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Safety and Reliability

Three-Dimensional Large Amplitude Body Motions in Waves

[+] Author and Article Information
Xinshu Zhang

Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109xinshuz@umich.edu

Robert F. Beck

Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI 48109rbeck@umich.edu

J. Offshore Mech. Arct. Eng 130(4), 041603 (Oct 01, 2008) (10 pages) doi:10.1115/1.2904949 History: Received June 22, 2007; Revised February 15, 2008; Published October 01, 2008

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength flat panels on the exact wetted body surface, the boundary integral equations are numerically solved at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous wetted body geometry. The desingularized method applied on the free surface produces nonsingular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant-strength flat panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceeded until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared to the experiments for both linear computations and body-exact computations.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Added-mass coefficients of a hemisphere by linear calculation, N=100, Δt=T0∕100, A33 is the added mass in the Z direction due to heave motion, k is the wave number of the radiated wave (k=ω2∕g in deep water), and R is the radius of the hemisphere

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Figure 2

Damping coefficients of a hemisphere by linear calculation, N=100, Δt=T0∕100, B33 is the damping in the Z direction due to the heave motion, k is the wave number of the radiated wave (k=ω2∕g in deep water), and R is the radius of the hemisphere

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Figure 3

Convergence of hydrodynamic radiation force acting on a sphere with changing time step size and number of panel on body, A=0.2R, ω2R∕g=1.0, 30 nodes per wavelength on free surface in each direction

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Figure 4

Convergence of hydrodynamic radiation force acting on a sphere with changing number of free surface nodes, A=0.2R, ω2R∕g=1.0, number of panel on body N=100, time step size Δt=T0∕100

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Figure 5

Vertical force acting on a sphere with heave motion amplitude A=0.2R, ω2R∕g=1.0, number of panel on body N=100, time step size Δt=T0∕100

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Figure 6

Vertical force acting on a sphere with heave motion amplitude A=0.5R, ω2R∕g=1.0, number of panel on body N=100, time step size Δt=T0∕100

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Figure 7

Wave resistance acting on a submerged spheroid with submerged depth H∕L=0.16, D∕L=0.2, Fn=0.35

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Figure 8

Wave resistance acting on a submerged spheroid with submerged depth H∕L=0.245, D∕L=0.2, Fn=0.35

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Figure 9

Vertical force acting on a submerged spheroid with submerged depth H∕L=0.16, D∕L=0.2, Fn=0.35

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Figure 10

Vertical force acting on a submerged spheroid with submerged depth H∕L=0.245, D∕L=0.2, Fn=0.35

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Figure 11

Pitch moment acting on a submerged spheroid with submerged depth H∕L=0.16, D∕L=0.2, Fn=0.35

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Figure 12

Pitch moment acting on a submerged spheroid with submerged depth H∕L=0.245, D∕L=0.2, Fn=0.35

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Figure 13

The calm water wave resistance of a Wigley hull, Fn=0.3

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Figure 14

Modified Wigley hull III at Fn=0.3, heave-heave added-mass coefficient

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Figure 15

Modified Wigley hull III at Fn=0.3, heave-heave damping coefficient

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Figure 16

Modified Wigley hull III at Fn=0.3, pitch-heave added-mass coefficient

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Figure 17

Modified Wigley hull III at Fn=0.3, pitch-heave damping coefficient

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Figure 18

Modified Wigley hull III at Fn=0.3, pitch-pitch added-mass coefficient

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Figure 19

Modified Wigley hull III at Fn=0.3, pitch-pitch damping coefficient

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Figure 20

Modified Wigley hull III at Fn=0.3, heave-pitch added-mass coefficient

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Figure 21

Modified Wigley hull III at Fn=0.3, heave-pitch damping coefficient

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Figure 22

Comparison of pitch moment component acting on a submerged spheroid undergoing forced pitch motion between using Tuck’s theorem and direct pressure integration, length L=10m submerged depth H∕L=3, ωL∕g=2.2, number of body panels N=600, B∕L=1∕10

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Figure 23

Surge force components due to the heave excitation, modified Wigley hull III at Fn=0.3, heave amplitude A∕T=0.48, ωL∕g=2.2

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Figure 24

Heave force components due to the heave excitation, modified Wigley hull III at Fn=0.3, heave amplitude A∕T=0.48, ωL∕g=2.2

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Figure 25

Pitch moment components due to the heave excitation, modified Wigley hull III at Fn=0.3, heave amplitude A∕T=0.48, ωL∕g=2.2

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Figure 26

Surge force components due to the pitch excitation, modified Wigley hull III at Fn=0.3, pitch amplitude=1.5deg, ωL∕g=2.2

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Figure 27

Heave force components due to the pitch excitation, modified Wigley hull III at Fn=0.3, pitch amplitude=1.5deg, ωL∕g=2.2

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Figure 28

Pitch moment components due to pitch excitation, modified Wigley hull III at Fn=0.3, pitch amplitude=1.5deg, ωL∕g=2.2

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Figure 29

Variation of added mass and damping with changing heave motion amplitude for a Modified Wigley hull III at Fn=0.3, ωL∕g=2.2. A is the motion amplitude, and T is the hull draft.

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