A methodology that allows for ef cient aerodynamic optimization of wings with a full account of typical viscous effects is proposed. It extends earlier work by A. Jameson 1¡ 3 on wing optimization for inviscid ows. The optimization process is based on control theory, which is employed to derive the adjoint equations. Accurate and consistent modeling of viscous effects is essential in wing design and is implemented in the approach described here by viscousinviscid interaction. The solution

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... es interaction between the Euler solver and the two-dimensional boundary layer. Although this technique is limited by the known assumptions of the boundary-layer approximation,it is very well suited for civil aircraft wing design in cruise conditions. For applications where large viscous-dominated regions of separation are present, substantially more expensive design methods based on the Navier-Stokes equations have to be used. The method developed in this work has resulted in a practical engineering tool because it combines the bene ts of the fast adjoint equation-based technique and a very economical boundary-layer approach. The cost required for viscous calculations is similar to that for inviscid ows. Results for three-dimensional wing design in viscous ow are possible, even with the use of a PC. The method is demonstrated for a single, clean wing, and wing-body con guration. Nomenclature A = wing surface area Cd = drag coef cient calculated by pressure integration C e = entrainment coef cient C f = skin-friction coef cient C f 0 = skin-friction coef cient in equilibrium ow in zero pressure gradient Cl = lift coef cient C p = pressure coef cient C ¿ = shear-stress coef cient H , N H , H 1 = velocity-pro le shape parameters M = Mach number p = current pressure pT = target pressure U e = mean component of streamwise velocity at edge of boundary layer X; Y; Z = Cartesian coordinates x = coordinate along surface 2 = momentum thicknesş = scaling factor on dissipation length Subscripts EQ = equilibrium conditions EQ 0 = equilibrium conditions in absence of secondary in uences on turbulent structure