DataCard - Cambridge University Engineering Department...

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Cambridge University Engineering Department 4A12: Turbulence Data Card Assume incompressible fluid with constant properties. Continuity: u i ∂x i =0 Mean momentum: u i ∂t + u j u i j = 1 ρ p i + ν∂ 2 u i /∂x 2 j u 0 i u 0 j j + g i Mean scalar: φ + u i φ i = D 2 φ 2 i u 0 i φ 0 i Turbulent kinetic energy ( k = u 0 i u 0 i / 2 ): ∂k + u j j = 1 ρ u 0 j p 0 j 1 2 u 0 j u 0 i u 0 i j + ν 2 k 2 j u 0 i u 0 j u i j ν ± ∂u 0 i j ² 2 + g 0 i u 0 i Scalar fluctuations ( σ 2 = φ 0 φ 0 ): ∂σ 2 + u j 2 j = D 2 σ 2 2 j 2 φ 0 u 0 j ∂φ 0 j 2 φ 0 u 0 j φ j 2 D ± 0 j ² 2 Energy dissipation: ε = ν ± 0 i j ² 2 u 3 L turb 62
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Scalar dissipation: 2 N =2 D ± ∂φ 0 ∂x j ² 2 2 ε k σ 2 Scaling rule for shear flow, flow dominant in direction x 1 : u L turb u 1 2 Kolmogorov scales: η K = ( ν 3 ) 1 / 4 τ K =( ν/ε ) 1 / 2 v K νε )
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This note was uploaded on 09/16/2011 for the course ME 563 taught by Professor Staff during the Spring '11 term at Auburn University.

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DataCard - Cambridge University Engineering Department...

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