This study shows that even small modifications of hull frames can yield a measurable reduction in propulsion power. This ship optimisation study was conducted by combining a parametrised local free-form deformation of hull frames together with a generalised Lackenby approach, designed to maintain the displacement and LCB. The KRISO Container Ship (KCS) is used as parent hull geometry. The hull was modified below the bilge, in the region close to the stern gondola. Modifications are contained within a realtively limited portion of the vessel, hence represent only local changes to its goemetry. This makes this ship optimisation approach appropriate for late design stages.
Stern hull frame modifications are parametrised with three different parameters. The tested combinations of parameters are determined using a design of experiments method. Differnt hull variants are evaluated by condicting self propulsion simulations using the actuator disc propeller modelling. The optimal stern hull shape is then selected (Variant 6 in the image below) showing a reduction in propulsion power of 1.6%. Variations in displacement and LCB were maintained below 0.1% withing the hull optimisation process.
The image at the top of the page shows the comparison of original (black) and optimised (red) hull lines at the aft portion of the vessel. The optimised hull curves have a more pronouced "S" shape in the bilge area, while the aft gondola is more slender. Interestingly, the optimal hull design is inferior to the original design in terms of towed hull resistance, but achieves better performance in self-propulsion conditions. This indicates that self-propulsion should be evaluated when conducting optimisation of the aft portion of the hull.
Images below show the original design, optimium design (No. 6), second best design (No. 21), and the worst-performing design (No. 25), and the wave fields that they generate. It is clearly visible that Hull No 6 and 21 have a smaller stern wave compared to the original and worst design.

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