Geometric Parameterisation and Aerodynamic Shape Optimisation

Aerodynamic optimisation plays an increasingly important role in the aircraft industry. In aerodynamic optimisation, shape parameterisation is the key technique, since it determines the design space. The ideal parameterisation method should be able to provide a high level of flexibility with a low number of design variables to reduce the complexity of the design space. In this work, the Class/Shape Function Transformation (CST) method is investigated for geometric representation of an entire transport aircraft for the purpose of aerodynamic optimisation. It is then further developed for an entire passenger transport aircraft, including such components as the wing, horizontal tail plane, vertical tail plane, fuselage, belly fairing, wingtip device, nacelle, flap tracking fairing and pylon. This work presents the parameterisation of these components in detail using the CST methods for the reference of future aerodynamic optimisation work. The intersection line calculation method between CST components is presented for future entire aircraft optimisation. The performance of the CST has been tested as well, and it found a few drawbacks of the CST methods; for example, it cannot provide some key intuitive design parameters and can lose the accuracy in the wing leading edge area. Therefore, two derivatives of the CST method are proposed: one is called the intuitive CST method (iCST), which is to transform the CST parameters to intuitive design parameters; the other is called the RCST method, which is able to increase the fitting accuracy of the original CST method with fewer design variables. Their performances are studied by comparing them regarding their accuracy in inversely fitting a wide range of aerofoils. Finally, the CST method is also developed to represent the shock control bump, which has better curvature continuity than cubic polynomials. The aerodynamic optimisation study based on adjoint approaches is carried out using the above parameterisation methods. Optimisation was performed on two-dimensional cases to make a preliminary investigation of the performances of the above parameterisation methods. The results showed that all of CST, iCST and RCST parameterisation methods are able to successfully reduce the drag. The results of the CST methods showed the lower order CST is able to provide fast convergence, and the high order CST is able to provide more flexibility and more local control of the shape to reach better optimal solution. The iCST providing intuitive parameters is improving the process of setup constraints, which is useful for aerofoil optimisation. The RCST showed good performance in aerodynamic optimisation in terms of convergence rate, number of design variables, low order of polynomials and smoothness of the shape. This work provides a reference to designer for choosing suitable parameterisation method in these three methods regarding specific requirement. The shock control bump optimisation on 2D aerofoil is performed to compare three shock control bump parameterisation methods. The results showed the CST parameterisation method is promising for shock control bump optimisation. Three-dimensional optimisation tests, including wing and winglet drag minimisation, were performed using the above parameterisation methods. The results showed that the CST methods are able to handle three-dimensional wing optimisation. It also investigated the effect of the order of CST method in optimisation. The results showed the lower order CST already performed well in optimisation in terms of optimal results and convergence rate. The optimisation also discussed the importance of using Cmx constraint in aerodynamic optimisation. In the winglet test cases, it showed the CST methods and adjoint approach are able to perform winglet optimisation. The drag of four winglets are successfully reduced. The downward winglet showed the potential benefits in terms of lower wing root bending momentum. At the end, the shock control bump optimisation using CST method on 3D wing has been performed. The results showed the mesh adjoint methods is able to identify the sensitive area for deploying shock control bumps and the CST shock control bump successfully reduced the wave drag.