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Resistance is one of the important areas that has to be taken into account in ship hull development. Prediction of ship resistance is in most cases based on results from experiments at model scale. If the resistance requirements are not fulfilled a modification of the hull shape is undertaken and another model test is carried out. This process forms a system for “manual optimization”.

In recent years computational methods (CFD) have been introduced in the design process to predict the flow around the hull and in some cases also the resistance of the hull. Different design alternatives may be compared based on computed results and the best one is then selected for verification by model tests. In this way CFD methods may help to speed up the “manual optimization” process by reducing the number of “iterations” that are needed to find the final shape.

Another interesting possibility is to combine a CFD method and a mathematical optimization method together with a program for hull form variation. This system can then be used to find a hull form that is optimized with respect to properties computed by the CFD method, like the resistance, maximum wave height, velocity in the propeller plane, etc. One or more constraints, for instance displacement and hull main dimensions, must then be introduced to limit the modifications of the hull. This forms a system for “automatic optimization”.

Many interesting works on hull form optimization from a hydrodynamic point of view have been presented through the years. Systems for “automatic optimization” as described above have been presented by Kim (1), Nowacki (2, 3), Papanikolaou et al. (4), Hsiung (5), Wyatt and Chang (6), Maisonneuve (7) and others. Different levels of approximation for the flow prediction, from thin ship theory for wave resistance and a simple formula like the ITTC-57 line for the viscous resistance to more advanced computational methods, both for the inviscid and the viscous flow, have been used.

Research in viscous and inviscid flow calculations has been carried out at SSPA Maritime Consulting and FLOWTECH International AB in collaboration with Chalmers University of Technology since about 1970. The computational methods developed in this research work, Xia (8), Kim (1), Larsson (9) and Broberg (10) are used in the present work together with an optimization method developed at the Royal Institute of Technology and at ALFGAM Optimization AB, Svanberg (11, 12) and Esping et al. (13, 14) to form a system for “automatic optimization” of ship hulls.

The Zonal approach

A zonal approach is used in SHIPFLOW to compute the flow around the ship hull. The flow domain is divided into three zones, figure 1, and a computational method is developed for each zone. The first zone covers the entire hull and a part of its surrounding free-surface. A free-surface potential-flow method of Rankine-source type is used. The second zone is a thin layer at the hull surface and a boundary layer method of the momentum integral type is used. The momentum integral equations are solved along streamlines traced from the potential flow solution. Finally, the third zone includes the aft part of the hull and extends about half a ship length downstream of the hull. It also covers about half a ship length in the radial direction. A Navier-Stokes method of the RANS type using the k–ε model and a wall-law is used in zone three. The zones are computed in sequence and boundary conditions are generated for succeeding zones. The reason for the division of the flow field into zones is that the computational time may be reduced considerably compared to the global approach where the Navier-Stokes method is used in the entire computational domain.

Fig. 1 The Zonal approach

The potential-flow method

Inviscid, irrotational flow is assumed and a velocity potential, whose gradient is equal to the local velocity may be defined. The potential is governed by the Laplace's equation which is an elliptic partial differential equation that requires boundary conditions on all boundaries of the computational domain. On the hull the flow in the hull surface normal direction must be zero and on the free-surface the flow must be tangent to the surface and the pressure must be constant. At infinity the disturbance due to the hull must vanish. One additional condition is also needed to prevent upstream waves. This condition is introduced together with the numerical method.

The potential-flow problem is non-linear and the free-surface boundary conditions have to be applied

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