Adaptive airfoils and wings can provide superior performance at the expense of increased cost and complexity. In this paper, an aerodynamic optimization algorithm is used to assess an adaptive airfoil concept for drag reduction at transonic speeds. The objective is to quantify both the improvements in drag that can be achieved and the magnitude of the shape changes needed. In an initial study, a baseline airfoil is designed to produce low drag at a fixed lift coefficient over a range of Mach numbers. This airfoil is compared with a sequence of nine airfoils, each designed to be optimal at a single operating point in the Mach number range. Shape changes of less than 2% chord lead to drag reductions of 4-6% over a range of Mach numbers from 0.68 to 0.76. If the shape changes are restricted to the upper surface only, then changes of less than 1% chord lead to drag reduction of 3-5%. In a second study, a baseline airfoil is designed based on a multi-point optimization over eighteen operating points, including dive and low-speed off-design requirements. Adaptive airfoils are designed through single-point optimization for the operating points corresponding to cruise conditions, producing drag reductions ranging from 9.7 to 16.7% with shape changes on the order of a few percent chord.

A Newton-Krylov algorithm for aerodynamic optimization is applied to the multipoint design of an airfoil for eighteen different operating conditions. The operating conditions include four cruise conditions and four long-range cruise conditions at maximum and minimum cruise weights and altitudes. In addition, eight operating points are included in order to provide adequate maneuvering capabilities under dive conditions at the same maximum and minimum weights and altitudes with two different load factors. Finally, two low-speed operating conditions are included at the maximum and minimum weights. The problem is posed as a multipoint optimization problem with a composite objective function that is formed by a weighted sum of the individual objective functions. The Newton-Krylov algorithm, which employs the discrete-adjoint method, has been extended to include the lift constraint among the governing equations, leading to an improved lift-constrained drag minimization capability. The optimized airfoil performs well throughout the flight envelope. This example demonstrates how numerical optimization can be applied to practical aerodynamic design.

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