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The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number

Published online by Cambridge University Press:  06 December 2010

GHANEM F. OWEIS ,
ERIC S. WINKEL ,
JAMES M. CUTBRITH ,
STEVEN L. CECCIO ,
MARC PERLIN  and
DAVID R. DOWLING
GHANEM F. OWEIS
Affiliation:
Department of Mechanical Engineering, Faculty of Engineering and Architecture, American University of Beirut, PO Box 11-0236, Riad El Solh, Beirut 1107 2020, Lebanon
ERIC S. WINKEL
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
JAMES M. CUTBRITH
Affiliation:
Carderock Division, Naval Surface Warfare Center, W. B. Morgan Large Cavitation Channel, 3001 Harbor Avenue, Memphis, TN 38113, USA
STEVEN L. CECCIO
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
MARC PERLIN
Affiliation:
Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA
DAVID R. DOWLING*
Affiliation:
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109, USA
*
∥Email address for correspondence: drd@umich.edu
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Abstract

Smooth flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century. However, there is a relative dearth of measurements at Reynolds numbers typical of full-scale marine and aerospace transportation systems (Reθ = Ueθ/ν > 105, where Ue = free-stream speed, θ = TBL momentum thickness and ν = kinematic viscosity). This paper presents new experimental results for the TBL that forms on a smooth flat plate at nominal Reθ values of 0.5 × 105, 1.0 × 105 and 1.5 × 105. Nominal boundary layer thicknesses (δ) were 80–90mm, and Karman numbers (δ+) were 17000, 32000 and 47000, respectively. The experiments were conducted in the William B. Morgan Large Cavitation Channel on a polished (k+ < 0.2) flat-plate test model 12.9m long and 3.05m wide at water flow speeds up to 20ms−1. Direct measurements of static pressure and mean wall shear stress were obtained with pressure taps and floating-plate skin friction force balances. The TBL developed a mild favourable pressure gradient that led to a streamwise flow speed increase of ~2.5% over the 11m long test surface, and was consistent with test section sidewall and model surface boundary-layer growth. At each Reθ, mean streamwise velocity profile pairs, separated by 24cm, were measured more than 10m from the model's leading edge using conventional laser Doppler velocimetry. Between these profile pairs, a unique near-wall implementation of particle tracking velocimetry was used to measure the near-wall velocity profile. The composite profile measurements span the wall-normal coordinate range from y+ < 1 to y > 2δ. To within experimental uncertainty, the measured mean velocity profiles can be fit using traditional zero-pressure-gradient (ZPG) TBL asymptotics with some modifications for the mild favourable pressure gradient. The fitted profile pairs satisfy the von-Kármán momentum integral equation to within 1%. However, the profiles reported here show distinct differences from equivalent ZPG profiles. The near-wall indicator function has more prominent extrema, the log-law constants differ slightly, and the profiles' wake component is less pronounced.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
Papers
Information
Journal of Fluid Mechanics , Volume 665 , 25 December 2010 , pp. 357 - 381
Copyright
Copyright © Cambridge University Press 2010

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Footnotes

†

Formerly at the University of Michigan, Ann Arbor, MI 48109, USA

‡

Present address: Design Research Engineering, Novi, MI 48377, USA

Present address: Mainstream Engineering Corporation, Rockledge, FL 32955, USA

References

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