Wave Drag and Vorticity in Two-Dimensional Viscous and Inviscid Flows

Recent methods based on flow vorticity and Lamb vector integration allow for a far-field formulation and decomposition of the whole aerodynamic force with identification of local flow structures associated with the force generation. Different exact and theoretically equivalent Lamb vector-based force formulations were proposed in the past and the decomposition of total drag into lift-induced and parasite contributions was subject of very recent papers. However, different results can be obtained in the practise when applying a selected force formula to numerically computed flow-fields, with sensitivity of the computed total force to additional degrees of freedom, such as the choice of the control volume or the location of the arbitrary pole appearing in Lamb vector-based formulations. Moreover, the separation of irreversible drag into viscous and wave drag contributions by Lamb vector field analysis is still questioned. In this paper, the accuracy of the total force formula and of the drag decomposition in lift-induced and parasite contributions is first analyzed, for a steady flow regime. Then, to verify the possibility to relate wave drag to Lamb vector integrals, the effectively inviscid flow around an airfoil in transonic flow is first studied, being, in this case, wave drag the only drag contribution. Finally, the study is completed by a viscous high Reynolds number analysis, where an approach to drag decomposition into physical constituents (viscous and wave contributions) is illustrated and results are compared against predictions obtained using consolidated thermodynamic-based methods.