Discrete boundary smoothing using control node parameterisation for aerodynamic shape optimisation

This paper presents an automated aerodynamic optimisation algorithm using a novel method of parameterising the search domain and geometry by employing user–defined control nodes. The displacement of the control nodes is coupled to the shape boundary movement via a ‘discrete boundary smoothing’. This is initiated by a linear deformation followed by a discrete smoothing step to act on the boundary during the mesh movement based on the change in its second derivative. Implementing the discrete boundary smoothing allows both linear and non-linear shape deformation along the same boundary dependent on the preference of the user. The domain mesh movement is coupled to the shape boundary movement via a Delaunay graph mapping. An optimisation algorithm called Modified Cuckoo Search (MCS) is used acting within the prescribed design space defined by the allowed range of control node displacement. In order to obtain the aerodynamic design fitness a finite volume compressible Navier-Stokes solver is utilized. The resulting coupled algorithm is applied to a range of case studies in two dimensional space including the optimisation of a RAE2822 aerofoil and the optimisation of an intake duct under subsonic, transonic and supersonic flow conditions. The discrete mesh–based optimisation approach outlined is shown to be effective in terms of its generalised applicability, intuitiveness and design space definition.