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The viscous sublayer revisited–exploiting self-similarity to determine the wall position and friction velocity

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Abstract

In experiments using hot wires near the wall, it is well known that wall interference effects between the hot wire and the wall give rise to errors, and mean velocity data from the viscous sublayer can usually not be used to determine the wall position, nor the friction velocity from the linear velocity distribution. Here, we introduce a new method that takes advantage of the similarity of the probability density distributions (PDF) or rather the cumulative distribution functions (CDF) in the near-wall region. By using the velocity data in the CDF in a novel way, it is possible to circumvent the problem associated with heat transfer to the wall and to accurately determine both the wall position and the friction velocity. Prior to its exploitation, the self-similarity of the distribution functions of the streamwise velocity fluctuations within the viscous sublayer is established, and it is shown that they can accurately be described by a lognormal distribution.

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Notes

  1. The situation for pipe flows is, due to the lack of both resolved experimental and numerical data spanning a sufficient Reynolds number range, unclear (Hultmark et al. 2010), although the recent pipe flow DNS by Wu and Moin (2009) indicates an increase in the limiting values with increasing Reynolds number.

  2. Equivalently, the lognormal distribution parameters, μ and σ, can be obtained through the mean and variance of the PDF, viz. \(\mu=\ln(\rm{mean}^2/\sqrt{\rm{var}+\rm{mean}^2})\) and \(\sigma=\sqrt{\ln(\rm{var}/\rm{mean}^2+1)}\).

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Acknowledgements

Financial support from the Swedish Research Foundation (VR) is gratefully acknowledged. Computer time was provided by SNIC (Swedish National Infrastructure for Computing) with a generous grant by the Knut and Alice Wallenberg (KAW) Foundation.

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Authors and Affiliations

  1. Linné FLOW Centre, KTH Mechanics, 100 44, Stockholm, Sweden

    P. Henrik Alfredsson, Ramis Örlü & Philipp Schlatter

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  1. P. Henrik Alfredsson
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  2. Ramis Örlü
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  3. Philipp Schlatter
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Correspondence to P. Henrik Alfredsson.

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Alfredsson, P.H., Örlü, R. & Schlatter, P. The viscous sublayer revisited–exploiting self-similarity to determine the wall position and friction velocity. Exp Fluids 51, 271–280 (2011). https://doi.org/10.1007/s00348-011-1048-8

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  • DOI: https://doi.org/10.1007/s00348-011-1048-8

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