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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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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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