Zonal structure of unbounded external-flow and aerodynamics

TL;DR

This paper reveals that the far-field behavior of external flows is more complex than previously thought, showing an unsteady, viscous, and compressible zone where disturbances decay exponentially, leading to a natural zonal structure that clarifies aerodynamic theories.

Contribution

It introduces a new zonal structure of unbounded external flow fields based on fundamental solutions of linearized Navier-Stokes equations, challenging traditional assumptions.

Findings

The furthest far-field zone is unsteady, viscous, and compressible.

Disturbances decay exponentially as sound waves in the far field.

Simplified flow models do not capture the true far-field behavior.

Abstract

This paper starts from the far-field behaviours of velocity field in externally-unbounded flow. We find that the well-known algebraic decay of disturbance velocity as derived kinematically is too conservative. Once the kinetics is taken into account by working on the fundamental solutions of far-field linearized Navier-Stokes equations, it is proven that the furthest far-field zone adjacent to the uniform fluid at infinity must be unsteady, viscous and compressible, where all disturbances degenerate to sound waves that decay exponentially. But this optimal rate does not exist in some commonly used simplified flow models, such as steady flow, incompressible flow and inviscid flow, because they actually work in true subspaces of the unbounded free space, which are surrounded by further far fields of different nature. This finding naturally leads to a zonal structure of externally-unbounded flow field. The significance of the zonal structure is demonstrated by its close relevance to existing theories of aerodynamic force and moment in external flows, including the removal of the difficulties or paradoxes inherent in the simplified models.