Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-19T05:09:32.177Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent boundary layer statistics at very high Reynolds number

Published online by Cambridge University Press:  17 August 2015

M. Vallikivi ,
M. Hultmark  and
A. J. Smits
M. Vallikivi
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
M. Hultmark*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
A. J. Smits
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Department of Mechanical and Aerospace Engineering, Monash University, Melbourne, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 371 - 389
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Afzal, N. 1982 Fully developed turbulent flow in a pipe: an intermediate layer. Ing.-Arch. 52, 355–377.CrossRefGoogle Scholar
Afzal, N. 1984 Mesolayer theory for turbulent flows. AIAA J. 22, 437–439.CrossRefGoogle Scholar
Bailey, S. C. C., Hultmark, M., Monty, J. P., Alfredsson, P. H., Chong, M. S., Duncan, R. D., Fransson, J. H. M., Hutchins, N., Marusic, I., McKeon, B. J., Nagib, H. M., Örlü, R., Segalini, A., Smits, A. J. & Vinuesa, R. 2013 Obtaining accurate mean velocity measurements in high Reynolds number turbulent boundary layers using Pitot tubes. J. Fluid Mech. 715, 642–670.Google Scholar
Bailey, S. C. C., Kunkel, G. J., Hultmark, M., Vallikivi, M., Hill, J. P., Meyer, K. A., Tsay, C., Arnold, C. B. & Smits, A. J. 2010 Turbulence measurements using a nanoscale thermal anemometry probe. J. Fluid Mech. 663, 160–179.CrossRefGoogle Scholar
Bailey, S. C. C., Vallikivi, M., Hultmark, M. & Smits, A. J. 2014 Estimating the value of von Kármán’s constant in turbulent pipe flow. J. Fluid Mech. 749, 79–98.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Mech. 4, 1–51.Google Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191–226.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Fernholz, 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
George, W. K. & Castillo, L. 1997 Zero-pressure-gradient turbulent boundary layer. Appl. Mech. Rev. 50, 689–729.Google Scholar
Hultmark, M. 2012 A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow. J. Fluid Mech. 707, 575–584.CrossRefGoogle Scholar
Hultmark, M. & Smits, A. J. 2010 Temperature corrections for constant temperature and constant current hot-wire anemometers. Meas. Sci. Technol. 21, 105404.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 1–5.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2013 Logarithmic scaling of turbulence in smooth- and rough-wall pipe flow. J. Fluid Mech. 728, 376–395.Google Scholar
Hutchins, N., Chauhan, K. A., Marusic, I., Monty, J. & Klewicki, J. 2012 Towards reconciling the large-scale structure of turbulent boundary layers in the atmosphere and laboratory. Boundary-Layer Meteorol. 145, 273–306.Google Scholar
Jiménez, J. M., Hultmark, M. & Smits, A. J. 2010 The intermediate wake of a body of revolution at high Reynolds numbers. J. Fluid Mech. 659, 516–539.Google Scholar
MacMillan, F. A.1957 Experiments on Pitot tubes in shear flow. No. 3028 Ministry of Supply, Aeronautical Research Council.Google Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3,1–3.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.CrossRefGoogle Scholar
McKeon, B. J., Li, J., Jiang, W., Morrison, J. F. & Smits, A. J. 2003 Pitot probe corrections in fully developed turbulent pipe flow. Meas. Sci. Technol. 14 (8), 1449–1458.CrossRefGoogle Scholar
McKeon, B. J., Li, J., Jiang, W., Morrison, J. F. & Smits, A. J. 2004 Further observations on the mean velocity distribution in fully developed pipe flow. J. Fluid Mech. 501, 135–147.Google Scholar
McKeon, B. J. & Smits, A. J. 2002 Static pressure correction in high Reynolds number fully developed turbulent pipe flow. Meas. Sci. Technol. 13, 1608–1614.Google Scholar
Meneveau, C. & Marusic, I. 2013 Generalized logarithmic law for high-order moments in turbulent boundary layers. J. Fluid Mech. 719, R1.Google Scholar
Metzger, M., McKeon, B. J. & Holmes, H. 2007 The near-neutral atmospheric surface layer: turbulence and non-stationarity. Phil. Trans. R. Soc. Lond. A 365 (1852), 859–876.Google Scholar
Millikan, C. B. 1938 A critical discussion of turbulent flows in channels and circular tubes. In Proceedings of the fifth International Congress for Applied Mechanics, pp. 386–392. Wiley/Chapman and Hall.Google Scholar
Nagib, H. M., Chauhan, K. A. & Monkewitz, P. A. 2007 Approach to an asymptotic state for zero pressure gradient turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 365 (1852), 755–770.Google Scholar
Österlund, J. M., Johansson, A. V., Nagib, H. M. & Hites, M. H. 2000 A note on the overlap region in turbulent boundary layers. Phys. Fluids 12 (1), 1–4.CrossRefGoogle Scholar
Patel, V. C. 1965 Calibration of the Preston tube and limitations on its use in pressure gradients. J. Fluid Mech. 23, 185–208.Google Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Pullin, D. I., Inoue, M. & Saito, N. 2013 On the asymptotic state of high Reynolds number, smooth-wall turbulent flows. Phys. Fluids 25 (1), 105116.CrossRefGoogle Scholar
Rosenberg, B. J., Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2013 Turbulence spectra in smooth- and rough-wall pipe flow at extreme Reynolds numbers. J. Fluid Mech. 731, 46–63.CrossRefGoogle Scholar
Smits, A. J. & Marusic, I. 2013 Wall-bounded turbulence. Phys. Today 25–30.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011a High Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Smits, A. J., Monty, J., Hultmark, M., Bailey, S. C. C., Hutchins, M. & Marusic, I. 2011b Spatial resolution correction for turbulence measurements. J. Fluid Mech. 676, 41–53.Google Scholar
Sreenivasan, K. R. & Sahay, A. 1997 The persistence of viscous effects in the overlap region and the mean velocity in turbulent pipe and channel flows. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R.), pp. 253–272. Comp. Mech. Publ.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vallikivi, M.2014 Wall-bounded turbulence at high Reynolds numbers. PhD thesis, Princeton University.Google Scholar
Vallikivi, M., Ganapathisubramani, B. & Smits, A. J. 2015 Spectra in boundary layers and pipes at very high Reynolds numbers. J. Fluid Mech. 771, 303–326.Google Scholar
Vallikivi, M., Hultmark, M., Bailey, S. C. C. & Smits, A. J. 2011 Turbulence measurements in pipe flow using a nano-scale thermal anemometry probe. Exp. Fluids 51, 1521–1527.CrossRefGoogle Scholar
Vallikivi, M., Hultmark, M. & Smits, A. J.2013 The scaling of very high Reynolds number turbulent boundary layers. In 8th International Symposium on Turbulence and Shear Flow Phenomena, Poitiers, France.CrossRefGoogle Scholar
Vallikivi, M. & Smits, A. J. 2014 Fabrication and characterization of a novel nano-scale thermal anemometry probe. J. Microelectromech. Syst. 23 (4), 899–907.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. C. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303–327.Google Scholar
Winkel, E. S., Cutbirth, J. M., Ceccio, S. L., Perlin, M. & Dowling, D. R. 2012 Turbulence profiles from a smooth flat-plate turbulent boundary layer at high Reynolds number. Exp. Therm. Fluid Sci. 40, 140–149.Google Scholar
Winter, K. G. & Gaudet, L.1970 Turbulent boundary-layer studies at high Reynolds numbers at Mach numbers between 0.2 and 2.8. R & M No. 3712. Aeronautical Research Council, Ministry of Aviation Supply, Royal Aircraft Establishment, RAE.Google Scholar
Wosnik, M., Castillo, L. & George, W. K. 2000 A theory for turbulent pipe and channel flows. J. Fluid Mech. 421, 115–145.Google Scholar
Zagarola, M. V. & Smits, A. J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 33–79.CrossRefGoogle Scholar
Zagarola, M. V., Williams, D. R. & Smits, A. J. 2001 Calibration of the Preston probe for high Reynolds number flows. Meas. Sci. Technol. 12, 495–501.Google Scholar