Constructing Geometry for Aerodynamic Shape Optimisation using Volume of Solid Driven Cellular Automata

A two and three dimensional volume of solid parameterisation method is explored that is based on the method of cellular automata. It is capable of using geometric refinement and representing complex topology, with the ability to handle merging or splitting of objects and internal voids. The cellular automata acts to maximise the cohesiveness of all occupied cells under the influence of a function to drive the overall number of occupied cells towards a target value within each volume of solid control cell. This creates a geometry of minimum surface length or area that conforms to the set of specified volume of solid parameters. This geometry is then smoothed to construct surfaces suitable for aerodynamic parameterisations. The presented method is capable of parameterising common test case aerofoils such as NACA 0012 and RAE 2822 to within Kulfan’s wind tunnel tolerance with 47 and 58 active parameters respectively, and is used to successfully optimise a supersonic aerodynamic geometry with a packaging constraint, achieving an approximately 95% reduction in drag coefficient compared to the initial shape.