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Unformatted text preview: ENU 4134 – Fluid Mechanics Review Part 2 – turbulence, velocity profile, pressure loss D. Schubring September 3, 2009 Topics I Turbulence I Transition from laminar behavior I Nature of turbulence, timeaveraged NS 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! Nature of Turbulence Smallscale, 3D, timedependent 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. TimeAveraged NS Equation (Enrichment) ~ v = ~ v + ~ v (3) ∂ ρ ~ v ∂ t + ∇ · ρ ~ v ~ v =∇ p + ∇ ~ ~ τ ρ~ v ~ v + ~ f (4) ~ ~ τ eff = ~ ~ τ ρ~ v ~ v > ~ ~ τ (5) (Remark: “Enrichment” = “Will not be on the test”) Understanding – or Tying To – Turbulence (Enrichment) Turbulence “cascade” – large eddies form smaller eddies, which form smaller eddies, etc.form smaller eddies, etc....
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This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.
 Spring '11
 Schubring

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