Efficient Optimisation Methods for Generic Aerodynamic Shape Optimisation

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


Aerodynamic shape optimisation amalgamates three, often independent, modules; a shape control system, a flow solver and an optimisation algorithm. The cornerstone is the shape control system, which governs the mapping between the real, continuous aerodynamic shape to the discretised surface that is used within the computational domain, using a set of design variables. The overall objectives of this work are to have efficient optimisation and design space exploration. Hence the focus of this work is first, shape control, and second, the optimisation algorithm.

First, a novel shape control system has been developed and is presented in this thesis that gives large design space coverage using very few design variables. The method uses a singular value decomposition (SVD) approach to extract the optimal reduced set of orthogonal aerofoil shape 'modes' from an existing library of aerofoils. Performing an SVD is guaranteed to produce an optimal representation of the original library; a powerful result. It is shown that different initial libraries of aerofoils result in different modes, each suited to their own design specification i.e. modes from transonic aerofoils are effective for transonic design. This method is shown to be highly efficient, with very few shape modes (fewer than ten, and sometimes as few as six) required to represent a wide range of aerofoils to within a typical wind tunnel tolerance. This is compared to the PARSEC method, which fails to represent any of the aerofoils tested to within the required tolerance, and the Hick-Henne method, that requires 12 to 16 bumps.

The efficiency that comes with the aerofoil modes can be fully exploited by performing global optimisation, and this is the second objective of this work. However, aerodynamic optimisation requires satisfaction of constraints. Constraint handling occurs using ad hoc techniques that are often not universally transferable between global optimisation algorithms. As such, an effective universal constraint handling framework has been developed and presented in this thesis. To demonstrate the universality of the framework, it is coupled to four different global optimisation algorithms (particle swarm, gravitational search, a hybrid of the two, and differential evolution) and used to optimise a number of analytical benchmark problems. It is compared, and shown to outperform, other universal constraint handling techniques that use penalty and feasible direction approaches, with feasibility rates shown to be higher than 90% with the new framework, compared to 50-80% for the other frameworks. When coupling differential evolution to the new framework, on a number of benchmark engineering problems, the results are equivalent to the best results published in the literature.

The development of efficient shape design variables and an effective constraint handling framework allows efficient global aerodynamic optimisation to be realised. A large number of transonic inviscid and viscous aerofoil optimisations are presented and it is demonstrated that as few as six aerofoil modes are sufficient to produce shock-free solutions for inviscid and viscous cases. Global wing planform optimisations are also considered. It is shown that when using chord variations only, two distinct minima are found that have almost equivalent drag reductions (around 25%) but at completely different locations within in the design space. The addition of further planform and non-planar design variables increases the multimodality found in the design space.
Date of Award6 Nov 2017
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorChristian B Allen (Supervisor) & Thomas C S Rendall (Supervisor)

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