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The stability of boundary layers on curved heated plates

Published online by Cambridge University Press:  17 February 2009

Jillian A. K. Stott  and
James P. Denier
Jillian A. K. Stott
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide SA 5005, Australia.
James P. Denier
Affiliation:
Department of Applied Mathematics, The University of Adelaide, Adelaide SA 5005, Australia.
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Abstract

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We consider the effect the competing mechanisms of buoyancy-driven acceleration (arising from heating a surface) and streamline curvature (due to curvature of a surface) have on the stability of boundary-layer flows. We confine our attention to vortex type instabilities (commonly referred to as Görtler vortices) which have been identified as one of the dominant mechanisms of instability in both centrifugally and buoyancy driven boundary layers. The particular model we consider consists of the boundary-layer flow over a heated (or cooled) curved rigid body. In the absence of buoyancy forcing the flow is centrifugally unstable to counter-rotating vortices aligned with the direction of the flow when the curvature is concave (in the fluid domain) and stable otherwise. Heating the rigid plate to a level sufficiently above the fluid's ambient (free-stream) temperature can also serve to render the flow unstable. We determine the level of heating required to render an otherwise centrifugally stable flow unstable and likewise, the level of body cooling that is required to render a centrifugally unstableflow stable.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 3 , January 2002 , pp. 333 - 358
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1965).Google Scholar
[2]Batchelor, G. K., An introduction to fluid dynamics (Cambridge University Press, London, 1967).Google Scholar
[3]Blackaby, N. D. and Choudhari, M., “Inviscid vortex motions in weakly three-dimensional boundary layers and their relation with instabilities in stratified shear flows”, Proc. R. Soc. Lond. (A) 440 (1993) 701–710.Google Scholar
[4]Denier, J. P. and Hall, P., “Fully nonlinear Görtler vortices in constricted channel flows and their effect on the onset of separation”, NASA/ICASE contractor report 92–29.Google Scholar
[5]Denier, J. P., Hall, P. and Seddougui, S. O., “On the receptivity problem for Görtler vortices: vortex motions induced by wall roughness”, Phil. Trans. R. Soc. Lond. (A) 335 (1991) 51–85.Google Scholar
[6]Denier, J. P. and Mureithi, E. W., “Weakly nonlinear wave motions in a thermally stratified boundary layer”, J. Fluid Mech. 315 (1996) 293–316.CrossRefGoogle Scholar
[7]Denier, J. P. and Stott, J. A. K., “Wave-mean flow interactions in thermally stratified Poiseuille flow”, Stud. Appl. Math. 102 (1999) 121–136.CrossRefGoogle Scholar
[8]Drazin, P. G. and Reid, W. H., Hydrodynamic stability (Cambridge University Press, London, 1981).Google Scholar
[9]Goldstein, J. L. and Sparrow, E. M., “Characteristics for flow in a corrugated wall channel”, J. Heat Transfer 99 (1977) 187–195.CrossRefGoogle Scholar
[10]Gschwind, P., Regele, A. and Kottke, V., “Sinusoidal wavy channels with Taylor-Görtler vortices”, Exp. Thermal Fluid Sci. 11 (1995) 270–275.CrossRefGoogle Scholar
[11]Hall, P., “The linear development of Görtler vortices in growing boundary layers”, J. Fluid Mech. 130 (1983) 41–58.CrossRefGoogle Scholar
[12]Hall, P., “Streamwise vortices in heated boundary layers”, J. Fluid Mech. 252 (1993) 301–324.CrossRefGoogle Scholar
[13]Hall, P. and Horseman, N. J., “The inviscid secondary instability of fully nonlinear longitudinal vortex structures in growing boundary layers”, J. Fluid Mech. 232 (1991) 357–375.CrossRefGoogle Scholar
[14]Hall, P. and Lakin, W. D., “The fully nonlinear development of Görtler vortices in growing boundary layers”, Proc. R. Soc. Lond. (A) 415 (1988) 421–444.Google Scholar
[15]Hall, P. and Morris, H., “On the instability of boundary layers on heated flat plates”, J. Fluid Mech. 245 (1992) 367–400.CrossRefGoogle Scholar
[16]Hall, P. and Seddougui, S. O., “On the onset of three-dimensionality and time-dependence in Görtler vortices”, J. Fluid Mech. 204 (1989) 405–420.CrossRefGoogle Scholar
[17]Jacobi, A. M. and Ramesh, K. S., “Air-sided flow and heat transfer in compact heat exchangers: a discussion of enhancement mechanisms”, Heat Trans. Eng. 19 (1998) 29–41.CrossRefGoogle Scholar
[18]Mangalam, S. M., Dagenhart, J. R., Hepner, T. E. and Meyers, J. F., “The Görtler instability on an airfoil”, AIAA Paper 85–0491, 1985.CrossRefGoogle Scholar
[19]Mureithi, E. W., “Effects of thermal buoyancy on the stability properties of boundary layer flows”, Ph. D. Thesis, University of New South Wales, 1998.Google Scholar
[20]Mureithi, E. W., Denier, J. P. and Stott, J. A. K., “The effect of buoyancy on upper branch Tollmien-Schlichting waves”, IMA J. App. Math. 58 (1997) 19–50.CrossRefGoogle Scholar
[21]Timoshin, S. N., “Asymptotic analysis of a spatially unstable Görtler vortex spectrum”, Fluid Dyn. 25 (1990) 25–33.CrossRefGoogle Scholar
[22]Wang, G. and Vanka, P., “Convective heat transfer in periodic wavy passages”, Int. J. Heat Mass Trans. 38 (1995) 3219–3230.CrossRefGoogle Scholar