The text book Flight Physics by Torenbeek and Wittenberg is used in the KTH course Fundamentals of Flight. Let is see how the course book presents the fundamentals in Chapter 4 Lift and Drag at Low Speeds:
- An aerofoil is a streamline body designed in such a way that, when set at a suitable angle to the airflow, it produces much more lift than drag.
- Similar to the situation with circulation around a cylinder, the flow around an aerofoil can be treated as a combination of two flow types;
- (a) In a frictionless flow there are two stagnation points: one near the nose point and one above and in front of the tail point.
- (b) A circulating flow. With airflow from the left and circulation in a clockwise direction, the velocity will increase on the upper aerofoil surface and slow down on the lower one.
- (c) The result of the superposition is a flow with a higher average velocity and a lower pressure on the upper surface than in case (a), whereas the pressure on the lower surface is higher.
- The pressure difference between both surfaces is experienced as lift.
- However, in contrast with the situation of a rotating cylinder, an aerofoil section is not rotating, which makes it unclear how circulation arises and what determines its value.
- Although just about every value of circulation seems possible, in reality nature takes care that a certain angle of attack only allows one type of flow.
- In 1902, W.M. Kutta first proposed – for a section with a sharp trailing edge – that the circulation adjusts to a value so that no air will flow around the sharp aerofoil tail from the lower to the upper surface, or vice versa... this so-called Kutta condition leads to a correct determination of the circulation and with that the velocity and pressure distribution, in other words: the lift force.
- The fundamental question how circulation occurs and remains in existence can be answered in principle by carrying out an experiment such as that done for the first time by Ludwig Prandtl. He placed an aerofoil in a water channel in which the flow was made visible by aluminium particles sprinkled on the surface.
- ...the viscous fluid cannot follow the corner at the tail point and will separate while creating a vortex above the trailing edge. At still higher velocity this vortex will move downstream, separate from the wing, and will become a cast-off or starting vortex. This will be quickly left behind and is eventually dissipated through the action of viscosity.
- Because the original flow did not contain circulation, a reverse circulation will occur around the aerofoil with the opposite direction.
- Its circulation causes the rear stagnation point to move towards the trailing edge.
- Since a starting vortex originates from viscosity, there is no circulation and also no lift created in ideal flow.
- Nevertheless, the lift on a section with a sharp tail can be determined by assuming the flow to be ideal and by making use of the Kutta condition. For small angles of attack, viscous effects are manifest only in the boundary layer and the lift is hardly affected by viscosity.
- The discussed model is therefore a good representation of the real flow.
We see here the classical Kutta-Zhukovsky 2d circulation theory conceived 100 years ago. There is massive evidence (see e.g. Swedish Aerodynamics Dissident) that the 2d flow thus described is unphysical and thus scientifically incorrect. We can see how the authors struggle to cope with this fact: It is not claimed that 2d potential flow + circulation describes the real physics, only that the model is a "good representation" and the flow can so "be treated" (the accepted way of handling the contradiction between 2d theory and 3d reality).
The unphysical circulation theory has survived only because a correct explanation of the actual real 3d physics of a wing has been missing. It is now available as New Theory of Flight and text books and university courses have to be revised:
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