A Helmholtz Velocity Decomposition Applied to Wave Drag Decompositions

Velocity decompositions are an essential component of modern, CFD based drag breakdowns, whether using classical far-field methods or the near-field partial-pressure methodology. To the knowledge of the authors, the currently employed velocity decompositions are incapable of deriving a vector field, instead relying on the projection of magnitudes. This limits the accuracy of these methods close to a lifting body. One possible alternative velocity decomposition is the Helmholtz velocity approach, a commonly used vector calculus theorem in fluid dynamics. The concept allows for the isolation of the divergence free velocity and the complementary irrotational component. As a result, it is reasonable to assume that the decomposition isolates the velocity directly attributable to compressibility effects. In this work, an assessment is made on the methods capabilities to decompose wave drag in two-dimensional flows. This is undertaken in both the near-field, using Partial-pressure fields, as well as in the far-field, through application of the velocity term to the conventional momentum deficit integrals. The method will be examined for several airfoil cases in the transonic regime as well as in the supersonic regime.