Vorticity Production at a Wall – How Does Vorticity get Produced? Author: John M. Cimbala, Penn State University Latest revision: 11 October 2007 Note: Consider steady, incompressible, Newtonian flow in which gravity is neglected and the wall is stationary. Equations of motion at the wall •Start with the Navier-Stokes equation (differential momentum equation), with gravity ignored, 2iijijijuuputxxxρ⎛⎞∂∂∂∂+=−+⎜⎟∂⎝⎠juxμ.(1)•Invoke the two vector identities discussed in class when the Bernoulli equation was derived. The result is ()121jikjjjijk kijkijuupuxxxxjωεωερρ⎡⎤∂∂+−=−+−⎢⎥∂∂⎢⎥⎣⎦.(2)•Simplify Eq. (2) by using incompressible continuity, steady flow, and the fact that at the wall, ui= 0 by the no slip condition. Right at the wall, then, all terms with uigo to zero; rearranging, 121kijkjjipxxxμμ∂=−−∂at the wall.(3)•
This is the end of the preview. Sign up
access the rest of the document.