Exploring the Benefit of Engaging the Coupled Aero-Elastic Adjoint Approach in MDO for Different Wing Structure Flexibilities

Abstract

By virtue of their efficiency, gradient-based algorithms can play a profound role in assessing wing designers overcome the challenges of decarbonizing the aviation industry. This role becomes more valuable when non-linearities increase in the corresponding physical discipline. The coupled aero-elastic adjoint approach, is used to efficiently compute the gradients of aerodynamic cost functions with respect to shape design parameters. This approach helps aerodynamic designers engage the effects of wing structure flexibility, earlier in the design process. To compute the gradients via the coupled aero-elastic adjoint approach, a fixed-point iteration between the aerodynamic adjoint equation and the structure adjoint equation is carried out. The cost of computing the coupled aero-elastic adjoint for a specific cost function is, hence, higher than that of computing the aerodynamic adjoint. In practice it costs three to ten times more, based on the structure flexibility. The aircraft industry tends currently to build wings with higher structure flexibility. This is the result of using composite materials instead of metal, in order to save structural mass, or advancing towards higher aspect ratio wings in order to improve the aerodynamic performance. These trends, which result in increased wing flexibility, motivate investigating the benefit of the coupled aeroelastic adjoint approach, over the aerodynamic adjoint approach. In the literature, some studies show the importance of employing the coupled adjoint, while others show barely any benefit for it. Hence, the aim of this study is to investigate, for the test case at hand, the relation between the wing flexibility and the necessity to employ the relatively costly, but ccurate, coupled aero-elastic adjoint approach. Five structure models were generated with different elasticities and were employed in two sets of optimizations; the first uses the aerodynamic adjoint to compute the gradients, and the other uses the coupled aero-elastic adjoint. This investigation was done for unconstrained as well constrained optimizations. The investigation showed that for the unconstrained optimization and for the design task at hand, a structure flexibility, that results in a normalized wing-tip deformation of 8% or higher, requires the use of the coupled aeroelastic adjoint. The normalized wing-tip deformation is defined, in this context, as the upward wing-tip deformation divided by half the wing span. For the constrained optimization, the investigation showed that the coupled aeroelastic adjoint always brought more improvements than the aerodynamic adjoint.