Defect force and viscous mechanical energy generation in aerodynamic flows

Abstract

A defect integral analysis of the 2D compressible steady-state viscous flow about unpowered aerodynamic bodies is derived in this paper based on momentum and mechanical energy conservation. The defect flowfield is obtained by subtracting the equivalent inviscid flowfield from the real viscous flow, thereby retaining only entropy-related perturbations within boundary and free shear layers that contribute to viscous drag and mechanical loss generation. First, a defect momentum balance is derived that introduces the notion of the defect force, its far-field decomposition, and its relation to the conventional viscous drag definition (profile drag minus wave drag). Next, a mechanical defect energy formulation is carried out in the relative reference frame that offers a means of explicitly and implicitly calculating the mechanical energy losses, including, for the first time, compressibility-induced losses for both adiabatic and nonadiabatic flows. Finally, a defect mechanical formulation is derived in the absolute reference frame that provides an energy-based decomposition of the defect and conventional drag power into its mechanical energy loss and viscous excess mechanical energy constituents. The result is a clear identification and traceability of the evolution of viscosity-induced mechanisms related to viscous drag, mechanical energy loss generation, and recoverable viscous mechanical energy, relevant for boundary-layer ingestion propulsion. The formulations are numerically and experimentally advantageous because they only require integration across the shear layer height, and all the momentum and mechanical energy terms can be implicitly calculated from surface integrations of readily available numerical and experimental data.