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Unformatted text preview: Fluids Lecture 18 Notes 1. Prediction of Lift 2. Vortex Sheets Reading: Anderson 3.17 Prediction of Lift Limitations of Source Sheets A point source has zero circulation about any circuit. Evaluating using its definition we have vector V dvectors = V r dr = r 2 r 1 2 r dr = 2 (ln r 2 ln r 1 ) = 0 which gives zero simply because r 1 = r 2 for any closed circuit, whether the origin is enclosed or not. A source sheet, which effectively consists of infinitesimal sources, must have zero circulation as well. x y V ds dr r 1 r 2 = 0 = 0 This zero-circulation property of source sheets has severe consequences for ow represen- tation. Any aerodynamic model consisting only of a freestream and superimposed source sheets will have = 0, and hence L = 0 as well. Hence, lifting ows cannot be represented by source sheets alone. This limitation is illustrated if we use source panels to model a ow expected to produce lift, such as that on an airfoil at an angle of attack. Examination of the streamlines reveals that the rear dividing streamline leaves the airfoil off one surface as shown in the figure. The model also predicts an infinite velocity going around the sharp trailing edge. V source sheet model reality smooth flowoff (Kutta condition) = 0 = 0 L L > 0 > 0 1 On real airfoils the ow always ows smoothly off the sharp trailing edge, with no large local velocities. This smooth ow-off is known as the Kutta condition , and it must be faithfully duplicated in any ow model which seeks to predict the lift correctly. Changingfaithfully duplicated in any ow model which seeks to predict the lift correctly....
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
- Fall '05