Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow

TL;DR

This paper validates a universal aerodynamic force theory for three-dimensional steady viscous and compressible flows through numerical simulations, confirming its accuracy across subsonic to supersonic regimes and explaining its physical basis.

Contribution

It provides the first numerical validation of the universal force theory in 3D steady viscous and compressible flows, demonstrating its practical accuracy and physical explanation.

Findings

Universal force formula agrees with traditional methods in simulations.

Turbulent viscosity in the wake enhances the theory's applicability.

Flow structures support the theory's physical basis.

Abstract

In a recent paper, Liu et al. [``Lift and drag in three-dimensional steady viscous and compressible flow'', Phys. Fluids 29, 116105 (2017)] obtained a universal theory for the aerodynamic force on a body in three-dimensional steady flow, effective from incompressible all the way to supersonic regimes. In this theory, the total aerodynamic force can be determined solely with the vorticity distribution on a single wake plane locating in the steady linear far field. Despite the vital importance of this result, its validity and performance in practice has not been investigated yet. In this paper, we performed Reynolds-averaged Navier-Stokes simulations of subsonic, transonic, and supersonic flows over a three-dimensional wing. The aerodynamic forces obtained from the universal force theory are compared with that from the standard wall-stress integrals. The agreement between these two formulas confirms for the first time the validity of the theory in three-dimensional steady viscous and compressible flow. The good performance of the universal formula is mainly due to the fact that the turbulent viscosity in the wake is much larger than the molecular viscosity therein, which can reduce significantly the distance of the steady linear far field from the body. To further confirm the correctness of the theory, comparisons are made for the flow structures on the wake plane obtained from the analytical results and numerical simulations. The underlying physics relevant to the universality of the theory is explained by identifying different sources of vorticity in the wake.