Effects of surface roughness on the drag coefficient of finite-span cylinders freely rolling on an inclined plane

We present an experimental investigation aimed at understanding the effects of surface roughness on the time-mean drag coefficient (CD) of finite-span cylinders (span/diameter = aspect ratio, 0.51 = AR = 6.02) freely rolling without slip on an inclined plane. While lubrication theory predicts an infinite drag force for ideally smooth cylinders in contact with a smooth surface, experiments yield finite drag coefficients. We propose that surface roughness introduces an effective gap (Geff) resulting in a finite drag force while allowing physical contact between the cylinder and the plane. This study combines measurements of surface roughness for both the cylinder and the plane panel to determine a total relative roughness (ξ) that can effectively describe Geff at the point of contact. It is observed that the measured CD increases as ξ decreases, aligning with predictions of lubrication theory. Furthermore, the measured CD approximately matches combined analytical and numerical predictions for a smooth cylinder and plane when the imposed gap is approximately equal to the mean peak roughness (Rp) for rough cylinders, and one standard deviation peak roughness (Rp,1σ) for relatively smooth cylinders. As the time-mean Reynolds number (Re) increases, the influence of surface roughness on CD decreases, indicating that wake drag becomes dominant at higher Re. The cylinder aspect ratio (AR) is found to have only a minor effect on CD. Flow visualisations are also conducted to identify critical flow transitions and these are compared with visualisations previously obtained numerically. Variations in ξ have little effect on the cylinder wake. Instead, AR was observed to have a more pronounced effect on the flow structures observed. The Strouhal number (St) associated with the cylinder wake shedding was observed to increase with Re, while demonstrating little dependence on AR.