Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Prediction of Radiation Forces on a Catamaran at High Froude Number
Prediction of Radiation Forces on a Catamaran at High Froude Number
Pages 5-20
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From page 5... ...
ABSTRACT Practical approach is investigated to predict three dimensional hydrodynamic interaction between two hulls of a catamaran oscillating and running at forward speed. Chapman's approach is tried to solve the boundary value problem for the unsteady velocity potential around twin hulls' section contour with retaining all the terms of the full linear free surface condition including forward speed effect.
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From page 6... ...
First we invesigate the far-field effect of unsteady bow flow caused by heave and pitch motions of the ship. There we describe a set of assumptions leading to the full linear free surface condition retaining the ~ derivatives in the near-field.
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From page 7... ...
Effect of the transverse waves might be taken into account approximately as follows. They satisfy the free surface condition far behind the bow region and satisfy the body boundary condition because of the approxi~nately zero normal velocity on section contours.
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From page 8... ...
to analyze the same problem. With this assumption, however, we once again end up with a non-linear free surface condition for the steady flow ¢5.
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From page 9... ...
Chapman (1975) presented a simplified highspeed theory satisfying the full linear free surface condition in the near field for a surface piercing flat plate in yaw and sway motion problems.
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From page 10... ...
, a far field approximation of the near field solution is to be obtained as follows. blur = e i(~/U)
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From page 11... ...
Ax Both hulls of a catamaran are considered to be within the near field of each other, the source density On both contours must be symmetrical with respect to fez plane. Each section contour is divided into a number of segments on which the source strength is assumed constant and the integral equation (30)
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From page 12... ...
s results we have shown here are too without A The present method and unified theory predict hydrodynamic forces al most similar in magnitude, while agreement is not consistent.
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From page 13... ...
However results obtained with the steady flow terns in the body boundary conditions and in the pressure equation taken into consideration, though it is inconsistent in our analysis, do not show better correlation. It may be concluded that our 'approach in predicting various factors, hydrodynamic forces and wave elevations etc.,associated with seakeeping of a catamaran at high speed seems to be promising front practical view point.
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From page 14... ...
Bow Flow and Added Re sistance of Slender Ships at High Froude Number and Low Wave Lengths.
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From page 15... ...
-- Unified theory FN=0-5 0.3h LFN=1.O ° l l 0 5 10 15 20 2 25 wg L Fig.5 Added Mass (Heaving) of a Single Hull Ship ~1 ~1 |~ Present Method(without mj)
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From page 16... ...
-W== ~ FN=0.89 ~° _ 0 ~ - - _ ~== ~ - - _ L FN=0 50 5 10 15 Fig.ll Damping (Heaving) of a Catamaran °~1 C33 pgL B2/2 0.5 ~N=05 /'/4FN= 0.89 / //~FN=0 ~15 //; ~ 1 ~/~ _ ~ ~0.5 15mm Heave Fig.14a Variation of Restoring Force (Heave)
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From page 17... ...
/~1 J I; I ^- ~~~5 0.6 / 0.8/ Fig.15 Wave Elevation TV For 0.89, ~ L-20, Pitching /'X-0.8 / / /0.6 / \` X-O.B cos ~ t 0.6 ' At' 0.~ 1 0.2> ~ a\ ~ 0.4 0.4 Fig.16 Wave Elevation 17
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From page 18... ...
. -L O L F.P A.P Fig.1/ Wave Elevation in the Far Field Y/L Y/L = 0.
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From page 19... ...
Indeed, our experience, as I recall, was that the terms associated with the change in waterline width need to be accounted for. In our calculations of those days, the mj terms involving the steady-state body potential was not included, but improvement over strip approximation was evident.
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