Flap-deflection optimization for transonic cruise performance improvement of supersonic transport wing

Wing flap-deflection angles of a supersonic transport are optimized to improve transonic cruise performance. Toward this end, a numerical optimization method is adopted using a three-dimensional unstructured Euler code and a discrete adjoint code. Deflection angles of 10 flaps, five for leading edge and five for trailing edge, are employed as design variables. An elliptic equation method is adopted to enable interior grid modification during the design process. Interior grid sensitivities are neglected for efficiency. Also tested is the validity of the approximate gradient evaluation method for the present design problem; it is found to be applicable for leading-edge flap design in cases where there are no shock waves on the wing surface. The Broydon-Fletcher-Goldfarb-Shanno method is used to minimize the drag with constraints on the lift and upper surface Mach numbers. Two design problems are considered; one involves a leading-edge flap design, and the other involves simultaneous design of leading-edge and trailing-edge flaps. The latter gave a smaller drag than the former by about two counts. Successful design results suggest that the present design method is valid and efficient.