The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
Currently Skimming:
Ship Wave Ray Tracing Including Surface Tension
Ship Wave Ray Tracing Including Surface Tension
Pages 157-174
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 157... ...
Eggers University of Hamburg Hamburg, Germany Abstract The aim of this work is to clarify the validity of slim wave ray theories at and near the ship's surface. As previous numerical investigations have led to ambiguities due to a breakdown of the ray analysis near the bow and stern stagnation points, we shall take care for the surface tension effect in order to Olden such deficiencies; then the wave length never surpasses a positive nimlun length which is attained at the boundary of a finite waveless zone around a stagnation point.
|
From page 158... ...
If we start rays from these boundaries rather than from the stagnation points, we apparently have a well defined initial value problem, even for blunt bow forms. In our computational investigations, we could confirm Maruo's experimental finding that capillarity effects can be significant even if the remodel speed exceeds the rnirumum wave speed considerably.
|
From page 159... ...
dY = g ~ (20) (witI~ c~ defined as the ray angle against the double body flow)
|
From page 160... ...
/2 (22) where c'', = .,,~'4'cg is the minimum velocity of capillarygravity waves and p—cm/U is a dimensionless pararneter of surface tension.
|
From page 161... ...
' including a termination of rays with short gravity waves with cg approaching negative values. We may retention that for a vertical circular cylinder, q2 increases up to 4.0, whereas for conventional forms q2 W]
|
From page 162... ...
') curves over the dotted dine for capillary waves; curves under the dotted lisle for gravity waves.
|
From page 163... ...
considered a quantity related to ~ P ~ as a (1isturbance parameter and came to the vexing conclusion that ray theory does not apply for bow entrance angles,B0 < 7r/3 as otherwise P is not bounded; on the other hand, Maruo (7] disclaimed the validity of ray theory for To ~ ~r/3 due to divergence of an integral representing the phase.
|
From page 164... ...
Due to inclusions of surface tension, steady components of bow capillary waves could be investigated as well. We traced rays with capillary waves from that part of the outer boundary of the short-life belt where the basic flow is incoming, and rays with gravity waves from the part with outgoing flow; the two domains have no common boundary, save the point where the basic flow is tangent to the belt.
|
From page 165... ...
Thus it seems that in this regard ray theory displays a certain value for predicting ship wave phenomena, although the re-entrance of rays or their reflection at the water line must be considered an open problem, among others. In any case, the authors would like to emphasize the need to take account of surface tension at low speeds, well in accord with Maruot74.
|
From page 166... ...
26pp (1988) 10 Eggers,K:"A comment on free surface conditions for slow ship theory and ray tracing." Schiffstechnik32 pp42-47~1985)
|
From page 167... ...
~ '~_ ~ ~—a~ ~ ~ p.O.1 Fig.7 Wave pattern of a rudder model of length () .3II with U = 0.65' 0.5 and 0.34 m/s (by courtesy of Prof.
|
From page 168... ...
4 ~ (l b 29 5 · · ~ ] = ~ PtC-'Ul'0.100 ~ = 0 ~ Fig.9 Rays of gravity waves for diffcrcnt entrance angles and bc)
|
From page 169... ...
under approach (~' U = ~ ~ ~ ~ Fig.l] Sow waves ~ front of ~ lacing cylinder with dinette D= 0.~ m' moving to the left' at the speeds of U=O.61 Oe7 ~ 0~9 m/s (From Ee OBEY L191 169
|
From page 170... ...
Il.B. it might not be the att ainable boundary of rays of gravi ty waves; and, it is not a boundary between ray families of gravityand capi llary- waves, p=O.1 ~ 170
|
From page 171... ...
But 0. 100 Fig,15 Rays of bow capillary waves (based upon (A)
|
From page 172... ...
If it is the case it is possible that the local phase velocity reaches to the minimum celerity of capillary gravity waves (=25 cm/see) and the capillary wave breaks.
|
From page 173... ...
Author's Reply Thank you for your congratulations and comments. The aim of this paper is to find out if surface tension is taken into consideration, the ambiguity and difficulties of the conventional Ray theory, as found by many others, can be overcome.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.