Proposed work aimed at developing efficient optimisation tools for NLF design where the cost function is the total drag (pressure and friction). The tool utilises efficient and accurate computation of gradients of objective functions as well as robust parametrisation of the geometry. Our approach uses Computational Fluid Dynamics followed by accurate boundary-layer stability analysis in order to find, by optimisation, geometries that damp growth of boundary-layer disturbances in order to delay the laminar-turbulence transition. Gradient-based optimisation and adjoint solvers are used in order to obtain the best numerical efficiency. The gradients are obtained through a chain of computations including adjoints of the flow equations and of the parabolized stability equations.

Our method was initially developed for airfoils and recently extended to 3D wing design. Here, the tool was improved by replacing the Euler equations of fluid dynamics by the Reynolds-Averaged Navier-Stokes (RANS) equations. This allowed us to account for the viscous-inviscid interactions and therefore obtain a more accurate evaluation of the aerodynamic performances such as the total drag, lift and pitching moment. In order to ensure high accuracy of the gradients, the adjoint of the RANS solver included an adjoint of the turbulence model. A mesh-less method based on Radial Basis Functions was used for deforming the RANS meshes. This approach was proven to be much faster than elliptic smoothers on meshes that are suitable for RANS computations. Here, two shape parametrisation methods suitable for industrial design were implemented and compared. Further, an automatic and efficient procedure for nonlocal stability analysis was implemented in order to facilitate the use of this approach in industrial projects.