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Scaling of the wall-normal turbulence component in high-Reynolds-number pipe flow

Published online by Cambridge University Press:  28 March 2007

RONGRONG ZHAO
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
ALEXANDER J. SMITS
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA

Abstract

Streamwise and wall-normal turbulence components are obtained in fully developed turbulent pipe over a Reynolds number range from 1.1 × 105 to 9.8 × 106. The streamwise intensity data are consistent with previous measurements in the same facility. For the wall-normal turbulence intensity, a constant region in v'r.m.s. is found for the region 200 ≤ y+ ≤ 0.1R+ for Reynolds numbers up to 1.0 × 106. An increase in v'r.m.s. is observed below about y+ ∼ 100, although additional measurements will be required to establish its generality. The wall-normal spectra collapse in the energy-containing region with inner scaling, but for the low-wavenumber region a y/R dependence is observed, which also indicates a continuing influence from the outer flow on the near-wall motions.

Type
Papers
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

DeGraaff, D. B. & Eaton, J. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.CrossRefGoogle Scholar
Fernholz, H. H. & Finley, P. J. 1996. Incompressible zero-pressure-gradient turbulent boundary layers: {A}n assessment of the data. Prog. Aerospace Sci. 32, 245311.CrossRefGoogle Scholar
Fernholz, H. H., Krause, E., Nockemann, N. & Schober, M. 1995. Comparative measurements in the canonical boundary layer at Reδ2 ≤ 6 × 104 on the wall of the German–Dutch windtunnel. Phys. Fluids 7, 12751281.CrossRefGoogle Scholar
Khoo, B. C., Chew, Y. T. & Li, G. L. 1997 Effects of imperfect spatial resolution on turbulence measurements in the very near-wall viscous sublayer region. Exps. Fluids 22, 327335.CrossRefGoogle Scholar
Klewicki, J. C. & Falco, R. E. 1990 On accurately measuring statistics associated with small-scale structure in turbulent boundary layers using hot-wire probes. J. Fluid Mech. 219, 119142.CrossRefGoogle Scholar
Kunkel, G. J. & Marusic, I. 2005 Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow. J. Fluid Mech. 548, 375402.CrossRefGoogle Scholar
Laufer, J. 1954 The structure of turbulence in fully developed pipe flow. NACA Rep. 1174.Google Scholar
Lawn, C. J. 1971 The determination of the rate of dissipation in turbulent pipe flow. J. Fluid Mech. 48, 477505.CrossRefGoogle Scholar
Marusic, I. & Kunkel, G. J. & Porte-Agel, F. 2001 Experimental study of wall boundary conditions for large-eddy simulation. J. Fluid Mech. 446, 309320.CrossRefGoogle Scholar
Marusic, I., Kunkel, G. J., Zhao, R. & Smits, A. J. 2004 Turbulence intensity similarity formulations for wall-bounded flows. In: Advances in Turbulence X, Proc. of the 10th European Turb. Conf., CIMNE, Barcelona, Spain (ed. Andersson, H. I. & Krogstad, P.-A.).Google Scholar
Marusic, I. & Perry, A. E. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support. J. Fluid Mech. 298, 389407.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, 37183726.CrossRefGoogle Scholar
McKeon, B. J., Ji, 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, 135147.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, 14491458.CrossRefGoogle Scholar
McKeon, B. J. & Morrison, J. F. 2005 Inertial scaling and the mixing transition in turbulent pipe flow. J. Fluid Mech. (Submitted).Google Scholar
McKeon, B. J. & Smits, A. J. 2003 Static pressure correction in high Reynolds number fully-developed turbulent pipe flow. Meas. Sci. Technol. 13, 16081614.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, 18191821.CrossRefGoogle Scholar
Morrison, J. F., McKeon, B. J., Jiang, W. & Smits, A. J. 2004 Scaling of the streamwise velocity component in turbulent pipe flow. J. Fluid Mech. 508, 99131.CrossRefGoogle Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005. Evidence of the k1−1 law in a high Reynolds number turbulent boundary layer. Phys. Review Lett. 95, 074501.CrossRefGoogle Scholar
Osterlund, J. 1999 Experimental studies of zero pressure-gradient turbulent boundary-layer flow. PhD thesis, Royal Institute of Technology, Stockholm.Google Scholar
Perry, A. E. 1982. Hot-Wire Anemometry. Oxford University Press.Google Scholar
Perry, A. E. & Abell, C. J. 1975 Scaling laws for pipe-flow turbulence. J. Fluid Mech. 67, 257271.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. M. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.CrossRefGoogle Scholar
Perry, A. E. & Li, J. 1990 Experimental support for the attached eddy hypothesis in zero-pressure-gradient turbulent boundary layers. J. Fluid Mech. 218, 405438.CrossRefGoogle Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361388.CrossRefGoogle Scholar
Shockling, M. A., Allen, J. J. & Smits, A. J. 2006 Effects of machined surface roughness on high-Reynolds-number turbulent pipe flow. J. Fluid Mech. 564, 267285.CrossRefGoogle Scholar
Townes, H. W., Gow, J. L., Powe, R. E. & Weber, N. 1972 Turbulent flow in smooth and rough pipes. J. Basic Engin. 94, 353362.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.Google Scholar
Wyngaard, A. A. 1968 Measurements of small-scale turbulence structure with hot wires. J. Sci. Instrum. 2, 1, 11051108.CrossRefGoogle Scholar
Zagarola, M. V. 1996 Turbulent pipe flow. PhD thesis, Princeton University, Princeton.Google Scholar
Zagarola, M. V. 1997 Scaling of high-Reynolds number turbulent boundary layers in the National Diagnostic Facility. PhD thesis, Illinois Institute of Technology, Chicago.Google Scholar
Zagarola, M. V. & Smits, A. J. 1998 Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 373, 3379.CrossRefGoogle Scholar
Zhao, R. 2005 High Reynolds number turbulent pipe flow. PhD thesis, Princeton University, Princeton.Google Scholar
Zhao, R., Li, J. & Smits, A. J. 2004 A new calibration method for crossed hot wires. Meas. Sci. Technol. 15, 19261931.CrossRefGoogle Scholar
Zhao, R. & Smits, A. J. 2006 Binormal cooling errors on crossed hot-wire measurements. Exps. Fluids 40 (2), 212217.CrossRefGoogle Scholar