Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern
Steady-State Hydrodynamics of High-Speed Vessels with a Transom Stern
Pages 191-205
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From page 191... ...
The latter component of the computation utilizes an integration of the resulting pressure distribution over the wetted surface of the vessel in an entirely consistent manner. Comparison of the theoretical results with a systematic series of twelve models shows excellent correlation with the towing-tank data.
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From page 192... ...
There, a simple virtual extension to the hull behind the transom was constructed in the computer program. The wave resistance for the vessel was deduced on the basis of an application of the Michell integral to the entire model and its extension, together with an estimate of the hydrostatic resistance due to the existence of the dry transom.
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From page 193... ...
On the other hand, numerical convergence tests for wave resistance, based on the two types of panels, showed that a similar number of panels was required in either case; namely, 40 panels in the longitudinal direction and 8 panels in the vertical direction. Equations for the Potential We start in the traditional manner by utilizing the potential ¢, whose gradient gives the perturbation velocity.
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From page 194... ...
Lego Ship Models 11 and 12 and the required arguments in the special function G4 are defined by x = Xi—xj + lax, + id—x') cost + iffy—y')
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From page 195... ...
In the current enhanced technique, the initial estimated profile of the hollow is assumed to be defined by the parabola that springs longitudinally from the bottom of the transom and meets the vertex on the (un(listurbed) free surface.
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From page 196... ...
, MP the bowup pressure moment, xprop the longitudinal lever arm for the propulsion force, Zprop the vertical lever arm for the propulsion force, Xprop the longitudinal component of the propulsion force, IF the vertical arm for the frictional force (measured to the centroid of the wetted surface) , Zs~ab the vertical lever arm to the stabilizers, Rub the resistance of the stabilizers (zero in the current work)
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From page 197... ...
Table 1 and Table 2 list the details of all twelve of these so-called Lego Ship Models. Results Numerical Convergence Tests The wave r esistance of a vessel without a transom stern, computed according to Equations (34)
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From page 198... ...
Resistance Components Figure 4 depicts the theoretical computations of the various resistance components referred to above, for four of the ship models. These show the hydrostatic resistance RH, the pressure resistance RP, the frictional resistance RF, the total resistance RT, and the total experimental resistance RT,E- In general, the correlation between the theory and the experiments is good at the higher speeds, which are of practical significance, that is, for a Froude number F of 0.6 or greater.
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From page 199... ...
Finally, we present Figure 8, which shows the dimensionless hollow length Lho~/L for the four Lego Ship Models. It is curious to note that there is little significant difference between the length of the hollow computed in the current hydrodynamic manner and the length of the hollow resulting from the simplified geometric approach of Doctors and Day (2000)
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From page 200... ...
Lego Ship Model 12 It is necessary to emphasize that, at least with regard to resistance, the current approach still uses a traditional estimator for the frictional component. That is, ideally, one might consider utilizing a form factor to correct the frictional resistance.
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From page 201... ...
E No T Yes T Yes T Yes T o of art' Series = Lego to Model = 12 ~Oo°° L =2.813 m O ° ° L/V1/3 = 9.889 T I I T I I 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 F Figure 5: Comparison of Resistance (d) Lego Ship Model 12 References COUSER, P.R., WELLICOME, J.F., AND MOLLAND, A.F.: "An Improved Method for the Theoretical Prediction of the Wave Resistance of Transom-Stern Hulls Using a Slender Body Approach", International Shipbuilding Progress, Vol.
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From page 202... ...
D OCTORS, L J .: "Improvement of the Correlation of Michell's Integral for Displacement Ves 10 x 10-3 Curve Holl 0 0 0 0 8 - Simp P,K P,K,L 6 4Series = Lego Model = 7 L = 1.875 m L/V1/3 = 7.615 / Free = Yes 1 O- 1 0.6 0.8 0 0.2 — — o o x10-3 Curve Holl a,, 5- 0 0 0 0 o 0 ~ Simp P,K 4— P,K,L 3xlO-3 2nData Exp Theory Theory ,Y to Series = Lego Model = 8 L = 2.063 m L/V1/3 = 8.187 Free = Yes 1 0.4 0.6 0.8 F Figure 6: Comparison of Sinkage (b)
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From page 203... ...
(a) Lego Ship Model 7 Holl Simp P,K P,K,L _ Data Exp Theory Theory Theory lo i, ~0°° Series = Lego ~ /' o Model = 11 o 0 0 oooOo° °OoO L =2.625 m L/V1/3 = 9.375 Free = Yes 1 1 1 1 1- 1 0.1 0.2 0.3 0.4 0.5 0.6 F Figure 7: Comparison of Trim (c)
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From page 204... ...
Lego Ship Model 7 16 xlo-2 12 8— 4O— A 16 xlo-2 12 _ 84 Curve Holl 0 0 0 0 Simp ~ Pa P,K,L Series = Lego Model = 8 L = 2.063 m Data Exp Theory Theory Theory / L/V1/3 = 8.187 Free = You / 00000000000000 0 0 ° .
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From page 205... ...
ccuterplaue source di.vribuuon I is because it is expected or presumed that the wave drag will be much smaller than She f ichona pa t. I propose Chat the model cou d be improved upon by using a desingu anzed panel method where She sources cou d be placed lid e inside the bounds y which wou d sell preserve She imp ined ca cu anon aspect and may work better in She sense of di using She prearm Fr on.
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