Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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A Coupled Time and Frequency Approach for Nonlinear Wave Radiation
A Coupled Time and Frequency Approach for Nonlinear Wave Radiation
Pages 67-84
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From page 67... ...
ABSTRACT In this paper we report on computations using a semi nonlinear time domain formulation for the threedimensional wave radiation problem with a free surface. The body boundary condition is applied at the actual time-depending body surface, and the free surface conditions are linearized.
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From page 68... ...
A method for the fast analysis of the steady-state radiated wave field, based on frequency domain Green functions for the body-nonlinear problem is also presented. A few additional results are given on the time domain approach of the wave resistance problem, in order to demonstrate the versatility of the time-domain body nonlinear formulation, which is basically able to cope with any free-surface linear problem.
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From page 69... ...
dSp (12) STEADY-STATE COMPONENTS FOR PERIODIC FORCED MOTIONS In the body-nonlin ear problem of the forced oscillations of a submerged body about a fixed mean position, the influence of the body boundary condition nonlinearity on forces and free-surface elevation is investigated.
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From page 70... ...
At last, for a quantification of the influence of the body boundary condition nonlinearity, the linear solution is systematically computed for comparison. REDUCTION OF COMPUTING TIME Apart from the use of frequency domain Green functions, the numerical implementation as described in the preceding paragraph is very classical.
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From page 71... ...
However, such an approach is not safe, for it is very difficult to estimate the influence of the truncation on the final results. In many particular problems of forced motions, an adequate choice of the time step allows a substantial reduction of the number of Green function evaluations without affecting the numerical results.
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From page 72... ...
The present results prove that at least for wave generation, a linear analysis is inadequate, the body nonlinearity having a very strong influence on the structure of the radiated wave field. This phenomenon, already highlighted using a frequency domain analysis of the problem by Clement & Ferrant (1987)
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From page 73... ...
non K1 = 0.25 KRIL3D+ -- Iineaire -0.6 - Differellce , 0 10 20 30 40 Figure 3 T* sqrt(g/R)
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From page 75... ...
Present computations simply intend to demonstrate the versatility of the body-nonlinear time domain formulation. CONCLUSION A systematic attention on computational efficiency has led to a time domain body-nonlinear code with Cpu requirements sufficiently low for intensive computations to become possible, as demonstrated on the problem of the heaving sphere.
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From page 76... ...
Harmonic Components K1- 0.100 1 0~= 0.316 Fo I A=O.
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From page 77... ...
n: O,OC~ cy 6 y t:)
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From page 79... ...
* 10-3 Submerged Ellitsoid Fr=0.40 *
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From page 80... ...
Houston, 1988. Liapis S., Beck R.F.,"Seakeeping computation using time domain analysis".
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From page 81... ...
15) where Cb is the curve defined by the intersection of the instantaneous body surface Sb and the free surface z=0 and Vc is the velocity of a point on Cb, we may write for Isf: 81
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From page 82... ...
. Although involving some tedious algebra, the results may be expressed in a very concise form, involving the frequency domain Green function for a fixed point source.
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From page 83... ...
2. Sine heave motion 2.1 Basic formulations Explicit forms of the body-nonlinear frequency domain Green functions may be derived by first imposing the analytic form of the source path, and then introducing appropriate formulations of Gino (Near-Field, Haskind, ...)
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