Abstract
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.
Highlights
Increases in computational power and improvements in computational fluid dynamics (CFD) tools have created the possibility of using CFD-based optimisation in industrial design
This paper presents the development of a parameterisation method which can handle topology changes while maintaining a compact design space, allowing the exploration of new aerodynamic optimisation problems
This paper presents development of the r-snake volume of solid (RSVS) method, an aerodynamic parameterisation that supports topological change while still performing efficiently on typical problems
Summary
Increases in computational power and improvements in computational fluid dynamics (CFD) tools have created the possibility of using CFD-based optimisation in industrial design. Parameterisation methods for aerodynamics need to be compact while not artificially limiting the geometric shapes that can be represented [1,2] This focus led to aerodynamic optimisation methods capable of efficiently handling small surface changes, using 10s to 100s of design variables in 2 dimensions and 100s to 1000s in 3 dimensions. The possibility to reduce designs to a set of external interactions and the Lagrangian formulation of CSD solvers facilitates the implementation of structural topological optimisation within existing designs There is no such separation in aerodynamics; the aerodynamic shape is intrinsically linked to the rest of the design by its need to be supported by an underlying structure. No current optimisation framework for external aerodynamics supports the exploration of topological changes, because none of the parameterisation methods commonly in use can represent different topologies with a homogeneous set of design variables. This paper presents the development of a parameterisation method which can handle topology changes while maintaining a compact design space, allowing the exploration of new aerodynamic optimisation problems
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