Multipoint Aerodynamic Shape Optimization Investigations of the Common Research Model Wing

The aerodynamic shape optimization of wings in transonic flow is an inherently challenging problem. In addition to the high computational cost of solving the Reynolds-averaged Navier–Stokes equations, there is a complex interdependence between the cross-sectional shape, wave drag, and viscous effects. Furthermore, it is necessary to perform multipoint optimizations to ensure good performance for a range of flight conditions. The choice of which flight conditions should be considered in a multipoint optimization and how many of these should be considered is still not well understood. This paper addresses this issue by solving a series of seven benchmark optimizations developed by the AIAA Aerodynamic Optimization Discussion Group. These optimization cases include a single-point optimization, four three-point optimizations, a nine-point optimization, and a five-point optimization. The optimizations consist in minimizing the weighted drag coefficient subject to lift, moment, thickness, and volume constraints. The optimizations were performed with respect to 768 shape design variables and an angle of attack for each flight condition. The single-point optimization was able to achieve an 8.1% drag reduction relative to the initial design, but it exhibited poor off-design performance. All the optimized designs were compared using a contour plot of ML/cD to evaluate the wing performance over the complete transonic flight operating envelope. Each of the four three-point optimizations successfully mitigated the poor off-design performance of the single-point design. However, the three-point optimization with widely spaced Mach numbers yielded a much more complex ML/cD contour with two distinct local maxima. Finally, the five- and nine-point optimizations yielded similar performance and the most robust off-design performance.