Inviscid circulatory-pressure field derived from the incompressible Navier-Stokes equations

The static-pressure field in the steady and incompressible Navier-Stokes momentum equation is decomposed into circulatory (inviscid) and dissipative (viscous) partial-pressure fields. It is shown analytically that the circulatory-pressure integral over the surface of a lifting body of thickness recovers the lift generating Kutta-Joukowski theorem in the far field, and results in Maskell's formula for the vortex-induced drag plus an additional pressure-loss term that tends to zero for an infinitely thin wake. A Poisson equation for the circulatory-pressure field is implemented as a transport equation into the FLUENT 13 solver. Numerical examples include a circular cylinder at Re = 8.5 × 10⁵, the S809 airfoil at Re = 2 × 10⁶, and the ONERA M6 wing at Re = 1 × 10⁶. It is shown that the circulatory-pressure field does indeed behave as an inviscid pressure field of a fully viscous solution, and provides insight into the nature of pressure drag and its contributions to local form and vortex-induced drag.