tisdag 21 augusti 2012

Circulation Theory of Lift Not Physical

The text book theory of lift of a wing is since 100 years the Kutta-Zhukovsky Circulation Theory based on 2d potential flow modified by large scale circulation around the wing section determined by the Kutta condition of zero flow velocity at the trailing edge.

Kutta-Zhukovsky Circulation Theory is presented as a "mathematical theory" based on the "trick" of the Kutta condition, to be compared with "physical theories" commonly connected to Newton and Bernoulli. This is presented as follows:
  • There are several ways to explain how an airfoil generates lift. Some are more complicated or more mathematically rigorous than others; some have been shown to be incorrect....but each appeals to a different audience. (Wikipedia)
  • The mathematical description of lift is a general term for the analysis tools of classical aerodynamics and computation aerodynamics. If the objective is to accurately compute the principle or aerodynamics of a wing, these are the tools to use, though the aerodynamic description is mathematical and not physical. (Understanding Flight)
  • There are different explanations of flight: 1. Mathematical, taught to aeronautical engineers. 2. Popular, taught at flight schools, NASA, in many cases fine but wrong. 3. Physical, presented by myself in this lecture. (Jefferson Lab Science Series/Eberhardt)
Circulation theory is thus described as a mathematical theory useful for computing lift, which however is not a physical theory. This fact is typically expressed as follows:  
  • How can potential flow be adapted to provide a reasonable theoretical model for the flow around an aerofoil that generates lift? The answer lies in drawing an analogy between the flow around an aerofoil and that around a spinning cylinder. For the latter it can be shown that when a point vortex is superimposed, a lifting flow is generated. (Aerodynamics for Engineering Students, 5th edition, by Houghton and Carpenter)
  • The airflow about an airfoil may be viewed as consisting of two superimposed patterns—one is the free-stream motion of the air about the airfoil and the other is a circulatory flow, or circulation, around the airfoil. (US Centennial Flight Commission)
The non-physical aspect of Circulation Theory is visible in expressions such as potential flow "be adapted" and airflow may "be viewed". 

It is thus generally acknowledged that Circulation Theory does not describe the actual physics of generation of lift. When now there is a New Theory of Flight describing the actual physics in mathematical terms, which can be used to compute both lift and drag, there is no longer any need for any unphysical Circulation Theory. This will come as a relief to many who have struggled to understand Circulation Theory over the years without success.

See also Unphysical Circulation Theory.

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