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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

REFERENCES

Afzal, N. 2001 Power law and log law velocity profiles in turbulent boundary layer flow: equivalent relations at large Reynolds numbers. Acta Mechanica 151, 195–216.CrossRefGoogle Scholar
Barenblatt, G. I., Chorin, A. J. & Prostokishin, V. M. 2000 A note on the intermediate region in turbulent boundary layers. Phys. Fluids 12, 2159–2161.CrossRefGoogle Scholar
Benedict, R. P. 1984 Fundamentals of Pressure, Temperature and Flow Measurements, pp. 340–349. Wiley.CrossRefGoogle Scholar
Bourassa, C. & Thomas, F. O. 2009 An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359–404.CrossRefGoogle Scholar
Buschmann, M. H. & Gad-el-Hak, M. 2003 Debate concerning the mean-velocity profile of a turbulent boundary layer. AIAA J. 41, 565–572.CrossRefGoogle Scholar
Compton, D. A. & Eaton, J. K. 1996 A high resolution laser Doppler anemometer for three dimensional turbulent boundary layers. Exp. Fluids 22, 111–117.CrossRefGoogle Scholar
Compton, D. A. & Eaton, J. K. 1997 Near-wall measurements in a three-dimensional turbulent boundary layer. J. Fluid Mech. 350, 189–208.CrossRefGoogle Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.CrossRefGoogle Scholar
Elbing, B. R., Winkel, E. S., Lay, K. A., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2008 Bubble-induced skin friction drag reduction and the abrupt transition to air-layer drag reduction. J. Fluid Mech. 612, 201–236.CrossRefGoogle Scholar
Etter, R. J., Cutbirth, J. M., Ceccio, S. L., Dowling, D. R. & Perlin, M. 2005 High Reynolds number experimentation in the US Navy's William B. Morgan Large Cavitation Channel. Meas. Sci. Technol. 16, 1701–1709.CrossRefGoogle Scholar
Fernholtz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245–311.CrossRefGoogle Scholar
Fernholtz, H. H., Krause, E., Nockermann, M. & Schober, M. 1995 Comparative measurements of the canonical boundary layer at Reδ2 ≤ 1.15 × 105 on the wall of the German–Dutch windtunnel. Phys. Fluids 7, 1275–1281.CrossRefGoogle Scholar
Fife, P., Wei, T., Klewicki, J. & McMurtry, P. 2005 Stress gradient balance layers and scale hierarchies in wall-bounded turbulent flows. J. Fluid Mech. 532, 165–189.CrossRefGoogle Scholar
Gad-el-Hak, M. & Bandyopadhyay, P. R. 1994 Reynolds number effects in wall-bounded turbulent flows. Appl. Mech. Rev. 47, 307–365.CrossRefGoogle Scholar
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50, 689–729.CrossRefGoogle Scholar
Knoblock, K. & Fernholtz, H.-H. 2002 Statistics, correlations, and scaling in a turbulent boundary layer at Reι2 ≤ 1.15 × 105. In IUTAM Symposium on Reynolds Number Scaling in Trubulent Flow (ed. Smits, A. J.), pp. 11–16. Springer.Google Scholar
Kunkel, G. J. & Marusic, I. 2006 Study of the new-wall-turbulent region of the high Reynolds number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375–402.CrossRefGoogle Scholar
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic Press.Google Scholar
Lindgren, B., Österlund, J. M. & Johansson, A. V. 2004 Evaluation of scaling laws derived from Lie group symmetry methods in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 502, 127–152.CrossRefGoogle Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 2461–2464.CrossRefGoogle Scholar
Marusic, I., Mckeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Marusic, I., Uddin, A. K. M. & Perry, A. E. 1997 Similarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers. Phys. Fluids 9, 3718–3726.CrossRefGoogle Scholar
McKeon, B. (ed.) 2007 Theme issue on scaling and structure in high Reynolds number wall bounded flows. Phil. Trans. R. Soc. Lond., Ser. A 365, 635–876.Google Scholar
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13, 692–701.CrossRefGoogle Scholar
Metzger, M. M., Klewicki, J. C., Bradshaw, K. L. & Sadr, R. 2001 Scaling the near-wall axial turbulent stress in the zero pressure gradient boundary layer. Phys. Fluids 13, 1819–1821.CrossRefGoogle Scholar
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2007 Self-consistent high-Reynolds number asymptotics for zero-pressure-gradient turbulent boundary layers. Phys. Fluids 19, 115101.CrossRefGoogle Scholar
Monkewitz, P. A., Chauhan, K. A. & Nagib, H. M. 2008 Comparison of mean flow similiarity laws in zero pressure gradient turbulent boundary layers. Phys. Fluids 20, 105102.CrossRefGoogle Scholar
Nagib, H. M. & Chauhan, K. A. 2008 Variations of the von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.CrossRefGoogle Scholar
Nagib, H. M., Christophorou, C. & Monkewitz, P. A. 2004 High Reynolds number turbulent boundary layers subjected to various pressure-gradient conditions. In IUTAM Symposium on One Hundred Years of Boundary Layer Research (ed. Meier, G. & Sreenivasan, K.), pp. 383–394. Springer.Google Scholar
Österlund, J. M., Johansson, A. V., Hagib, H. M. & Hites, M. H. 1999 Wall shear stress measurements in high Reynolds number boundary layers from two facilities. In 30th AIAA Fluid Dynamics Conference, Norfolk, VA (AIAA Paper no. 99–3814).Google Scholar
Österlund, J. M., Johansson, A. V. & Nagib, H. 2000 a A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 1–4.CrossRefGoogle Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. & Hites, M. H. 2000 b Comment on ‘A note on the intermediate region in turbulent boundary layers [Phys. Fluids 12, 2159]’. Phys. Fluids 12, 2360–2363.CrossRefGoogle Scholar
Panton, R. C. 2002 Evaluation of the Barenblatt–Chorin–Prostokishin power law for turbulent boundary layers. Phys. Fluids 14, 180-1808.CrossRefGoogle Scholar
Park, J. T., Cutbirth, J. M. & Brewer, W. H. 2003 Hydrodynamic performance of the Large Cavitation Channel (LCC). In Proceedings of the 4th ASME_JSME Joint Fluids Engng Conference, Honolulu, HI.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds numbers. J. Fluid Mech. 268, 333–372.CrossRefGoogle Scholar
Sanders, W. C., Winkel, E. S., Dowling, D. R., Perlin, M. & Ceccio, S. L. 2006 Bubble friction drag reduction in a high Reynolds number flat plate turbulent boundary layer. J. Fluid Mech. 552, 353–380.CrossRefGoogle Scholar
Schultz-Grunow, F. 1941 New frictional resistance law for smooth plates. NACA Tech. Memorandum 17–18, 1–24.Google Scholar
Sreenivasan, K. R. 1989 The turbulent boundary layer. Frontiers Exp. Fluid Mech. 46, 159–209.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe, and channel flows. J. Fluid Mech. 522, 303–327.CrossRefGoogle Scholar
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.Google Scholar
Winkel, E. S., Oweis, G. F., Vanapalli, S. A., Dowling, D. R., Perlin, M., Solomom, M. J. & Ceccio, S. L. 2009 High Reynolds number turbulent boundary layer friction drag reduction from wall-injected polymer solutions. J. Fluid Mech. 621, 259–288.CrossRefGoogle Scholar
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