A note on the Kutta condition in Glauert's solution of the thin aerofoil problem

Glauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the rôle of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied. It is shown here that if Glauert's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series. Furthermore, the present method provides a very direct way to construct other, more singular solutions. A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion

Experimental Analysis of a Wind-Turbine Rotor Blade Airfoil by means of Temperature-Sensitive Paint

Knowledge on the boundary-layer transition location at large chord Reynolds numbers (Re ≥ 3 million) is essential to evaluate the performance of airfoils designed for modern wind-turbine rotor blades, which rotor diameters can be of the order of hundred meters. In the present work, a temperature-sensitive paint (TSP) was used to systematically study boundary-layer transition on the suction side of a DU 91-W2-250 airfoil. The experiments were performed in the High-Pressure Wind Tunnel Göttingen at chord Reynolds numbers up to Re = 12 million and angles-of-attack from -14° to 20°. The coefficients of airfoil lift, drag, and pitching moment were also obtained after integration of the pressure distributions measured on the wind-tunnel model surface and in the model wake. The surface data obtained by means of TSP enabled not only to analyze the evolution of the transition location with varying angle-of-attack and chord Reynolds number, but also to provide an explanation for the evolution of the aerodynamic coefficients measured at stall and post-stall conditions. The stability of the laminar boundary layers investigated in the experiments was analyzed according to linear stability theory. The results of the stability computations supported the experimentally observed variations in the transition location. The amplification factors of boundary-layer disturbances at transition were also determined by correlating the experimental and numerical results