Two-dimensional High-Lift Aerodynamic Optimization Using the Continuous Adjoint Method

An adjoint-based Navier-Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-Averaged Navier-Stokes (RANS) equations are used as a flow model together with the Spalart-Allmaras turbulence model to account for high Reynolds number effects. Using a viscous continuous adjoint formulation, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite difference methods. A previous study of accuracy of the gradient information provided by the adjoint method, in comparison with finite differences and an inverse design of a single-element airfoil are also presented for validation of the present viscous adjoint method.tack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparisons with experimental data. Finally, several design results that verify the effectiveness of the method for high-lift system design and optimization, are presented. Firstly, C^ is minimized and Cf is maximized for a single-element airfoil. Secondly, a multi-element inverse design problem is presented that attempts to match a pre-specified target pressure distribution using the shape of all elements in the airfoil, as well as their relative positions. Finally, the lift-to-drag ratio of a multi-element airfoil is maximized with fixed Cj, or fixed Q. Introduction T HE motivation for this study is twofold: on the one hand, we would like to improve the takeoff and landing performance of existing high-lift systems using an adjoint formulation. On the other hand, we would like to setup a numerical optimization procedure that can be useful to the aerodynamicist in the rapid design and development of high-lift system configurations and that can also provide derivative information regarding the influence of various design parameters (gap, overlap, slat and flap deflection angles, etc.) on the performance of the system. The primary goal of an aerodynamic high-lift system is to increase payload capacity and reduce takeoff and landing distances by increasing both the lift coefficient at a given angle of attack and the maximum lift coefficient. Traditionally, high-lift designs have been realized by careful wind tunnel testing which is both expensive and difficult due to the extremely complex flow interactions. Recently computational fluid dynamics (CFD) analyses have also been incorporated to the high-lift design process. 1 In particular, automatic design procedures, which use CFD combined with gradient-based optimization techniques, have made it possible to remove the difficulties in the decision making process (traditionally taken by …