söndag 29 juli 2012

Making of the Prandtl Myth by Prandtl

The Father of Modern Aerodynamics inspecting the Ho III 1938 Rhön Contest Challenger:
Did Germany lose the war because of incorrect aerodynamics?

On the request by NACA (US National Advisory Committee for Aeronautics) in 1921, Ludwig Prandtl "prepared for the reports of the committee a detailed treatise on the present condition of those applications of hydrodynamics which lead to the calculation of the forces acting on airplane wings and airship bodies" (NACA Report 116 Applications of Modern Hydrodynamics to Aeronautics). 

Prandtl "acceded to the request all the more willingly because the theories in question have at this time reached a certain conclusion where it is worth while to show in a comprehensive manner the leading ideas and the results of these theories and to indicate what confirmation the theoretical results have received by tests".

Prandtl states in his report defining the state-of-the-art with my comments in parenthesis:

1. Friction between fluid and solid body never comes into consideration in the fields of application to be treated here, because it is established by reliable experience that fluids like water and air never slide on the surface of the body; what happens is, the final fluid layer immediately in contact with the body is attached to it (is at rest relative to it), and all the friction of fluids with solid bodies is therefore an internal friction with the fluid. (This is Prandtl's dictate of no-slip boundary condition which made 20th century fluid mechanics into uncomputable magics).

2. In this layer, which we call the boundary layer, the forces due to viscosity are of the same order of magnitude as the forces due to inertia, as may be seen without difficulty. (This is misleading: both forces due to viscosity and inertia can be small.)

3. Closer investigation concerning this shows that under certain conditions there may occur a reversal flow in the boundary layer which is set in rotation by the viscous forces, so that, further on, the whole flow is changed owing to the formation of vortices. (This is Prandtl's main thesis: The boundary layer changes the whole flow).

4. In the rear of blunt bodies vortices are formed…on the other hand, in the rear of very tapering bodies…there is no noticeable formation of vortices. The principal successful results of hydrodynamics apply to this case…the theory can be made useful exactly for those bodies which are of most technical interest. (Prandtl's theory is based on the formation of vortices in the boundary layer, which Prandtl claims are not formed in the cases of interest: Missing logic).

5. On resistance of airships: It is seen that the agreement (pressure distribution) is very complete; at the rear end, however, there appears a characteristic deviation in all cases, since the theoretical pressure distribution reaches the full dynamical pressure at the point where the flow reunites again, while actually this rise in pressure, owing to the influence of the layer of air retarded by friction, remains close to the surface. (Prandtl suggests that the lack of pressure rise at separation in real flow is du to boundary layer friction. We show that this is incorrect: It is instead caused by 3d rotational separation.)

6. As is well known there is no resistance for the theoretical flow in a nonvoscpus fluid (potential flow). The actual drag consists of two parts, one resulting from all the noral forces (pressures) acting on the surface of the body, the other from all tangential forces (friction). The pressure resistance, arises in the main from the deviation mentioned at the rear end, and is, as is known, very small. (This is incorrect: Pressure drag is the main part of drag in slightly viscous flow)

7. We shall concern ourselves in what follows only with non viscous and incompressible fluid, also called "ideal fluid". (Confusing since friction forces are supposed to change the flow.)

8. In order that the flow may be like the actual one, the circulation must always be so chosen that the rear rest point coincides with the trailing edge….We are accordingly, by the help of such constructions, in the position of being able to calculate the velocity at every point in the neighborhood of the wing profile…. The agreement on the whole is as good as can be expected from a theory which neglects completely the viscosity. (Empty statement.)

9. That a circulatory motion is essential for the production of lift of an aerofoil is definitely established. The question is then how to reconcile this with the proposition that the circulation around a fluid line in a non viscous fluid remains constant.... There is instantly formed at the trailing edge a vortex of increasing intensity… (This is the mystery of circulation theory: If circulation generates lift, the question is how circulation is generated. The standard answer is by a non-real sharp trailing edge and starting vortex. This is however not the real physics of 3d rotational separation at a real rounded trailing edge.)

Concluding analysis: Prandtl's message of 1921 has become the text book canon, which however is non-physical and thus incorrect.

1 kommentar:

  1. Q: Did Germany lose the war because of incorrect aerodynamics?

    A: No, Germany lost the war because of “incorrect” adversary. Hitler should have heeded wise Bismarck who advised Germans never initiate a war against Russia.

    Our cause is just – we will prevail (Joseph Stalin). So, we did.