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Comprehensive shear stress analysis of turbulent boundary layer profiles

Published online by Cambridge University Press:  27 September 2019

Kristofer M. Womack Open the ORCID record for Kristofer M. Womack [Opens in a new window] ,
Charles Meneveau Open the ORCID record for Charles Meneveau [Opens in a new window]  and
Michael P. Schultz Open the ORCID record for Michael P. Schultz [Opens in a new window]
Kristofer M. Womack
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Charles Meneveau
Affiliation:
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD 21218, USA
Michael P. Schultz*
Affiliation:
Department of Naval Architecture and Ocean Engineering, United States Naval Academy, Annapolis, MD 21402, USA
*
†Email address for correspondence: mschultz@usna.edu
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Abstract

Motivated by the need for accurate determination of wall shear stress from profile measurements in turbulent boundary layer flows, the total shear stress balance is analysed and reformulated using several well-established semi-empirical relations. The analysis highlights the significant effect that small pressure gradients can have on parameters deduced from data even in nominally zero pressure gradient boundary layers. Using the comprehensive shear stress balance together with the log-law equation, it is shown that friction velocity, roughness length and zero-plane displacement can be determined with only velocity and turbulent shear stress profile measurements at a single streamwise location for nominally zero pressure gradient turbulent boundary layers. Application of the proposed analysis to turbulent smooth- and rough-wall experimental data shows that the friction velocity is determined with accuracy comparable to force balances (approximately 1 %–4 %). Additionally, application to boundary layer data from previous studies provides clear evidence that the often cited discrepancy between directly measured friction velocities (e.g. using force balances) and those derived from traditional total shear stress methods is likely due to the small favourable pressure gradient imposed by a fixed cross-section facility. The proposed comprehensive shear stress analysis can account for these small pressure gradients and allows more accurate boundary layer wall shear stress or friction velocity determination using commonly available mean velocity and shear stress profile data from a single streamwise location.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 879 , 25 November 2019 , pp. 360 - 389
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Copyright
© 2019 Cambridge University Press 

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