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Influence of variable properties on the stability of two-dimensional boundary layers

Published online by Cambridge University Press:  26 April 2006

H. Herwig  and
P. Schäfer
H. Herwig
Affiliation:
Institut für Thermo- und Fluiddynamik, Ruhr-Universität. D-4630 Bochum, Germany
P. Schäfer
Affiliation:
Institut für Thermo- und Fluiddynamik, Ruhr-Universität. D-4630 Bochum, Germany
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Abstract

Classical linear stability theory is extended to include the effects of temperature- and pressure-dependent fluid properties. These effects are studied asymptotically by using Taylor series expansions for all the properties with respect to temperature and pressure. In this asymptotic approach all effects are well separated from each other, and only the Prandtl number remains as a parameter. In their general form the asymptotic solutions hold for all Newtonian fluids. A shooting technique with Gram-Schmidt orthonormalization for the zero-order equation (classical Orr-Sommerfeld problem) and a multiple shooting method for all other equations is applied to solve the stiff differential equations. In particular the zero- and first-order equations are solved for a flat-plate boundary-layer flow with temperature-dependent viscosity. PhysicalhT. this corresponds to a fluid with a linear viscosity/temperature relation. The results show that decreasing the viscosity in the near-wall region of the boundary layer stabilizes the flow, whereas it would be destabilized for a uniformly decreased viscosity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 243 , October 1992 , pp. 1 - 14
Copyright
© 1992 Cambridge University Press

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References

Asfar, O. R., Masad, J. A. & Nayfeh, A. H. 1990 A method for calculating the stability of boundary layers. Computers Fluids 18, 305–315.Google Scholar
Chen, Y. M. & Pearlstein, A. J. 1989 Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots. J. Fluid Mech. 198, 513–541.Google Scholar
Gersten, K. & Herwig, H. 1984 Impuls- und Wärmeübertragung bei variablen Stoffwerten für die laminare Plattenströmung. Wärme-und Stoffübertragung 18, 25–35.Google Scholar
Hauptmann, E. G. 1968 The influence of temperature dependent viscosity on laminar boundary-layer stability. Intl J. Heat Mass Transfer 11, 1049–1052.Google Scholar
Herwig, H. 1987 An asymptotic approach to compressible boundary-layer flow. Intl J. Heat Mass Transfer 30, 59–68.Google Scholar
Herwig, H. 1990 ACFD: An Asymptotic/Computational Approach to Complex Problems. In Advanced Computational Methods in Heat Transfer: Proc. 1st. Intl Conf., Portsmouth. UK. (ed. Wrobel), vol. 1, pp. 333–344.
Kümmerer, H. 1973 Numerische Untersuchungen zur Stabilität ebener laminarer Grenzschichtströmungen. Dissertation, Universität Stuttgart, Germany.
Lee, H. R., Chen, T. S. & Armaly, B. F. 1990 Non-parallel thermal instability of forced convection flow over a heated. non-isothermal horizontal flat plate. Intl J. Heat Mass Transfer 33, 2019–2028.Google Scholar
Mack, L. M. 1976 A numerical study of the temporal eigenvalue spectrum of the Blasius boundary layer. J. Fluid Mech. 73, 497–520.Google Scholar
Mack, L. M. 1984 Boundary-layer linear stability theory. AGARD Rep. 709.
Sabhapathy, P. & Cheng, K. C. 1986 The effects of temperature-dependent viscosity and coefficient of thermal expansion on the stability of laminar, natural convective flow along an isothermal, vertical surface. Intl J. Heat Mass Transfer 29, 1521–1529.Google Scholar
Schlichting, H. 1982 Grenzschicht-Theorie. Karlsruhe: G. Braun.
Squire, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls.. Proc. R. Soc. Lond. A 142, 621–628.Google Scholar
Stoer, J. & Bulirsch, R. 1978 Einführung in die Numerische Mathematik II, Springer.
Wazzan, A. R., Keltner, G., Okamura, T. T. & Smith, A. M. O. 1972 Spatial stability of stagnation water boundary layers with heat transfer. Phys. Fluids 15, 2114–2118.Google Scholar
Wazzan, A. R., Taghavi, H. & Hsu, W.-C. 1978 Combined effects of pressure gradient and heating on the stability of freon-114 boundary layer. Phys. Fluids 21, 2141–2147.Google Scholar
Yih, C.-S. 1955 Stability of two-dimensional parallel flows for three-dimensional disturbances. Q. Appl. Maths. 12, 434–435.Google Scholar