Sonic Boom Adjoint Methodology and its Applications

Abstract

This paper presents an approach to predict the sensitivity of the sonic boom ground signatures by numerically solving the augmented Burgers’ equation along with its discrete adjoint. The discrete adjoint equations are derived and solved. The exactness of the adjoint sensitivities is veri ed against derivatives obtained using the complex variable approach. Underand o -track ground signature sensitivities to di erent design variables may be obtained e ciently. The formulation of the coupling between boom adjoint and CFD adjoint is derived and discussed. This formulation represents the rst time in literature that boom propagation and CFD are formally coupled for the purpose of obtaining gradients of a ground based objective with respect to the aircraft shape design variables. The coupled formulation is e ective in calculating discretely accurate sensitivities, and should be an extremely useful tool in the design of supersonic cruise low-boom aircraft.