16100lectre43_cj

16100lectre43_cj - Linearized Compressible Potential Flow...

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Unformatted text preview: Linearized Compressible Potential Flow Governing Equation Recall the 2-D full potential eqn is: 2 ) ( 1 1 ) ( 1 1 2 2 2 2 2 = + xy y x yy y xx x a a a Where [ ] 2 2 2 2 ) ( ) ( 1 y x o a a + = As you saw, for small perturbations to a uniform flow, the linearized form of the equation was: Where y x J y j x i v u u u u u = = + = + = v v v v v v This equation is valid for both 1 < M and 1 > M . Note, though, it is not correct for 1 M or for M large, say greater than about 2 or so. So what happens to the linearized potential equation for : 1 > M It also turns out that ) 1 ( 2 = + yy xx M is much easier to solve when 1 > M . Define 1 2 2 = = yy xx M Then, ) ( ) , ( = y x where y x = is a solution to the linearized potential. To see this:...
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16100lectre43_cj - Linearized Compressible Potential Flow...

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