Introduction to turbulence and turbulence modeling

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Introduction to turbulence and turbulence modeling
Henry Chang University of Texas, Austin
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Outline

• Turbulence phenomenon
• Levels of modeling
• Computer simulation methods

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Turbulence Phenomenon

• Regimes of fluid flow
• Turbulent flows are ubiquitous
• Characteristics of turbulence
• Chaotic (seemingly random) fluctuations
• Vortical structures
• Large range of scales
• 3 dimensional
• High Reynolds number VL/n
• High dissipation and mixing

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Levels of modeling

• Particle physics
• Quantum mechanics
• Molecular dynamics
• Continuum mechanics
• Navier Stokes equations

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Computer Simulation

• Discretize domain in space and time
• Solve Navier Stokes equations numerically
• 3 methods for turbulence
• Direct Numerical Simulation (DNS)
• Large Eddy Simulation (LES)
• Reynolds Averaged Navier Stokes (RANS)

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Direct Numerical Simulation

• Simulate all scales of turbulence
• Largest scale L
• Smallest scale h, known as Kolmogorov scale
• L/h O(Re3/4)
• Computation time O(Re3)
• Currently limited simple geometry, low Re,
  fundamental research

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Reynolds Averaged Navier Stokes

• Reynolds decomposition u(x,t) u(x) u'(x,t)
• Solution u contains no turbulent fluctuations
• Closure problem depends on
• Reynolds stress must be modeled
  averaged effect of fluctuations of all time
  scales
• Well-suited for steady flow engineering problems

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Large Eddy Simulation

• Simulate only the large scale fluctuations model
  the small scales
• Large scales defined through filter G
• Example Top-hat filter
• G(x-x') 1/D if x-x' lt D/2 (zero
  otherwise)
• D is filter width, often equal to cell width

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Large Eddy Simulation

• Filter Navier Stokes equation
• Subgrid stress tensor
  modeled averaged effect of all subgrid scale
  fluctuations
• Unsteady flows, possibly more general classes of
  problems and geometries

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Errors in simulations

• Continuous space/time domain approximated by
  finite number of spatial points and time steps
• Differential or integral equations approximated
  by numerical schemes
• Continuous range of fluctuation scales
  approximated by finite number of scales (not
  applicable to RANS)
• Closure modeling for small scale fluctuations
  (not applicable to DNS)

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References

• Pierre Sagaut, Large Eddy Simulation for
  Incompressible Flows, 2nd ed., Springer, 2002.
• Robert Moser, TAM 538 Turbulence Fall 2004,
  Illini Union Bookstore.
• Stephen Pope, Ten questions concerning the
  large-eddy simulation of turbulent flows, New
  Journal of Physics 6 (2004) 35.