Shape and Topology Optimisation of External Flows

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The work in this thesis develops methods for aerodynamic topology optimisation (ATO), in particular, and, in general the automatic exploration of physical design spaces. To be suitable for aerospace applications, the framework developed in this work is compatible with boundary fitted meshes; which contrasts with recent methods for ATO which do not maintain an explicit boundary. This makes this work compatible with existing aerodynamic shape optimisation frameworks, and gives those methods the potential to explore radically new designs though topology optimisation.

Development of a parameterisation with a smooth and intuitive geometric response in two and three dimensions is one of the key requirements for TO and the primary focus of this thesis. The new parameterisation, the restricted snakes volume of solid (RSVS), is defined as the profile minimising the length and containing the area specified by a set of volume fractions defined on a grid. This formulation is shown to extend to any layout of volume fractions, and, an analytical equivalence to NURBS is analytically derived. The parameterisation is extended to three dimensions following the natural reformulation of its definition as the geometry minimising area under volume constraints. Like the two dimensional parameterisation, the 3D-RSVS is shown to have intrinsic links to methods in discrete differential geometry.

The new parameterisation is integrated into a modular optimisation framework which supports gradient and agent based optimisation; with geometric, structural and aerodynamic objective functions. The framework is shown to match expected results on the geometric matching of traditional and multi-body aerofoils, the topology optimisation of structural geometries, and, the minimisation of drag on a standard aerodynamic shape optimisation (ASO) benchmark case. This framework outperformed known analytical optima and shape optimisation results on the minimisation of drag at supersonic speeds under area constraints; which have analytical optima, where it successfully explored topology.

Meanwhile flexibility is achieved by using hierarchical design variables both inside the RSVS and through integration with multi-level subdivision optimisation (MLSO). The combination of MLSO and RSVS enables very efficient exploration of complex design spaces, revealing the intricate interactions between geometric and flow topology in supersonic benchmarks. Beyond strict minimisation, this method revealed discontinuous flow behaviours and degenerate multi-modality in the design space. By discovering the properties of the search region, the integrated RSVS-MLSO method shows the potential of flexible automatic design methods to enhance a designers understanding of the physical design space.
Date of Award12 May 2020
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorThomas C S Rendall (Supervisor) & Chris J Allen (Supervisor)

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