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exact_soln_BL - MECH 371 Boundary Layer Theory Exact...

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1 MECH 371 Boundary Layer Theory: Exact Solution MECH 371 Boundary Layer Theory To start the derivation of the Falkner-Skan and Blasius equations, we must come up for an expression of the flow external to the boundary layer on a plane surface. Let's say there's a possible potential flow solution in polar coordinates: ! r, " ( ) = C r m + 1 sin m + 1 ( ) " # $ % & where ! satisfies the Laplace Eq. 2 ! = 0 ( ! is a valid potential flow solution. The radial streamlines act as walls for a wedge (ramp flow), expansion corner or convergent-divergent wedge (Jeffery-Hamel flow). We'll define ) as ) = 2m m + 1 ( ) . Then Inviscid Flow Past Wedges and Corners
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2 MECH 371 Boundary Layer Theory ! 1 2 " m " 0 , ! 2 " # " 0 : flow around an expansion corner of turning angle # $ 2 m = 0 , # = 0 : a flat plate 0 " m " % , 0 " # " 2 : flow against a wedge of half angle & = # $ 2 m = 1 , # = 1 : the plane stagnation point ( & = 180 ! ) MECH 371 Boundary Layer Theory m = ! 2 , " = +4 : This can be modeled by doublet flow near a plane wall m = ! 5 3 , " = +5 : This can be modeled by doublet flow near a 90 !
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