Analytic sensitivities and approximations in supersonic and subsonic wing/control surface unsteady aerodynamics

Abstract

Development of efe cient, design-oriented analysis techniques and associated approximations for wing/ control surface unsteady aerodynamics is crucial to the success of any multidisciplinary aeroservoelastic optimization of airplanes including active control technology. A design-oriented capability for unsteady supersonic aerodynamics for planar wing/control surface cone gurations is presented here. Explicit expressions for aerodynamic ine uence coefe cients make it possible to efe ciently obtain analytic sensitivities of generalized aerodynamic loads with respect to planform shape. Examination of the mathematical structure of the discretization used, similar to other aerodynamic panel methods, reveals sources of discontinuity of derivatives with respect to shape in the supersonic case. Sources of nonsmooth behavior of the unsteady aerodynamic loads in subsonic e ow are identie ed and eliminated. The accuracy and computational cost of alternative approximation techniques are studied. A second-order approximation technique based on the direct and adjoint solutions at a reference cone guration is presented. Experience and insight are gained in the area of design-oriented and approximate unsteady aerodynamics, to be used in the nonlinear programming/approximation concepts approach to engineering optimization.