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On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes

Published online by Cambridge University Press:  26 April 2006

J. C. Klewicki  and
R. E. Falco
J. C. Klewicki
Affiliation:
Turbulence Structure Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226. USA
R. E. Falco
Affiliation:
Turbulence Structure Laboratory, Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824-1226. USA
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Abstract

Spanwise vorticity measurements have been performed in zero-pressure-gradient boundary layers over the range 1010 < Rθ < 4850 (Rθ ≡ U∞ θ/ν, where U∞ is the free-stream velocity and θ is the momentum deficit thickness) using a four-wire probe. In addition, experiments quantifying the spatial and temporal resolution required to obtain an accurate statistical representation of the small-scale structure of wall-bounded turbulence were performed. Furthermore, a thorough investigation of statistical convergence for a variety of fluctuating quantities was performed. Comparisons with earlier high-resolution studies indicate that the maximum value of u′/uτ increases with increasing Reynolds number over the given Rθ range (u′ ≡ r.m.s. u, and uτ is the friction velocity). It is suggested that detecting this dependence provides a good measure of probe resolution. In general it was found that statistics of velocity gradients were distinctly more sensitive to finite probe size than velocity statistics. Wire spacing experiments suggest that Wyngaard's (1969) criterion is to a good approximation valid even under anisotropic conditions. Furthermore, it was found that instantaneously spatial averaging of ∂u/∂t caused significant attenuation in the resulting r.m.s., and that this averaging procedure is sensitive to the level of mean shear. A simple method of estimating how noise in the u-velocity signals enters into the ∂u/∂y signals is presented. The convergence study shows that statistical convergence criteria developed from free-shear flows severely underestimates the averaging times required in boundary layers. A table of general convergence criteria is provided.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 219 , October 1990 , pp. 119 - 142
Copyright
© 1990 Cambridge University Press

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