Restricted snakes volume of solid (RSVS): A parameterisation method for topology optimisation of external aerodynamics

•A topology parameterisation method for boundary-fitted CFD analyses is proposed.•A Hierarchical topology optimisation method allows recovery of multi-body airfoils.•Drag minimisation in supersonic flow shows the local optimality of Spitzer bullets.•Topological flexibility enables the exploration of drag reducing aerospike.•Topology optimisation allows a 70% reduction in drag compared to shape optimisation. An approach for aerodynamic shape optimisation is derived which is capable of handling topological design changes as well as detailed surface control. The technique applies a material distribution, or volume of solid approach where design variables specify a volume fraction of solid on a fixed mesh. To convert this data to a solid surface, a contour is constructed around the volumes by moving points on the surface until the final shape satisfies those specified volumes. The objective of this construction procedure is to minimise the surface length, subject to the preset volume constraints. As a result, the method reproduces circular arcs exactly. Shape function analysis is then used to explore the theoretical behaviour of the parameterisation, and to prevent oscillatory surfaces from forming, thereby ensuring good optimiser convergence. The method is extended to allow for anisotropic refinement of the parameter mesh. Final test cases include geometric fitting of arbitrary shapes, as well as drag minimisation of topologies in supersonic flow, and show the parameterisation is able to explore single and multi-body aerodynamic design problems.