- #1
leviterande
- 106
- 0
Hello everyone!
I am interested in roughly calculating the lift from an airfoil that has air circulating around its full circumference, (can be done by a treadmill skin but probably best done in practice by blowing air from slots around the entire circumference as seen in Fig.1)
As we know, 2D lift from rotating cylinders or ordinary airplane airfoils in a free-stream airspeed can be roughly calculated using the Kutto-Joukowski Theorem circulation equation where the force per unit span is:
L = p v r
Where p is the air density, the free-stream velocity and r is the total amount of air vorticity around the object.
A rotating cylinder:
The r value here is simply the vortex strength which is the rotational speed times the circumference of the cylinder.
A fixed wing inclined/cambered airfoil
The r value or circulation value can be computed from the different air speeds resulting on top and bottom sides of the airfoil.
What about a circulation airfoil in Fig.1?
How do I obtain the circulation value r
My question is, how would you go about in approximately calculating the lift from the proposed air-circulating airfoil in FIG.1, where the air is circulating around the ENTIRE airfoil by for example blowing slots? That is, if I know the blown net average rotating air speed around the airfoil circumference and if I also know the free-stream velocity, how do I go about calculating the lift here?
My attempt:
I Do I just go about calculating just as if it was an ordinary fixed airfoil, and for the r value I just use the resulting different speeds on top and bottom of the circulating airfoil(as the p airfoil is going through the stream)? But, I am not sure really.
Thank you for your time and help
Regards
Levi
(NOTE: I am aware of the current state of art trailing edge Circulation Control WIng blowing at the round training edge. I just can't see why they don't make a full blowing : upper and lower side + trailing edge,+ leading edge blowing instead of only trailing edge blowing. But that's perhaps a different subject.)
I am interested in roughly calculating the lift from an airfoil that has air circulating around its full circumference, (can be done by a treadmill skin but probably best done in practice by blowing air from slots around the entire circumference as seen in Fig.1)
As we know, 2D lift from rotating cylinders or ordinary airplane airfoils in a free-stream airspeed can be roughly calculated using the Kutto-Joukowski Theorem circulation equation where the force per unit span is:
L = p v r
Where p is the air density, the free-stream velocity and r is the total amount of air vorticity around the object.
A rotating cylinder:
The r value here is simply the vortex strength which is the rotational speed times the circumference of the cylinder.
A fixed wing inclined/cambered airfoil
The r value or circulation value can be computed from the different air speeds resulting on top and bottom sides of the airfoil.
What about a circulation airfoil in Fig.1?
How do I obtain the circulation value r
My question is, how would you go about in approximately calculating the lift from the proposed air-circulating airfoil in FIG.1, where the air is circulating around the ENTIRE airfoil by for example blowing slots? That is, if I know the blown net average rotating air speed around the airfoil circumference and if I also know the free-stream velocity, how do I go about calculating the lift here?
My attempt:
I Do I just go about calculating just as if it was an ordinary fixed airfoil, and for the r value I just use the resulting different speeds on top and bottom of the circulating airfoil(as the p airfoil is going through the stream)? But, I am not sure really.
Thank you for your time and help
Regards
Levi
(NOTE: I am aware of the current state of art trailing edge Circulation Control WIng blowing at the round training edge. I just can't see why they don't make a full blowing : upper and lower side + trailing edge,+ leading edge blowing instead of only trailing edge blowing. But that's perhaps a different subject.)