Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Nonlinear Free-Surface Effects on the Resistance and Squat of High-Speed Vessels with a Transom Stern
Nonlinear Free-Surface Effects on the Resistance and Squat of High-Speed Vessels with a Transom Stern
Pages 502-516
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From page 502... ...
Introduction Previous Work Previous work on the subject of prediction of resistance of marine vehicles, such as monohulls and catamarans, has shown that the trends in the curve of total resistance with respect to speed can be predicted with excellent accuracy, using the traditional linearized Michell (1898) wave-resistance theory, together with a suitable formulation for the component of frictional resistance.
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From page 503... ...
This approach involves apolYin~ the Kutta condition to the edge of the transom stern and also adjusting the length of the hull to minimize the deviations of the pressure from atmospheric. Current Work The primary aim of the current work is to study the possibly of incorporating nonlinear wave effects in the analysis of the vessel.
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From page 504... ...
Finally, a tertiary aspect of the study is to develop a semi-empirical model for the water flow withers the transom-sterrz hollow at low speeds. The need for this improvement was made apparent from previous work on this subject, where it was recognized that assuming that the water was fully separated, even at low speeds, resulted in predictions for the resistance which were impractically high.
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From page 505... ...
(4) These different approaches are summarized Enhanced Viscous Effects In previous work by the authors, the frictional resistance RF was estimated using only a suitable friction line based on a semi-empirical method, such as the 1957 International Towing Tank Committee (ITTC)
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From page 506... ...
Low-E'roude-Number Regime The assumption that the water separates cleanly at the sharp edge of the transom stern has Length ~ ~ = rat 1 0.000 0.0000 0.7500 0.6666 2 0.000 0.1875 0.9375 0.7290 3 0.000 0.3750 1.1250 0.7499 4 0.000 0.5625 1.3125 0.7290 5 0.750 0.0000 1.5000 0.8332 6 0.750 0.1875 1.6875 0.8494 7 0.750 0.3750 1.8750 0.8499 8 0.750 0.5625 2.0625 0.8275 9 1.500 0.0000 2.2500 0.8888 10 1.500 0.1875 2.4375 0.8957 11 1.500 0.3750 2.6250 0.8928 12 1.500 0.5625 2.8125 0.8735 Table 5: Lego Ship Models (Variable Data) been shown to be a reasonable approach for modeling the physical situation at most Froude numbers of practical interest.
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From page 507... ...
Finally, the total resistance can be found by 6 ~ ~ ~ Model 12 Model 10 Figure 2: Towing-Tank Models (b) Lego Ship Models 10 and 12 the simple summation of the pressure resistance RP, the frictional resistance RF discussed earlier in this paper, and the correlation resistance RA.
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From page 508... ...
Table 4 and Table 5 list the details of all twelve of these so-called Lego Ship Models. Results Numerical Convergence Tests The three parts of Figure 3 show a test of convergence for Lego Ship Model 8, for three physical parameters of interest.
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From page 509... ...
Resistance Components Figure 4 depicts the theoretical computations of the various resistance components referred to earlier, 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.
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From page 510... ...
As for the case Data Exp Field Linear NL—1 NL—2 NL—3 Series = Logo Model= 8 L = 206~3 m B/L = 0.0727~3 Visc = Simple I' K~i o O.~ 1 1 1 1 1 1 02 0.23 0.4 Q5 0.6 0.7 0.8 0.9 F Figure 5: Comparison of Resistance (b) Lego Ship Model 8 Data Exp Field Linear NL—1 NL—2 _ NL—3 Series = LeB° Model = 12 L = 2813 m B/L = 0.053 Visc = Simple ~ ," 0.1 0~2 0.13 0.4 0.5 0.6 0 F Figure 5: Comparison of Resistance (d)
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From page 511... ...
Hence, the favorable impact of the displacement thickness on the total resistance will be even less on a relative basis. Data Exp Linear NL—1 NL—2 NL—3 _1 14 X10 ~ 12— 10 8— 6— I_ 2— O— 0.8 0 Series = Lego Model = 8 ~ _ '' I!
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From page 512... ...
Lego Ship Model 6 40 xlO~3 Curve 0 0 0 0 30 20 ~ _ 10— O— —10 Data Exp Linear NL—1 NL—2 NL—:3 / ~ ,/ in_,/ ~ ~ /x /~ -I 0 ,'~°Series= Lego ,c~ Model— 10 B/L = 0.06154 Visc = Simple 1 1 1 1 1 1 0 0.1 02 0.13 0.4 0.5 0.6 0.7 0 F Figure 7: Comparison of Trim (c) Lego Ship Model 1O three curves are plotted rather than just two.
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From page 513... ...
That is, the idea of applying distortion to the hull body in order to generate a more correct longitudinal distribution of the immersed hull volume usually gave worse pre1 12 32 xlo-s 28 ~ 24R 2016 12 8Series = IRgo Model= 8 L = 2063 m B/L = 0.07273 Data = Linear Free = No | Curve | Visa | — 1~ 1 0 0.1 02 0.3 0.4 0.5 0.6 0.7 0.8 0.9 F Figure 8: Viscous Effects without Squat (b) Lego Ship Model 8 4.5— X10 ~ 40— 35— ~ 3020— 15 10 5— Series = Len Model = 8 L = 2~063 m B/L = 0.07273 of Data = NL—1 Free = Yes i/ Curve Vise Simple ~ ..~ ~.
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From page 514... ...
Lego Ship Model 12 will be obtained, if one could just develop a simple approximate dependence of the transom-stern pressure coefficient on the form of the ship hull (the longitudinal rate of change of the sectional area) just ahead of the transom stern.
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From page 515... ...
SAHOO, P.K., DOCTORS, L.J., AND RENILSON, M.R.: "Theoretical and Experimental Investigation of Resistance of High-Speed Round-Bilge Hull Forms", Proc. Fifth International Conference on Fast Sea Transportation (FAST '99J, Seattle, Washington, pp 803-814 (August-September 1999)
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From page 516... ...
While the analysis of these results is still at an early stage, we have demonstrated that the associated wave-elevation-prediction computer program provides wave profiles which are verified by the experiments within a few percent. Differences are mainly in the phasing of the waves rather than in their elevation and, hence, the energy density in the wave system and the resulting wave resistance is expected to be predicted well - as demonstrated by the total resistance predictions presented in our paper.
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