5 - 1 Turbulence mixing Turbulence mixing 4th lecture FACE 8 2007 Turbulence mixing 2 Program 08:15-08:45 08:45-09:00 09:00-09:15 09:15-10:00

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1 Turbulence & mixing Turbulence & mixing 4 th lecture FACE 8 2007
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2 Turbulence & mixing ·P r o g r a m 08:15-08:45 Lecture: The LES approach 08:45-09:00 Exercise: RANS+ Questions 09:00-09:15 Break 09:15-10:00 Lecture: Smagorinsky SGS model 10:00-11:30 Exercise: Test case in Fluent 11:20-12:00 presentations in plenum ·L i t e r a t u r e Frölich and Rodi’s introduction to LES Suggested reading: Fluent user guide Sagaut’s LES for incompressible flows
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3 Turbulence & mixing · Turbulence structure · How to simulate this?
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4 Turbulence & mixing · DNS (Direct Numerical Simulation) Idea: Just use the NS-equations… Problem: Need to resolve the time and length scales of turbulence / Conclusion: Not practical possible for most problems ·L E S (Large Eddy Simulation) Idea: Okay, let just resolve the larger time and length scales then Problem: Still very demanding + difficult to setup Conclusion: We only want to use LES for specific problems ·R A N S (Reynolds Averaged Navier Stokes) Idea: Lets forget about eddies and whirls and try to find some way to model the effect of turbulence on the overall flow Problem: This is an oversimplification of the problem which yields erroneous results and require an insight to use Conclusion: This is the fast solution and we must be skeptical of the result; but we’ll probably be using RANS models most of the time! More time More computational demanding
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5 Turbulence & mixing ·R A N S · Boussinesq approximation · Mixing length () ij i ij i j i jj j uu u P S tx x x ρ τ ρρ −∂ ′′ += +− + ∂∂ Turbulent stress or Reynolds stresses: τ T j i TT j i u u xx τμ ⎛⎞ ≈+ ⎜⎟ ⎝⎠ Turbulent or eddy viscosity T l u μ∝ Velocity scale Length scale
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6 Turbulence & mixing · Structure of turbulence Energy is extracted from the main flow to produce large eddies Energy is transferred from larger eddies to smaller eddies The smallest eddies dissipates due to the viscosity of the flow
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7 Turbulence & mixing · Local isotropy Large eddies transport the majority of the turbulent kinetic energy Large eddies are problem dependent ; they are dictated by the geometry/ boundaries of the flow Large eddies are more anisotropic
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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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5 - 1 Turbulence mixing Turbulence mixing 4th lecture FACE 8 2007 Turbulence mixing 2 Program 08:15-08:45 08:45-09:00 09:00-09:15 09:15-10:00

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