Joukowski transformation velocity. Slider C = circulation.
Joukowski transformation velocity. Slider T = apply transformation. One of the ways of finding the flow patterns (streamlines), velocities, and pressures around a shape (similar to an “ airfoil “) in a potential flow field is to apply a mathematical “ conformal mapping ” (called, “ Joukowski transformation “) to the potential flow solution for a circular cylinder. One of the more important potential flow results obtained using conformal mapping are the solutions of the potential flows past a family of airfoil shapes known as Joukowski foils. The plots indicate the analytic solution of a rotating cylinder in cross flow to the transformation of the flow over a Joukowski airfoil. Happy clicking/dragging! The Joukowsky transformation maps a circle of greater than unit radius with the origin offset from (0,0) to the upper and lower surface of a wing with its trailing edge at +2. Slider C = circulation. Airfoil's Meanline curvature, Thickness, and Angle of Attack are adjustable. The following simulation shows the uniform flow past the circular cylinder c 1 and its transformation to the Joukowsky airfoil. First, overall lift is proportional to the circulation generated; second, the magnitude of the circulation must be such as to keep the velocity finite at the trailing edge in accordance with the Kutta condition. The cylinder can be mapped to a variety of shapes and by knowing the derivative of the transformation, the velocities in the mapped flow field can be found as a function of the known velocities around the cylinder. i4z 8wwi jrrla xuyvoye t6 2ajn ec zspts fo4b0l anabwe
Back to Top
