Abstract
The conventional extrapolation of ship resistance from model tests to full scale presumes that the coefficient of wave-making resistance (Cw) depends on the Froude number only. This leads to the assumption that Cw of a ship is identical to Cw of its scaled model. However, this assumption is challenged in shallow water due to viscous effects, which are represented by the Reynolds number (Re). In this study, different scales (different Re) of the Wigley hull and the KCS hull are used to investigate the scale effects on Cw numerically. After verification and validation, systematic computations are performed for both ships and their scaled models in various shallow-water conditions. Based on the results, significantly larger values of Cw are found for the KCS at model scale in very shallow water, suggesting that the conventional extrapolation has to be reconsidered. Additionally, this study reveals the relationship between the changes in frictional resistance coefficient (Cf) and the changes in Cw caused by shallow water, which benefits the prediction of shallow water effects on Cw. Finally, use of a larger ship model, where the Re is also higher, is recommended for resistance tests in shallow water to reduce scale effects on Cw.
Highlights
It is not easy to obtain the resistance of a full-scale ship directly
coefficient of wave-making resistance (Cw) of the Wigley hull is insensitive to Reynolds number (Re) at this Frh, which indicates that the ship form plays an important role in the scale dependency of Cw;
The conventional extrapolation of ship resistance from model tests can be applied in shallow water without any corrections
Summary
It is not easy to obtain the resistance of a full-scale ship directly. Conducting ship model tests, acts as an important technique to predict the full-scale ship resistance. Cw remains identical for a ship and its scaled model (ITTC, 2017a) This assumption acts as the basis of resistance extrapolation from model scale to full scale after model tests. Small errors might be caused due to the damping if one uses wave-cut analysis (Sharma, 1963) to obtain Cw. As indicated by Stern (1986), the development of the ship’s boundary layer is influenced by ship waves. According to the numerical calculations conducted by Raven et al (2008), the wave height of ship-generated waves at full scale is larger than that at model scale, indicating that the computed Cw at model scale underestimates a real ship’s wave-making resistance. More recently Terziev et al (2018), using a geosim analysis, argued that Cw does not show clear relationship with neither scale factors nor Re
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