The Limitations of using "ra" to describe surface roughness

Martin N. Goodhand, Karl Walton, Liam Blunt, Hang W. Lung, Robert J. Miller, Reg Marsden

Research output: Contribution to journalArticlepeer-review

46 Citations (Scopus)


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 (q1u1Ra/l1) 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.

Original languageEnglish
Article number101003
Number of pages8
JournalJournal of Turbomachinery
Issue number10
Early online date26 Apr 2016
Publication statusPublished - 1 Oct 2016


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