Abstract
Aerodynamic shape optimisation, which involves the coupling of optimisation search algorithms with computational fluid dynamics tools to improve upon a design objective, is now a mature field of research in academia and industry. An aerodynamic shape optimisation framework relies on three technologies in particular: a computational fluid dynamics solver; an optimisation search algorithm; and a shape control or parameterisation method. Despite much research and development across all areas, aerodynamic shape optimisation still remains a computationally costly process to perform, particularly for large or complex geometries and meshes. Moreover, there is much variety in the tools and approaches used, the choice of which can have significant effect on both the final result (effectiveness) and computational cost (efficiency) of the optimisation process as a whole. In this thesis, focus has been given to these two aspects of aerodynamic shape optimisation - effectiveness and efficiency - and in particular how the numerical treatment of geometry affects them.The handling of geometry is central to the formulation of a shape optimisation problem since it interfaces between the physical problem being modelled, such as fluid flow, and the optimisation search algorithm, which manipulates the shape to improve the objective function. In this thesis, two geometry components are considered in detail: volume mesh deformation and shape control.
A new formulation for performing mesh deformation using radial basis function (RBF) interpolation is developed which captures global and local motions at multiple scales. The new multiscale formulation overcomes the cost and conditioning issues associated with standard RBF interpolation and permits an efficient sparse implementation that is cheaper than existing 'greedy' type methods. Importantly, the multiscale method uses all surfaces points and so, unlike existing point-reduction methods, it does not require a secondary correction stage. Mesh deformation using the new multiscale RBF method is incorporated into the shape optimisation framework used in the rest of the thesis.
Next, shape control is considered and it is shown that smoothness and linear independence are important for a well-posed shape optimisation problem. This is demonstrated by formulating explicit constraints on surface continuity which remove non-smooth and oscillatory shapes from the design space. This filtering approach reduces the effective degrees of freedom in a geometrically meaningful way while still allowing the high-fidelity design space to be exploited. When tested on a challenging two-dimensional inviscid drag minimisation problem the constraint-based approach is shown to have an optimisation convergence rate independent of both numerical grid resolution and shape control fidelity, and achieves the lowest published optimised drag value for equivalent mesh resolution.
Based on the constraint-based approach a new shape control methodology is then developed by reformulating the linear smoothness constraints to derive orthogonal shape modes with design variable bounds
that maintain surface smoothness in the same way. Not only does this enforce the smoothness condition without needing a large number of linear constraints, but it also generalises the concept of orthogonal modes to arbitrary shape optimisation problems; this is because, unlike existing approaches, the new methodology does not require a database of historic or representative geometry. Hence, the new generic modes can be applied to three-dimensional geometry such as wings without restriction. Effectiveness of the new method is demonstrated on two-dimensional geometric recovery and aerodynamic
optimisation problems, and three-dimensional geometric recovery.
| Date of Award | 22 Mar 2022 |
|---|---|
| Original language | English |
| Awarding Institution |
|
| Supervisor | Christian B Allen (Supervisor) & Thomas C S Rendall (Supervisor) |