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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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