Using Surface Sensitivity for Adjoint Aerodynamic Optimisation of Shock Control Bumps

The purpose of this research is to use the surface sensitivity to aid the design and placement of flow control devices and to develop a new and efficient method of calculating the surface sensitivity using the mesh adjoint equations. The mesh adjoint equation provides a implification of the adjoint optimisation framework which can speed up an optimisation by removing the bottleneck of needing to calculate the mesh sensitivity.
The surface sensitivity can be used as a design tool a designer to the most important regions on an aircraft surface. This thesis focusses on using shock control bumps and surface contour bumps in drag sensitive regions on transonic aerofoils and wings to reduce drag. Usually a designer has the surface pressure and streamlines to guide the device placement, however these can mislead as it is not clear which areas will have the most impact on drag reduction. The drag surface sensitivity gives a direct link between the drag coefficient and a potential change in the wing surface in the form of a derivative. This method was proved successful for reducing drag when optimisation was localised to the drag sensitive regions on the wing.
A new method for calculating the surface sensitivity using the Delaunay Graph Mapping (DGM) mesh movement has been developed. This provides an explicit and efficient mapping of the mesh sensitivity to the surface senstivity. Previously, this required the solution of a large and costly linear system using a mesh movement such as Linear Elasticity (LE) to move the mesh. The DGM method is compared
against analytical solutions, finite difference and the LE mesh adjoint to show that the DGM mesh adjoint will provide an accurate calculation of the gradients on the wing surface. The DGM mesh adjoint has been shown to successfully find a minima when optimising shock bumps on a 3D geometry showing that it is a robust and capable method for optimisation.