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

  • GHANEM F. OWEIS (a1), ERIC S. WINKEL (a2), JAMES M. CUTBRITH (a3), STEVEN L. CECCIO (a2), MARC PERLIN (a4) and DAVID R. DOWLING (a2)...

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.

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Corresponding author

Email address for correspondence: drd@umich.edu

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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

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References

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Afzal, N. 2001 Power law and log law velocity profiles in turbulent boundary layer flow: equivalent relations at large Reynolds numbers. Acta Mechanica 151, 195216.
Barenblatt, G. I., Chorin, A. J. & Prostokishin, V. M. 2000 A note on the intermediate region in turbulent boundary layers. Phys. Fluids 12, 21592161.
Benedict, R. P. 1984 Fundamentals of Pressure, Temperature and Flow Measurements, pp. 340349. Wiley.
Bourassa, C. & Thomas, F. O. 2009 An experimental investigation of a highly accelerated turbulent boundary layer. J. Fluid Mech. 634, 359404.
Buschmann, M. H. & Gad-el-Hak, M. 2003 Debate concerning the mean-velocity profile of a turbulent boundary layer. AIAA J. 41, 565572.
Compton, D. A. & Eaton, J. K. 1996 A high resolution laser Doppler anemometer for three dimensional turbulent boundary layers. Exp. Fluids 22, 111117.
Compton, D. A. & Eaton, J. K. 1997 Near-wall measurements in a three-dimensional turbulent boundary layer. J. Fluid Mech. 350, 189208.
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.
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, 201236.
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, 17011709.
Fernholtz, H. H. & Finley, P. J. 1996 The incompressible zero-pressure-gradient turbulent boundary layer: an assessment of the data. Prog. Aerosp. Sci. 32, 245311.
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, 12751281.
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, 165189.
Gad-el-Hak, M. & Bandyopadhyay, P. R. 1994 Reynolds number effects in wall-bounded turbulent flows. Appl. Mech. Rev. 47, 307365.
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50, 689729.
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. 1116. Springer.
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, 375402.
Launder, B. E. & Spalding, D. B. 1972 Mathematical Models of Turbulence. Academic Press.
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, 127152.
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15, 24612464.
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.
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, 37183726.
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, 635876.
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, 692701.
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, 18191821.
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.
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.
Nagib, H. M. & Chauhan, K. A. 2008 Variations of the von Kármán coefficient in canonical flows. Phys. Fluids 20, 101518.
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. 383394. Springer.
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).
Österlund, J. M., Johansson, A. V. & Nagib, H. 2000 a A note on the overlap region in turbulent boundary layers. Phys. Fluids 12, 14.
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, 23602363.
Panton, R. C. 2002 Evaluation of the Barenblatt–Chorin–Prostokishin power law for turbulent boundary layers. Phys. Fluids 14, 180-1808.
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.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds numbers. J. Fluid Mech. 268, 333372.
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, 353380.
Schultz-Grunow, F. 1941 New frictional resistance law for smooth plates. NACA Tech. Memorandum 17–18, 1–24.
Sreenivasan, K. R. 1989 The turbulent boundary layer. Frontiers Exp. Fluid Mech. 46, 159209.
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, 303327.
White, F. M. 2006 Viscous Fluid Flow, 3rd edn. McGraw-Hill.
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, 259288.
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The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number

  • GHANEM F. OWEIS (a1), ERIC S. WINKEL (a2), JAMES M. CUTBRITH (a3), STEVEN L. CECCIO (a2), MARC PERLIN (a4) and DAVID R. DOWLING (a2)...

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