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Defining an equivalent homogeneous roughness length for turbulent boundary layers developing over patchy or heterogeneous surfaces

Defining an equivalent homogeneous roughness length for turbulent boundary layers developing over patchy or heterogeneous surfaces
Defining an equivalent homogeneous roughness length for turbulent boundary layers developing over patchy or heterogeneous surfaces
A new approach based on the power mean is suggested for defining an equivalent homogeneous roughness length which takes into account patchiness or heterogeneous distribution of roughness on ship hulls and can be readily incorporated into existing full-scale drag prediction methods. In the limit where patch sizes are much greater than the boundary layer thickness, it is readily shown that the relationship between drag coefficient and roughness length is non-linear, highlighting an obvious source of error with current approaches that attempt to define an equivalent homogeneous roughness through an area-weighed arithmetic mean. The degree of error is dependent on the roughness distribution, but is estimated to exceed 16% for highly skewed beta heterogeneous distributions. For fully-rough models, the power-mean approach returns errors of % for the distributions tested here. The efficacy of the power-mean approach is also evaluated in the transitional regime and with different transitional roughness models (Nikuradse and Colebrook) and retains accuracy for most realistic operating scenarios.
Biofouling, Heterogeneous roughness, Hull roughness, Rough wall bounded turbulence
0029-8018
Hutchins, N.
10ef0e3e-266c-4569-90ae-598ed9fb5edd
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052
Schultz, M.P.
ca79afb7-5d45-48da-94f9-9fb6f6b63aa2
Pullin, D.I.
920b5885-0adb-4bcd-985a-fbf537b9782d
Hutchins, N.
10ef0e3e-266c-4569-90ae-598ed9fb5edd
Ganapathisubramani, B.
5e69099f-2f39-4fdd-8a85-3ac906827052
Schultz, M.P.
ca79afb7-5d45-48da-94f9-9fb6f6b63aa2
Pullin, D.I.
920b5885-0adb-4bcd-985a-fbf537b9782d

Hutchins, N., Ganapathisubramani, B., Schultz, M.P. and Pullin, D.I. (2023) Defining an equivalent homogeneous roughness length for turbulent boundary layers developing over patchy or heterogeneous surfaces. Ocean Engineering, 271, [113454]. (doi:10.1016/j.oceaneng.2022.113454).

Record type: Article

Abstract

A new approach based on the power mean is suggested for defining an equivalent homogeneous roughness length which takes into account patchiness or heterogeneous distribution of roughness on ship hulls and can be readily incorporated into existing full-scale drag prediction methods. In the limit where patch sizes are much greater than the boundary layer thickness, it is readily shown that the relationship between drag coefficient and roughness length is non-linear, highlighting an obvious source of error with current approaches that attempt to define an equivalent homogeneous roughness through an area-weighed arithmetic mean. The degree of error is dependent on the roughness distribution, but is estimated to exceed 16% for highly skewed beta heterogeneous distributions. For fully-rough models, the power-mean approach returns errors of % for the distributions tested here. The efficacy of the power-mean approach is also evaluated in the transitional regime and with different transitional roughness models (Nikuradse and Colebrook) and retains accuracy for most realistic operating scenarios.

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equivelent_homogeneous_roughness - Accepted Manuscript
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Accepted/In Press date: 16 December 2022
e-pub ahead of print date: 28 January 2023
Published date: 1 March 2023
Additional Information: Funding Information: NH gratefully acknowledges support from the Australian Research Council (ARC) and as Millikan Visiting Professor at the California Institute of Technology. DP acknowledges support from the ARC as an international partner investigator. MPS acknowledges support from the US Office of Naval Research . BG gratefully acknowledges support from EPSRC, United Kingdom (Grant ref No: EP/V00199X/1 ).
Keywords: Biofouling, Heterogeneous roughness, Hull roughness, Rough wall bounded turbulence

Identifiers

Local EPrints ID: 475363
URI: http://eprints.soton.ac.uk/id/eprint/475363
ISSN: 0029-8018
PURE UUID: 3244c6fa-f7f3-4152-b252-a080552dfb2e
ORCID for B. Ganapathisubramani: ORCID iD orcid.org/0000-0001-9817-0486

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Date deposited: 16 Mar 2023 17:37
Last modified: 17 Mar 2023 02:42

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Contributors

Author: N. Hutchins
Author: M.P. Schultz
Author: D.I. Pullin

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