16100lectre24_cg

16100lectre24_cg - Method of Assumed Profiles Here are the...

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Method of Assumed Profiles Here are the basic steps: 1. Assume some basic boundary velocity profile for ) , ( y x u . For example, this is a crude approach but illustrates the ideas: ,0 ( ) (, ) () 1, e y yx uxy x ux δ ≤< = where ) ( x is the single unknown describing the velocity distribution. 2. Calculate ) ( , * H or θ , and f C for the assumed profile: 2 * 00 0 1 11 2 e uy y dy dy y u δδ  =− =    ∫∫ * 1 2 = 23 2 0 ee uu y y yy dy dy =−=   1 6 = Note: * 1 2 3 1 6 H == = Finally, to find f C we need 0 w y u y τµ = = , for 0 e e u ∂∂ <
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Method of Assumed Profiles 16.100 2002 2 22 2 11 e w f ee u C u uu µ τ δ ρ ρρ === 3. Plug results from step 2 into integral b.l. equation: dx du H u dx d C e e f ) 2 ( 2 + + = θ So, for our assumed linear profile: 15 66 e e dd u ud x u d x µδ ρδ =+ (1) where ) ( x is the only unknown. We can solve this by specifying ) ( x u e , setting an initial value for at 0 = x (i.e. the leading edge) and then integrate in x .
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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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16100lectre24_cg - Method of Assumed Profiles Here are the...

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