What is the Theoretical Solution for Lift at High Angles of Attack for Airfoils?

[OrangeDog]

I need a reference for the exact solution for lift at high angles of attack, when an airfoil behaves like a flat plate. I am pretty sure the theoretical solution is CL = 2 sin(α)*cos(α) based on two papers I read on lift through 180 degrees angle of attack, but I can't find in any of my books where this is stated. This would also be consistent with the small angle approximation for flat plate lift, as the cosine term becomes 1 and the sin term equals α.

See the Sandia publication:
Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections Through 180-Degree Angle of Attack for Use in Aerodynamic Analysis of Vertical Axis Wind Turbines"

 

[boneh3ad]

Have you checked a source like Theory of Wing Sections by Abbott and von Doenhoff? I don't recall off the top of my head if this is covered in there and my copy is at home, not with me at work, but it would probably be the first place I would look.

 

[OrangeDog]

Im at work now and can't check. ToWS only covers up to stall for their studies so I doubt it would be in there. I checked von Mises book "Theory of Flight" (my favorite aeronautics book by the way) and it only used the small angle approximation. For the life of me I can't remember where I found the high AoA solution...

 

[boneh3ad]

Yeah, basically all of my aeronautics books that don't involve compressible flow are at home right now or I'd do a quick flip through them.

On the other hand, if you were looking for sources on waves, compressible flows, hydrodynamic stability, or turbulence, then my stash of books at work would be of some help. Alas, you are not.

 

[OrangeDog]

My line of work is strictly pertaining to IC flows :( I just need to compare the theoretical solution with some data.