Thermodynamic decomposition of compressible wave drag in the euler equations

Abstract

To support the development of ultra-efficient, commercial transport aircraft, the origins of wave drag within the Euler equations are explored with an ultimate goal of fundamentally decoupling it from the vortex-induced drag. A strategy for performing a thermodynamic decomposition of a compressible, inviscid flow field is presented based on the momentum deficit downstream of a shockwave. Two partial pressure fields are suggested in tandem with partial volume (density) fields, which are intended to reflect the reversible and irreversible processes. The behavior of these fields are illustrated based on numerical solutions of the Euler equations for transonic flow over an airfoil. In subsequent analyses, it is assumed that the shockwave is relatively weak (i.e. an incoming Mach number less than 1.3), and through series expansions and linearizations, a classic expression for wave drag is exactly recovered from the irreversible partial pressure field.