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Research Papers

The Limitations of Using “Ra” to Describe Surface Roughness

[+] Author and Article Information
Martin N. Goodhand

Whittle Laboratory,
University of Cambridge,
Cambridge CB2 3BU, UK
e-mail: mng24.cam@gmail.com

Karl Walton

Centre for Innovative Manufacturing
in Advanced Metrology,
University of Huddersfield,
Huddersfield HD1 3DH, UK
e-mail: karl.walton@hud.ac.uk

Liam Blunt

Centre for Innovative Manufacturing
in Advanced Metrology,
University of Huddersfield,
Huddersfield HD1 3DH, UK
e-mail: l.a.blunt@hud.ac.uk

Hang W. Lung

Rolls-Royce Plc,
Derby DE24 8BJ, UK
e-mail: Hang.Lung@rolls-royce.com

Robert J. Miller

Whittle Laboratory,
University of Cambridge,
Cambridge CB2 3BU, UK
e-mail: rjm76@cam.ac.uk

Reg Marsden

Rolls-Royce Plc,
Derby DE24 8BJ, UK
e-mail: Reg.Marsden@rolls-royce.com

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 26, 2015; final manuscript received October 31, 2015; published online April 26, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(10), 101003 (Apr 26, 2016) (8 pages) Paper No: TURBO-15-1210; doi: 10.1115/1.4032280 History: Received September 26, 2015; Revised October 31, 2015

Current criteria used to determine whether rough surfaces affect skin friction typically rely on a single amplitude parameter to characterize the roughness. The most commonly used criteria relate the centerline averaged roughness, Ra, to an equivalent sandgrain roughness size, ks. This paper shows that such criteria are oversimplified and that Ra/ks is dependent on the roughness topography, namely, the roughness slope defined as the roughness amplitude normalized by the distance between roughness peaks, Ra/λ. To demonstrate the relationship, wake traverses were undertaken downstream of an aerofoil with various polished surfaces. The admissible roughness Reynolds number (ρ1u1Ra1) at which the drag rose above the smooth blade case was determined. The results were used to demonstrate a 400% variation in Ra/ks over the roughness topographies tested. The relationship found held for all cases tested, except those where the roughness first initiated premature transition at the leading edge. In these cases, where the roughness was more typical of eroded aerofoils, the drag was found to rise earlier.

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References

Bons, J. P. , 2010, “ A Review of Surface Roughness Effects in Gas Turbines,” ASME J. Turbomach., 132(2), p. 021004. [CrossRef]
Schlichting, H. , 1962, Boundary Layer Theory, 3rd ed., McGraw-Hill, New York.
Goodhand, M. N. , 2015, “ Admissible Roughness in Turbomachines,” ASME Paper No. GT2015-43326.
Feindt, E. G. , 1957, “ Untersuchungen uber die Abhangigkeit des Umschlages laminar-turbulent von der Oberflachenrauhigkeit und der Druckverteilung,” Diss. Braunschweig, Jb. 1956 Schiffbautechn. Gessellschaft 50, pp. 180–203.
Brinich, P. F. , 1954, “ Boundary Layer Transition at Mach 3.12 With and Without Single Roughness Element,” Report No. NACA TN-3267.
Küsters, B. , Schreiber, H. A. , Köller, U. , and Mönig, R. , 2000, “ Development of Advanced Compressor Airfoils for Heavy-Duty Gas Turbines, Part II: Experimental and Theoretical Analysis,” ASME J. Turbomach., 122(3), pp. 406–415. [CrossRef]
Henderson, A. , Walker, G. J. , and Hughes, J. , 2008, “ Unsteady Transition Phenomena at a Compressor Blade Leading Edge,” ASME J. Turbomach., 130(2), p. 021013. [CrossRef]
Tropea, C. , Yarin, A. L. , and Foss, J. F. F. , Springer Handbook of Experimental Fluid Dynamics, Springer-Verlag, Berlin.
Baals, D. D. , and Mourhess, M. J. , 1945, “ Numerical Evaluation of the Wake Survey Equations for Subsonic Flow Including the Effect of Energy Addition,” NACA Report No. ARRL5H27.
Walton, K. , 2016, “ High Fidelity Replication of Surface Texture and Geometric Form of a High Aspect Ratio Aerodynamic Test Component,” Surf. Topogr.: Metrol. Prop., 4(2), p. 025003.

Figures

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Fig. 1

Can Ra alone describe roughness? Examples of topographies with the same Ra, but which have the potential to affect the flow differently

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Fig. 2

Schematic of tunnel working section and Mach number distribution. (a) Experimental setup and (b) Mach numbers.

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Fig. 3

Turbulent wedges caused by roughness-induced transition

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Fig. 4

Samples of raw, unstretched, roughness profiles

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Fig. 5

Changes in roughness metrics during polishing

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Fig. 6

Effect of roughness and Reynolds number on drag coefficient

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Fig. 7

Effect of roughness and Reynolds number on drag coefficient

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Fig. 8

The effect of Reynolds number on transition for the different roughness levels

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Fig. 9

The effect of different roughness topographies on the sandgrain roughness correlation

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Fig. 10

Different roughness profiles tested

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Fig. 11

The effect of independently varying the slope and skew on the sandgrain roughness correlation. (a) Correlation with the roughness slope and (b) correlation with the roughness skew.

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