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Unformatted text preview: vector Fluids Lecture 16 Notes 1. Vortex 2. Lifting ow about circular cylinder Reading: Anderson 3.14 3.16 Vortex Flowfield Definition A vortex ow has the following radial and tangential velocity components C V r = 0 , V = r where C is a scaling constant. The circulation around any closed circuit is computed as 2 C V dvectors = V r d = r d = C ( 2 1 ) 1 r y y x V ds d r d The integration range 2 1 = 2 if the circuit encircles the origin, but is zero otherwise. 2 C , (circuit encircles origin) = 0 , (circuit doesnt encircle origin) y y 2 1 x 2 1 x In lieu of C , it is convenient to redefine the vortex velocity field directly in terms of the circulation of any circuit which encloses the vortex origin. V = 2 r 1 x A positive corresponds to clockwise ow, while a negative corresponds to counterclock- wise ow. Cartesian representation The cartesian velocity components of the vortex are u ( x, y ) = 2 y x 2 + y 2 v ( x, y ) = 2 x x 2 + y 2 and the corresponding potential and stream functions are as follows....
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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