The Behaviour of Evolutionary Algorithms for the CFD-Driven Design Optimisation of Aerofoils

This thesis utilises aerodynamic shape optimisation software AerOpt and FLITE2D, to explore the behaviour of three Evolutionary Algorithms, Differential Evolution (DE), Modified Cuckoo Search (MCS), and Particle Swarm Optimisation (PSO), to optimise a 2D nonsymmetric aerofoil, providing an evaluation of their aerodynamic optimising capabilities.The aerofoil used in test cases is the NACA21120, where a variation of control node approaches are utilised to alter the aerofoil’s geometry. In the first set of test cases, a control node is placed on the upper surface to allow the thickness to be altered, and in the second set of cases, six control nodes are arranged along the boundary of the aerofoil, to examine the overall shape change.A mesh convergence study helped to determine the best mesh settings for the given problem. Each algorithm is tested in a subsonic, transonic, and supersonic flow regime to ensure the test cases fulfil the CFD aspect of the research. All flow regimes were treated as viscous with the relevant Reynolds number applied. To provide an analysis on how tuning the input parameters affects the algorithm’s behaviour, the number of agents were inputted were varied from 10 to 50 to 99. The generations number was set to 99, and the fitness objective was to optimise for the lift-drag ratio (L/D), throughout all optimisations.The first set of results (one control node) found that fitness improvements were largest in the transonic cases, increasing the L/D by an average percentage of 213%. The aerofoil’s L/D at Mach 0.5 was improved by an average of 80%, and Mach 1.5 by 33%. Each algorithm showed a similar trend in which the control node was positioned at the final generation in the design space, this varied depending on the Mach number being optimised for, either resulting in an increase or decrease in the aerofoil thickness. Varying the number of agents inputted, had a more significant effect on MCS, whereas DE and PSO showed more consistent results regardless of the number of inputted agents. Generally, PSO displayed fastest convergence of all the agents, shortly followed by DE, followed by MCS.The second set of results (six control nodes) were optimised for identical input parameters but for simplicity, at a single flow regime, Mach 1.5. Differing from the first set of results showing similar control node placement within the design space, the second set of results showed the algorithm’s position some of the control nodes in different locations within the design space. Despite the similar fitness improvement values seen between DE and PSO, the final geometries were observed to be somewhat varied, where DE reduced the thickness of the trailing edge, but PSO increased it. MCS displayed similar geometry change to PSO but with more conservative control node movement

Our friend in the north: the origins, evolution and appeal of the cult of St Duthac of Tain in later Middle Ages

St Duthac of Tain was one of the most popular Scottish saints of the later middle ages. From the late fourteenth century until the reformation devotion to Duthac outstripped that of Andrew, Columba, Margaret and Mungo, and Duthac's shrine in Easter Ross became a regular haunt of James IV (1488-1513) and James V (1513-42). Hitherto historians have tacitly accepted the view of David McRoberts that Duthac was one of several local saints whose emergence and popularity in the fifteenth century was part of a wider self-consciously nationalist trend in Scottish religious practice. This study looks beyond the paradigm of nationalism to trace and explain the popularity of St Duthac from the shadowy origins of the cult to its heyday in the early sixteenth century