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Experimental investigation of added frictional resistance by paint rough surface using a rotating cylinder

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Abstract

Ship hull paint roughness considerably affects ship’s resistance. During the ship design stage, the added resistance coefficient, ΔCF, is used as the parameter of added resistance due to roughness. ΔCF is commonly estimated by the ITTC1978 formula using Ks as the roughness parameter. Ks is measured as the average hull roughness (AHR). AHR is composed of the average of Pt50 values (difference between the maximum peak height and the maximum valley depth in the evaluation length of 50 mm) collected from multiple locations on the ship’s hull. However, it has been indicated that not only the roughness height parameter but also the wavelength parameter can affect frictional resistance. In this study, we try to develop a new method for estimating the added frictional resistance using the rotating cylinder test. The relation between the friction increase rate (FIR) (%) and the roughness Reynolds number (k+) is investigated. FIR (%) is dependent not only on the height parameter but also on the wavelength parameter. The projected area of the “cones” above the non-effective thickness, δs, to stream direction per unit area, Aall, which is called the cone projected area (CPA), is calculated using the roughness parameter Rc (i.e., the average height of roughness components) and the wavelength parameter RSm (i.e., the average length of roughness components). The strong positive correlation between the FIR (%) and CPA is confirmed. Using this relationship, the FIR (%) of the roughness cylinder can be easily estimated from Rc, RSm, and δs.

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Abbreviations

Re:

Reynolds number (–) \({\text{Re}} = \frac{\text{VL}}{\nu }\)

L:

Length scale

Re_C :

Reynolds number of cylinder test (length scale as circumferential length) (–) \({\text{Re}}_{{\_{\text{C}}}} = \frac{{V_{0} c}}{\nu }\)

C :

Circumference of the outer cylinder of cylinder test (m)

Re_G :

Reynolds number (length scale as gap between the inner and outer cylinder) (–) \({\text{Re}}_{{\_{\text{G}}}} = \frac{{V_{0} G}}{\nu }\)

G :

Gap between the inner and the outer cylinder (m)

V o :

Circumferential velocity of outer cylinder (m/s)

ν :

Kinematic viscosity coefficient (pa s)

C F :

Friction resistance coefficient (–)

C f :

Local friction stress coefficient (–)

ΔC F :

Added resistance due to roughness (–)

τ w :

Wall shear stress on inner cylinder (N/m2)

τ w0 :

Wall shear stress on smooth cylinder (N/m2)

τ wr :

Measured wall shear stress on rough cylinder (N/m2)

ρ :

Density (kg/m3)

u τ :

Friction velocity (m/s)

y + :

Non-dimensional distance from wall (–)

k + :

Roughness Reynolds number (–)

δ s :

Non-effective thickness (μm)

n :

Revolution per minute of outer cylinder (rpm)

H :

Height of the inner cylinder (m)

D :

Diameter of the inner cylinder (m)

r :

Radius of the inner cylinder (m)

S :

Sidewall area of the inner cylinder (m2)

T :

Torque acting on the inner cylinder (N m)

Ks :

Roughness height (AHR) (μm)

Rz :

Maximum height of roughness profile (μm)

Rc :

Average height of element of roughness profile (μm)

RSm :

Average length of element of roughness profile (μm)

RKu :

Kurtosis of roughness profile (–)

FIR (%):

Friction increase ratio (%)

CPA:

Cone projected area Aall (m2/m2)

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Acknowledgements

The research could not have been accomplished without great support and corporation of Professor Yasuo Kawaguchi of Tokyo university of Science, Professor Kaoru Iwamoto of Tokyo University of Agriculture and Technology, and Mr. Hideki Kawashima and Mr. Hiromoto Ando of National Maritime Research Institute. The research was also carried out for the project “Next generation environmental related technology development support program” of Japanese Ministry of Land, Infrastructure, Transport and Tourism, and as a joint research with ClassNK, both entitled “Method to estimate the changing ratio of in situ frictional resistance using the data of reduced surface roughness and roughness parameters of hull coating”. The authors would like to thank MARUZEN-YUSHODO Co., Ltd. for the English language editing (https://kw.maruzen.co.jp/kousei-honyaku/).

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Authors and Affiliations

  1. Chugoku Marine Paints, LTD., 1-7, Meijishinkai, Otake, Hiroshima, 739-0652, Japan

    Hirohisa Mieno

  2. Ocean-Bottom Exploration Center, Kobe University, 5-1-1, Fukaeminami, Higashinada, Kobe, 658-0022, Japan

    Tokihiro Katsui

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  1. Hirohisa Mieno
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  2. Tokihiro Katsui
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Correspondence to Hirohisa Mieno.

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Mieno, H., Katsui, T. Experimental investigation of added frictional resistance by paint rough surface using a rotating cylinder. J Mar Sci Technol 26, 1–15 (2021). https://doi.org/10.1007/s00773-020-00717-6

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