Study Based on the AIAA Aerodynamic Design Optimization Discussion Group Test Cases

Abstract

Three model problems associated with aerodynamic drag minimizations are studied. These test cases have been proposed by the aerodynamic design optimization discussion group, and they include an inviscid NACA0012 nonlifting airfoil, a viscous RAE2822 lifting airfoil, and a viscous lifting wing based on the NASA Common Research Model. Various optimization methods are used, including MDOPT, TRANAIR, SYN83, and SYN107. The resulting designed and associated baseline geometries are cross analyzed by several computational fluid dynamics codes, including OVERFLOW, TRANAIR, GGNS, and FLO82. Pathological issues are unveiled in both of the simple airfoil model problems. Designed geometries for the inviscid symmetric test case exhibit strong tendencies to permit nonsymmetric flow solutions. Designed airfoils for the viscous lifting case also support nonunique solutions and hysteresis loops at or near the design point in Reynolds-averaged Navier–Stokes and integral boundary-layer method simulations. These results provide further evidence that single-point aerodynamic optimization is often ill posed. In extreme cases, it can yield designs with very undesirable aerodynamic characteristics, at least as analyzed by Reynolds-averaged Navier–Stokes and integral boundary-layer methods occurring at offdesign, and even ondesign, conditions. These examples are used to further document the multiple-solution and pseudosolution phenomena for steady-state Reynolds-averaged Navier–Stokes. This provides evidence that, even in practical engineering settings, numerical methods to assess stability and uniqueness of steady-state solutions and/or predict the bifurcations of these solutions have value. The single-point wing design problem is likewise ill posed in the spanwise direction. A multipoint design with a potentially large number of points or the inclusion of inequality constraints can regularize the problem.