Dynamic behaviour of a rotatable airfoil, at constant and variable flow field

[prezza]

Homework Statement

While I was learning about drag and lift on airfloils, I imagined a special airfoil which is fixed at a certain elevation and cannot move vertically (y axis) but can be rotated around its axis (z). Let's assume the direction of the flow to be the x axis.
I try to predict the dynamic behaviour of the airfoil after being subjected to a moving fluid. How does the angle of the airfoil change with time when it is subjected to a one dimensional constant velocity flow at x direction.

Homework Equations

The second question: What is the effect of increasing flow velocity on the angle of airfoil?

The Attempt at a Solution

In the case of constant velocity flow, I know that the airfoil tries to reach an equilibrium angle. One equilibrium angle can be the one, at which the velocity of the fluid at the top and bottom of the airfoil are equal. So there will be no driving force for rotation. But right after we apply an angle of attack, pressure difference of two sides of the airfoil causes a clockwise rotation. This will continue until stall is occurred. What happens next? Does the airfoil ever reach a steady state or it continues to rotate?

 

[CWatters]

Not sure I've understood your axis but...

I believe most conventional aerofoils have a negative (leading edge down) pitching moment. They aren't stable in pitch on their own, that's one reason why aircraft have tails.

Bit old but basic book on the subject..
http://www.amazon.com/dp/1854861905/?tag=pfamazon01-20

Special sections have been designed for tailless aircraft but that's another story..

http://www.mh-aerotools.de/airfoils/index.htm

 

[prezza]

Thanks for the references.

What I mean is not the airfoil in its conventional usage. Just a geometry like an airfoil. and the rotation axis is parallel to its surface. I am not talking about aircrafts at all. Just wondering about the physics of the flow and forces on such a geometry.

 

[rcgldr]

Cambered airfoils generate a torque in the downwards pitch direction. If free to rotate, some flat airfoils may end up spinning. I'm not sure if a conventional airfoil would flap back and forth or spin. Do a seb search for spinning wings often used a lawn decorations, which do not fly, as an example.

 

[CWatters]

some flat airfoils may end up spinning

Now that's a blast from the past. More than 35 years ago when I was at school we would take small strips of paper about 3 inches long and 1 inch wide (perhaps a bit less). Fold down the short sides 90 degrees to form vertical surfaces about 1/2 inch tall at each end. They would spin as described. (eg They pitch up and keep pitching up). Sometimes they needed to be given an initial "flip" when launched to set them spinning (eg pull down on the trailing edge as you launch them). They would fly considerable distances if launched from the maths tower building.