. & Liu, C. K. 1969 An experimental study of turbulent natural convection boundary layers. J. Heat Transfer 91, 517–531.Google Scholar
Warner, C. 1966 Turbulent natural convection in air along a vertical flat plate. Ph.D. thesis, University of Michigan.
Warner, C. & Arpaci, V. S. 1968 An experimental investigation of turbulent natural convection in air at low pressure along a vortical heated plate. Int. J. Heat Mass Transfer 11, 397–406.Google Scholar