Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

Abstract

This paper presents an approach to shape an aircraft to equivalent-area-based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed the augmented Burgers equation or direct conversion of off-body pressures into equivalent areas. Formal coupling with computational fluid dynamics allows computation of sensitivities of equivalent-area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent-area cost functionals are discussed and further refined using ground loudness-based objectives.