Application of Control Point-Based Aerodynamic Shape Optimization to Two-Dimensional Drag Minimization

An investigation is presented that considers various aspects of an aerodynamic shape optimization framework. A two-dimensional aerofoil transonic zero-lift drag minimization test case is used to investigate the effect of dimensionality, shape deformation parameters, and optimizer on the results from the shape optimization process. A flexible control point-based parameterization is implemented which decouples the design variables from the surface, such that control point deformations determine the surface and volume mesh deformations in a unified manner. A gradient-based optimizer (feasible sequential quadratic programming) and global search algorithm (gravitational search algorithm) are tested on the constrained optimization case. The results show, as expected, that an increase in the number of dimensions produces a greater design space coverage and better optimization results, and the gradient-based method is prone to terminating in local optima or at constraint boundaries, so the global search algorithm is more reliable at locating optima. Efficient, reduced, and orthogonal shape deformation parameters are defined here by singular value decomposition extraction, and are shown to be particularly effective, demonstrating a 99.7% drag reduction for the case considered.