The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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The Effect of the Steady Perturbation Potential on the Motions of a Ship Sailing in Random Seas
The Effect of the Steady Perturbation Potential on the Motions of a Ship Sailing in Random Seas
Pages 375-390
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From page 375... ...
The theory of small forward speed motion computations is extended in order to allow larger horizontal distances in the Green's functions by deriving a proper asymptotic expansion of the low speed Green's function. Also an alternative formulation for the wave drift forces has been derived, based on the momentum balance as e.g.
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From page 376... ...
The calculation of the wave drift forces is done in two alternative ways, one is the integration of the pressures over the mean wetted surface of the body and secondly using the Maruo expression for the wave drift forces corrected for the small forward speed parameter. The nature of the non-uniformity in the asymptotic expansions will be studied in this paper and extended to uniform expansions.
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From page 377... ...
with D = 0, while the Green's function fulfills the homogeneous adjoins free surface condition: -~2G + 2i~UG`+ +U2G`` + gG: = 0 at ~ = 0 (9) This Green's function has the form Gf x, g j U)
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From page 378... ...
because the pressure is calculated at the ship's hull and we assume the horizontal length scales large compared to the vertical length scale. To get more insight in the structure of the source function we deform the contour L in the complex plane.
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From page 379... ...
One for the computation of the far field wave and one for the computation of the integral equation. In the far field the exact value of the wave number has to be taken into account, while in the latter case a first order correction of the wave number is sufficient to arrive at solutions valid up to second order.
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From page 380... ...
The steady perturbation potential is determined using a boundary integral technique for the steady double body flow, which originally comes from a Hess and Smith type of algorithm. The steady double body flow is calculated separately and is then incorporated into the free surface integral.
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From page 381... ...
we described a way to compute the first order forces and the second order wave drift forces. The method we used there was based on a direct pressure integration of the first and second order pressures respectively.
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From page 382... ...
In our case we follow the same reasoning to obtain similar results for the slow forward speed case. Our velocity potential has the form: flex, t)
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From page 383... ...
A critical reader will notice that formally we have to deal with a non-uniformity due to the fact that we have a first order 'uniform' solution. The phase correction is of first order.
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From page 384... ...
The analysis of the results of the wave drift forces using the pressure distribution integration, as shown in 384
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From page 385... ...
6. Forward speed wave drift forces 60 Drift force on sphere Influence stationary potential .
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From page 386... ...
This can be made plausable by observing that the expression for the wave drift forces from the momentum balance only simple source distribution integration over the mean wetted hull is required. It is our opinion that due to the integration of higher order derivatives in the pressure distribution for the forward speed case the results are more sensitive for the way the integration is performed.
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From page 387... ...
13 and 14. From these results one is tempted to conclude that the influence of the stationary potential on the drift forces in this case is restricted to the sway drift force results, however, previous observations also indicate that the use of a pressure integration for the calculation of the wave drift forces with forward speed are somewhat doubtful, due to the large dependency on the panel discretization of the body.
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From page 388... ...
and Hermans, A.J., "A fast algorithm for the calculation of 3-D ship motions at moderate forward speed", Proceedings of 4th Numerical Ship Hydrodynamic Conference, Washington (1985~.
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From page 389... ...
In the zero speed case there is sufficient evidence that this procedure, using 3-D diffraction theory results, will lead to meaningful results. In the non-zero speed case however this evidence is lacking and to the author's opinion the accuracy of the f irst order results based on 3-D diffraction results with forward speed must be even more accurate than the zero speed results due to the fact that in the evaluation of the pressure distribution, gradients of the water velocity distribution are required.
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