Non-Uniform Rational B-Spline Parameterization for Aerodynamic Shape Optimization

Through this study, direct geometric parameterization framework is introduced, using non-uniform rational B-splines (NURBS), for aerodynamic shape optimization. A NURBS geometry generation suite is integrated with the high-fidelity SU2 multiphysics simulation and design software and IPOPT to handle high-dimensional, nonlinear design problems. The framework is evaluated for two-dimensional aerodynamic shape optimization with NURBS curves using the standardized RAE 2822 test case from the AIAA Aerodynamic Design Optimization Discussion Group. A three-dimensional implementation is also introduced using NURBS surfaces applied to aerodynamic shape optimization of a Blended Wing Body (BWB) concept. The study compares the NURBS framework with a conventional free-form deformation (FFD) method, keeping all other conditions equivalent. Different optimization barrier update schemes are demonstrated for both the NURBS and FFD optimization. The NURBS parameterization shows a drag reduction of 45.5% compared to FFD's 34.45% on the RAE 2822 case when subject to lift, pitching-moment, and area constraints. Initial iterations of the BWB aerodynamic shape optimization using the NURBS framework demonstrate a drag reduction of 7.47% compared to FFD's 0.53% for a fixed lift constraint. These results reveal the superior performance of NURBS for these shape optimization problems for identical bound constraints imposed on the design variables.