Vorticity based breakdown of the aerodynamic force in three-dimensional steady 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 postprocessing computational-fluid-dynamics solutions around wings. The possibility to extend this definition also to the case of compressible flows is investigated in this paper. An exact expression of the aerodynamic force in three-dimensional flows is discussed; it allows for a breakdown of the aerodynamic force (both drag and lift) in its physical contributions. Its applicability is analyzed in case of Reynolds-averaged Navier–Stokes numerical solutions around an elliptic wing in subsonic and transonic conditions. A rigorous and unambiguous definition of lift-induced drag is obtained. It still depends on the vortex force of the flow (the volume integral of the Lamb vector field), but a compressibility correction term is also to be taken into account. Both viscous and wave drag components can be computed by a surface integral of the Lamb vector field in the body wake.