Drag Decomposition Using Partial-Pressure Fields in the Compressible Navier–Stokes Equations

Abstract

The static-pressure field in the steady and compressible Navier–Stokes equations is decomposed into Euler (inviscid) and dissipative (viscous) partial-pressure fields as a generalization of the incompressible pressure decomposition previously reported by Schmitz and Coder (“Inviscid Circulatory-Pressure Field Derived from the Incompressible Navier–Stokes Equations,” AIAA Journal, Vol. 53, No. 1, 2015, pp. 33–41). The primary purpose of partial-pressure fields is to provide a means of dissecting local drag contributors over a lifting body. The analysis shows that the integral of the Euler pressure over the surface of a lifting body of thickness recovers the Kutta–Joukowski theorem for lift, and results in Maskell’s formula for the vortex-induced drag in the limit of high Reynolds number; the combined integral of the dissipative pressure and wall shear stress results in a generalized form of Oswatitsch’s formula for entropy-flux drag. Transport equations are derived with well-posed boundary conditions for both the Euler and dissipative partial-pressure fields for implementation in computational fluid dynamics codes as a complement to far-field and volumetric methods for drag decomposition of complex aircraft configurations.