Stability-Constrained Aerodynamic Shape Optimization of Flying Wings

The optimal shape of flying wings for subsonic and transonic speeds is examined using a suite of tools developed around a three-dimensional, time-spectral, Euler computational fluid dynamics solver. The first result in the study is a lift-constrained drag minimization, performed on an unswept, rectangular wing. When the spanwise twist distribution of the wing is varied, the elliptic optimum predicted by the low-speed inviscid theory can be reproduced. With this result as a reference, three different optimization formulations are explored. These formulations consider the addition of bending moment constraints, static-stability constraints, and dynamic-stability constraints. In each case, the design space of the problem is explored using both planform and shape variables to determine the optimal shape. These techniques are used to show that the addition of stability constraints has a significant impact on the optimal surface shape of the wing. In particular, it is shown that at lower speeds, the airfoil shape is sufficient to satisfy static-stability constraints, whereas dynamic-stability constraints require the addition of sweep. It is also shown that at higher speeds, the airfoil shape is insufficient to satisfy the stability constraint, either static or dynamic, and that the addition of sweep is necessary.