Optimization of airfoils using the adjoint approach and the influence of adjoint turbulent viscosity

The adjoint approach in gradient-based optimization combined with computational fluid dynamics is commonly applied in various engineering fields. In this work, the gradients are used for the design of a two-dimensional airfoil shape, where the aim is a change in lift and drag coefficient, respectively, to a given target value. The optimizations use the unconstrained quasi-Newton method with an approximation of the Hessian. The flow field is computed with a finite-volume solver where the continuous adjoint approach is implemented. A common assumption in this approach is the use of the same turbulent viscosity in the adjoint diffusion term as for the primal flow field. The effect of this so-called ""frozen turbulence"" assumption is compared to the results using adjoints to the Spalart-Allmaras turbulence model. The comparison is done at a Reynolds number of Re=2×106 for two different airfoils at different angles of attack.