Turbulence lecture 32

Turbulence lecture 32 - Turbulence Lecture 32 1....

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Turbulence Lecture 32 1. Clarification – Leibnitz rule Does () ( ) ( ) 00 UU xx d y δδ ∂∂ −=   ∫∫ d y The “naturally” occurring form. Leibnitz’s rule for integration ( ) () () () () ( ) ,, , , bx ax df f xyd y fx bxbx fxaxax y dx y ′′ =−+ For our case () () () () () () ()( )() ( ) () () () ( ) () () 0 0 b U , , U , 0 0 , 0 a x d x x dx f xy U xy x U xy fxbx fx Ux fxax δ =⇒ = =⇒= =−  == − = ±²³² ´± ²³²´ () ( ) 0 U, 0 xUx 0 0 dd d y d y dx dx = a Q.E.D. Displacement thickness Physical interpretation of * Consider 1
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() * 12 UU ee e mh m d y U h ρ ρρ δ ′′ == =+− + ±± / 0 Udy Prime means per unit depth * 0 e e hU d y h U + Solve for * 00 * 0 0U 1 e e Udy dy dy dy U δδ δρ =− − =− ∫∫ U * 0 1 U U dy    for incompressible flow Alternate representation Makes a bigger hypothetical airfoil for inviscid calculations. Physical interpretation of θ . Thickness of potential flow having a momentum flux equal to that lost by the presence of a boundary layer.
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Turbulence lecture 32 - Turbulence Lecture 32 1....

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