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OCR for page 719
Summary of the Group Discussion on Rankine Source Methods Chairman: A. J. Musker Admiralty Research Establishment Haslar, England Co-cha~rman: S. Ogiwara Ishikawajima-Har~ma Heavy Industries Co. Yokohama, Japan The Groupe Discussion on Rankine Source Methods was attended by approximately 50 leading researchers from 12 nations. Attention was focussed on the following items, although there was necessarily a high degree of overlap between the topics: (i) Radiation condition and its application (ii) Resolution of divergent waves -higher order panels (iii) Water-line problem -effect on stability (iv) Calculation of wave resistance (v) Existance and uniqueness Three different approaches to satisfying the radiation condition were discussed: Dawson's approach, involving a one-sided finite difference operator (eg Larsson,Musker), staggered collocation points (Jensen, Ando, Nakatake) and a hybrid approach, first suggested by Gadd, involving a Kelvin source density distributed on the hull and a Rankine source density distributed on the free- surface but confined to the nearfield (Yim). The errors associated with various formulations of a four-point Taylor series operator were discussed (Van). A recent study had drawn the same conclusions as Dawson, namely that the 2nd and 4th derivatives should be eliminated in its formulation. 719 The method of staggered or shifted collocation points was discussed at some length. Jensen described the change in wave pattern resulting from different ways of staggering the free-surface grid. Waves were found to propagate upstream and downstream depending on the chosen configuration. The question remained as to whether a regime could be identified for which the results were realistic as well as being insensitive to small changes in mesh geometry. The lack of rigour in treating the radiation condition used in the more popular methods described in recent years was criticised by Bail Suggestions that the approaches were nearer to art than science were quickly refuted by the more pragmatic users of the methods since the experience has been that the methods do provide good engineering predictions provided the algorithms remain stable. There was general agreement about the desire to use higher order panels to resolve the divergent wave system and to better model the larger gradients in the bow region (Yim, Larsson, Mori, Baubeau). Larsson referred to the 1977 paper by Hess which addressed the two dimensional problem of the flow over a submerged vortex. His conclusion was that a higher order line source method was required. For ship- flows, the case for higher order panels is not as strong if the panels are not positioned in the calm-water plane (Baubeau, Musker), although the stability

OCR for page 719
of the solution algorithms does seem to improve. Larsson made a strong case that the higher order method is more economical in terms of computing requirements and that an additional benefit arose in that the pressure integration around the body, required in the caluculation of resistance, was more accurate. It was the general feeling that the resistance should be calculated by pressure integration and not by momentum considerations. This recommendation was largely the result of experience in comparing both methods with experiment rather than a rigorous appraisal of the numerical issues involved. Numerical damping in the far-field probably accounts for the disparity. Difficulties remain in the vicinity of the water-line. Whilst the available methods behave reasonably well with the Wigley and Series 60 hulls, great difficulties have been experienced with the HSVA tanker (Jensen, Larsson). In Jensen's case, the collocation points near to the water-line were suppressed to achieve convergence. The existence of solutions to the potential flow formulation of the wave resistance problem was discussed at some length in the context of instabilities near the water-line. In the real world, we know that spray and wave-breaking occur -especially near the bow; both viscous and surface tension effect are present (Jensen). Thus the potential flow model cannot be expected to cope with these complexities and it is then necessary to consider whether, when these (non-linear) regimes are being approached in a Rankine-Source calculation, a solution exists at all. Divergence of a scheme may then be truly reflecting the mathematics - not the numerical techniques invoked (Musker,Larsson), in which case it might be possible to identify an upper limit in terms of the utility of such methods. A consensus on this issue could not be reached. Notwithstanding the above difficulties, however, it was agreed that Rankine-Source methods had a very definite role to play in ship design to predict wave resistance and that they should also be used, in conjunction with NavJer-Stokes methods, to investigate the wave-viscous interaction problem (Yin). 720