Turbulence Modelling: Large Eddy Simulation

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Turbulence Modelling Large Eddy Simulation
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Turbulence Modeling Large Eddy Simulation and
Hybrid RANS/LES

• Introduction
• LES Sub-grid Models
• Numerical aspect and Mesh
• Boundary conditions
• Hybrid approaches
• Sample Results

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Turbulence Structures
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Introduction LES / other Prediction Methods

• Different approaches to make turbulence
  computationally tractable
• DNS Direct Simulation.
• RANS Reynolds average (or time or ensemble)
• LES Spatially average (or filter)

LES 3D, unsteady
DNS 3D, unsteady
RANS Steady / unsteady
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RANS vs LES
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Why LES?

• Some applications need explicit computation of
  accurate unsteady fields.
• Bluff body aerodynamics
• Aerodynamically generated noise (sound)
• Fluid-structure interaction
• Mixing
• Combustion

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LES difficulties

• Cpu expensive for atmospheric modelling
• Unsteady simulation
• Turn around time is weeks/months (rans is hours
  or days)
• Cannot afford grid independence testing
• Still open research issues
• combustion, acoustics, high Prandtl, shmidt
  mixing problem, uns.
• Wall bounded flows
• Need expertise to reduce cpu, human cost
• Mesh models strategy
• Analysis of the instantaneous flow
• Knowledge about turbulent instabilities,
  turbulent structures

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Energy Spectrum
e
Eu,ET
k,f

• Large eddies
• responsible for the transports of momentum,
  energy, and other scalars.
• anisotropic, subjected to history effects, are
  strongly dependent on boundary conditions, which
  makes their modeling difficult.

• Small eddies
• tend to be more isotropic and less flow-dependent
  (universal), mainly dissipative scales, which
  makes their modeling easier.

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LES Filtering - Decomposition
Energy spectrum against the length scale
Isotropic Homogeneous Universal
Anisotropic Flow dependent
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Filtering

• The large or resolved scale field is a local
  average of the complete field.
• e.g., in 1-D,
• Where G(x,x) is the filter kernel.
• Exemple box filter G(x,x) 1/D if
  x-xltD/2, 0 otherwise

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Filtered Navier-Stokes Equations

• Filtering the original Navier-Stokes equations
  gives filtered Navier-Stokes equations that are
  the governing equations in LES.

N-S equation
Filter
Filtered N-S equation
Needs modeling
Sub-grid scale (SGS) stress
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Available SGS model

• Subgrid stress turbulent viscosity
• Smagorinsky model (Smagorinsky, 1963)
• Need ad-hoc near wall damping
• Dynamic model (Germano et al., 1991)
• Local adaptation of the Smagorinsky constant
• Dynamic subgrid kinetic energy transport model
  (Kim Menon 2001)
• Robust constant calculation procedure
• Physical limitation of backscatter

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Smagorinskys Model

• Hypothesis local equilibrium of sub-grid scales
• Simple algebraic (0-equation) model (similar to
  Prandtle Mixing length model in RANS)
• Cs 0.065 0.25
• The major shortcoming is that there is no Cs
  universally applicable to different types of
  flow.
• Difficulty with transitional (laminar) flows.
• An ad hoc damping is needed in near-wall region.
• Turbulent viscosity is always positive so no
  possibility of backscatter.

with
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Dynamic Smagorinskys Model

• Based on the similarity concept and Germanos
  identity (Germano et al., 1991 Lilly, 1992)
• Introduce a second filter, called the test filter
  with scale larger than the grid filter scale
• The model parameter (Cs ) is automatically
  adjusted using the resolved velocity field.
• Overcomes the shortcomings of the Smagorinskys
  model.
• Can handle transitional flows
• The near-wall (damping) effects are accounted
  for.
• Potential Instability of the constant

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Dynamic Smagorinskys Model

• Basic Idea consider the same smagorinsky model
  at two different scales, and adjust the constant
  accordingly
• Constant value error minimization using least
  square method and Germanos Identity

Test Filter
Grid Filter
Tij
Error minimization
?ij
Lij
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Dynamic Subgrid KE Transport Model

• Kim and Menon (1997)
• One-equation (for SGS kinetic energy) model
• Like the dynamic Smagorinskys model, the model
  constants (Ck, Ce) are automatically adjusted
  on-the-fly using the resolved velocity field.
• Backscatter better accounted for

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Mesh
Energie E(k) Dissipation D(k)

• Grid resolution
• Constraint Based on LES hypothesis
• Explicit Resolution of production mechanism
  (whereas production is modeled with RANS)
• Resolution of anisotropic and energetic large
  scales
• Cell size must be included inside the inertial
  range, in between the integral scale (L) and the
  Taylor micro-scale (l).
• Integral scale L
• Energy peaks at the integral scale. These scales
  must be resolved (with several grid points).
• Crude Estimation of L
• Use correlation (mixing layer, jet) for L
• Perform RANS calculation and compute L k3/2 / e
  

1/?
1/L
1/?
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Mesh

• Grid resolution
• Taylor micro-scale l
• Dissipation rate peaks at l.
• Not necessary to resolve l but useful to define a
  lower bound for the cell size.
• Estimation of l L ReL-1/2
• ( for an homogeneous and isotropic turbulence
  151/2 L ReL-1/2)
• Temporal resolution resolve characteristic time
  scale associated to the cell size (ie CFLU Dt /
  Dx lt1).
• As for the numerical scheme (minimization of
  numerical errors) use of hexa and high quality of
  mesh (very small deformations) is recommended

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Numerics time step

• Dt must be of the order (or even less for
  acoustic purpose) of the characteristic time
  scale t corresponding to the smallest resolved
  scales.
• As tDx/U , it correspond to approx CFL 1
  (Courant Dreidrich Levy Number) (where U is the
  velocity scale of the flow)

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Numerics discretization scheme

• Discretization scheme in space should minimize
  numerical dissipation
• LES is much more sensitive to numerical diffusion
  than RANS
• 2nd Order Central Difference Scheme (CD or BCD)
  perform much better than high order upwind scheme
  for momentum
• A commonly used remedy is to blend CD and FOU.
• With a fixed weight (G 0.8), this blending
  scheme has been found to still introduce
  considerable numerical diffusion
• Bad idea!
• Most ideally, we need a smart, solution-adaptive
  scheme that detects the wiggles on-the-fly and
  suppress them selectively.

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Boundary Conditions (LES)

• Near-wall resolving
• Near-wall modelling
• Inlet Boundary Conditions

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Inlet Boundary Conditions

• Inlet Boundary conditions
• Laminar case
• Random noise is sufficient for transition
• Turbulent case

• Precursor domain
• Realistic inlet turbulence
• Cpu cost not universal
• Vortex Method
• Coherent structures preserving turbulence
• Need to use realistic profiles (U, k, e)
  otherwise risk to force the flow
• Spectral synthesizer
• No spatial coherence
• Flexibility for inlet (profiles of full reynolds
  stress or k-e, constant values, correlation)

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Boundary Conditions

• Near Wall treatment
• 1/ Near Wall Resolving
• All the nearwall turbulent structures are
  explicitly computed down to the viscous
  sub-layer.
• 2/ Near Wall Modeling
• All the near-wall turbulent structures are
  explicitly computed down to a given y gt1
• 3/ DES
• No turbulent structures are computed at all
  inside the entire boundary layer (all B.L. is
  modeled with RANS).

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Boundary Conditions

• 1/ Near wall resolving explicit resolution of
  the boundary layer.
• Motivation separated flows, complex physics
  (turbulence control)
• High resolution requirement due to the presence
  of (anisotropic) wall turbulent structures so
  called streaks.
• Necessary to resolved correctly these near wall
  production mechanisms
• Boundary layer grid resolution
• ylt2
• Dx 50-150, Dz 15-40
• Not only wall normal constraints, but also
  Span-wise and stream-wise constraints due to the
  streaky structures

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Boundary Conditions

• Near wall modeling
• Wall function
• Schumann/Grozbach
• Instantaneous wall shear stress at walls and
  instantaneous tangential velocity in the wall
  adjacent cells are assumed to be in phase.
• Log law apply for mean velocity (necessary to
  perform acquisition)
• Werner Wengle (6.2)
• Instantaneous wall shear stress at walls and
  instantaneous tangential velocity in the wall
  adjacent cells are assumed to be in phase.
• Filtered Log law (power 1/7) applied to
  instantaneous quantities

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Hybrid LES-URANS

• Near Walls URANS 1-equation model
• Core region LES 1-equation SGS model

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Hybrid LES-URANS

• Navier Stokes time averaged in the near wall and
  filtered in the core region reads

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LES-URANS hybrid

• Use 1-equation model in both LES and URANS
  regions

LES region
RANS region
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LES-URANS hybrid

• Problems
• LES region is supplied with bad BC from the URANS
  regions
• The flow going from URANS to LES region has no
  proper time or length scale of turbulence
• Solution
• Add synthesized isotropic fluctuations as the
  source term of the momentum equations at the
  LES-URANS interface.

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Inlet BC and forcing
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LES of a realistic Car model exposed to Crosswind
35 M 65 M
Side Box (max) 8 mm 6 mm
Rear Box (max) 8 mm 6 mm
Nb Prism layer 5 5
Volume mesh Gambit  Sizing Functions  to
control both growth rate and cell size in
specified box
Rear box
Side box
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Results
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Simulation of flow over a 3D mountain
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Comparision between RANS and LES-RANS hybrid model

• RANS using SST model
• Hybrid RANS-LES model

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Conclusion

• RANS/URANS is not always reliable.
• LES is closer to reality than RANS/URANS.
• LES is computationally very expensive.
• In the absence of enough experimental data one is
  left with no choice but to use LES wherever
  feasible.