When Steady State Turbulence Models are not good Enough - When and how to use Unsteady Turbulence Models
Duhwan Lee TAESUNG Software and Engineering, INC
 
Turbulence Models
Motivation for Scale-Resolving Simulations (SRS)
• Accuracy Improvements over RANS  – Reduce uncertainty in CFD simulations relative to RANS
 – Flows with large separation zones (stalled airfoils/wings
, flow past buildings, flows with swirl instabilities, etc.)
• Additional information required  – Acoustics
RANS
• resolution of vortex required
 
Why not Unsteady RANS (URANS)
• URANS means the application of existing
conventional RANS models in unsteady mode (k-e 
SST, RSM, …) 
with strong flow instabilities
- URANS typically provides unphysical large
scales – no turbulence spectrum
tonal noise
relative to RANS but not reliably
• However – this is not a principal problem of URANS
and can be improved
Scale-Adaptive Simulation (SAS)
   
 
   
 
 j j j j k k 
U U U U     U  U U L
 x x x x x x U    


    3/ 2
 j j k j
t x L x x  
 
 
     
SAS Modell - 2D Periodic Hill
Scale-Adaptation based on t
t  = 0.045 h/U B 
SAS Modell - 2D Periodic Hill
Time averaged velocity profiles U
 
Detached Eddy Simulation (DES)
• LES „ detached “ regions. 
Switch of model:
• Different numerical treatment in RANS and LES regions.
RANS
region
Detached Eddy Simulation (DES) for SST  –   Strelets (2000)
),,max(   z  y x  
t x L x x  
            
 

t x C x x  
            
 


U k k k k   P 
t x L C x x  
            
 


Classical Derivation of LES
leads to additional stress
terms in NS equations
for Lt<
ij ij
ˆ ˆ ˆ i j ji i
t 
t x x x x x
      

SGS Models: Summary
WALE model (Nicoud & Ducros 1999) • Correct asymptotic near wall behaviour
Dynamic model (Germano et al., 1991) • Local adaptation of the Smagorinsky constant
Dynamic sub-grid kinetic energy transport model (Kim & Menon 2001) (Fluent only)
• Robust constant calculation procedure
• Physical limitation of backscatter
 
 

 
 

 
 











2
Sub-grid stress : turbulent viscosity
Periodic Channel Flow
Nx Ny Nz Lx Ly Lz x+ y1 + z+
180 Mesh 1 73 75 73 2h 2 h 15.7 0.254 7.85
590 Mesh 2 120 100 110 2h 2 h 30 1 15
• Near the wall turbulent streaks appear
• They have to be resolved to obtain
correct wall shear stress and heat
transfer
• Wall flows can only be computed with
LES for small domains and low Re
numbers
Periodic Channel Flow
U+ DNS
U+ DSM
U+ WALE
0,00E+00
1,00E+00
2,00E+00
3,00E+00
4,00E+00
5,00E+00
6,00E+00
7,00E+00
8,00E+00
9,00E+00
1,00E+01
1,00E+0
U+ DNS
U+ DSM
0,00E+00
1,00E+00
2,00E+00
3,00E+00
4,00E+00
5,00E+00
6,00E+00
7,00E+00
8,00E+00
9,00E+00
1,00E+00 1,01E+02 2,01E+02 3,01E+02 4,01E+02 5,01E+02
uu+ DNS
uu+ DSM
NACA 0012 Airfoil Noise
Velocity inlet
Pressure outlet
71.3 m/s
 
WB Unstructured Hex Mesh
Leading edge Trailing edge
• WALE LES model
• Periodicity in spanwise
Q-criterion ( 2-S2): Q=109 , colored by z-velocity:
Q-criterion
Leading edge Trailing edge
• Due to high Re number and moderate a, it looks still ok near trailing edge even
though span=0.05c
5%chord, 11M cells, t=1.5 s
Pressure and skin friction coefficients
Even on this grid cf is too low -> WMLES (see later)
0.000
0.005
0.010
0.015
0.020
Cf
x/chord
2-D RANS
WMLES: Near Wall Scaling
number
decreases with increasing Re number
• Turbulent structures inside sublayer are
damped out
get “exposed” as Re increases 
• WMLES: models small near wall structures
with RANS and only resolve larger structures
 – less dependent on Re number
• Some Re number dependence for boundary
layer remains as boundary layer thickness
decreases with Re number
WMLES-Concept  –  Algebraic Model
A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities
Mikhail L. Shur , Philippe R. Spalart , Mikhail K. Strelets , Andrey K. Travin , Int. J of Heat and Fluid Flow 29, 2008
dw  - Wall distance
  - Modified grid spacing
f d  - damping function
 
• The model has been modified and optimized for usage in ANSYS-
Fluent and ANSYS-CFX
Re τ   Cells
395 384 000 384 000 81×81×61 40.0 20.0
760 480 000 1 500 000 81×101×61 76.9 38.5
1100 480 000 4 000 000 81×101×61 111.4 55.7
2400 528 000 19 000 000 81×111×61 243.0 121.5
18000 624 000 1 294 676 760 81×131×61 1822.7 911.4
• Very large savings between
WMLES and wall-resolved LES
WMLES  –  Channel Flow Tests
WMLES  –  Channel Flow at Different Re Numbers
• Solutions at very different Re numbers look essentially identical
• Differences can only be seen near the wall.
• Visible is higher Eddy-Viscosity for higher Re number close to wall
Re =395 Re
WMLES  –  Flat Plate Grid
Normal, Spanwise)
 – Y+~0.05 (to allow for higher Re
numbers)
ΔX+  ΔY+  ΔZ+ 
 
WMLES  –  Boundary Layer
NACA0012 at 7.3 AoA, Re=1.1106 
• Skin friction coefficient on the suction side 
 
Inflow Boundary Conditions
• It is often important to specify a realistic turbulent inflow
velocity for accurate prediction of the (downstream) flow
• Two methods are available for time-dependent inflow
boundary condition for LES:

Vortex Method 
(Sergent, Bertoglio, Laurence, 2000)
Biot-Savart’s law
Vortex Method
xr
• Input from turbulence model in form of Lt and w.
• Produces Karman spectrum
  , ,
n


2
1
  ,  N 
SRS - Model Summary
• LES and WMLES assume that all wall boundary layers are
covered in unsteady Scale-Resolving mode (turbulence
structures resolved)
- LES costs excessive for moderate to high RE number wall bounded flows
- Even for WMLES, this is still very expensive, as one needs ~5000 cells to cover one
boundary layer volume ( x  x )
- On the other hand, LES of free shear flows is much less demanding
• Hybrid RANS-LES models are therefore being developed which compute all
wall boundary layers in RANS mode and switch to LES only for the free shear
flow regions
- Simulations can be performed on grids much closer to the RANS grid
- Still - expensive time integration is needed
 
Embedded/Zonal Large Eddy Simulation (ELES, ZFLES)
• Suitable if zone with high accuracy demands is embedded into larger domain which can be covered properly by RANS models
• Limited zone can then be covered by LES or Wall- Modelled WMLES model
• LES zone needs to be coupled to RANS zone through interfaces
• LES zone requires suitable (WM)LES resolution in time and space
LES zone Rest: RANS zone
 
Coupled Zonal Modelling
interaction at this interface since
models are different in Zone 1 →
2 and Zone 2 → 3
Shadow face 1 acting as B.C. for
model1 in zone2
model2 in zone3
In ELES/ZFLES e.g. MODEL2 can be LES turbulence model embedded
in a RANS or SAS model (MODEL1), or vice versa
ZONE 3
RANS Model
Embedded LES and Zonal Forced LES
• In many flows an area where (WM)LES is required is embedded in a larger RANS region
• In such cases, a zonal method is advantageous
• RANS and LES regions are separately defined and use different models
 
• Types of highly unstable flows:  –  Flows with strong swirl instabilities
 –  Bluff body flows, jet in crossflow
 –  Massively separated flows
• Physics  –  Resolved turbulence is generated quickly by flow instability
 –  Resolved turbulence is not dependent on details of turbulence in upstream RANS region (the RANS model can determine the separation point but from there ‘new’ turbulence is generated) 
• Models  –  SAS: Most easy to use as it converts quickly into LES mode, and
automatically covers the boundary layers in RANS. Has RANS fallback solution in regions not resolved by LES standards (t, x)
 –  DDES: Similar to SAS, but requires LES resolution for all free shear flows (t, x) (jets etc.)
 –  ELES: Not really required as RANS model can cover boundary layers. Often difficult to place interfaces for synthetic turbulence.
Flow Types: Globally Unstable Flows
Green-recommended, Red=not recommended
• Physics  –  Flow instability is weak – RANS/SAS models stay steady state.
 –  Can typically be covered with reasonable accuracy by RANS models.
 –  DDES and LES models go unsteady due to the low eddy-viscosity provided by the models. Only works on fine LES quality grids and time steps. Otherwise undefined behavior.
• Models  –  SAS: Stays in RANS mode. Covers upstream boundary layers in
RANS mode. Can be triggered into SRS mode by RANS-LES interface.
 –  DDES: Can be triggered to go into LES mode by fine grid and small t. Careful grid generation required. Covers upstream boundary layers in RANS mode.
 –  ELES: LES mode on fine grid and small t. Careful grid generation required. Upstream boundary layer (pipe flow) in expensive LES mode. Alternative – ELES with synthetic turbulence RANS-LES interface.
Flow Types: Locally Unstable Flows
Green-recommended, Red=not recommended
35 © 2014 ANSYS, Inc. May 15, 2014 ANSYS Confidential
• Types of marginally unstable flows:  –  Pipe flows, channel flows, boundary layers, ..
• Physics  –  Transition process is slow and takes several boundary layer
thicknesses.
 –  When switching from upstream RANS to SRS model, RANS-LES interface with synthetic turbulence generation required.
 –   RANS-LES interface needs to be placed in non-critical (equilibrium) flow portion. Downstream of interface, full LES resolution required.
• Models  –  SAS: Stays in RANS mode. Typically good solution with RANS. Can
be triggered into SRS mode by RANS-LES interface.
 –  DDES: Can be triggered to go into LES mode by fine grid and small t. Careful grid generation required. Covers upstream boundary layers in RANS mode.
 –  ELES: LES mode on fine grid and small t. Careful grid generation required. Upstream boundary layer (pipe flow) in RANS mode. Synthetic turbulence RANS-LES interface.
Flow Types: Stable Flows
Green-recommended, Red=not recommended
Globally Unstable Flow  –  Jets in Crossflow
• Problem:
heats wall
 
Generic Jet in Cross Flow Configuration
Infrared Thermography Particle Image Velocimetry
Laser Doppler Anemometry Hot and Cold Wire Measurements
 
 
Hexahedral Mesh
12,900,000 Elements
 
Scale Resolvability of Turbulence Models Q-criterion:
SAS DDES
ELES URANS
 
Hybrid Tetrahedral Mesh
 
Hybrid Cartesian Mesh
 
Time Averaged Temperature Distribution Turbulence models (on hex)
• Lateral spreading of temperature in good a greement with all three SRS
• Poor URANS prediction due to unphysical
damping of lateral jet wake movement
Meshing strategies (with SAS)
• Generally very good agreement
ter
 
Mean Thermal Efficiency on Wing Surface
 
 
 
Geometry of the Cavity
L = 5 D, W = D
Lx  x Ly x Lz = 18 D x 17 D x 9 D
M = 0.85
Inlet Side
 
Turbulent structure by q-criterion. SAS Model
 
Wave propagation by Fluctuating Density, SAS Model
 
SAS: k20  –  k25 k20
SAS: k26  –  k29 k20
Stable Flow Example
http://cfd.mace.manchester.ac.uk/twiki/bin/view/ATAAC/WebHome
• Geometry:
ness).
• Grid:
wise direction
layer (Dx/d=10, Dz/d~20, NY~40).
EU project ATAAC
Flow over a wall mounted hump
Q criterion:
53 © 2014 ANSYS, Inc. May 15, 2014 ANSYS Confidential
Flow over a wall mounted hump Wall Shear Stress and Wall Pressure
• The Re number at the
RANS-LES interface is
with a standard LES
solution smoothly across
Overall Summary
Different types of model recommended for different types of applications
Currently favored methods within ANSYS software:
• SAS – globally unstable flows
• ELES/WMLES stable flows
• Synthetic turbulence is good – but far from perfect
• WMLES requires special grid resolution – not as generic as other model
s (inherited from LES)