Non k-type behaviour of roughness when1 in-plane wavelength approaches the2 boundary layer thickness3

Abstract

A surface roughness from a recently cleaned and painted ship hull was scanned, scaled and replicated for laboratory testing to systematically investigatethe influence of the ratio of in-plane roughness wavelength,λ, with respect to the boundary layer thickness δ. The experiments were performed by geometrically scaling the surface which maintains a constant effective slopeESxand solidityΛ, while the ratio ofλ~δis varied. Here we scale the scanned roughness topography by a factor of 2.5 and, and measure the18mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of freestream velocities and streamwise measurement locations. The results show that the 2.5×scaled roughness, which hasλ~δ≪1 behaves in the expectedk-21type manner, with a roughness function∆U+that is proportional to the viscous scaled roughness height. The 15×surface, however, which hasλ~δ≈1, exhibits very different nonk-type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the 2.5×case despite the six-fold increase in the roughness height. Measurements on a spanwise/wall-normal plane reveal that the 15×surface has introduced a large scale spanwise variation in mean streamwise velocity (dispersive stresses) that extend far beyond the logarithmic region. Together this evidence suggests that a demarcation betweenk-type and nonk-type behaviour can occur in situations where the in-plane roughness wavelength approachesthe boundary layer thickness. This finding has important implications to how we scale smallscale roughness from high Relarge-scale applications for testing in lowResmall-scale laboratory facilities or simulations.

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ORCID for Bharathram Ganapathisubramani: orcid.org/0000-0001-9817-0486

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