The aerodynamic shape optimization of transonic wings requires Reynolds-averaged Navier-Stokes (RANS) modeling due to the strong nonlinear coupling between airfoil shape, wave drag, and viscous effects. While there has been some research dedicated to RANS-based aerodynamic shape optimization, there has not been an benchmark case for researchers to compare their results. In this investigations, a series of aerodynamic shape optimizations of the Common Research Model wing defined for the Aerodynamic Design Optimization Workshop are presented. The computational fluid dynamics solves Reynolds-averaged Navier-Stokes equations with a Spalart-Allmaras turbulence model. A gradient-based optimization algorithm is used in conjunction with a discrete adjoint method that computes the derivatives of the aerodynamic forces. The drag coefficient at the nominal flight condition is minimized subject to lift, pitching moment and geometric constraints. A multilevel acceleration technique is used to reduce the computational cost A total of 768 shape design variables are considered, together with a grid with 28.8 million cells. The drag coefficient of the optimized wing is reduced by 8.5% relative to the baseline. The single-point design has a sharp leading edge that is prone to flow separation at off-design conditions. A more robust design is achieved through a multipoint optimization, which achieves more reliable performance when lift coefficient and Mach number are varied about the nominal flight condition. To test the design space for local minima, randomly generated initial geometries are optimized, and a flat design space with multiple local minima was observed.
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