Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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Complete Cancellation of Ship Waves in a Narrow Shallow Channel
Complete Cancellation of Ship Waves in a Narrow Shallow Channel
Pages 428-440
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From page 428... ...
INTRODUCTION By purely theoretical analysis, albeit inspired partly by previous experimental results, Chen & Sharma discovered and reported in (1996, 1997) that when a slender ship moves in a narrow shallow channel at a supercritical speed, its bow and stern waves can be made to cancel each other so completely by a proper choice of hull-channel geometry that there are no free waves behind the ship and so it experiences theoretically no wave resistance.
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\~N ~~ V .~ > 1 Nigh z~,~. / / ,,, ~~ ~~ z~ Figure 1: Schematic of ship wave pattern at supercritical speed in a narrow shallow channel.
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2. Figure 2: Theoretic solution of the ship wave pattern in the narrow channel.
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Luckily, the curve decays exponentially so that an approximate practical hull form of finite length can be acquired by simple truncation of the bow and stern cusps. In absolute terms, we decided upon a round ship length of 6 m leaving the stem and stern as sharp edges of 2.7 mm thickness.
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The former is claimed to be the true friction line for infinitely thin smooth plates in fully turbulent, two-dimensional flow, while the latter incorporates a constant viscous form factor of about 1.12, believed to be the minimum value for realistic hull forms. As theoretically predicted, the measured total resistance in the narrow channel drops dramatically at the exact design speed, whereas nothing conspicuous happens in the wide tank.
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. 0.41 0.2t iO ~:~ Figure 6: Measured wave profiles at the design depth Froude number Fob = 1.414 (h = 0.2 m and V = 1.98 m/s)
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wave profiles at design depth Froude number Fnh = 1.414 in the design narrow channel; graphs from top to bottom are cuts at y/h = 1.5, 3.0, 4.5, 6.0, 7.5 and 9.0.
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Nevertheless, the numerically simulated wave profiles at the design Froude number, almost adjacent to the transcritical range, are obviously in fair agreement with the theoretical and experimental profiles. The numerical wave resistance calculated by integrating the pressure on the hull surface in the Euler solution is compared in Fig.
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. , ~ 0 5 0.75 1 1.25 1.5 depth Froude number 1.75 2 Figure 9: Comparison of measured residuary resistance from model experiment (solid line connecting dots)
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CONCLUSIONS The purely theoretical prediction of a state of no trailing waves and hence zero wave-resistance for a ship of an ingenious mathematical hull form moving at a chosen supercritical design speed in a rectangular channel of appropriate depth and width has been verified by numerical simulation using a nonlinear 3D Euler solver and validated by physical model experiments conducted in a specially erected narrow shallow-water channel. ACKNOWLEDGMENT We thank the management and staff of VBDEuropean Development Centre for Inland and Coastal Navigation at Duisburg, Germany, for their valuable support in conducting the model experiments.
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. -1 0 1 Figure 12: Measured wave profiles at the off-design depth h = 0.3 m (in the narrow channel of 3.8 m width)
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D., "Zero wave resistance for ships moving in shallow channels at supercritical speeds," J Fluid Mechanics, Vol.
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. It is true for almost any ship model in a shallow channel of rectangular cross-section that if ship length and speed are in the right proportion to channel depth and width, the bow waves reflected from channel sidewalls would significantly cancel the stern waves and, hence, result in a corresponding reduction of wave resistance.
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