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Turbulence_Part_One_web - ENU 4133 Turbulence Part 1 March...

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ENU 4133 – Turbulence – Part 1 March 5, 2010
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Duct Flows Coverage I Time Averaging I Reynolds Decomposition and RANS (Reynolds Averaged Navier-Stokes) I Law of the Wall and Velocity Profiles I Kolmogorov hypotheses and scales I Mixing length modeling of turbulence I Multi-equation models of turbulence ( k - , k - ω ) I Computational techniques for turbulence (including large eddy simulation – LES & direct numerical simulation – DNS) In general – Part 1 is more basic, quantitative, and rather closely parallels Section 6.5 in the text. Part 2 is more complex, qualitative, and will be driven from the notes & references.
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Example Fluctuations Sufficient time for u and p to converge – couple/few seconds (White recommends 5).
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Time-Average Operator f = 1 T Z T 0 fdt (1) ~ V = 1 T Z T 0 ~ V dt (2) p = 1 T Z T 0 pdt (3) Rules ( f , g scalar/vector/tensor functions, h scalar variable) f = f (4) f + g = f + g (5) f g = f g (6) fg 6 = f g (7) f h = f h (8)
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Reynolds Decomposition Fluctuations ~ V 0 and p 0 : ~ V 0 ( ~ r , t ) = ~ V ( ~ r , t ) - ~ V (9) p 0 ( ~ r , t ) = p ( ~ r , t ) - p (10) Mean fluctuation: ~ V 0 = 1 T Z T 0 ~ V - ~ V dt
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