Optimisation of Natural Laminar Flow Aerofoils and Wings for Robustness to Critical Transition Amplification Factor

This thesis investigates the use of robust design and optimisation methods to improve natural laminar flow (NLF) aerofoil and wing robustness to variations both in operating conditions and uncertainty in surface and flow quality. NLF is a promising method for aircraft drag reduction but has high sensitivity to operating conditions, flow quality and surface finish. Existing research on this topic has looked to improve NLF designs at a range of operating conditions, but uncertainty in surface and flow quality has not been considered. In this work, surface and flow quality are represented by the critical transition amplification factor, or N-factor, from the eN transition model. A probabilistic distribution and quantification method for uncertainty in critical N-factor is first selected. This is then used to assess NLF aerofoil performance with uncertainty in critical N-factor. Transition location sensitivity to critical N-factor is found to be linked to transition location sensitivity to lift coefficient; and drag robustness is found to be closely related to transition location robustness. Robust optimisation is then used to design NLF aerofoils that are insensitive to uncertainty in critical N-factor. This is found to be effective; however, the robustness at off-design flight conditions deteriorates as a result. Many designs with no laminar flow are also generated. These are inherently robust to critical N-factor uncertainty but of no practical use. A method is then developed that enables the coupling of multi-point and robust optimisation without an increase in computational costs. This uses the N-factor envelope from eN stability analysis to predict transition locations over the critical N-factor range. Multi-point robust optimisation of NLF aerofoils with critical N-factor uncertainty is then carried out. This is able to produce NLF aerofoils with good robustness to critical N-factor uncertainty over a range of lift coefficients and Mach numbers. This envelope sampling method is then extended to account for three-dimensional flows and is used to optimise swept and tapered wing sections for NLF with uncertainty in critical N-factor. Overall, this work demonstrates that robust design and optimisation method are well suited to the design of NLF aerofoils and wings. Furthermore, it shows that the N-factor envelope from eN stability analysis can be used to reduce the dimensionality of robust NLF design, making it no more computationally expensive than current multi-point optimisation problems. It therefore makes an original contribution to the field of NLF design and optimisation.