Kutta Condition

When a smooth symmetric body, such as a cylinder with oval cross-section, moves with zero angle of attack through a fluid it generates no lift. There are two stagnation points on the body - one at the front and the other at the back. If the oval cylinder moves with a non-zero angle of attack through the fluid there are still two stagnation points on the body - one on the underside of the cylinder, near the front edge; and the other on the topside of the cylinder, near the back edge. The circulation around this smooth cylinder is zero and no lift is generated, despite the positive angle of attack.

If an airfoil with a sharp trailing edge begins to move with a positive angle of attack through air, the two stagnation points are initially located on the underside near the leading edge and on the topside near the trailing edge, just as with the cylinder. As the air passing the underside of the airfoil reaches the trailing edge it must flow around the trailing edge and along the topside of the airfoil toward the stagnation point on the topside of the airfoil. Vortex flow occurs at the trailing edge and, because the radius of the sharp trailing edge is zero, the speed of the air around the trailing edge should be infinitely fast! Real fluids cannot move at infinite speed but they can move very fast. The very fast airspeed around the trailing edge causes strong viscous forces to act on the air adjacent to the trailing edge of the airfoil and the result is that a strong vortex accumulates on the topside of the airfoil, near the trailing edge. As the airfoil begins to move it carries this vortex, known as the starting vortex, along with it. Pioneering aerodynamicists were able to photograph starting vortexes in liquids to confirm their existence. [2] [3] [4]

The vorticity in the starting vortex is matched by the vorticity in the bound vortex in the airfoil, in accordance with Helmholtz's second theorem. [5] As the vorticity in the starting vortex progressively increases...