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Non-$k$-type behaviour of roughness when in-plane wavelength approaches the boundary layer thickness

Published online by Cambridge University Press:  22 January 2021

B. Nugroho Open the ORCID record for B. Nugroho [Opens in a new window] ,
J. P. Monty Open the ORCID record for J. P. Monty [Opens in a new window] ,
I. K. A. P. Utama Open the ORCID record for I. K. A. P. Utama [Opens in a new window] ,
B. Ganapathisubramani Open the ORCID record for B. Ganapathisubramani [Opens in a new window]  and
N. Hutchins Open the ORCID record for N. Hutchins [Opens in a new window]
B. Nugroho
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
J. P. Monty
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
I. K. A. P. Utama
Affiliation:
Department of Naval Architecture, Institut Teknologi Sepuluh Nopember, Surabaya60111, Indonesia
B. Ganapathisubramani
Affiliation:
Aerodynamics and Flight Mechanics Research Group, University of Southampton, SouthamptonSO171BJ, UK
N. Hutchins*
Affiliation:
Department of Mechanical Engineering, The University of Melbourne, Victoria3010, Australia
*
†Email address for correspondence: nhu@unimelb.edu.au
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Abstract

A surface roughness from a recently cleaned and painted ship's hull was scanned, scaled and replicated for laboratory testing to systematically investigate the influence of the ratio of in-plane roughness wavelength, $\lambda$, with respect to the boundary layer thickness $\delta$. The experiments were performed by geometrically scaling the surface which maintains a constant effective slope $ES_x$ and solidity $\varLambda$, while the ratio of $\lambda /\delta$ is varied. Here we scale the scanned roughness topography by a factor of 2.5 and 15, and measure the mean velocity profiles in the turbulent boundary layers developing over these surfaces at a range of free stream velocities and streamwise measurement locations. The results show that the $2.5\times$ scaled roughness, which has $\lambda /\delta \ll 1$, behaves in the expected $k$-type manner, with a roughness function ${\rm \Delta} U^+$ that is proportional to the viscous-scaled roughness height. The $15\times$ surface, however, which has $\lambda /\delta \approx 1$, exhibits very different non-$k$-type behaviour. This larger surface does not approach the fully rough asymptote and also exhibits a drag penalty that is comparable to the $2.5\times$ case despite the sixfold increase in the roughness height. Measurements on a spanwise–wall-normal plane reveal that the $15\times$ 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 between $k$-type and non-$k$-type behaviour can occur in situations where the in-plane roughness wavelength approaches the boundary layer thickness. This finding has important implications to how we scale small-scale roughness from high Reynolds number (Re) large-scale applications for testing in low Re small-scale laboratory facilities or simulations.

JFM classification

Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A1
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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