Uncertainty analysis of the von Kármán constant

Uncertainty analysis of the von Kármán constant In 1930, von Kármán presented an expression for the mean velocity distribution in channel and pipe flows that can be transformed into the today well-known logarithmic velocity distribution. At the same time, he also formulated the logarithmic skin friction law and obtained a value of 0.38 for the constant named after him through pipe flow pressure drop measurements. Different approaches to determine the von Kármán constant from mean velocity measurements have been proposed over the last decades, sometimes giving different results even when employed on the same data, partly because the range over which the logarithmic law should be fitted is also under debate. Up to today, the research community has not been able to converge toward a single value and the favored values range between 0.36 and 0.44 for different research groups and canonical flow cases. The present paper discusses some pitfalls and error sources of commonly employed estimation methods and shows, through the use of boundary layer data from Österlund (1999) that von Kármán’s original suggestion of 0.38 seems still to be valid for zero pressure gradient turbulent boundary layer flows. More importantly, it is shown that the uncertainty in the determination of the von Kármán constant can never be less than the uncertainty in the friction velocity, thereby yielding a realistic uncertainty for the most debated constant in wall turbulence. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Experiments in Fluids Springer Journals

Uncertainty analysis of the von Kármán constant

Loading next page...
 
/lp/springer_journal/uncertainty-analysis-of-the-von-k-rm-n-constant-2PU19c0bTH
Publisher
Springer-Verlag
Copyright
Copyright © 2013 by Springer-Verlag Berlin Heidelberg
Subject
Engineering; Engineering Fluid Dynamics; Fluid- and Aerodynamics; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
0723-4864
eISSN
1432-1114
D.O.I.
10.1007/s00348-013-1460-3
Publisher site
See Article on Publisher Site

Abstract

In 1930, von Kármán presented an expression for the mean velocity distribution in channel and pipe flows that can be transformed into the today well-known logarithmic velocity distribution. At the same time, he also formulated the logarithmic skin friction law and obtained a value of 0.38 for the constant named after him through pipe flow pressure drop measurements. Different approaches to determine the von Kármán constant from mean velocity measurements have been proposed over the last decades, sometimes giving different results even when employed on the same data, partly because the range over which the logarithmic law should be fitted is also under debate. Up to today, the research community has not been able to converge toward a single value and the favored values range between 0.36 and 0.44 for different research groups and canonical flow cases. The present paper discusses some pitfalls and error sources of commonly employed estimation methods and shows, through the use of boundary layer data from Österlund (1999) that von Kármán’s original suggestion of 0.38 seems still to be valid for zero pressure gradient turbulent boundary layer flows. More importantly, it is shown that the uncertainty in the determination of the von Kármán constant can never be less than the uncertainty in the friction velocity, thereby yielding a realistic uncertainty for the most debated constant in wall turbulence.

Journal

Experiments in FluidsSpringer Journals

Published: Feb 1, 2013

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off