Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Ship Motions by a Three-Dimensional Rankine Panel Method
Ship Motions by a Three-Dimensional Rankine Panel Method
Pages 21-40
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From page 21... ...
Computations of the steady ship wave patterns reveal significant detail in the Kelvin wake a significant distance downstream of the ship, permitted by the cubic order and zero numerical damping of the panel method. The wave pattern appears to be sensitive to the selection of the freesurface condition only for full ship forms.
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From page 22... ...
A comparison of the wave patterns obtained form the Neumman-Kelvin and the more general double body free-surface conditions reveals good agreement for the Wigley hull, while evident differences appear in the respective Series-60 wakes. Predictions of the heave and pitch added-mass and damping coefficients and exciting forces are found to be in very good agreement with experimental measurements both for the Wigley and the Series-60 hull.
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From page 23... ...
(2.6) The double-body flow is chosen as the basis flow, a selection primarily motivated by the body boundary condition as well as the simplifications it allows in the ensuing analysis.
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From page 24... ...
for i, j = 1, ..., 6. The exciting forces Xi and the added mass and damping coefficients, aij and bit are therefore functions of the forward speed and the frequency of oscillation w.
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From page 25... ...
for the steady and unsteady flows is obtained using a Panel Method. The systematic methodology for the study of the numerical properties of Rankine Panel Methods for free surface flows developed in Sclavounos and Nakos (1988)
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From page 26... ...
This section presents converged computations of the steady and time harmonic wave patterns around a Wigley and a Series60 hull. The Wigley model has parabolic sections and waterlines, a length-to-beam ratio L/B = 10 and beam-to-draft ratio B/T = 1.6.
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From page 27... ...
I 1 _ _ ~_ F = 0.35 F = ~ 25 l~t~ble~Bod' -0 75 J -1 TO -1 .00 - 0.50 0.00 0.50 O.SO o.oo -0.25 -0. 75 -0 75 ~ = 0.4C (/~/~//~< ~ J Neumann-Kelvin ~ - 1.50 - 1.00 -0.50 0.00 O.SO I 0.00 -0.25 -0 75 Figure 2: Contour plots of the steady wave patterns due to the parabolic Wigley model advance ig at Froude numbers F = 0.25, 0.35, 0.40.
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From page 28... ...
,1 , , , , , , ,) , ~ , -1.50 - 1 .00 - 0.50 0.00 0.50 I I I I I I I ~ I I _ Double-Body ~7 _ F = 0.35 -0 75 -0.75 - 1.50 - 1 too -0.50 0.so 0.00 Figure 3: Contour plots of the steady wave patterns due to the Series-60-cb =0.6 Yesse1 advancing at Froude numbers F = 0.20, 0.25, 0.35.
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From page 29... ...
Figure d: Snapshots of the time-harmonic wave patterns due to a modified Wigley model advaDcing at F=0.20 while oscillating in heave at frequencies wp7ij=3.0,5.0.
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From page 30... ...
Computations of the heave and pitch added-mass and damp ing coefficients obtained from these grids, are illustrated in Figure 7. The convergence rate is very satisfactory and Figure 5: Snapshots of the time-harmonic wave patterns due to a modified Wigley model advsacing at F-0.30 while oscillating in heave at frequencies 7= 3.0, 5.0.
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From page 31... ...
The Neumman-Kelvin curve is obtained from the solution of the linearized problem using the present Rankine panel method and is obtained by approximating the steady flow by the uniform stream -Up both in the free-surface and body boundary conditions. The agreement between SWAN and experiments is quite satisfactory and represents an improvement over strip theory.
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From page 32... ...
. · °2.00 3.00 ~ 00 w47~; 5.00 6.00 Figure 7: Numerical convergence study for the heave and pitch hydrodynamic coefficients of a modified Wigley model advancing at F = 0.3.
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From page 33... ...
. 02.00 ~ Do ~ Do w\~7; 5.00 6.00 Figure 8: Diagonal hydrodynamic coefficients in heave and pitch for a modified Wigley model advancing at Eroude number F=0.3.
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From page 34... ...
Strip Theory - SWAN ~Neumann-KelYin . o ~ , ~ 10~ I trio o 0 Experiments -- Strip Theory SWAN Neumann Kelvin cat _ o '2.00 3.00 `.00 a _ s.oo 6.00 2.0 3.0 To w~77 5.0 6.0 Figure 9: Cross coupling hydrodynamic coefficients between heave and pitch for a modified Wigley model advancing at Froude number F=0.3.
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From page 35... ...
'~ . 2.0 2.5 ab.s t.0 t.5 2.0 2.5 A/L Figure 10: Heave and pitch exciting forces and motions of a modified Wigley model advancing at Froude number F=0.3 through regular head waves.
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From page 36... ...
Computations of steady and time-harmonic ship wave patterns illustrate the capability of the method to resolve considerable detail in the wave disturbance and at a significant downstream of the ship. Predictions of the heave and pitch added-mass, damping coefficients, exciting forces and motions of a Wigley and the Serie~60 hull are found to be in very good agreement with experiments and present a significant improvement over strip theory.
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From page 37... ...
Future research towards the further development of the present rankine panel method in the steady problem, will concentrate upon the determination of the ship wave spec trum from the available numerical data over the discretized portion of the free surface. This information is useful for the characterization of ships from their Kelvin wake and the accurate and robust evaluation of the wave resin lance.
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From page 38... ...
o °~.5 1~ _. .0 1.5 A/L 2.0 2.5 Figure 13: Heave and pitch motions of the Series-60-cb =0.7 vessel advancing at Froude number F = 0~2 through regular head waves.
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From page 39... ...
We are also indebted to the Computer Aided Design Laboratory of the Department of Ocean Engineering at MIT for their assistance in the preparation of the time-harmonic ship wave patterns on their IRIS Workstation. REFERENCES Chang, M.-S., 1977, 'Computations of three-dimensional ship motions with forward speed', 2nd International Conference on Numerical Ship Hydrodynamics, USA.
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From page 40... ...
Raven for implementing and testing the free surface condition proposed in this paper. The differences of the wave patterns, as predicted by different free surface linearization models are indeed reflected on the corresponding wave resistance calculations.
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