This work focused on reducing the drag of the ship by changing the shape of the bulbous bow, visualized in the figure below. Two shape changing parameters were defined and allowed the bulbous bow to translate in both the X and Z-axis. The RBF Morph tool was employed for changing the shape of the bulbous bow, as specified by the parameters. This tool is used to make smooth shape changes to the ship geometry by relocating grid nodes within the solver. This removes the need for manually changing and remeshing the geometry.

The Latin Hypercube Sampling Design Of Experiments method was applied to get a set of design points that provide an optimal range of parameter variations for the development of a surrogate model. Design points are a set of input parameters with corresponding output parameter value. The output parameter is the total drag of the ship hull, which was calculated with dedicated CFD simulations. A response surface is a surrogate model that correlates design points. The response surface provides an increased number of data points for the optimization algorithm by correlating and extrapolating the calculated design points within given bounds. The response surface is visualized in the figure below. In this figure the grey squares in the response surface are the design points on which the surrogate model is based upon. A verification CFD simulation was executed to check the validity of the response surface and gave a deviation in drag of 0.5%.

A Multi-Objective Genetic Algorithm was used to solve the optimization problem. The objective of the optimization algorithm was to minimize the ship hull drag with minimal movement in the X direction and free movement in the Z direction. For a multi-objective optimization it is not possible to find one optimum, since improving on one parameter would at some point always reduce the quality of another parameter. Therefore, such an optimization results in a range of optimum points, known as the Pareto front. With strong deviations in the Pareto front it is required to execute a CFD simulation of all candidate points. In this case the deviation of the estimated drag is within 1 percent point for the feasible candidate points, hence it was chosen to continue based on one candidate point.

A new CFD simulation was executed to evaluate the candidate point and check the actual drag. It was found that the total ship hull drag was reduced by 4.6%. The effect of the shape change on the drag is visualized in the figure below for individual sections of the ship. An increase in drag was found at the bulb section itself, but the drag decreased at the bow section of the ship. The change in drag at the rear sections is negligible.

In the figure below the vortex core regions are visualized by the Q-criterion for the base and optimal case. The bulbous bow shape change resulted in a decrease of a separation area on top of the bulb. This in turn reduced the vortex that is generated by this separation zone, visualized in the figure below.

The shape optimization results have demonstrated that with a limited number of parameters, for only a small section of the ship an improved ship design could be created. The total drag has reduced by 4.6% with relatively small changes to the bulb design. Extending the number of parameters in the optimization process could lead to more improvements and a better ship design.

The work demonstrated that this design optimization methodology can be a good alternative to the traditional iterative ship design process.