Қанат шеттеріндегі ағын динамикасы және Кутта шарты

Fluid dynamics principle regarding bodies with sharp corners

The Kutta condition is a principle in steady flow fluid dynamics, especially aerodynamics, that is applicable to solid bodies with sharp corners, such as the trailing edges of airfoils. It is named for German mathematician and aerodynamicist Martin Kutta. Kuethe and Schetzer state the Kutta condition as follows:

The vorticity in the starting vortex is matched by the vorticity in the bound vortex in the airfoil, in accordance with Kelvin's circulation theorem. As the vorticity in the starting vortex progressively increases the vorticity in the bound vortex also progressively increases and causes the flow over the topside of the airfoil to increase in speed. The starting vortex is soon cast off the airfoil and is left behind, spinning in the air where the airfoil left it. The stagnation point on the topside of the airfoil then moves until it reaches the trailing edge. When an airfoil is moving with an angle of attack, the starting vortex has been cast off and the Kutta condition has become established, there is a finite circulation of the air around the airfoil. The airfoil is generating lift, and the magnitude of the lift is given by the Kutta–Joukowski theorem. The Kutta condition gives some insight into why airfoils have sharp trailing edges, even though this is undesirable from structural and manufacturing viewpoints. In irrotational, inviscid, incompressible flow (potential flow) over an airfoil, the Kutta condition can be implemented by calculating the stream function over the airfoil surface. The same Kutta condition implementation method is also used for solving two dimensional subsonic (subcritical) inviscid steady compressible flows over isolated airfoils. The viscous correction for the Kutta condition can be found in some of the recent studies.

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 can have abrupt changes in velocity, in reality viscosity smooths out sharp velocity changes. If the trailing edge has a non zero angle, the flow velocity there must be zero. At a cusped trailing edge, however, the velocity can be non zero although it must still be identical above and below the airfoil. 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 airfoil where the flow speed is zero) begins on the top surface of an airfoil (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.