turb+mixing%202007%203MM

turb+mixing%202007%203MM - FACE8 Turbulence and Mixing...

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1 FACE8 Turbulence and Mixing FACE8 2007 Turbulence and Mixing 3rd lecture Boundary layers revisitted Free shear flows
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2 FACE8 Turbulence and Mixing Laminar/viscous sublayer Turbulence free Buffer layer High dissipation Turbulent boundary layers
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3 FACE8 Turbulence and Mixing The layer structure of turbulent boundary layers · Sublayer and buffer layer Shear stress nearly constant Flow governed by τ w , ν , ρ and y We define the friction velocity u * And introduce the Law of the Wall ρ τ w u = * () * * y f y u f u u = = ν
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4 FACE8 Turbulence and Mixing The layer structure of turbulent boundary layers · Outer (free) layer The deficit law · At interface, the two expressions must have same gradient Differentiate both expressions and set equal to each other Law of the wall Deficit law = δ y g u u U * () κ ν 1 ' ' * * 2 * = = = y g u y f u y u 2 * 1 * * ln 1 ln 1 C y u u U C y u u u + = + = 1 2 0.40 0.41, 4.9. ..5.5 2.5 C C
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5 FACE8 Turbulence and Mixing The viscous sublayer profile · For the viscous sublayer u is linear Æ ν y u u u * * =
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6 FACE8 Turbulence and Mixing Near-wall velocity profiles
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7 FACE8 Turbulence and Mixing Single parameter approximations for turbulent boundary layers · The sublayer corresponds to approximately 1% of the boundary layer thickness Æ negligible. .. · Wecanusethelawo f±thewa l ld irect lyas ± approximation · Which is related to the von Kármán equation by n y u C u u 1 * 1 * = ν () 2 * 2 2 / = = = U u U U dx d w w ρ τ θ
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8 FACE8 Turbulence and Mixing Reynolds number, n and C 1 Power law profiles 12.0 9.6x10 7 10 11.0 3.8x10 7 9 10.1 1.4x10 7 8 9.1 3.3x10 6 7 7.1 5x10 3 6 C 1 Re x n
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turb+mixing%202007%203MM - FACE8 Turbulence and Mixing...

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