16100lectre22_cg

16100lectre22_cg - Integral Boundary Layer Equations...

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Integral Boundary Layer Equations Displacement Thickness The displacement thickness * δ is defined as: * 00 11 ee e compressible incompressible flow flow uu dy dy ρ ∞∞  =−   ∫∫ ±²²³²² ´± ² ²³²²´ The displacement thickness has at least two useful interpretations: Interpretation #1 0 0 (1) e u dy u dy = = A A+B So, the difference is in area B . * “represents” the decrease in mass flow due to viscous effects, i.e. lost * e e visc u m = µ y u / u e u / u e (y) A B
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Integral Boundary Layer Equations 16.100 2002 2 Interpretation #2 Conservation of mass: 11 1 1 00 0 0 () 1 yy y e ee y y e u dy udy udy yu yu u u dy u yd y u +∆ = =+ ⇒∆ =  ∆=   ∫∫ Taking the limit of 1 y gives * 0 1 e u y u δ ⇒∆ = = So, the external streamline is displaced by a distance * away from the body due to viscous effects. Outer flow sees an “effective body” s tre am line y δ *(x) y y 1 u(y) x u e
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.

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16100lectre22_cg - Integral Boundary Layer Equations...

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