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Rough-wall turbulent boundary layers in the transition regime

Published online by Cambridge University Press:  21 April 2006

Promode R. Bandyopadhyay
Promode R. Bandyopadhyay
Affiliation:
Mail Stop 163. NASA Langley Research Center, Hampton, VA 23665-5225, USA
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Abstract

This paper describes an experimental study of turbulent boundary layers over two-dimensional spanwise groove and three-dimensional sandgrain roughnesses in the ‘transition regime’ between hydraulically smooth and fully rough conditions. Mean-flow measurements show that a state of kinematic near-self-preservation is also reached by sandgrain roughness and not just by d-type grooved roughness alone as commonly believed; sandgrain roughness simply requires an order-of-magnitude-longer length to reach such a state. The two roughness Reynolds numbers demarcating the boundaries of the transition regime of k-type roughnesses are found to decrease with increasing roughness-element spanwise aspect ratio (span/height). A more important role of the upper-Reynolds-number limit of the transition regime in the drag behaviour is indicated. The two Reynolds-number limits of the transition regime correlate with the two critical Reynolds numbers that describe the stability of the vortex-shedding process existing behind a similar but isolated roughness element lying submerged in an otherwise laminar boundary layer. The results provide a guideline for reducing k-type rough-wall drag by lowering the spanwise aspect ratio of the roughness elements. The vortex-shedding process in rough-wall turbulent boundary layers is described by the stability parameter $U\tau (\overline{T}/\nu)^{\frac{1}{2}}$ whose value is the same for all roughnesses examined herein; here Uτ is the friction velocity, $\overline{T}$ is the mean time period of vortex shedding and v is the kinematic viscosity of the fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 231 - 266
Copyright
© 1987 Cambridge University Press

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