Constrained Adjoint-based Shape Optimization for Aerodynamic Design on Unstructured Grids

In this paper, the effect of different kind of constraints on two and three dimensional adjoint-based shape optimization of aerodynamic design in inviscid and turbulent flows has been investigated. To assess the accuracy and efficiency of the adjoint-based approach, a complete set of optimization problem is investigated: from none to fully aerodynamic and geometrical constraints. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. Drag forces was chosen to be the objective function. Hicks–Henne shape functions and free form deformation parameters are adopted for the surface geometry perturbations, for two and three dimensional geometries, respectivelyThe drag minimization results show that the adjoint equation converges well and with specifying the suitable constraints, the designed shape approaches to the most optimized level without the loss of performance.