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Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to $\mathbf{Re}_{\boldsymbol{\theta}}{=}$13650

Published online by Cambridge University Press:  04 March 2014

Sébastien Deck ,
Nicolas Renard ,
Romain Laraufie  and
Pierre-Élie Weiss
Sébastien Deck*
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
Nicolas Renard
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
Romain Laraufie
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
Pierre-Élie Weiss
Affiliation:
ONERA, The French Aerospace Lab, F-92190 Meudon, France
*
†Email address for correspondence: [email protected]
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Abstract

A numerical investigation of the mean wall shear stress properties on a spatially developing turbulent boundary layer over a smooth flat plate was carried out by means of a zonal detached eddy simulation (ZDES) technique for the Reynolds number range $3060\leq Re_{\theta }\leq 13\, 650$. Some asymptotic trends of global parameters are suggested. Consistently with previous findings, the calculation confirms the occurrence of very large-scale motions approximately $5\delta $ to $6 \delta $ long which are meandering with a lateral amplitude of $0.3 \delta $ and which maintain a footprint in the near-wall region. It is shown that these large scales carry a significant amount of Reynolds shear stress and their influence on the skin friction, denoted $C_{f,2}$, is revisited through the FIK identity by Fukagata, Iwamoto & Kasagi (Phys. Fluids, vol. 14, 2002, p. L73). It is argued that $C_{f,2}$ is the relevant parameter to characterize the high-Reynolds-number turbulent skin friction since the term describing the spatial heterogeneity of the boundary layer also characterizes the total shear stress variations across the boundary layer. The behaviour of the latter term seems to follow some remarkable self-similarity trends towards high Reynolds numbers. A spectral analysis of the weighted Reynolds stress with respect to the distance to the wall and to the wavelength is provided for the first time to our knowledge and allows us to analyse the influence of the largest scales on the skin friction. It is shown that structures with a streamwise wavelength $\lambda _x >\delta $ contribute to more than $60\, \%$ of $C_{f,2}$, and that those larger than $\lambda _x >2\delta $ still represent approximately $45\, \%$ of $C_{f,2}$.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulence simulation
Type
Papers
Information
Journal of Fluid Mechanics , Volume 743 , 25 March 2014 , pp. 202 - 248
Copyright
© 2014 Cambridge University Press 

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