Turbulence lecture 12

Turbulence lecture 12 - Turbulence Lecture 12 Energetics...

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Turbulence Lecture 12 Energetics (of the mean flow) Multiply the mean momentum equation by U , and, contract . i i () 22 2 ii jj i i j UU P U S txx x ρρ µ ∂∂∂ ∂ j i j u u ρ += + − ∂∂∂ 2 2 i j j ij i i i j i j ij ij ij U U U P SU U uu uu S S S tx x ρµ   ∂∂ + +     ±²²²³²²²´ time rate of change of KE mean flow pressure work viscous of following the mean flow Note: i j i i j i j U u U u u u u Uu x xx =− symmetric j Note: 2 ji i j i i j UP US Uuu x µρ −+ ±²²²²²²³²²²²²²´ j Spatial distribution of mean flow KE due to pressure, viscosity, and Reynolds stresses iji j - loss (sometimes gain) of mean flow KE to turb KE 2 ij ij SS - rate of loss of mean flow KE to internal engery. Note: j i U µµ = i j S 2 i ij j U S x {} N 2 2 i j i i j j V i j i i j j A Uuu dV x Uuu ndP + of boundary Unit normal of C.V.
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0 = for most B.C.’s Except for example wind water waves where pressure can do work on surface.
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.

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Turbulence lecture 12 - Turbulence Lecture 12 Energetics...

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