Invariant Vortex-Force Theory Extending Classical Aerodynamic Theories to Transonic Flows

Abstract

Recent studies about the Lamb vector have led to the development of the vortex-force theory: a formulation able to predict the aerodynamic force in compressible flows and decompose it into lift, lift-induced drag, and profile drag. Here, a revised formulation of the vortex-force theory developed at ONERA in collaboration with the University of Naples is presented and applied to steady transonic flows. In the mathematical developments, special care is given to the presence of shock wave discontinuities within the flowfield. The equivalence between the new definition, the Kutta–Joukowski lift theorem, Maskell’s lift-induced drag formula (“Progress Towards a Method for the Measurement of the Components of the Drag of a Wing of Finite Span,” Procurement Executive, Ministry of Defence, Royal Aircraft Establishment TR 72232, Farnborough, England, U.K., 1972) and Betz’s profile drag formula (“A Method for the Direct Determination of Wing-Section Drag,” NACA TM 337, 1925) are emphasized. The revised formulation also presents several practical advantages: the decomposition is naturally invariant to the reference point chosen for the calculation of moment transformations, and the computation can be performed in a fine part of the grid, close to the body skin. The formulation is finally tested on the NASA Common Research Model wing–fuselage configuration in cruise flight conditions.