The Multipoint Global Shape Optimization of Flying Configuration with Movable Leading Edges Flaps

Abstract

The aerodynamical global optimized (GO) shape of flying configuration (FC), at two cruising Mach numbers, can be realized by morphing. Movable leading edge flaps are used for this purpose. The equations of the surfaces of the wing, of the fuselage and of the flaps in stretched position are approximated in form of superpositions of homogeneous polynomes in two variables with free coefficients. These coefficients together with the similarity parameters of the planform of the FC are the free parameters of the global optimization. Two enlarged variational problems with free boundaries occur. The first one consists in the determination of the GO shape of the wing-fuselageFC, with the flaps in retracted position, which must be of minimum drag, at higher cruising Mach number. The second enlarged variational problem consists in the determination of the GO shape of the flaps in stretched position in such a manner that the entire FC shall be of minimum drag at the second lower Mach number. The iterative optimum-optimorum (OO) theory of the author is used for the solving of these both enlarged variational problems. The inviscid GO shape of the FC is used only in the first step of iteration and the own developed hybrid solutions for the compressible Navier-Stokes partial-differential equations (PDEs) are used for the determination of the friction drag coefficient and up the second step of iteration of OO theory.

Keywords

• Aerodynamical global shape optimization
• Multipoint design by morphing
• Supersonic flow
• Hybrid and meshless solutions for the three-dimensional compressible Navier-Stokes PDEs