Range-Based Problem with Varying Design Point for Transonic Aerodynamic Wing Optimization

Drag minimization of aerodynamic shapes in transonic flow can lead to shock-free solutions with poor off-design performance. The work here explores whether optimizing range, augmented by the addition of the operating point as a design variable, is an appropriate objective for inviscid transonic wing optimization. Gradient-based optimizations are performed, showing that the range formulation allows the optimizer to increase drag divergence to maximize speed which in turn allows a lower lift coefficient to minimize induced drag. The result is a shocked solution, with the shock moving further aft on the wing for higher weight, which can be managed via a pitching moment constraint. Range optimizations lead to higher optimum Mach numbers which raise drag divergence. Similar behavior is seen with multi-point optimization with a high-speed point included, though the range optimizations have better global off-design performance (via a larger region of high performance around the optimum performance point), better local off-design performance (via lower sensitivity in range to changes in speed and lift) and are further from drag divergence.