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Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
the flowfield about the airfoil can be represented by distributing vortices along the mean camber line. An infinite number of solutions are possible for the distribution of the strengths of the vortices as a function of chord. All but one of these solutions is eliminated by applying the Kutta condition. The Kutta condition essentially requires that the flow be physically realistic in that the fluid cannot flow around a sharp trailing edge. More specifically, it states that the following be true: (1) the value of the circulation, Γ, is such that the flow leaves the trailing edge smoothly; (2) if the included angle at the trailing edge is finite, then the trailing edge is a stagnation point; and (3) if the trailing edge is cusped (zero included angle), then the velocities from the upper and lower surfaces are equal in magnitude and direction at the trailing edge. Thin airfoil theory then yields a lift slope of 2π, so in the case of symmetric airfoil C1=2πα. For relatively thin airfoils, less than about 12%, this prediction is accurate to within several percent of experimentally determined values.
Elementary Aerodynamics
Published in Rama B. Bhat, Principles of Aeroelasticity, 2018
To make the theory compatible with the physically observed phenomenon, a circulation with correct intensity around the airfoil must be imposed so that the downstream stagnation point is moved all the way back to the trailing edge of the airfoil, thus allowing the flow to leave the airfoil smoothly at the trailing edge. This is called the Kutta condition, named after the German mathematician and aerodynamicist Martin Wilhelm Kutta. Ideal-flow theory then shows that the magnitude of circulation required to maintain the rear stagnation point at the trailing edge (Kutta condition) of a symmetrical airfoil with a small angle of attack, α, is given by Γ=πcV0α
Numerical Methods for Inviscid Flow Equations
Published in Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar, Computational Fluid Mechanics and Heat Transfer, 2020
Dale A. Anderson, John C. Tannehill, Richard H. Pletcher, Munipalli Ramakanth, Vijaya Shankar
In the lifting case, the circulation must be imposed and determined by satisfying the Kutta condition on the airfoil. The far-field boundary condition in this case takes the form of a vortex with the value of circulation determined by the Kutta condition. For development of the far-field boundary condition, the papers by Ludford (1951) and Klunker (1971) are recommended.
BEM applied to the cup effect on the partially submerged propeller performance prediction and ventilation pattern
Published in Journal of Marine Engineering & Technology, 2022
Ehsan Yari, Ali Barati Moghadam
A Kutta condition is required at the trailing-edge to uniquely specify the circulation. In its most general form, it states that the flow velocity at the trailing-edge remains bounded .