The Limitations of Using “R_a” to Describe Surface Roughness

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, R_a, to an equivalent sandgrain roughness size, k_s. This paper shows that such criteria are oversimplified and that R_a/k_s is dependent on the roughness topography, namely, the roughness slope defined as the roughness amplitude normalized by the distance between roughness peaks, R_a/λ. To demonstrate the relationship, wake traverses were undertaken downstream of an aerofoil with various polished surfaces. The admissible roughness Reynolds number (ρ₁u₁R_a/μ₁) at which the drag rose above the smooth blade case was determined. The results were used to demonstrate a 400% variation in R_a/k_s 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.