Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Nonlinear Ship Waves
Nonlinear Ship Waves
Pages 439-452
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From page 439... ...
singularities on the body and on the true location of the free surface, which must be obtained by iteration. The key is the iterative algorithm for determining the free surface and wave resistance using a new one parameter family of upstream finite difference methods A verification of numerical modeling is made using Wigley hull and validity of computer program is examined carefully by comparing the details of wave profiles and wave-making resistance with Series 60, CB =0.60 model.
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- Uo2) We denote ¢° and (° the velocity potential and the wave profiles, respectively, obtained from the previous step and introduce two small parameters 6o and b: with respect to the previous solution.
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, it would be necessary to consider a higher order panel geometry definition for the sake of consistency. Specifically, we assume that the singularity strength ~ at a point ~ A, 11, ~ ~ on a panel S is given by o(t,11)
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The iteration starts from the solution which satisfies the well-known linearized free surface condition. In each iteration the free surface panels as well as body surface panels are adjusted according to the newly computed wavy surface and boundary conditions are applied to the updated boundaries.
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Although the higher order panel method gives better results, we used linearly varying source strength distribution across curved panel for the ship hull and constant source strength across flat panel for free surface during computation because of the following reasons: (1) The higher order panel method requires a much longer computing time, normally 3 or 4 times longer with the same number of panels.
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The wave profiles obtained from linearized free surface condition are also plotted together. The nonlinear solution significantly improves the wave profiles, in particular, at the bow and the first trough and after that the difference between linear and nonlinear results seems insignificant.
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Using the contour plots we can more easily visualize the quality of computational results and choices of truncation regions and panel densities which often may be misjudged just looking the local flow characteristics such as the wave profile or streamline tracing along the ship hull or especially a scaler quantity such as wave resistance alone. We have found that numerical instability sometimes starts at the edge of a boundary with negligibly small magnitude, and it progressively grows and spreads as iteration continues.
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and D Jenkins, "Trim and Sinkage Here Effects on Wave Resistance with Series60, CB=0.60," DTNSRDC/SPD-1013-01, 1981.
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5. Wave Profile Comparisons Wigley Hull at Fn=O.
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Contour Plots of Wave Height and Source Strength Series60, CB=0.60 at Fn=0.32 448 .
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I was wondering if it will be possible for you to compare your results with theirs. To my recollection, their stern wave profiles do not have as good an agreement with experiments as yours.
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In our numerical experiments, we shifted the collocation points forward between 10% and 50% of the characteristic length of each panel. Our numerical results showed that the shifting apparently removed the oscillation of wave profiles, in particular near the bow region, but decreased the wave amplitude proportionally as we increased the shifting.
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Table A Wave-Making Resistance Comparisons Series60, Cg=0.60(Model Fixed) En i Linear I Nonlinear 0.22 0.369 0.255 .
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Fig.B. Series60, CB=O.8O at Fn=0.250 .o 0.5 cot ~ o.o _' ._ o at -0.5 -1.0 _ I S~nbolSVIFr l ~Linear Have _ l ~Iteration No.
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