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The Kutta Condition in Aerodynamics
The Kutta condition allows an aerodynamicist to incorporate a significant effect of viscosity while neglecting viscous effects in the underlying conservation of momentum equation. It is important in the practical calculation of lift on a wing.
The equations of conservation of mass and conservation of momentum applied to an inviscid fluid flow, such as a potential flow, around a solid body result in an infinite number of valid solutions. One way to choose the correct solution would be to apply the viscous equations, in the form of the Navier-Stokes equations. However, these normally do not result in a closed-form solution. The Kutta condition is an alternative method of incorporating some aspects of viscous effects, while neglecting others, such as skin friction and some other boundary layer effects.
The condition can be expressed in a number of ways. One is that there cannot be an infinite change in velocity at the trailing edge. Although an inviscid fluid (a theoretical concept that does not normally exist in the everyday world) can have abrupt changes in velocity, in reality viscosity smooths out sharp velocity changes. If the trailing edge has a nonzero angle, the flow velocity there must be zero. At a cusped trailing edge, however, the velocity can be nonzero although it must still be identical above and below the aerofoil. Another formulation is that the pressure must be continuous at the trailing edge.
The Kutta condition does not apply to unsteady flow. Experimental observations show that the stagnation point (one of two points on the surface of an aerofoil where the flow speed is zero) begins on the top surface of an aerofoil (assuming positive effective angle of attack) as flow accelerates from zero, and moves backwards as the flow accelerates. Once the initial transient effects have died out, the stagnation point is at the trailing edge as required by the Kutta condition.
Mathematically, the Kutta condition enforces a specific choice among the infinite allowed values of circulation.
