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This paper describes the application of optimization technique based on control theory for natural-laminar-∞ow airfoil and wing design in viscous compressible ∞ow modeled by the Reynolds averaged Navier-Stokes equations. A laminar-turbulent transition prediction module which consists of a boundary layer method and two e N -database methods for Tollmien-Schlichting and cross∞ow instabilities is coupled with ∞ow solver to predict and prescribe transition locations automatically. Results of the optimization will demonstrate that an airfoil can be designed to have the desired favorable pressure gradient for laminar ∞ow and the new airfoil can be redesigned for higher Mach number for performance beneflts while still maintains reasonable amount of laminar ∞ow. For 3D wing, the redesigned wing conflguration will demonstrate an overall improvement not only at a single design point, but also at ofi-design conditions. The results prove the feasibility and necessary of incorporating laminar-turbulent transition prediction with ∞ow solver in natural laminar-∞ow wing design.

Natural-Laminar-Flow Airfoil and Wing Design by Adjoint Method and Automatic Transition Prediction