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Research Papers: Fundamental Issues and Canonical Flows

The Application of Wall Similarity Techniques to Determine Wall Shear Velocity in Smooth and Rough Wall Turbulent Boundary Layers

[+] Author and Article Information
Jessica M. Walker

National Centre for Maritime
Engineering and Hydrodynamics,
Australian Maritime College,
University of Tasmania,
Locked Bag 1395,
Launceston, Tasmania, Australia, 7248
e-mail: Jessica.Walker@utas.edu.au

These data are readily available at http://torroja.dmt.upm.es/turbdata/

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 10, 2012; final manuscript received January 12, 2014; published online March 11, 2014. Assoc. Editor: Mark F. Tachie.

J. Fluids Eng 136(5), 051204 (Mar 11, 2014) (10 pages) Paper No: FE-12-1612; doi: 10.1115/1.4026512 History: Received December 10, 2012; Revised January 12, 2014

Smooth and rough wall turbulent boundary layer profiles are frequently scaled using the wall shear velocity u*, thus it is important that u* is accurately known. This paper reviews and assesses several wall similarity techniques to determine u* and compares results with data from the total stress, Preston tube, and direct force methods. The performance of each method was investigated using experimental repeatability data of smooth and rough wall turbulent boundary layer profiles at Reθ of 3330 and 4840, respectively, obtained using laser Doppler velocimetry (LDV) in a recirculating water tunnel. To validate the results, an analysis was also performed on the direct numerical simulation (DNS) data of Jimenez et al. (2010, “Turbulent Boundary Layers and Channels at Moderate Reynolds Numbers,” J. Fluid Mech., 657, pp. 335–360) at Reθ = 1968. The inner layer similarity methods of Bradshaw had low experimental uncertainty and accurately determined u* and ε for the DNS data and are the recommended wall similarity methods for turbulent boundary layer profile analysis. The outer layer similarity methods did not perform well, due to the need to simultaneously solve for three parameters: u*, ε, and Π. It is strongly recommended that the u* values determined using wall similarity techniques are independently verified using another method such as the total stress or direct force methods.

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References

Townsend, A., 1976, The Structure of Turbulent Shear Flow (Cambridge Monographs on Mechanics and Applied Mathematics), Cambridge University Press, Cambridge, UK.
Krogstad, P. A., Antonia, R. A., and Browne, L. W. B., 1992, “Comparison Between Rough- and Smooth-Wall Turbulent Boundary Layers,” J. Fluid Mech., 245, pp. 599–617. [CrossRef]
Keirsbulck, L., Labraga, L., Mazouz, A., and Tournier, C., 2002, “Surface Roughness Effects on Turbulent Boundary Layer Structures,” ASME J. Fluids Eng., 124, pp. 127–135. [CrossRef]
Tachie, M. F., Bergstrom, D. J., and Balachandar, R., 2004, “Roughness Effects on the Mixing Properties in Open Channel Turbulent Boundary Layers,” ASME J. Fluids Eng., 126, pp. 1025–1032. [CrossRef]
Tachie, M. F., Bergstrom, D. J., and Balachandar, R., 2000, “Rough Wall Turbulent Boundary Layers in Shallow Open Channel Flows,” ASME J. Fluids Eng., 122, pp. 533–541. [CrossRef]
Flack, K. A., Schultz, M. P., and Shapiro, T. A., 2005, “Experimental Support of Townsend's Reynolds Number Similarity Hypothesis on Rough Walls,” Phys. Fluids, 17, p. 035102. [CrossRef]
Shockling, M. A., Allen, J. J., and Smits, A. J., 2006, “Roughness Effects in Turbulent Pipe Flow,” J. Fluid Mech., 564, pp. 267–285. [CrossRef]
Kunkel, G. J., Allen, J. J., and Smits, A. J., 2007, “Further Support for Townsend's Reynolds Number Similarity Hypothesis in High Reynolds Number Rough-Wall Pipe Flow,” Phys. Fluids, 19(5), p. 055109. [CrossRef]
Walker, J. M., Sargison, J. E., and Henderson, A. D., 2013, “Turbulent Boundary-Layer Structure of Flows Over Freshwater Biofilms,” Exp. Fluids, 54(12), p. 1628. [CrossRef]
Wu, Y. and Christensen, K. T., 2007, “Outer-Layer Similarity in the Presence of a Practical Rough-Wall Topography,” Phys. Fluids, 19, p. 085108. [CrossRef]
Krogstad, P. A., and Efros, V., 2010, “Rough Wall Skin Friction Measurements Using a High Resolution Surface Balance,” Int. J. Heat Fluid Flow, 31, pp. 429–433. [CrossRef]
Jimenez, J., Hoyas, S., Simens, M. P., and Mizuno, Y., 2010, “Turbulent Boundary Layers and Channels at Moderate Reynolds Numbers,” J. Fluid Mech., 657, pp. 335–360. [CrossRef]
Clauser, F. H., 1954, “Turbulent Boundary Layers in Adverse Pressure Gradients,” J. Aerosp. Sci., 21, pp. 91–108.
Bradshaw, P., 1959, “A Simple Method of Determining Skin Friction From Velocity Profiles,” J. Aerosp. Sci., 26, p. 841. [CrossRef]
Winter, K. G., 1977, “An Outline of the Techniques Available for the Measurement of Skin Friction in Turbulent Boundary Layers,” Prog. Aerosp. Scie., 18, pp. 1–57. [CrossRef]
Spalding, D. B., 1961, “A Single Formula for the “Law of the Wall”,” J. Appl. Mech., 28, pp. 455–458. [CrossRef]
Musker, A., 1979, “Explicit Expression for the Smooth Wall Velocity Distribution in a Turbulent Boundary Layer,” AIAA J., 17, pp. 655–657. [CrossRef]
Chauhan, K., Monkewitz, P., and Nagib, H., 2009, “Criteria for Assessing Experiments in Zero Pressure Gradient Boundary Layers,” Fluid Dyn. Res., 41(2), p. 021404. [CrossRef]
Perry, A. E., and Joubert, P. N., 1963, “Rough-Wall Boundary Layers in Adverse Pressure Gradients,” J. Fluid Mech., 17, pp. 193–211. [CrossRef]
Lewthwaite, J., Molland, A., and Thomas, K., 1985, “An Investigation Into the Variation of Ship Skin Frictional Resistance With Fouling,” Trans. RINA, 127, pp. 269–284.
Barton, A., 2007, “Friction, Roughness and Boundary Layer Characteristics of Freshwater Biofilms in Hydraulic Conduits,” Ph.D. thesis, University of Tasmania, Hobart, Australia.
Schultz, M. P., 1998, “The Effect of Biofilms on Turbulent Boundary Layer Structure,” Ph.D. thesis, Florida Institute of Technology, Melbourne, FL.
Perry, A. E., Schofield, W. H., and Joubert, P. N., 1969, “Rough Wall Turbulent Boundary Layers,” J. Fluid Mech., 37(2), pp. 383–413. [CrossRef]
Perry, A. E., and Li, J. D., 1990, “Experimental Support for the Attached-Eddy Hypothesis in Zero-Pressure-Gradient Turbulent Boundary Layers,” J. Fluid Mech., 218, pp. 405–438. [CrossRef]
Coles, D., 1956, “The Law of the Wake in the Turbulent Boundary Layer,” J. Fluid Mech., 1, pp. 191–226. [CrossRef]
Hama, F. R., 1954, “Boundary-Layer Characteristics for Smooth and Rough Surfaces,” Soc. Nav. Archit. Mar. Eng., Trans., 62, pp. 333–351.
Bandyopadhyay, P. R., 1987, “Rough-Wall Turbulent Boundary Layers in the Transition Regime,” J. Fluid Mech., 180, pp. 231–266. [CrossRef]
Bradshaw, P., 1987, Turbulent Shear Flows 5—Selected Papers from the Fifth International Symposium on Turbulent Shear Flows, Springer-Verlag, New York.
Candries, M., 2001, “Drag, Boundary-Layer and Roughness Characteristics of Marine Surfaces Coated With Antifoulings,” Ph.D. thesis, University of Newcastle-Upon-Tyne, Newcastle, UK.
Akinlade, O. G., Bergstrom, D. J., Tachie, M. F., and Castillo, L., 2004, “Outer Flow Scaling of Smooth and Rough Wall Turbulent Boundary Layers,” Exp. Fluids, 37, pp. 604–612. [CrossRef]
Granville, P. S., 1976, “A Modified Law of the Wake for Turbulent Shear Layers,” ASME J. Fluids Eng., 98, pp. 578–580. [CrossRef]
Coles, D., 1969, “Turbulent Boundary Layers in Pressure Gradients: A Survey Lecture Prepared for the 1968 Stanford Conference on Computation of Turbulent Boundary Layers,” United States Air Force Project RAND, Santa Monica, CA, Technical Report No. RM-6412-PR.
Chauhan, K., Nagib, H., and Monkewitz, P., 2007, “On the Composite Logarithmic Profile in Zero Pressure Gradient Turbulent Boundary Layers,” Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Paper No. AIAA 2007-532, pp. 1–18.
Schultz, M. P., and Flack, K. A., 2007, “The Rough-Wall Turbulent Boundary Layer From the Hydraulically Smooth to the Fully Rough Regime,” J. Fluid Mech., 580, pp. 381–405. [CrossRef]
Brown, K. C., and Joubert, P. N., 1969, “The Measurement of Skin Friction in Turbulent Boundary Layers With Adverse Pressure Gradients,” J. Fluid Mech., 35(4), pp. 737–757. [CrossRef]
Hakkinen, R. J., 2004, “Reflections on Fifty Years of Skin Friction Measurement,” Proceedings of the 24th AIAA Aerodynamic Measurement Technology and Ground Testing Conference, Portland, OR, AIAA Paper No. 2004-2111, pp. 1–13.
Preston, J. H., 1954, “The Determination of Turbulent Skin Friction by Means of Pitot Tubes,” J. R. Aeronaut. Soc., 58, pp. 109–121.
Patel, V., 1965, “Calibration of the Preston Tube and Limitations of Its Use in Pressure Gradients,” J. Fluid Mech., 23(1), pp. 185–208. [CrossRef]
McKeon, B., Li, J., Morrison, J., and Smits, A. J., 2003, “Pitot Probe Corrections in Fully Developed Turbulent Pipe Flow,” Meas. Sci. Technol., 14, pp. 1449–1458. [CrossRef]
Sargison, J., Barton, A., Walker, G., and Brandner, P., 2009, “Design and Calibration of a Water Tunnel for Skin Friction Research,” Aust. J. Mech. Eng., 7(2), pp. 1–14.
Andrewartha, J., Perkins, K., Sargison, J., Osborn, J., Walker, G., Henderson, A., and Hallegraeff, G., 2010, “Drag Force and Surface Roughness Measurements on Freshwater Biofouled Surfaces,” Biofouling, 26(4), pp. 487–496. [CrossRef] [PubMed]
Andrewartha, J., 2010, “The Effect of Freshwater Biofilms on Turbulent Boundary Layers and the Implications for Hydroelectric Canals,” Ph.D. thesis, University of Tasmania, Hobart.
Zhang, Z., and Eisele, K., 1995, “Off-Axis Alignment of an LDA-Probe and the Effect of Astigmatism on Measurements,” Exp. Fluids, 19, pp. 89–94.
Karlsson, R. I., Eriksson, J., and Persson, J., 1993, “LDV Measurements in a Plane Wall Jet in a Large Enclosure,” Proceedings of the 6th International Symposium on LDA, Lisbon, Portugal, pp. 311–332.
Reynolds, A., 1974, Turbulent Flows in Engineering, John Wiley and Sons Ltd., Chichester.
McKeon, B., Li, J., Jiang, W., Morrison, J., and Smits, A. J., 2004, “Further Observations on the Mean Velocity Distribution in Fully Developed Pipe Flow,” J. Fluid Mech., 201, pp. 135–147. [CrossRef]
Coleman, H., and Steele, W., 1995, “Engineering Application of Experimental Uncertainty Analysis,” AIAA J., 33(10), pp. 1888–1895. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Smooth wall repeatability data for each wall similarity analysis method at Reθ = 3330: − · − smooth wall law of the wall using constants of κ = 0.43 and C = 5.85

Grahic Jump Location
Fig. 2

Rough wall repeatability data for each wall similarity analysis method at Reθ = 4840: − · − smooth wall law of the wall using constants of κ = 0.43 and C = 5.85

Grahic Jump Location
Fig. 3

Log law and velocity defect plots of the DNS data [12] at Reθ = 1968 analyzed using wall similarity methods to determine u* and ε: (a) low law plot of unmodified data, (b) log law plot of data with noise and offset, (c) velocity defect plot of unmodified data, and (d) velocity defect plot of data with noise and offset

Grahic Jump Location
Fig. 4

Modified Hama methods applied to the unmodified DNS data of Jiménez et al. [12]: (a) upper limit set to y/δ <0.9, and (b) upper limit set to y/δ < 0.6

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