Optimal aerodynamic shape design with transition prediction

A two-dimensional Newton-Krylov aerodynamic shape optimization algorithm with laminar-turbulent transition has been developed. The coupled Euler and boundary-layer solver, MSES, is used to obtain transition locations, which are then used in the compressible Reynolds-Averaged Navier-Stokes (RANS) solver with the one-equation Spalart-Allmaras turbulence model. The sensitivity of the objective function to transition location perturbation is obtained from the RANS solutions. MSES is used to obtain the sensitivity of transition point movement to shape changes. These two sensitivities are combined to modify the discrete-adjoint objective function gradient. A unique design example demonstrates that the modified algorithm is able to design an airfoil very similar to one of the high-lift airfoils designed by Robert Liebeck. The design examples demonstrate that the optimizer is able to control the transition point locations to provide optimum performance, in effect designing optimized natural laminar-flow airfoils.