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Research Papers: Fundamental Issues and Canonical Flows

Dynamic Analysis of a Slender Body of Revolution Berthing to a Wall

[+] Author and Article Information
Q. X. Wang

School of Mathematics, University of Birmingham Edgbaston, Birmingham B15 2TT, UK

S. K. Tan

Maritime Research Centre, Nanyang Technological University, 50 Nanyang Avenue, Singapore 630798, The Republic of Singapore

J. Fluids Eng 131(1), 011205 (Dec 02, 2008) (7 pages) doi:10.1115/1.3026727 History: Received August 10, 2007; Revised September 01, 2008; Published December 02, 2008

A slender body of revolution berthing to a wall is studied by extending the classical slender body theory. This topic is of practical importance for a ship berthing to a quay wall. The flow problem is solved analytically using the method of matched asymptotic expansions. The lateral force and yaw moment on the body are obtained in a closed form too. The translation and yawing of the body are modeled using the second Newton law and coupled with the flow induced. Numerical analyses are performed for the dynamic lateral translation and yawing of a slender spheroid, while its horizontal translation parallel to the wall is prescribed at zero speed, constant speed, and time varying speed, respectively. The analysis reveals the interesting dynamic features of the translation and yawing of the body in terms of the forward speed and starting angle of yaw of the body.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A slender body of revolution at an angle of yaw in a dynamic motion near a wall

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Figure 2

The conformal mapping of (a) the domain outside two circles C1 and C2 in the cross-flow plane Q=Y+iZ to (b) the domain between two concentric circles B1 and B2 in the plane ς=ρeiΘ

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Figure 3

The control volume, for a slender body moving near a wall, surrounded by the body surface Sb, the wall Sw, and the upper half of a large sphere surface S∝ in far field

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Figure 4

A slender spheroid falls to a wall at ρs/ρf=1.05. (a) The lateral distance of the body center to the wall H0, (b) the lateral force Fz, (c) the angle of yaw α, and (d) the yawing moment My versus time.

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Figure 5

Dynamic motion of a slender spheroid at constant horizontal velocity U=1.0. (a) The lateral distance of the body center to the wall H0, (b) the lateral force Fz, (c) the angle of yaw α, and (d) the yawing moment My versus time.

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Figure 6

Dynamic motion of a slender spheroid at the horizontal velocity of U=exp(-δT) and δ=0.25, compared with that at constant horizontal velocity U=1.0(δ=0.0). (a) The lateral distance of the body center to the wall H0, (b) the lateral force Fz, (c) the angle of yaw α, and (d) the yawing moment My versus time.

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