Surface modification method for aerodynamic design optimization

A new geometry modification method for aerodynamic design optimization is developed using surface mesh coordinates as design variables. Surface meshes are modeled as a spring system with tension and bending springs, and a negative gradient vector of a design objective function is imposed on the spring system as fictitious external forces. Corresponding deformation of the surface spring system is considered as a smoothed vector of the objective function gradient and used for a line search to find an optimum solution along the smoothed vector. This provides a rich design space, which is limited only by the surface mesh density. It also enables smooth variation of design surfaces even for singular gradient vectors. As design examples, sample aerodynamic optimization problems are conducted utilizing two- and three-dimensional computational-fluid-dynamics codes for flow analyses and discrete adjoint codes for sensitivity analyses. A recommendation on the selection of a required parametric value is made based on the design results.