A novel mid-field breakdown of the aerodynamic force in compressible flows

A vorticity based exact theory for the computation and breakdown of the aerodynamic force is here applied to the analysis of three-dimensional aircraft configurations in steady transonic flow conditions by post-processing numerical CFD solutions. A rigorous and unambiguous definition of lift-induced drag in compressible flows and its distinction from the profile components (viscous and wave) has been obtained. The equation is based on field integrals of the Lamb vector field, the cross product of vorticity times velocity. It highlights the generation of the aerodynamic force in the rotational part of the flow only (mid field formula).
The encountered numerical difficulties are described; they arise in particular when the freestream Mach number approaches one. They have been overcome by a proper treatment of the numerical integration in the shock region where the accuracy of the numerical flow solution is poorer. Thus, a new exact formula is obtained for an accurate aerodynamic force computation in high transonic and supersonic flows.
Applications are shown in the case of two-dimensional airfoil, elliptic wing (in transonic flow) and for the NASA CRM wing-body configuration. Comparisons with with classical drag breakdown methods based on the entropy drag concept are also presented and the improvements obtained in particular in the lift induced drag analysis are discussed.