AIAA 2002–0844 Design Optimization of High–Lift Configurations Using a Viscous 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 study of the 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. The high-lift configuration design method uses a compressible RANS flow solver, FLO103-MB, a point-to-point matched multi-block grid system and the Message Passing Interface (MPI) parallel solution methodology for both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack 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 potential of the method for high-lift system design and optimization, are presented. The design examples include a multi-element inverse design problem and the following problems: C l maximization, lift-to-drag ratio, L/D, maximization by minimizing C d at a given C l or maximizing C l at a given C d (α is allowed to float to maintain either C l or C d), and the maximum lift coefficient, C l max , maximization problem for both the RAE2822 single-element airfoil and the 30P30N multi-element airfoil. A ERODYNAMIC shape design has long been a challenging objective in the study of fluid dynamics. Computational Fluid Dynamics (CFD) has played an important role in the aerodynamic design process since its introduction for the study of fluid flow. However, CFD has mostly been used in the analysis of aerodynamic configurations in order to aid in the design process rather than to serve as a direct design tool in aerodynamic shape optimization. Although several attempts have been made in the past to use CFD as a direct design tool, 1–5 it has not been until recently that the focus of CFD applications has shifted to aerodynamic design. 6–11 This shift has been mainly motivated by the availability of high performance computing platforms and by the development of new and efficient analysis and design algorithms. In particular, automatic design procedures which …