The conventional extrapolation of ship resistance from model tests to full scale presumes that the coefficient of wave-making resistance (C_w) depends on the Froude number only. This leads to the assumption that C_w of a ship is identical to C_w 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 C_w 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 C_w 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 (C_f) and the changes in C_w caused by shallow water, which benefits the prediction of shallow water effects on C_w. 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 C_w.

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Understanding the characteristics of the waves generated by a ship can improve the prediction of ship’s wave resistance. Such waves generated in deep water have been studied in detail whereas in shallow water, the existing methods, mostly derived from inviscid flow, are not fully coping with physical phenomena. In this study, the changes in the height and length of ship-generated waves in shallow water are explored as well as the effects of waterbed friction. A Computational Fluid Dynamics (CFD) approach is selected as the main tool and a Wigley hull is chosen due to the availability of validating data. It is found that the wave cut analysis will slightly underestimate the wave resistance. The effects of bottom friction are perceivable and should be considered if a highly accurate prediction is required. This study, which improves the understanding of ship-generated waves, is expected to contribute to the prediction of ship’s wave resistance in shallow water.@en

Accurate resistance prediction for ships sailing in vertically restricted waterways is highly required to improve the design and operation for large ships entering harbors and for vessels navigating in inland waters. The methods derived from deep water may lead to large errors, and studies considering shallow water effects are needed. As most ships sailing in shallow water operate at a low Froude number, the viscous resistance dominates the total resistance and becomes the main concern. In this study, a Wigley hull and the KCS (KRISO Container Ship), which have available benchmark data, are applied. A typical 86 m long inland ship is then chosen to further investigate the influence of a different hull form. Results show that the friction and the viscous pressure resistance depend on ship types, speeds, and water depths. A formula to predict a ship's friction in shallow water is given with some constants determined based on ship's characteristics. A form factor defined based on computed ship's friction is suggested, and an empirical expression is provided for each ship applied. With the investigations for three ship forms, this study is expected to provide inspirations to further improve the prediction of ship's viscous resistance in shallow water.@en

The traditional approach of extrapolating the experimentally measured model resistance of a ship to full scale is based on the Froude assumption or the form factor assumption, where the viscous part and wave-making part of the resistance are dealt with in deep water. In shallow water, however, the water-depth dependency of flat-plate/ship frictional resistance as well as form- and wave effects are expected. It is found in this research that all of these three properties are deviating more or less clearly from the traditional understanding from certain water depths. In this dissertation, a correct understanding of the resistance of ships in shallow water from the very basis is provided to build a new approach to improve resistance prediction considering the water-depth dependency of the three features mentioned above. A method is proposed to improve the extrapolation of ship resistance for model-scale tests carried out in shallow water. The effects of limited water depths on the three components of ship resistance (i.e., frictional resistance, viscous pressure resistance, and wave-making resistance) have been studied individually. Empirical formulas have been developed for three ship types in various water depths. This approach can benefit all further qualities of the ship, e.g., a reliable performance prediction, truly valid rules for ship design and even future work on understanding ship propulsion in (extremely) shallow water when navigating in inland waterways and coastal waters. It also allows the further application of the well-accepted extrapolation method with at the same time taking into account the inherent deviations in shallow water.@en

In ship model tests, a model-ship correlation line (e.g., the ITTC57 formula) is used to calculate the frictional resistance of both the ship and its scaled model. However, this line is designed for deep water and the effects of water depth is not considered. Research has been conducted to improve the correlation line in shallow water, but studies of the extremely shallow water case (depth/draft, h/T < 1.2) are rare. This study focuses on the friction of two ship types in extremely shallow water, where the ship’s boundary layer cannot develop freely. The physical details are analyzed based on the data generated with Computational Fluid Dynamics (CFD) calculations. The results show that for certain ship types at the same Reynolds number, the frictional resistance becomes smaller when the water is shallower. The geometry of the ship, in addition to the Reynolds number, becomes essential to the prediction of ship’s friction in extremely shallow water. Therefore, this scenario is different from intermediate shallow and deep water, and the prediction method should be considered separately. The data and analysis shown in this study can help to improve the understanding and prediction of ship’s frictional resistance in extremely shallow water.@en

CFD (Computational Fluid Dynamics) calculations have been making dramatic contributions to ship resistance prediction. Since the virtual models used are always simplifications of the real ships and fluid, results need to be validated by experiments. However, although a certain number of model tests can be found, the publicly available resistance tests in shallow to extremely shallow water (water depth-to-draft ratio h/T ≤ 2.0) are rare. Therefore, to provide data for validation, a test of an inland ship model in shallow water is performed in a towing tank. Four shallow water depths are applied and one deep water case is added for comparison. The uncertainties in this test are analyzed for the measuring instruments as well as the resistance, trim and sinkage. This test is motivated to provide the path for the ongoing research by the authors on the improved prediction of ship resistance in shallow water and enables the benchmark for other researchers, who investigate ship resistance in extremely shallow water, with experimental data to validate CFD calculations@en

The ITTC57 correlation line, which is derived based on the assumption that the water in which ships advance is infinite deep and wide. However, for ships sailing in the waterway with limited water depth, the frictional resistance will be influenced leading to a decreasing accuracy of the prediction with this correlation line. In this study, a modification of the ITTC57 correlation line is proposed to correct the effects in very shallow water specifically for the flat area of the bottom of the ship. Under some assumptions, this area can be simplified to a 2D flat plate with a parallel wall close to it to study how the shallow water conditions of two interacting boundary conditions are affecting the flat plate friction coefficient. Computational fluid dynamics (CFD) calculations are applied to investigate how a friction line specifically in shallow water deviates from the conventional lines. Such deviations may severely affect the extrapolation of a ship model’s resistance to full scale and, therefore, the accuracy of ship’s performance prediction. Cases at ten Reynolds numbers from 10⁵ to 10⁹ are simulated on the 2D flat plate. Seven different distances between the flat plate and the parallel wall were chosen to generate various shallow water conditions, and consequently, a database including frictional resistance coefficients, Reynolds numbers and the distance between those two walls is built. Results indicate that thinner boundary layers are observed in shallow water conditions, and the scale effects which has a significant impact on resistance extrapolation are also observed. Furthermore, the assumption of the zero pressure gradients (ZPG) which is commonly used in deep water is no longer valid in extremely shallow ones. Finally, a modification for the ITTC57 correlations line considering shallow water effects is proposed, which is willing to improve the prediction of the frictional resistance of those ships with a large area of flat bottom and sail in shallow water.

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Inland vessels generally experience a resistance increment when the water in which they sail is extremely shallow. In this case, resistance extrapolation from ship model to full scale becomes complicated, and the traditional approaches do not often lead to satisfactory predictions. In this study, both numerical and experimental methods were applied to investigate the ship resistance, trim and sinkage in extremely shallow water. In the numerical calculations, the model initially has a trim and sinkage obtained from the model tests. The overset mesh technique was used to save the meshing effort. A 1/30 scaled model, which is only allowed to pitch and heave, was used in the model tests. It was found that, in extremely shallow water, the ITTC57 correlation line is not sufficient to extrapolate the resistance.@en