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Scaling of adverse-pressure-gradient turbulent boundary layers

Published online by Cambridge University Press:  26 April 2006

P. A. Durbin  and
S. E. Belcher
P. A. Durbin
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
S. E. Belcher
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305-3030, USA
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Abstract

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y½ behaviour in the overlap layer between the wall and transition regions.

The analysis is done in the context of eddy viscosity closure modelling. It is found that k-ε-type models are suitable to the wall region, and have a power-law solution in the y½ layer. The outer-region scaling precludes the usual ε-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 238 , May 1992 , pp. 699 - 722
Copyright
© 1992 Cambridge University Press

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