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DataCard - Cambridge University Engineering Department 4A12...

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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 ∂x j = 1 ρ p ∂x i + ν∂ 2 u i /∂x 2 j u i u j ∂x j + g i Mean scalar: φ ∂t + u i φ ∂x i = D 2 φ ∂x 2 i u i φ ∂x i Turbulent kinetic energy ( k = u i u i / 2 ): ∂k ∂t + u j ∂k ∂x j = 1 ρ u j p ∂x j 1 2 u j u i u i ∂x j + ν 2 k ∂x 2 j u i u j u i ∂x j ν ∂u i ∂x j 2 + g i u i Scalar fluctuations ( σ 2 = φ φ ): ∂σ 2 ∂t + u j ∂σ 2 ∂x j = D 2 σ 2 ∂x 2 j 2 φ u j ∂φ ∂x j 2 φ u j φ ∂x j 2 D ∂φ ∂x j 2 Energy dissipation: ε = ν ∂u i ∂x j 2 u 3 L turb 62
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Scalar dissipation: 2 N = 2 D ∂φ ∂x j 2 2
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