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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