Vortex force and lift induced drag in compressible flows

Recently a definition of the lift induced drag in terms of a field integral of the Lamb vector has been proposed in case of incompressible high Reynolds number flow and verified by post processing CFD solutions around wings. The possibility to extend this definition also to the case of compressible flows is investigated in this paper. In particular an exact expression of the aerodynamic force is discussed and its applicability is analyzed in case of RANS numerical solutions around an elliptic wing in subsonic and transonic conditions. A rigorous and unambiguous definition of lift induced drag is obtained. The lift induced drag still depends on the vortex force of the flow (the volume integral of the Lamb vector field), but a compressibility correction term (providing a thrust contribution) is also to be taken into account for.