Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Accuracy of Wave Pattern Analysis Methods in Towing Tanks
Accuracy of Wave Pattern Analysis Methods in Towing Tanks
Pages 147-160
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From page 147... ...
developed by Newman ~ and Sharma 1 is based on the analysis of wave height measurements along a semi-infinite line parallel t& the model's axis assuming infinite depth, far field waves, and no reflection. In practice, the signal is cut before the reflected waves are measured and a correction has to be made for the lost momentum.
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From page 148... ...
Since, for moderate Froude numbers, the larger part of the wave resistance is generated by transverse waves, the point where the signal is cut, and the accuracy of the correction, play a large part in the accuracy of the computed wave resistance. For higher speed models the contribution of transverse waves to the resistance diminishes as shown in figure 2.
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From page 149... ...
were fitted as follows: Rw(0 < 35° ~ _ -AFT <6' Rw _ _ ~ _ %, The difference in the contribution to Rw from the transverse waves between two consecutive truncation points is defined as follows: Truncation ei=R '(+~ l~withi=1; x~=10C; el=0 (7) Once the minimal distance from the probe to the model axis has been selected, it is possible to study the influence of signal length on the computed resistance.
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From page 150... ...
and~= 1 (10) tan(19°28' ~ In order to reduce errors introduced by the near field waves to less than loo we take y > 5.
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From page 151... ...
Hence, a numerical study was performed to evaluate the robustness of this method based on computed longitudinal cuts at different distances Ye using near field and far field waves. The test case used for a similar study in 5 was modelled following thin ship theory: an infinitely long, thin strut, 2 m in chord, in a 13 m wide tank, at 1, 2 and 4 m/s.
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From page 152... ...
Compared to the LCM method in which, through the Fourier transform, the wave amplitude components are solved independently, the DDM method solves for all components simultaneously through the resolution of a linear system. Hence, errors in the higher frequency, divergent wave components tend to introduce errors on the lower frequency, transverse wave components.
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From page 153... ...
k (17) k=0 If we consider the measurement of Imax wave heights at abscissa xi along a line of constant y, the far field wave elevation at each position (xi ,y)
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From page 154... ...
The results obtained in terms of maximum difference compared to theoretical value using both DDM and SDIM methods are tabulated below: Table 1: Error in % between calculated and theoretical wave resistance using DDM and SDI\I methods Method ~ DDM | SDIM Nm5 1 0.70 % T 0 43 % N=O 1 no solution ~ 1.2 To ~ These early tests confirmed the potential of the SDIM method to obtain very accurate results, even with a limited signal length. Near field wave correction The knowledge of the singularity distribution enables the calculation of near field waves.
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From page 155... ...
A further example of the global agreement between the slender ship model and the identified source distribution is the comparison between the wave elevations generated by POTFLO and by the equivalent source distribution (figure 9~. The small differences between the two signals are due to the presence of near field waves close to the ship and to the oscillations due to the line integral term in POTFLO.
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From page 156... ...
, the agreement between measured and reconstructed SDIM wave elevations for x<-15, indicates that the wave resistance calculated by S DIM is closer to the real value. Different tests performed on the parameters of the SDIM method did not succeed in obtaining a perfect agreement between measured and calculated wave elevations.
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From page 157... ...
T i. -- Nr=0 Nr= 1 Nr=2 20 ~ ~ £ ~ I Nr=3 3 15- ~ Pa 10 -- -- - Nr=4 ~ ~ -- 1 ~-1 1 -am '-am 6 7 8 9 10 0 1 2 3 -- Nr=5 4 5 Figure 12: Wave spectra identified by SDIM for different signal lengths (or number or reflections)
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From page 158... ...
'1' y' , , .V 7.One R 0 20 40 6() 80 zone C 100 120 140 160 180 200 Figure 13: Measured wave elevations indicating the selected signal segments zone A zone B I ~ ~ ~ ~ ~ ~ zone C 1 2 3 4 s 6 7 8 9 10 Figure 14: Wave amplitude spectra computed for each of the zone identified in figure 14 using SDIM 158
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From page 159... ...
Numerical tests have shown this method capable of taking into account the near field wave components through an iterative process, and of providing very accurate estimates of wave resistance independently of signal length (large number of reflections) and transverse position of the probe.
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From page 160... ...
(nf Off 1 =COS ~ Near field wave elevation. Far field wave elevation.
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