On the spurious effects in Lamb-vector-based force decomposition methods

Recent methods based on 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 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 studies. However, inconsistencies were also reported, raising questions on the physical role of a non-zero induced drag found in two-dimensional flows. Moreover, the effect of the arbitrary pole (appearing in Lamb-vector-based formulas) on the numerical accuracy of such methods was never investigated. Additionally, the separation of parasite drag into viscous and wave drag contributions by Lamb vector field analysis is still questioned. In this paper, the accuracy of different force formulas and of the drag decomposition in lift-induced and parasite contributions is first analyzed, for steady flows. Two-dimensional numerical solutions around RAE2822 and NACA0012 airfoils are considered, the latter in both inviscid and viscous flows (at low and high Reynolds number), to analyze consistency between lift-induced/parasite drag definitions and the drag generated in isentropic flow conditions (reversible drag) or due to entropy production (irreversible drag). A spurious induced drag contribution (related to the streamwise momentum perturbation) is identified, resulting in negative induced drag values in two-dimensional flows. The effect of a shift in the pole location is also analysed, with reference to its impact on the total force and on drag decomposition accuracy, then a new approach to parasite drag breakdown into physical constituents (viscous and wave contributions) is proposed and results are compared against predictions obtained using consolidated thermodynamic-based methods and against available results from recent literature.