NUS Turbulence
Workshop, Aug. ‘04
Large Eddy Simulation in Aid of RANS Modelling
M A Leschziner
Imperial College London
RANS/LES simulation of flow
around a highly-swept wing
Collaborators
Lionel Temmerman
Anne Dejoan
Sylvain Lardeau
Chen Wang
Ning Li
Fabrizio Tessicini
Yong-Jun Jang
Ken-ichi Abe
Kemo Hanjalic
The Case for RANS
RANS may be something of a ‘can of worms’, but is here to stay
Decisive advantages:
 Economy, especially in
 statistical homogeneous 2d flows
 when turbulence is dominated by small, less energetic scales
 in the absence of periodic instabilities
 Good performance in thin shear and mildly-separated flows, especially
near walls
Predictive capabilities depend greatly on
 appropriateness of closure type and details relative to flow characteristics
 quality of boundary conditions
 user competence
Challenges to RANS
Dynamics of large-scale unsteadiness and associated non-locality
Massive separation – large energetic vortices
Unsteady separation from curved surfaces
Reattachment (always highly unsteady)
Unsteady instabilities and interaction with turbulence
Strong non-equilibrium conditions
Interaction between disparate flow regions

post reattachment recovery

wall-shear / free-shear layers
Highly 3d straining – skewing, strong streamwise vorticity
Separation from Curved Surfaces - Tall Order for RANS?
LES instantaneous realisations
AL model with k - w equation
Reverse flow
Y/H
(Separation : X/H = 0.26, Reattachment : X/H = 4.7)
3
RANS
2
1
X/H
0
0
1
2
3
4
5
6
7
8
9
Dynamics of Separated Flow
Steady
Unsteady
Separation
Dynamics of Separated Flow
Steady Reattachment
Attached
Recovery
RANS Developments
Desire to extent generality drives RANS research
 Non-linear eddy-viscosity models
 Explicit algebraic Reynolds-stress models
 Full second-moment closure
 Structure-tensor models
 multi-scale models…
Simulation plays important role in aiding development and validation
Traditionally, DNS for homogeneous and channel flow at low Re
used
Increasingly, LES exploited for complex flow
The Argument for Resolving Anisotropy
Generalised eddy-viscosity hypothesis:
 U i U j
ui u j   t 

xi
 xi
 2
  k ij ; U i  {U ,V ,W }; xi  {x, y, z}
 3
Wrongly implies that eigenvalues of stress and strain tensors aligned
Wrong even in thin-shear flow:
Channel flow
2
u 2  v 2  w2  k
3
Which is
wrong
u2
v2
The Argument for Resolving Anisotropy
Exact equations imply complex stress-strain linkage
U j

U i 
 uiu j 
    uiuk
+ u j uk
    Body -force production
 xk
 xk 

Pij
Analogous linkage between scalar fluxes and production

 ui 
     uiuk


U i 
+ ui
     Body -force production
 xk
 xk 
Pu 
i
Can be used to demonstrate
 Origin of anisotropy in shear and normal straining
 Experimentally observed high sensitivity of turbulence to curvature, rotation,
swirl, buoyancy and and body forces
 Low generation of turbulence in normal straining
 Inapplicability of Fourier-Fick law for scalar/heat transport
 Inertial damping of near-wall turbulence by wall blocking
Reynolds-Stress-Transport Modelling
Closure of exact stress-transport equations
Duiu j
Dt
U j

U i 
=   uiuk
+ u j uk
  Redistribution
 xk
 xk 

Cij  AdvectiveTransport
Pij  Production
 Diffusion  Dissipation
Modern closure aims at realisability, 2-component limit, coping
with strong inhomogeneity and compressibility
Additional equations for dissipation tensor
 ij
At least 7 equations in 3D
Numerically difficult in complex geometries and flow
Can be costly
Motivated algebraic simplifications
Homogeneous Straining
Axisymmetric expansion
Homogeneous Straining
Homogeneous shear and plain strain
Near-Wall Shear
Channel flow
Explicit Algebraic Reynolds-Stress Modelling
Arise from the explicit inversion of
Duiu j
Dt
Cij  AdvectiveTransport
U j

2 Dk
U i 

 ij =   uiuk
+ u j uk
  Redistribution
3 Dt
 xk
 xk 

Pij  Production
0
 Diffusion  Dissipation
Transport of anisotropy (and shear stress) ignored
Redistribution model linear in stress tensor
Lead to algebraic equations of the form uiu j  f (Sij , ij .....k ,  )
Most recent variant: Wallin & Johansson (2000)
Recent modification (Wallin & Johansson (2002/3)):
approximation of anisotropy transport by reference to streamlineoriented frame of reference
Non-linear EVM
Constitutive equation
 Sij
a  2 t s
 ui u j

 k


 ij 
3

2
ij
 1 (s 2  13 {s 2 }I )   2 (ws  sw ) 
  3 (w 2  13 {w 2 }I )
Quadratic
  1{s 2 }s   2 {w 2 }s
Quasi-cubic
  3 (w 2 s  sw 2  {w 2 }s  23 {wsw}I )
  4 (ws 2  s 2 w )
Cubic (=0 in
2d)
Transport equation for turbulence energy and length-scale
surrogate (ε, ω…)
Coefficients determined by calibration
Large Eddy Simulation – An alternative?
Superior in wall-remote regions
Resolution requirements rise only with Re 0.4
Near wall, resolution requirement rise with Re 2
Near-wall resolution can have strong effect on separation process
Sensitivity to subgrid-scale modelling
At high Re, increasing reliance on approximate near-wall
treatments
 Wall functions
 Hybrid RANS-LES strategies
 DES
 Immersed boundary method
 Zonal schemes
Spectral content of inlet conditions
Achilles heal of
LES
Realism of LES – Channel Constriction
Effects of Resolution – no-slip condition
x=2h
x=6h
Re=21900
Distance of nodes closest to wall
5
y/H
4
Sensitivity of Reattachment to Separation
Abe, Jang and Leschziner
3
2
1
0
0
10
x/H
20
Δxreat=7 Δxsep
0.4
0.05
30
Realism of LES – Channel Constriction
Effects of near-wall treatment (WFs) on 0.6M mesh
Realism of LES – Channel Constriction
Sensitivity to SGS modelling
Realism of LES – Stalled Aerofoil
High-lift aerofoil – an illustration of the resolution problem
Re=2.2M
Experiments
Realism of LES – Stalled Aerofoil
High-lift aerofoil
Realism of LES – Stalled Aerofoil
Effect of the spanwise extent
Realism of LES – Stalled Aerofoil
5
• Mesh 1: 320 x 64 x 32 = 6.6 • 10 cells
Effect of the mesh
6
• Mesh 2: 768 x 128 x 64 = 6.3 • 10 cells
6
• Mesh 3: 640 x 96 x 64 = 3.9 • 10 cells
6
• Mesh 4: 1280 x 96 x 64 = 7.8 • 10 cells
Streamwise velocity at x/c = 0.96
Prediction of the friction coefficient
High-Lift Aerofoil - RSTM & NLEVM
RSTM
NLEVM
The Case for LES for RANS Studies
Experiments traditionally used for validation
 Very limited data resolution
 Boundary conditions often difficult to extract
 Errors – eg 3d contamination in ‘2d’ flow
 Reliance on wind-tunnel corrections
Example: 3d hill flow (Simpson and Longe, 2003)
Y
Mid Coarse Grid
Tauw vector
Z
X
TAUW
0.006
0.0055
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
New Experimental Information
Flow visualisation vs. LDV
1.2
0.3 Uref
x/H  0.18
separation in oilflow
1
-2
TKE contour, velocity
vector and streamline
+
yL = 145 micron, y = 8 based on 2D Utau
-1.8
TKE/Uref 2
-1.6
4.37E-02
4.12E-02
3.87E-02
3.62E-02
3.37E-02
3.12E-02
2.87E-02
2.62E-02
2.37E-02
2.12E-02
1.87E-02
1.62E-02
1.37E-02
1.12E-02
8.65E-03
-1.4
z/H
-1.2
-1
-0.8
-0.6
0.8
Uref
-0.4
-0.2
y/H
0
x/H  0.7
attachment in oilflow
0.6
0
0.5
1
1.5
2
x/H
x/H  2.0
attachment in oilflow
Large bump#3
0.4
Separation in
CCLDV data
0.2
x/H  1.5
separation in oilflow
0
0
0.2
0.4
0.6
0.8
1
x/H
1.2
1.4
1.6
1.8
2
The Case for LES for RANS Studies
Well-resolved LES a superior alternative
 Close control on periodicity and homogeneity
 Reliable assessment of accuracy
 SGS viscosity and stresses relative to resolved
 Spectra and correlations
 Ratio of Kolmogorov to grid scales
 Balance of budgets (eg zero pressure-strain in k-eq.)
 Reliable extraction of boundary conditions
 Second and possibly third moments available
 Budgets available
Attention to resolution and detail essential
LES for RANS Studies
Considered are five LES studies contributing to RANS
 2d separation from curved surfaces
 3d separation from curved surfaces
 Wall-jet
 Separation control with periodic perturbations
 Bypass transition
Study of Non-Linear EVMs for Separation
Constitutive equation
 Sij
a  2 t s
 ui u j

 k


 ij 
3

2
ij
 1 (s 2  13 {s 2 }I )   2 (ws  sw ) 
  3 (w 2  13 {w 2 }I )
Quadratic
  1{s 2 }s   2 {w 2 }s
Quasi-cubic
  3 (w 2 s  sw 2  {w 2 }s  23 {wsw}I )
  4 (ws 2  s 2 w )
Cubic (=0 in
2d)
2C-Limit Non-linear EVM
Recent forms aim to adhere to wall-asymptotic behaviour
Example: NLEVM/EASM of Abe, Jang & Leschziner (2002)
 Anisotropy cannot be represented by functions of
Sij , ij alone
 Thus, addition of near-wall-anisotropy term, calibrated by reference
to channel-flow DNS
 Involve “wall-direction indicators”, d i , Kolmogorov as well as macro
time scales and viscous-damping function
aij  1aij  2 aij  w aij



aij  Cd f w ( Rt )  di d j  ij d k d k   f  d Sij , d ij ,invariants 
3


ld
Ni
l
di 
Ni  d ld - wall distance
xi
Nk Nk
w
2C-Limit Non-Linear EVM
Performance of AJL model in channel flow ( and  variants) by
reference to DNS
2C-Limit Non-linear EVM
Performance of AJL model in channel flow ( and  variants)
Turbulence
energy
budget
w

A-priori Study of Non-Linear EVMs
Quadratic terms represent anisotropy
‘cubic’ terms represent curvature effects
Example:
 Streamwise normal stress across separated zone
2d periodic hill,
Re=21500
 Accurate simulation data used for model investigation

Modelled stresses determined from constitutive equation with
mean-flow solution inserted

Comparison with simulated stresses

Linear, quadratic and cubic contributions can be examined
separately
Jang et al, FTC, 2002
Highly-Resoved LES Data
Two independent simulations of 5M mesh
Highly-Resolved LES Data
Turbulence-energy budget at x/h = 2.0
Near-wall velocity profiles at 3
streamwise locations (wall units)
IJHFF (2003), JFM (2005)
Highly-Resolved LES Data - Animations
U-velocity
Q-criterion
W-velocity
Pressure
Streamlines
5
4
Abe, Jang and Leschziner
y/H
3
2
1
0
LES solution (Temmerman & Leschziner, 2001)
(Separation : X/H = 0.22, Reattachment : X/H = 4.72)
Y/H
0
10
20
x/H
30
RSM (Jakirlic & Hanjalic, 1995)
(Separation : X/H = 0.26, Reattachment : X/H = 5.9)
Y/H
3
3
LES
2
2
1
1
X/H
0
0
1
2
3
4
5
6
7
8
9
0
k -  (Launder & Sharma, 1974) (LS)
(Separation : X/H = 0.35, Reattachment : X/H = 3.42)
Y/H
X/H
0
1
2
3
4
5
6
7
8
9
Cubic k -  (Apsley & Leschziner, 1998) (AL)
(Separation : X/H = 0.26, Reattachment : X/H = 5.3)
Y/H
3
3
k-
2
2
1
1
X/H
0
0
1
2
3
4
5
6
7
8
9
0
Cubic k -  (Craft, Launder & Suga, 1996) (CLS)
(Separation : X/H = 0.26, Reattachment : X/H = 5.9)
Y/H
3
2
2
1
1
X/H
0
1
2
3
4
5
6
7
1
8
9
2
3
4
5
6
7
8
9
Abe k - w
(Separation : X/H = 0.31, Reattachment : X/H = 4.90)
Y/H
3
0
X/H
0
Abe et al
X/H
0
0
1
2
3
4
5
6
7
8
9
Velocity Profiles
(x/h=2.0)
(x/h=6.0)
LS- 
AL- 
WJ- w
CLS- 
AJL- w
LES
LS- 
AL- 
WJ- w
CLS- 
AJL- w
LES
-0.2
0
0.2
0.4 0.6
U/Ub
0.8
1
-0.2
0
0.2
0.4 0.6
U/Ub
0.8
1
Shear-Stress Profiles
3
(x/h=2.0)
(x/h=6.0)
LS- 
AL- 
WJ- w
CLS- 
AJL-w
LES
LS- 
AL- 
WJ- w
CLS- 
AJL-w
LES
2.5
2
1.5
1
0.5
0
-0.04
-0.02
uv/U2b
0
0.02 -0.04
-0.02
uv/U2b
0
0.02
A-priori Study – modelled vs. simulated stresses
Linear EVM
Symbols : a-priori analysis
Lines
: LS model
(X/H=2.0)
L*
L
L*
L**
L
L*
ñ 2/3k
L **
*
L *
L *
L *
ñ L
L *
L *
L *
L
*
ñ uu(=2/3k+L)
L
**
L
L
**
L
L
uu-2/3k (actual
L
**
L
L
**
L
L
**
L
L
*
L
L **
L
**
L
L
**
L
L
*
L
*
L
L
**
L
*
L
*
L
L
**
L
*
L
*
L
L **
3
2.5
Y/H
2
1.5
1
0.5
0
0
0.02 0.04 0.06 0.08
0.1
2/3k, mean strain and normal stress
Symbols : a-priori analysis
Lines
: Abe-w model
3
2.5
Y/H
2
1.5
1
0.5
0
LES)
L
L
L
(X/H=2.0)
(X/H=2.0)
LS model
a-priori analysis
uu-2/3k (actual LES)
L
L
L
uu
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
0
0.01
0.02
(L=)Linear term of uu/U2b
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
LS model
a-priori analysis
Actual LES
L
L
L
L
L
L
L
L
L
L
L
L
L
-0.04 -0.03 -0.02 -0.01
uv/U2b
L
L
L
0
uv
0.01
0.02
Quadratic 2c limit EVM Abe,Jang &Leschziner, 2003
L
* (X/H=2.0)
L
L* *
L*
L
L **
ñ 2/3k
L *
*
L *
L *
L *
ñ L+Q
L
L **
L
**
L
ñ uu(=2/3k+L+Q)
L
**
L
L
**
L
L
uu-2/3k (actual LES)
L
**
L
L
**
L
L
**
L
L
**
L
L
**
L
L
**
L
L
L
**
L
*
L
*
L
L
**
L
*
L
L
**
L
L
**
L
*
*L
0
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
0.02
0.04
0.06
0.08
0.1
2/3k, mean strain and normal stress
(X/H=2.0)
(X/H=2.0)
Abe-w model
a-priori analysis
Abe-w model
a-priori analysis
uu
(quadr)
uu
(linear)
0
0.01
0.02
(L=)Linear term of uu/U2b
0.03
0
0.01
0.02
(Q=)Quadratic term of uu/U2b
0.03
A-priori Study – modelled vs. simulated stresses
Linear EVM
Symbols : a-priori analysis
Lines
: LS model
(X/H=2.0)
L*
L
L*
L**
L
L*
ñ 2/3k
L **
*
L *
L *
L *
ñ L
L *
L *
L *
L
*
ñ uu(=2/3k+L)
L
**
L
L
**
L
L
uu-2/3k (actual
L
**
L
L
**
L
L
**
L
L
*
L
L **
L
**
L
L
**
L
L
*
L
*
L
L
**
L
*
L
*
L
L
**
L
*
L
*
L
L **
3
2.5
Y/H
2
1.5
1
0.5
0
LES)
3
2.5
Y/H
2
1.5
1
0.5
0
L
L
0
0.02 0.04 0.06 0.08
0.1
2/3k, mean strain and normal stress
Symbols : a-priori analysis
Lines : CLS model
L*
L
L*
L*
L **
L *
L *
*
L *
L *
L
**
L
L
**
L
L
**
L
L
**
L
L
L
**
L
L
**
L
L
*
L
**
L
L
**
L
L
**
L
L
L
**
L
*
L
L **
L
L *
L*
L**
L
L *
L *
L *
L **
*L
0
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
(X/H=2.0)
(X/H=2.0)
LS model
a-priori analysis
uu-2/3k (actual LES)
L
L
L
L
L
L
uu
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
0
0.01
0.02
(L=)Linear term of uu/U2b
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
LS model
a-priori analysis
Actual LES
L
L
L
L
L
L
L
L
L
L
L
uv
L
L
L
L
-0.04 -0.03 -0.02 -0.01
uv/U2b
L
0
0.01
0.02
Cubic EVM Craft, Launder & Suga, 2003
(X/H=2.0)
ñ 2/3k
ñ L+Q+C
(X/H=2.0)
(X/H=2.0)
(X/H=2.0)
CLS model
a-priori analysis
CLS model
a-priori analysis
CLS model
a-priori analysis
ñ uu(=2/3k+L+Q+C)
uu-2/3k (actual LES)
0.02
0.04
0.06
0.08
0.1
2/3k, mean strain and normal stress
uu
(linear)
0
0.01
0.02
(L=)Linear term of uu/U2b
uu
(‘cubic’)
uu
(quadr)
0.03
0
0.01
0.02
(Q=)Quadratic term of uu/U2b
0.03
0
0.01
0.02
(C=)Cubic term of uu/U2b
0.03
A-priori Study – modelled vs. simulated stresses
Linear EVM
Symbols : a-priori analysis
Lines
: LS model
(X/H=2.0)
L*
L
L*
*
L
L*
L*
ñ 2/3k
L **
*
L *
L *
L *
ñ L
L *
L *
L *
L
*
ñ uu(=2/3k+L)
L
**
L
L
**
L
L
uu-2/3k (actual
L
**
L
L
*
L
**
L
L
**
L
L
L **
L
**
L
L
**
L
L
*
L
*
L
*
L
*
L
L
**
L
L
**
L
*
L
*
L
L **
3
2.5
Y/H
2
1.5
1
0.5
0
2.5
Y/H
2
1.5
1
0.5
0
L*
L
L*
L*
L*
*
L*
L*
L*
L*
L*
L*
L *
L *
L *
L *
L *
L *
L *
L *
L
L **
L
L **
L *
L *
L *
L *
L *
L
L **
L
L **
L *
L
L *
L **
L
L *
L *
L **
L *
L *
L*
L
L
0
L
LS model
a-priori analysis
uu-2/3k (actual LES)
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
LS model
a-priori analysis
Actual LES
L
uv
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
0
0.01
0.02
(L=)Linear term of uu/U2b
L
L
L
L
L
L
L
L
L
L
L
L
L
-0.04 -0.03 -0.02 -0.01
uv/U2b
L
L
L
0
0.01
0.02
Explicit ASM Wallin &Johansson, 2000
(X/H=2.0)
*
(X/H=2.0)
(X/H=2.0)
uu
LES)
0
0.02 0.04 0.06 0.08
0.1
2/3k, mean strain and normal stress
Symbols : a-priori analysis
Lines
: WJ-LS model
3
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
L
ñ 2/3k
ñ L+Q
(X/H=2.0)
(X/H=2.0)
WJ-LS model
a-priori analysis
WJ-LS model
a-priori analysis
ñ uu(=2/3k+L+Q)
uu-2/3k (actual LES)
0.02
0.04
0.06
0.08
0.1
2/3k, mean strain and normal stress
uu
(linear)
0
0.01
0.02
(L=)Linear term of uu/U2b
uu
(quadr.)
0.03
0
0.01
0.02
(Q=)Quadratic term of uu/U2b
0.03
3D-Hill - Motivation
Efforts to predict flow around 3d hill with anisotropy-resolving closures
Y
Z
X
3
-4
1
y/H
2
-2
0
0
0
x/H 2
4
6
4
8
2
z /H
6
LDA Experiments by Simpson et al (2002)
Re=130,000, boundary-layer thickness = 0.5xh
Computations with up to 170x135x140 (=3.3 M) nodes
Several NLEVMs and RSTMs
Topology – Experiment vs. NLEVM Computation
Y
Mid Coarse Grid
Tauw vector
Z
X
TAUW
0.006
0.0055
0.005
0.0045
0.004
0.0035
0.003
0.0025
0.002
0.0015
0.001
0.0005
0
Chen et al, IJHFF, 2004
Pressure and Skin Friction on Centreline
0.6
AJL- w
AL- 
SSG- 
WJ- w
Exp., z>0
Exp., z<0
0.05
0.4
0.2
0.04
0
U /U ref
Cp
-0.2
AJL- w
AL- 
SSG- 
WJ- w
Exp.
-0.4
-0.6
0.03
-0.8
-1
-1.2
-2
0.02
-1
0
1
2
x/H
3
4
5
6
0
0.5
1
1.5
z/H
2
2.5
3
Corrected Experimental Information
1.2
0.3 Uref
1
y/H
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x/H
1.2
1.4
1.6
1.8
2
3D Hill - LES
Can origin of discrepancies be understood?
Wall-resolved LES at Re=130,000 deemed too costly
LES and RSTM computations undertaken at Re=13,000
Identical inlet conditions as at Re=130,000
Grid: 192 x 96 x 192 = 3.5M cells (y+=O(1))
LES scheme
 Second-order + ‘wiggle-detection’, fractional-step, AdamsBashforth
 Solves pressure equation with SLOR + MG
 Fully parallelised
 WF and LES/RANS hybrid near-wall approximations
 SGS models: Smag + damping, WALE
Temmerman et al,
ECCOMAS, 2004
Computational Aspects - LES
Re=13000 128 x 64 x 128 cells
CFL=0.2
d=0.003
CPU cost: 32 x 30 CPUh on Itanium2 cluster
Statistics connected over 10 flow-through times, after initial 6 initial
sweeps
Near-wall grid:
Overall View - LES
Short-span integral of skin-friction lines
LES / RANS Comparison – topology maps
LES /RANS Comparisons – pressure & skin friction
LES – subgrid-scale viscosity
LES/RANS – cross-sectional flow field
x/h = 1.5625
AL Model
U: -0.10 -0.01 0.08 0.17 0.26 0.35 0.44 0.53 0.61 0.70 0.79 0.88 0.97 1.06 1.15
x/h = 1.5625
SSG+Chen Model
U: -0.10 -0.01 0.08 0.17 0.26 0.35 0.44 0.53 0.61 0.70 0.79 0.88 0.97 1.06 1.15
LES/RANS – cross-sectional flow field
x/h = 2.8125
AL Model
U: -0.10 -0.01 0.08 0.17 0.26 0.35 0.44 0.53 0.61 0.70 0.79 0.88 0.97 1.06 1.15
x/h = 2.8125
SSG+Chen Model
U: -0.10 -0.01 0.08 0.17 0.26 0.35 0.44 0.53 0.61 0.70 0.79 0.88 0.97 1.06 1.15
LES / RANS Comparison – streamwise velocity
LES / RANS Comparison – turbulence energy
Subgrid-scale energy
LES, Re=130,000 – near-wall grid
Grid: 192 x 96 x 192 cells
LES / RANS Comparison, Re=130,000 – pressure coefficient
LES /RANS Comparison, Re=130,000 – Topology maps
RANS
LES
LES / RANS Comparison, 130,000 - velocity
LES / RANS Comparison, 130,000 - velocity
Wall Jet
Motivation
 RANS models perform poorly in ‘interactive’ flows
 Example: post-reattachment recovery
 Key feature: interaction between upper (free) shear layer
and developing boundary layer
 Wall jet is a similar ‘interactive’ flow
 LES solutions allow physics of interaction to be studied
 Budgets allow a-priori studies of closure assumptions
 Requirements for highly-resolved LES
 Simulations for real wall as well as shear-free wall
 allow viscous and blocking effects to be separated
Dejoan & Leschziner, PoF, 2005
Wall Jet
Geometry and flow conditions
Grid: 420x208x96
Wall Jet
Time evolution
Grid: 420x208x96
Wall Jet
Resolution indicators
Wall Jet
Q-structure criterion
Wall Jet
Log law & Equilibrium
Wall Jet
Shear-strain / stress dislocation
Wall Jet
Stress diffusion and budgets
Wall Jet
Comparison of stresses: AJL NLEVM / SSG RSTM / LES
Wall Jet
Comparison of budgets: SSG RSTM / LES


xk

k u2u2 
 Cd uk ul



x
l


Wall Jet
Comparison of budgets: SSG RSTM / LES


xk

k u1u2 
 Cd uk ul



x
l


Wall Jet
Comparison of stress diffusion: SSG RSTM / LES
Transitional Wake-Blade Interaction - NLEVM
Key issue: unsteady transition in high-pressure turbine blades
Lardat &
Leschziner, J AIAA,
C&F, FTC, 2004
Transitional Wake-Blade Interaction - NLEVM
Unsteady wake-induced separation on suction side
Transitional Wake-Blade Interaction - NLEVM
Time-space representation of shape factor (unsteady transition)
Bypass Transition
Experimental evidence: substantial ‘turbulence’ ahead of ‘transition’
T3A
Concept of laminar turbulence
Necessity to include a specific transport equation for so-called
“laminar-kinetic energy” fluctuations (Mayle and Schulz, 1997)
Dkl
kl
k
 Pk ,l   2  2 2
Dt
y
y
In laminar region, shear production assumed = 0; rise in k attributed
to k- diffusion by pressure fluctuation (pressure diffusion)
Model proposed:
Pk ,l  Cw
U 2

k  k e
 y / C 
LES of Bypass Transition
Finite-volume code, second order in time and space
Localized Lagrangian-averaged dynamic eddy-viscosity model
Re=500 (based on displacement thickness * at the inflow)
Correlated perturbation field in the free-stream, with a specified
energy spectrum
Dimension of the domain : (Lx,Ly,Lz)=(200*,40*,35*),
(nx,ny,nz)=(256,84,92)
LES of transition over a flat plate
Streamwise fluctuations in the near-wall region
LES of transition over a flat plate
Turbulence budgets in the transitional region
New transition-specific model
T3A
T3B
New transition-specific model
T3A
T3B
New transition-specific model
VKI blade test case, TUFS = 1%
Displacement thickness
Momentum thickness
Shape factor
New transition-specific model
VKI blade test case, TUFS = 1%
Turbulence energy profiles along the suction side of the blade
Separation Control
Context: flow control
 Reducing recirculation by external periodical forcing
 Exploiting sensitivity of mean flow and turbulence to forcing frequency
Specific motivation of study
 Ability of URANS to emulate response observed experimentally and in
simulations
 Challenge: coupling between turbulence time scale and perturbation
time scale
Subject of study
 External periodical forcing by mass-less jet applied to a separated flow
over a backward-facing step
 Assessment of URANS modelling by reference to well-resolved LES
data and experiment
Dejoan & Leschziner, IJHFF, 2004,
ASME FED, 2004
Separation Control - LES
Expts. by S.Yoshioka, S. Obi andS. Masuda (2001))
Inlet channel:
-3h <x<0, 0<y<2
Downstream the step:
0<x<12h; -h<y<2h
Spanwise direction
homogeneous, Lz=4p/3
Reynolds number: Re=Uc h / =3700
Strouhal number:
St=fe h / Uc = 0.2
Optimum frequency
Separation Control - Effect on Recirculation Length
St
Exp.
LES
LS
AJL-
0.0
x r,o=5.5 h
x r,o=7 h
x r,o=6.5 h
x r,o=8 h
0.2
x r=3.8 h
x r=5.5 h
x r=4.6 h
x r=5.5 h
Skin Friction Coefficient
Separation Control – Effect on Shear Stress
LES
LS
model
Separation Control – Effect on Shear Stress
LES
AJL-
model
Separation Control – Phase-Averaged Features
Streamlines
Reynolds Shear Stress
Separation Control – Phase-Averaged Features
Streamline
Reynolds Shear Stress
Separation Control – Phase-Averaged Features
Streamline
Reynolds Shear Stress
Concluding Remarks
RANS will remain principal approach for many years to come
Recognised by industry – hence increased interest in model
generality
Research pursued on two-point closure, structure modelling, multilength-scale modelling…. but practical prospects are uncertain
Progress is incremental, slow and costly
Serious model improvements must encompass a broad range of
conditions – homogeneous 1D flows to complex 3D flows
There is a need to extend further efforts to complex 3D conditions
– the real challenge
Concluding Remarks
LES (& hybrid LES/RANS) of increasing interest – periodicity, shedding,
large-scale motion
LES is no panacea and faces significant obstacles in near-wall flows
Poses serious problems in high-Re conditions – wall resolution, grid,
cost…
LES can play a very useful role in support of RANS modelling
 elucidating physics
 providing wealth of data for validation and a-priori study of closure
proposals, especially budget
Necessarily a very costly approach, because of resolution demands
 can only be done at relatively low Re
Hybrid RANS / LES strategies hold some promise, but difficult
 very active area of research
NUS Turbulence
Workshop, Aug. ‘04
Near-Wall Modelling in LES
M.A. Leschziner
Imperial College London
Hybrid RANS-LES
Wall resolved LES is untenable in high-Re near-wall flow
Near-wall treatment is key to utility of LES in practice
Several approaches:
 Wall functions
 Zonal methods – thin-shear-flow equations near wall
 Hybrid RANS-LES (+ synthetic turbulence)
All pose difficult fundamental and practical questions:
 Compatibility of averaging with filtering
 Applicability of RANS closure – time-scale separation
 Interface conditions
LES / Wall-Functions
Channel flow, Re=12000, 96x64x64 grid
LES / Wall-Functions
2d hill flow, Re=2.2x104, 0.6M nodes
LES / Wall-Functions
Hydrofoil trailing edge, Re=2x106, 384x64x24 grid
Hybrid RANS-LES
Methodology
Interface
conditions
Superimposed
RANS layer
Target
 Velocity
U
RANS
int
 Turbulent viscosity
 Turbulence energy
U
LES
int
LES
 tRANS


,int
t ,int
k
RANS
mod,int
k
LES
mod,int
Hybrid RANS-LES
Implementation

RANS
mod


RANS
mod
 C l k
LES
mod
C ,int 
0.5

or
LES
 mod,int
0.5
l k RANS
,int
RANS
mod
 C k /
< . > : spatial average
in the homogeneous directions.
Alternative: instantaneous value
C ( y )  0.09   C ,int
2
1  exp   y   
 0.09 
1  exp   yint int  
Hybrid RANS-LES
Typical variation of mean C
model
at interface
in channel flow , 1-eq. RANS
across RANS layer
Hybrid RANS-LES
Variations of mean and instantaneous C in channel flow, 1-eq.
RANS model
Hybrid RANS-LES
Channel flow, Re=42200
64  64  32
512  128  128

yint
 135 - j  17
Hybrid RANS-LES
Channel flow, Re=42200
Resolved
Modelled
DES
Hybrid RANS-LES
Channel flow, Re=42200, velocity and shear stress distributions
for two interface positions
Hybrid RANS-LES
Variations of mean and instantaneous C in channel flow, 2-eq.
RANS model, Re=2000
Hybrid RANS-LES
Velocity in channel flow, 2-eq. RANS model, Re=2000, average
and instantaneous input of C
Hybrid RANS-LES
Structure (streamwise vorticity) in channel flow, 2-eq. RANS
model, Re=2000
Interface y+=120
Interface y+=610
Hybrid RANS-LES
2d-hill flow, Re=21500, interface conditions
Grid: 112x64x56=4x105
against reference of 4.6x106
Hybrid RANS-LES
2d-hill flow, Re=21500, variations of C
Hybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity against log-law
Hybrid RANS-LES
2d-hill flow, Re=21500, variations of turbulent viscosity
Two-Layer Model
Methodology
Low-Re solution
In sublayer
Two-Layer Model
Methodology
 Near-wall control volume
divided into subgrid volumes
 Transport equations solve
across the subgrid for:
Mean-flow parameters: U, W
 Wall-normal V-velocity from
continuity within subgrid
Two-Layer Model
Methodology
Wall-parallel pressure
gradient (dP/dx) calculated
from main-grid and assumed
constant across subgrid
 wall calculated from subgridPk , 
solution
 wall applied to main-grid as in
standard wall-function
treatments
U
U
U
dP  
U 
 V

   t 
x
y
dx y 
y 
Two-Layer Model
Numerical solution in sublayer

Similar to 1-D convection-diffusion problem

Finite-volume method

Central differences for diffusion and for convection

Tri-diagonal matrix algorithm

Average solution in time

No need to solve Poisson equation

Very fast!
Desider: 6 month meeting
Two-Layer Model
Trailing-edge separation from
hydrofoil; Re=2.2x106
 512x128x24 nodes
Comparison with highly-resolved
LES by Wang, 1536x96x48 nodes

 Sub-layer thickness y  40
Streamwise velocity
pressure
Two-Layer Model
Streamwise-velocity contours
Wall model
Two-Layer Model
Velocity magnitude
B
C
D
X/h
|U|/U_e
Full LES
Wall model (dynamic SGS)
E
F
G
Two-Layer Model
Turbulence energy
Full LES
Wall model (dynamic SGS)
Two-Layer Model
Streamwise velocity in wake
Full LES
Wall model (dynamic SGS)
Two-Layer Model
Skin friction
Full LES
Wall model (dynamic SGS)
Concluding Remarks
The jury is out on the prospect of approximate wall modelling as a
general approach
There is evidence that some offer ‘credible’ solutions and gains in
economy
There is a price to pay (sometimes high) in terms of physical
realism (e.g. near-wall structure)
Particular problem: loss of small-scale near-wall components
It is not clear what to do in very complex near-wall flow –
separation, severe 3d straining
Particular problems when near-wall flow has a strong effect on
global flow features
Hybrid RANS-LES and zonal modelling work, but much more
research is required to identify applicability and limitations