Abstract
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 Furthermore, the assumption of the zero pressure gradients (ZPG) which is commonly used in deep water is no longer valid in extremely shallow ones.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.
Highlights
An improved understanding of the characteristics of friction/ correlation lines in various conditions can contribute a better model-ship extrapolation, which is in turn beneficial for ship design and optimization
The number of grid cells in the y-direction (Ny) was varied according to the distance between the flat plate and the parallel wall
When lg(Re) = 5.6, the increase of Cf can reach almost 50% compared to the deep water condition;
Summary
An improved understanding of the characteristics of friction/ correlation lines in various conditions can contribute a better model-ship extrapolation, which is in turn beneficial for ship design and optimization. Researchers have provided several friction lines, e.g. Schoenherr [1], Grigson [2] and Katsui [3] proposed friction lines for flat plates and 1957 ITTC [4] correlation line is frequently used to predict the frictional resistance of ships These methods were based on the results of experiments and/or numerical simulations with an unrestricted incoming flow. To improve the prediction of ship’s friction, after applying ITTC57 correlation line for all wetted surface, this proposed line can be used to correct the shallow water effects on a ship’s flat bottom. The combination of these two lines is considered as a suitable method for predicting the frictional resistance in the pure shallow water.
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