Gradient-Based Aerodynamic Optimisation for Two- and Three-Dimensional Supersonic Flows Using a Volume-of-Solid Parameterisation

A topology-free parameterisation is used to optimise geometries in supersonic flow under a volume constraint, using a gradient-based method. In two-dimensions, these geometries recover parabolic shapes for a small volume constraint, and shapes with a similar forebody but truncated afterbody when the volume constraint is increased. All cases presented provide a reduction in Cd compared to the two-dimensional parabolic optimal geometries of equivalent area. In three dimensions, small volume constraints lead to a Sears-Haack like shape, but when the volume is increased, the Sears-Haack body becomes truncated and terminates in a crenellated boat-tail. This type of afterbody is unusual and only possible due to the flexibility of the volume-of-solid parameterisation used. This appears to provide an advantage in terms of drag from Euler computations, although it is not known if such an advantage would be seen in a real flow. Neither case presented in three dimensions improves over the Sears-Haack geometry of equivalent volume, however this appears to be due to an excessively coarse parameterisation.