Optimized Natural-Laminar-Flow Airfoils

Abstract

A two-dimensional Newton-Krylov aerodynamic shape optimization algorithm has been modied to incorporate the prediction of laminar-turbulent transition. Modications to the discrete-adjoint gradient computation were required to allow the optimization algorithm to manipulate the transition point through shape changes. The coupled Euler and boundary-layer solver, MSES, is used to obtain transition locations, which are then used in Optima2D, a Newton-Krylov discrete-adjoint optimization algorithm based on the compressible Reynolds-averaged Navier-Stokes equations. The algorithm is applied to the design of airfoils with maximum lift-drag ratio, endurance factor, and lift coecien t. The design examples demonstrate that the optimizer is able to control the transition point locations to provide optimum performance, in eect designing optimized natural-laminar-o w airfoils. In particular, the optimization algorithm is able to design an airfoil that is very similar, in terms of both shape and performance, to one of the high-lift airfoils designed by Liebeck (J. of Aircraft, 10:610-617, 1973) in the 1970’s.