An Aero-Structure Adjoint Formulation for Efficient Multidisciplinary Wing Optimization

Computational fluid dynamics is today a reliable tool for the analysis of the flow past wings, and is increasingly used in aircraft design. Since the wing is a coupled fluid-structure system, stationary elastic deflection has to be taken into account during the design. If the design is performed by means of gradient-based optimization techniques, it is necessary to include the effect of static elasticity in the gradient computation, since this can significantly alter the values of the sensitivities. On the other hand, the prediction of highly non-linear effects such as shock arise in transonic flow, and shock-shock interaction in supersonic flow is critical to perform a detailed optimization; this demands the use of high fidelity flow models. Since these models are extremely computationally expensive, an efficient computation of the gradient in turn requires the use of an advanced mathematical tool: the adjoint method. Both these critical requirements can be met by a coupled aero-elastic adjoint formulation, where the coupling is carried out firstly in the physical variables of the two systems, and then in the adjoint variables, which are subsequently used to calculate the sensitivity. The multidisciplinary extension of the adjoint method also allows the evaluation of gradients of cost functions or constraints containing terms coming from the structure side, as in the case of the Breguet formula for aircraft range. In the present work, a completely continuous formulation of the aeroelastic coupled adjoint method is presented and applied to test cases relevant to aircraft design, through an implementation within the software FLOWer from DLR and MSC-Nastran. The test cases are based on the AMP wing in the transonic regime, while the shape parametrization is based on the free-form deformation method. A comparative study of optimization histories is presented, showing the necessity of a high number of design variables to maximize the effectiveness of the optimization, as well as the necessity for accurate sensitivities that contain the effect of aeroelasticity. The sensitivities obtained from the coupled adjoint have allowed to perform in relatively short time optimizations with high number of design variables, aimed to reduce drag at constant lift and angle of attack and to increase range by means of the Breguet formula, assuming a stress penalty for the structural weight and again constant lift and angle of attack. A comparison of these two cases shows that the aerodynamically optimal minimal drag design differs from the multidisciplinary optimal design.