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Design optimization of high-lift configurations using a viscous adjoint-based method

Aerodynamic Shape Optimization (ASO) has long been a challenging problem in the study of fluid dynamics. A continuous adjoint method for ASO using the compressible Reynolds-Averaged Navier-Stokes (RANS) equations was implemented and tested. Using a viscous continuous adjoint formulation, the necessary aerodynamic gradient information was obtained with large computational savings over traditional finite-difference methods. The resulting implementation was used to determine the accuracy in the calculation of aerodynamic gradient information for use in ASO problems. The accuracy of the derivative information was assessed by direct comparison with finite-difference gradients. Design examples, including inverse problems, drag minimization, and lift maximization were performed for a single-element airfoil. The method was also used to demonstrate the feasibility of aerodynamic design of twodimensional multi-element airfoils, although more complete studies are needed to generate realistic configurations. The viscous design method used a RANS multi-block solver, FLO103-MB, a point-to-point matched multi-block grid system and the Message Passing Interface (MPI) communication standard for both the flow and adjoint calculations. The Spalart-Allmaras turbulence model was implemented to account for high Reynolds number effects. Airfoil shape, element positioning, and angle of attack were used as design variables. Design results that verify the mathematical correctness of the gradient calculation method for high-lift system design and optimization were also shown.