Turbulence lecture 31

Turbulence lecture 31 - Turbulence Lecture 31 Since P = Pe...

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Turbulence Lecture 31 Since () 2 12 u e PPx ρ =− 2 2 11 u e P P 1 x xx ρρ ∂∂ In external flow (outside B.L.) Bernoulli’s equation applies (inviscid, etc.). 2 1 constant 2 1 20 2 1 ee t e e PU P U U += = = Combine with x -momentum equation. Term from 2 x - dir integration / 2 22 1 1 2 1 2 2 12 1 2 2 1 May be important for flows approaching separation. We will neglect for well-behaved B-L's. e e U UU U u u UU U u u xx xx x x ν ′′ +=+− − − ∂∂ ∂∂ ±²³ ²´ With 1 2 , , U e Vuu vu u U U Uu == = = = 2 2 U U 0 U u UV v x yxy xy ∂∂ ∂∂∂ y 2 equations, 3 unknowns. U assumed known. Evaluation of U. 1
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a. External Flows - Let U be potential flow velocity on surface for 1 st approximation. b. Internal Flow Apply Continuity () 11 2 2 0 UU 22 ww U δ =− + y Solve for - integrated form of continuity. 2 U Possible Closures: 1. 2 uu uv yy ∂∂ ′′ A −= 2. u y τ ν ′′ = But we will pursue a different approach.
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Turbulence lecture 31 - Turbulence Lecture 31 Since P = Pe...

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