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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 720
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
Representative terms from entire chapter:
radiation condition
