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On a class of compressible laminar boundary-layer flows and the solution behaviour near separation

Published online by Cambridge University Press:  20 April 2006

Antonios Liakopoulos  and
Chen-Chi Hsu
Antonios Liakopoulos
Affiliation:
Department of Engineering Sciences, University of Florida, Gainesville, Florida 32611
Chen-Chi Hsu
Affiliation:
Department of Engineering Sciences, University of Florida, Gainesville, Florida 32611
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Abstract

A class of compressible laminar boundary-layer flows subject to adverse pressure gradients of different magnitude is studied using a finite-element–differential method in which the assumed solutions are represented by classical cubic spline functions. The numerical integration process for the reduced initial-value problem has been carried out directly to at least one integration step upstream of the separation point, and very accurate numerical results have been obtained for a large number of integration steps extremely close to separation. The skin-friction and heat-transfer coefficients for nearly zero-heat-transfer, cooled-wall and heated-wall cases, computed under the assumption of constant Prandtl number Pr = 1.0 as well as Pr = 0.72, have clearly exhibited the same distinctive behaviour near separation. It is deduced that Buckmaster's series expansions for the solution near separation, derived on the assumptions of cooled wall and Pr = 1.0, are valid for all the cases considered. By matching the numerical results with Buckmaster's expansions, accurate distributions of skin friction and heat transfer have been obtained up to the separation point. Moreover, the importance of Prandtl number on the solution is evidenced from the numerical results presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 149 , December 1984 , pp. 339 - 353
Copyright
© 1984 Cambridge University Press

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