On the sensitivity and efficiency of aerodynamic shape optimisation

Abstract

Computational fluid dynamics (CFD) has become the method of choice for aerodynamic shape optimisation of complex engineering problems. To date, however, the sensitivity of the optimal solution to numerical parameters has been largely underestimated. Meanwhile, aerodynamic shape optimisation based on high-fidelity CFD remains a computationally expensive task. The thesis consists of two research streams aimed at addressing each of the challenges identified, namely revisiting the optimal solution and developing an efficient optimisation framework. This work primarily focuses on the assessment of optimal design sensitivity and computational efficiency in gradient-based optimisation of aeronautical applications.

Two benchmark cases for NACA0012 and RAE2822 aerofoil optimisation are investigated using the open-source SU2 code. Hicks-Henne bump functions and free-form deformation are employed as geometry parameterisation methods. Gradients are computed by the continuous adjoint approach. The optimisation results of NACA0012 aerofoil exhibit strong dependence on virtually all numerical parameters investigated, whereas the optimal design of RAE2822 aerofoil is insensitive to those parameter settings. The degree of sensitivity reflects the difference in the design space, particularly of the local curvature on the optimised shape. The closure coefficients of Spalart-Allmaras model affect the final optimisation performance, raising the importance of quantifying uncertainty in turbulence modelling calibration. Non-unique flow solutions are found to exist for both cases, and hysteresis occurs in a narrow region near the design point.

Wing twist optimisations are conducted using two aerodynamic solvers of different levels of fidelity. A multi-fidelity aerodynamic approach is proposed, which contains three components: a linear vortex lattice method solver, an infinite swept wing solver, and a coupling algorithm. For reference, three-dimensional data are obtained using SU2. Two optimisation cases are considered, featuring inviscid flow around an unswept wing and viscous flow around a swept wing. A good agreement in terms of lift distribution and aerodynamic shape between the multi-fidelity solver and high-fidelity CFD is obtained. The numerical optimisation using the multi-fidelity approach is performed at a negligible computational cost compared to the full three-dimensional CFD solver, demonstrating the potential for use in early phases of aircraft design.

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Identifiers

ORCID for Guangda Yang: orcid.org/0000-0002-8029-8518

ORCID for Andrea Da Ronch: orcid.org/0000-0001-7428-6935

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