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FMreviewPart2_web

# FMreviewPart2_web - ENU 4134 Fluid Mechanics Review Part 2...

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ENU 4134 – Fluid Mechanics Review Part 2 – turbulence, velocity profile, pressure loss D. Schubring September 3, 2009

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Topics I Turbulence I Transition from laminar behavior I Nature of turbulence, time-averaged N-S equation I Wall coordinates and velocity profiles I Pressure losses – gravity, acceleration, form, friction I Application to rod bundles (subchannels)
Reynolds Number Criterion Re = ρ vL μ = ρ vD h μ (1) For tubes ( D h = D ) D h = 4 A P w (2) I Below 2,100 – Laminar I Above 10,000 – Turbulence I Between 2,100 and 10,000 – Transition Not directly applicable to other geometries – D h does not work in laminar flow!

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Nature of Turbulence Small-scale, 3-D, time-dependent eddies Enhance convection (warm fluid moved away from wall) With an eddy, d ~ v / d ~ x is larger than without – increases shear, pressure loss, required pumping power Reason: the d ~ v / d ~ x does not have sufficient driving force to maintain it, eddies dissipate in time.
Time-Averaged N-S Equation (Enrichment) ~ v = ~ v + ~ v 0 (3) ρ ~ v t + ∇ · ρ ~ v ~ v = -∇ p + ~ ~ τ - ρ~ v 0 ~ v 0 + ~ f (4) ~ ~ τ eff = ~ ~ τ - ρ~ v 0 ~ v 0 > ~ ~ τ (5) (Remark: “Enrichment” = “Will not be on the test”)

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Understanding – or Tying To – Turbulence (Enrichment) Turbulence “cascade” – large eddies form smaller eddies, which form smaller eddies, etc.
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