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Large Eddy Simulation in Aid of RANS ModellingLarge Eddy Simulation in Aid of RANS Modelling
M A Leschziner
Imperial College London
RANS/LES simulation of flow around a highly-swept wing
NUS Turbulence NUS Turbulence Workshop, Aug. ‘04Workshop, Aug. ‘04
CollaboratorsCollaborators
Lionel Temmerman
Anne Dejoan
Sylvain Lardeau
Chen Wang
Ning Li
Fabrizio Tessicini
Yong-Jun Jang
Ken-ichi Abe
Kemo Hanjalic
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
The Case for RANSThe Case for RANS
Challenges to RANSChallenges 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?Separation from Curved Surfaces - Tall Order for RANS?
0 1 2 3 4 5 6 7 8 90
1
2
3
AL model with k - equation(Separation : X/H = 0.26, Reattachment : X/H = 4.7)Y/H
X/H
Reverse flow
LES instantaneous realisations
RANS
Dynamics of Separated FlowDynamics of Separated Flow
Steady
Unsteady
Separation
Dynamics of Separated FlowDynamics of Separated Flow
Steady Reattachment
Recovery
Attached
RANS DevelopmentsRANS 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
2 ; { , , }; { , , }
3ji
i j t ij i ii i
UUu u k U U V W x x y z
x x
2 2 2 2
3u v w k
Channel flow
2u
2v
Which is wrong
Generalised eddy-viscosity hypothesis:
Wrongly implies that eigenvalues of stress and strain tensors aligned
Wrong even in thin-shear flow:
The Argument for Resolving AnisotropyThe Argument for Resolving Anisotropy
The Argument for Resolving AnisotropyThe Argument for Resolving Anisotropy
Exact equations imply complex stress-strain linkage
Analogous linkage between scalar fluxes and production
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
-
ij
j ii i k j kj
k k
P
U Uu u u u + u u Body force production
x x
-
ui
ii i k i
k k
P
Uu u u + u Body force production
x x
Reynolds-Stress-Transport ModellingReynolds-Stress-Transport Modelling
Closure of exact stress-transport equations
Modern closure aims at realisability, 2-component limit, coping
with strong inhomogeneity and compressibility
Additional equations for dissipation tensor
At least 7 equations in 3D
Numerically difficult in complex geometries and flow
Can be costly
Motivated algebraic simplifications
ijij
i j j ii k j k
k k
C AdvectiveTransport P Production
Du u U U = u u + u u Redistribution
Dt x x
Diffusion Dissipation
ij
Homogeneous StrainingHomogeneous Straining
Axisymmetric expansionAxisymmetric expansion
Homogeneous StrainingHomogeneous Straining
Homogeneous shear and plain strain
Near-Wall ShearNear-Wall Shear
Channel flow
Explicit Algebraic Reynolds-Stress ModellingExplicit Algebraic Reynolds-Stress Modelling
Arise from the explicit inversion of
Transport of anisotropy (and shear stress) ignored
Redistribution model linear in stress tensor
Lead to algebraic equations of the form
Most recent variant: Wallin & Johansson (2000)
Recent modification (Wallin & Johansson (2002/3)):
approximation of anisotropy transport by reference to streamline-
oriented frame of reference
2
3
ijij
iji j j i
i k j kk k
C AdvectiveTransport P Production
Du u U U = u u + u u Redistribution
Dt x x
Diffus
D
D
i n
k
o D
t
issipation
( , ..... , )i j ij iju u f S k
0
Non-linear EVMNon-linear EVM
Constitutive equation
Transport equation for turbulence energy and length-scale surrogate (ε, ω…)
Coefficients determined by calibration
2 211 23
2 213 3
2 21 2
2 2 2 23 3
2 24
2
( { } ) ( )
( { } )
{ } { }
( { } { } )
( )
t
a s
s s I ws sw
w w I
s s w s
w s sw w s wsw I
ws s w
ijS
2
3
i jij
k
u u
ij
Cubic (=0 in 2d)
Quadratic
Quasi-cubic
Large Eddy Simulation – An alternative?Large Eddy Simulation – An alternative?
Superior in wall-remote regions
Resolution requirements rise only with
Near wall, resolution requirement rise with
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
0.4Re2Re
Achilles heal of LES
Realism of LES – Channel ConstrictionRealism of LES – Channel Constriction
Effects of Resolution – no-slip conditionx=2h x=6h
Re=21900
Distance of nodes closest to wall
Sensitivity of Reattachment to SeparationSensitivity of Reattachment to Separation
Δxreat=7 Δxsep
x/H
y/H
0 10 20 300
1
2
3
4
5 Abe, Jang and Leschziner
0.050.4
Realism of LES – Channel ConstrictionRealism of LES – Channel Constriction
Effects of near-wall treatment (WFs) on 0.6M mesh
Realism of LES – Channel ConstrictionRealism of LES – Channel Constriction
Sensitivity to SGS modelling
Realism of LES – Stalled AerofoilRealism of LES – Stalled Aerofoil
Experiments
High-lift aerofoil – an illustration of the resolution problem
Re=2.2M
Realism of LES – Stalled AerofoilRealism of LES – Stalled Aerofoil
High-lift aerofoil
Effect of the spanwise extent
Realism of LES – Stalled AerofoilRealism of LES – Stalled Aerofoil
Effect of the mesh
Streamwise velocity at x/c = 0.96
Prediction of the friction coefficient
Realism of LES – Stalled AerofoilRealism of LES – Stalled Aerofoil
• Mesh 1: 320 x 64 x 32 = 6.6 • 105 cells
• Mesh 2: 768 x 128 x 64 = 6.3 • 106 cells
• Mesh 3: 640 x 96 x 64 = 3.9 • 106 cells
• Mesh 4: 1280 x 96 x 64 = 7.8 • 106 cells
High-Lift Aerofoil - RSTM & NLEVMHigh-Lift Aerofoil - RSTM & NLEVM
RSTM
NLEVM
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)
The Case for LES for RANS StudiesThe Case for LES for RANS Studies
X
Y
Z
TAUW0.0060.00550.0050.00450.0040.00350.0030.00250.0020.00150.0010.00050
Mid Coarse GridTauw vector
x/H 1.5separation in oilflow
Separation inCCLDV data
x/H 0.7attachment in oilflow
x/H 0.18separation in oilflow
Large bump#3
x/H 2.0attachment in oilflow
x/H
y/H
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.20.3 Uref
x/H
z/H
0 0.5 1 1.5 2
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
4.37E-024.12E-023.87E-023.62E-023.37E-023.12E-022.87E-022.62E-022.37E-022.12E-021.87E-021.62E-021.37E-021.12E-028.65E-03
TKE/Uref 2
Uref
TKE contour, velocity vector and streamlineyL = 145 micron, y+ = 8 based on 2D Utau
New Experimental InformationNew Experimental Information
Flow visualisation vs. LDV
The Case for LES for RANS StudiesThe 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 StudiesLES 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
Constitutive equation
2 211 23
2 213 3
2 21 2
2 2 2 23 3
2 24
2
( { } ) ( )
( { } )
{ } { }
( { } { } )
( )
t
a s
s s I ws sw
w w I
s s w s
w s sw w s wsw I
ws s w
ijS
2
3
i jij
k
u u
ij
Cubic (=0 in 2d)
Quadratic
Quasi-cubic
Study of Non-Linear EVMs for SeparationStudy of Non-Linear EVMs for Separation
2C-Limit Non-linear EVM2C-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 alone
Thus, addition of near-wall-anisotropy term, calibrated by reference
to channel-flow DNS
Involve “wall-direction indicators”, , Kolmogorov as well as macro
time scales and viscous-damping function
1 2
( ) , , invariants3
- wall distance
wij ij ij ij
ijwij d w t i j k k d ij d ij
i di i d
ik k
a a a a
a C f R d d d d f S
N ld N l
xN N
,ij ijS
id
ld
2C-Limit Non-Linear EVM2C-Limit Non-Linear EVM
Performance of AJL model in channel flow ( and variants) by reference to DNS
2C-Limit Non-linear EVM2C-Limit Non-linear EVM
Performance of AJL model in channel flow ( and variants)
Turbulence energy budget
A-priori Study of Non-Linear EVMsA-priori Study of Non-Linear EVMs
Quadratic terms represent anisotropy
‘cubic’ terms represent curvature effects
Example: Streamwise normal stress across separated zone
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
2d periodic hill,
Re=21500
Jang et al, FTC, 2002
Two independent simulations of 5M mesh
Highly-Resoved LES DataHighly-Resoved LES Data
Turbulence-energy budget at x/h = 2.0 Near-wall velocity profiles at 3 streamwise locations (wall units)
Highly-Resolved LES DataHighly-Resolved LES Data
IJHFF (2003), JFM (2005)
U-velocity
PressureQ-criterion
Highly-Resolved LES Data - AnimationsHighly-Resolved LES Data - Animations
W-velocity
StreamlinesStreamlines
0 1 2 3 4 5 6 7 8 90
1
2
3
Cubic k - (Apsley & Leschziner, 1998) (AL)(Separation : X/H = 0.26, Reattachment : X/H = 5.3)Y/H
X/H
0 1 2 3 4 5 6 7 8 90
1
2
3
Abe k -(Separation : X/H = 0.31, Reattachment : X/H = 4.90)Y/H
X/H
0 1 2 3 4 5 6 7 8 90
1
2
3
RSM (Jakirlic & Hanjalic, 1995)(Separation : X/H = 0.26, Reattachment : X/H = 5.9)Y/H
X/H
0 1 2 3 4 5 6 7 8 90
1
2
3
LES solution (Temmerman & Leschziner, 2001)(Separation : X/H = 0.22, Reattachment : X/H = 4.72)Y/H
X/H
0 1 2 3 4 5 6 7 8 90
1
2
3
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 90
1
2
3
Cubic k - (Craft, Launder & Suga, 1996) (CLS)(Separation : X/H = 0.26, Reattachment : X/H = 5.9)Y/H
X/H
Abe et al
LES
x/H
y/H
0 10 20 300
1
2
3
4
5 Abe, Jang and Leschziner
k-
Velocity ProfilesVelocity Profiles
U/Ub
-0.2 0 0.2 0.4 0.6 0.8 1
LS-AL-WJ-CLS-AJL-LES
(x/h=6.0)
U/Ub
-0.2 0 0.2 0.4 0.6 0.8 1
LS-AL-WJ-CLS-AJL-LES
(x/h=2.0)
Shear-Stress ProfilesShear-Stress Profiles
uv/Ub2
-0.04 -0.02 0 0.020
0.5
1
1.5
2
2.5
3
LS-AL-WJ-CLS-AJL-LES
(x/h=2.0)
uv/Ub2
-0.04 -0.02 0 0.02
LS-AL-WJ-CLS-AJL-LES
(x/h=6.0)
*******************************************
LL
LLLLLLLLLLLLLLLLLLLLLLL
LL
LLLL
LL
LLLL
LL
LLLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L
uu(=2/3k+L)
Symbols : a-priori analysisLines : LS model
uu-2/3k (actual LES)
LL
LL
LLLLLLLLLLLLLLLLLL
LL
LL
LL
LL
LL
LL
LL
LL
LL
LL
L
(L=)Linear term of uu/Ub2
0 0.01 0.02
LS modela-priori analysisuu-2/3k (actual LES)L
(X/H=2.0) LL
LL
LL
LL
LL
LLLLLLLLLLLL
LL
LL
LL
LLL
LL
LL
LL
LL
LL
LL
uv/Ub2
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02
LS modela-priori analysisActual LESL
(X/H=2.0)
(Q=)Quadratic term of uu/Ub2
0 0.01 0.02 0.03
Abe-w modela-priori analysis
(X/H=2.0)
(L=)Linear term of uu/Ub2
0 0.01 0.02 0.03
Abe-w modela-priori analysis
(X/H=2.0)*******************************************
LL
LLLLLLLLLLLLLLLLLLLLLL
LL
LLLLL
LL
LL
LL
LL
LLLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L+Q
uu(=2/3k+L+Q)
Symbols : a-priori analysisLines : Abe-w model
uu-2/3k (actual LES)
uu uv
uu (linear)
uu (quadr)
Linear EVM
Quadratic 2c limit EVM Abe,Jang &Leschziner, 2003
A-priori Study – modelled vs. simulated stressesA-priori Study – modelled vs. simulated stresses
(L=)Linear term of uu/Ub2
0 0.01 0.02 0.03
CLS modela-priori analysis
(X/H=2.0)
(Q=)Quadratic term of uu/Ub2
0 0.01 0.02 0.03
CLS modela-priori analysis
(X/H=2.0)
(C=)Cubic term of uu/Ub2
0 0.01 0.02 0.03
CLS modela-priori analysis
(X/H=2.0)*******************************************
LL
LLLLLLLLLLLLLLLLLLLLLL
LL
LLLLL
LL
LL
LL
LL
LLLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L+Q+C
uu(=2/3k+L+Q+C)
Symbols : a-priori analysisLines : CLS model
uu-2/3k (actual LES)
*******************************************
LL
LLLLLLLLLLLLLLLLLLLLLLL
LL
LLLL
LLL
LLLL
LL
LLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L
uu(=2/3k+L)
Symbols : a-priori analysisLines : LS model
uu-2/3k (actual LES)
LL
LL
LLLLLLLLLLLLLLLLLL
LL
LL
LL L
LL
LLL
LL
LLL
LLL L
(L=)Linear term of uu/Ub2
0 0.01 0.02
LS modela-priori analysisuu-2/3k (actual LES)L
(X/H=2.0) LL
LL
LLL
LL
LLLLLLLLLLLLL
LL
LL
LLL
LL
LL L
LL
L LL
LL
L L
uv/Ub2
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02
LS modela-priori analysisActual LESL
(X/H=2.0)
A-priori Study – modelled vs. simulated stressesA-priori Study – modelled vs. simulated stresses
Linear EVM
Cubic EVM Craft, Launder & Suga, 2003
uu uv
uu (linear) uu
(quadr)
uu (‘cubic’)
*************************** ****************
LL
LLLLLLLLLLLLLLLLLLLLLL
LL
LLLLL
LL
LL
LL
LL
LLLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L+Q
uu(=2/3k+L+Q)
Symbols : a-priori analysisLines : WJ-LS model
uu-2/3k (actual LES)
(L=)Linear term of uu/Ub2
0 0.01 0.02 0.03
WJ-LS modela-priori analysis
(X/H=2.0)
(Q=)Quadratic term of uu/Ub2
0 0.01 0.02 0.03
WJ-LS modela-priori analysis
(X/H=2.0)
*******************************************
LL
LLLLLLLLLLLLLLLLLLLLLLL
LL
LLLL
LL
LLLL
LL
LLLL
2/3k, mean strain and normal stress
Y/H
0 0.02 0.04 0.06 0.08 0.10
0.5
1
1.5
2
2.5
3
*
L
(X/H=2.0)
2/3k
L
uu(=2/3k+L)
Symbols : a-priori analysisLines : LS model
uu-2/3k (actual LES)
LL
LL
LLLLLLLLLLLLLLLLLL
LL
LL
LL
LL
LL
LL
LL
LL
LL
LL
L
(L=)Linear term of uu/Ub2
0 0.01 0.02
LS modela-priori analysisuu-2/3k (actual LES)L
(X/H=2.0) LL
LL
LL
LL
LL
LLLLLLLLLLLL
LL
LL
LL
LLL
LL
LL
LL
LL
LL
LL
uv/Ub2
-0.04 -0.03 -0.02 -0.01 0 0.01 0.02
LS modela-priori analysisActual LESL
(X/H=2.0)
A-priori Study – modelled vs. simulated stressesA-priori Study – modelled vs. simulated stresses
Linear EVM
Explicit ASM Wallin &Johansson, 2000
uu (linear) uu
(quadr.)
uu uv
-4
-2
0
2
4
6
8
x/H 0
2
4
6
z/H
0
1
2
3
y/H
X
Y
Z
3D-Hill - Motivation3D-Hill - Motivation
Efforts to predict flow around 3d hill with anisotropy-resolving closures
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 ComputationTopology – Experiment vs. NLEVM Computation
X
Y
Z
TAUW0.0060.00550.0050.00450.0040.00350.0030.00250.0020.00150.0010.00050
Mid Coarse GridTauw vector
Chen et al, IJHFF, 2004
Pressure and Skin Friction on CentrelinePressure and Skin Friction on Centreline
x/H
Cp
-2 -1 0 1 2 3 4 5 6-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
AJL-AL-SSG-WJ-Exp.
z/H
U/U
ref
0 0.5 1 1.5 2 2.5 3
0.02
0.03
0.04
0.05AJL-AL-SSG-WJ-Exp., z>0Exp., z<0
x/H
y/H
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.20.3 Uref
Corrected Experimental InformationCorrected Experimental Information
3D Hill - LES3D 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, Adams- Bashforth
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
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:
Computational Aspects - LESComputational Aspects - LES
Overall View - LESOverall View - LES
Short-span integral of skin-friction lines
LES / RANS Comparison – topology mapsLES / RANS Comparison – topology maps
LES /RANS Comparisons – pressure & skin frictionLES /RANS Comparisons – pressure & skin friction
LES – subgrid-scale viscosityLES – subgrid-scale viscosity
LES/RANS – cross-sectional flow fieldLES/RANS – cross-sectional flow field
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 = 1.5625AL 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 = 1.5625SSG+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
x/h = 2.8125SSG+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
x/h = 2.8125AL Model
LES/RANS – cross-sectional flow fieldLES/RANS – cross-sectional flow field
LES / RANS Comparison – streamwise velocityLES / RANS Comparison – streamwise velocity
LES / RANS Comparison – turbulence energyLES / RANS Comparison – turbulence energy
Subgrid-scale energy
LES, Re=130,000 – near-wall gridLES, Re=130,000 – near-wall grid
Grid: Grid: 192 x 96 x 192 cells
LES / RANS Comparison, Re=130,000 – pressure coefficientLES / RANS Comparison, Re=130,000 – pressure coefficient
RANS LES
LES /RANS Comparison, Re=130,000 – Topology mapsLES /RANS Comparison, Re=130,000 – Topology maps
LES / RANS Comparison, 130,000 - velocityLES / RANS Comparison, 130,000 - velocity
LES / RANS Comparison, 130,000 - velocityLES / RANS Comparison, 130,000 - velocity
Wall JetWall 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 JetWall Jet
Geometry and flow conditions
Grid: 420x208x96
Wall JetWall Jet
Time evolution
Grid: 420x208x96
Wall JetWall Jet
Resolution indicators
Wall JetWall Jet
Q-structure criterion
Wall JetWall Jet
Log law & Equilibrium
Wall JetWall Jet
Shear-strain / stress dislocation
Wall JetWall Jet
Stress diffusion and budgets
Wall JetWall Jet
Comparison of stresses: AJL NLEVM / SSG RSTM / LES
Wall JetWall Jet
Comparison of budgets: SSG RSTM / LES
2 2d k l
k l
k u uC u u
x x
Wall JetWall Jet
Comparison of budgets: SSG RSTM / LES
1 2d k l
k l
k u uC u u
x x
Wall JetWall Jet
Comparison of stress diffusion: SSG RSTM / LES
Transitional Wake-Blade Interaction - NLEVMTransitional Wake-Blade Interaction - NLEVM
Key issue: unsteady transition in high-pressure turbine blades
Lardat & Leschziner, J AIAA, C&F, FTC, 2004
Unsteady wake-induced separation on suction side
Transitional Wake-Blade Interaction - NLEVMTransitional Wake-Blade Interaction - NLEVM
Time-space representation of shape factor (unsteady transition)
Transitional Wake-Blade Interaction - NLEVMTransitional Wake-Blade Interaction - NLEVM
T3A
Experimental evidence: substantial ‘turbulence’ ahead of ‘transition’
Bypass TransitionBypass Transition
Concept of laminar turbulenceConcept of laminar turbulence
, 2 22l l
k l
Dk k kP
Dt y y
2/
,y C
k l w
UP C k k e
Necessity to include a specific transport equation for so-called
“laminar-kinetic energy” fluctuations (Mayle and Schulz, 1997)
In laminar region, shear production assumed = 0; rise in k attributed
to k- diffusion by pressure fluctuation (pressure diffusion)
Model proposed:
LES of Bypass TransitionLES 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 plateLES of transition over a flat plate
Streamwise fluctuations in the near-wall region
Turbulence budgets in the transitional region
LES of transition over a flat plateLES of transition over a flat plate
New transition-specific modelNew transition-specific model
T3A T3B
T3A T3B
New transition-specific modelNew transition-specific model
New transition-specific modelNew transition-specific model
VKI blade test case, TUFS = 1%
Displacement thickness Momentum thickness Shape factor
Turbulence energy profiles along the suction side of the blade
New transition-specific modelNew transition-specific model
VKI blade test case, TUFS = 1%
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
Separation ControlSeparation Control
Dejoan & Leschziner, IJHFF, 2004, ASME FED, 2004
Separation Control - LESSeparation Control - LES
Reynolds number: Re=Uc h / =3700
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=4/3
Strouhal number: St=fe h / Uc = 0.2
Optimum frequency
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 Recirculation LengthSeparation Control - Effect on Recirculation Length
LES
LS
model
Separation Control – Effect on Shear StressSeparation Control – Effect on Shear Stress
LES
AJL-model
Separation Control – Effect on Shear StressSeparation Control – Effect on Shear Stress
Streamlines
Reynolds Shear Stress
Separation Control – Phase-Averaged FeaturesSeparation Control – Phase-Averaged Features
Streamline
Reynolds Shear Stress
Separation Control – Phase-Averaged FeaturesSeparation Control – Phase-Averaged Features
Streamline
Reynolds Shear Stress
Separation Control – Phase-Averaged FeaturesSeparation Control – Phase-Averaged Features
Concluding RemarksConcluding 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, multi- length-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
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
Concluding RemarksConcluding Remarks
NUS Turbulence NUS Turbulence Workshop, Aug. ‘04Workshop, Aug. ‘04
Near-Wall Modelling in LESNear-Wall Modelling in LES
M.A. Leschziner
Imperial College London
Hybrid RANS-LESHybrid 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-FunctionsLES / Wall-Functions
Channel flow, Re=12000, 96x64x64 grid
LES / Wall-FunctionsLES / Wall-Functions
2d hill flow, Re=2.2x104, 0.6M nodes
LES / Wall-FunctionsLES / Wall-Functions
Hydrofoil trailing edge, Re=2x106, 384x64x24 grid
Hybrid RANS-LESHybrid RANS-LES
Methodology
Target
Velocity
Turbulent viscosity
Turbulence energy
SuperimposedRANS layer
Interface conditions
LESRANS UU intint LESt
RANSt int,int,
LESRANS kk intmod,intmod,
Hybrid RANS-LESHybrid RANS-LES
Implementation
mod modRANS LES
0.5 2mod mod or / RANS RANSC l k C k
mod,int,int 0.5
,int
LES
RANS
Cl k
< . > : spatial average in the homogeneous directions.
,int
int int
1 exp( ) 0.09 0.09
1 exp
yC y C
y
Alternative: instantaneous value
Hybrid RANS-LESHybrid RANS-LES
Typical variation of mean in channel flow , 1-eq. RANS model
C
at interface across RANS layer
Hybrid RANS-LESHybrid RANS-LES
Variations of mean and instantaneous in channel flow, 1-eq. RANS model
C
Hybrid RANS-LESHybrid RANS-LES
512 128 128
326464
Channel flow, Re=42200
17 - 135int jy
Hybrid RANS-LESHybrid RANS-LES
Channel flow, Re=42200
Resolved
Modelled
DES
Hybrid RANS-LESHybrid RANS-LES
Channel flow, Re=42200, velocity and shear stress distributions for two interface positions
Hybrid RANS-LESHybrid RANS-LES
Variations of mean and instantaneous in channel flow, 2-eq.
RANS model, Re=2000
C
Hybrid RANS-LESHybrid RANS-LES
Velocity in channel flow, 2-eq. RANS model, Re=2000, average and instantaneous input of C
Hybrid RANS-LESHybrid RANS-LES
Structure (streamwise vorticity) in channel flow, 2-eq. RANS
model, Re=2000
Interface y+=610Interface y+=120
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, interface conditions
Grid: 112x64x56=4x105
against reference of 4.6x106
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of C
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity and shear stress
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of velocity against log-law
Hybrid RANS-LESHybrid RANS-LES
2d-hill flow, Re=21500, variations of turbulent viscosity
Low-Re solution
In sublayer
Two-Layer ModelTwo-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 ModelTwo-Layer Model
Methodology
Wall-parallel pressure gradient (dP/dx) calculated from main-grid and assumed constant across subgrid
calculated from subgrid solution
wall ,kP
applied to main-grid as in standard wall-function treatments
wall
y
U
ydx
dP
y
UV
x
UU t
Two-Layer ModelTwo-Layer Model
Methodology
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
Numerical solution in sublayer
Two-Layer ModelTwo-Layer Model
pressureStreamwise velocity
Two-Layer ModelTwo-Layer Model
Trailing-edge separation from hydrofoil; Re=2.2x106
512x128x24 nodesComparison with highly-resolved LES by Wang, 1536x96x48 nodes Sub-layer thickness
40y
Two-Layer ModelTwo-Layer Model
Streamwise-velocity contours
Wall model
B C D E F G
X/h
|U|/U_e
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Velocity magnitude
Two-Layer ModelTwo-Layer Model
Full LESWall model (dynamic SGS)
Turbulence energy
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Streamwise velocity in wake
Full LESWall model (dynamic SGS)
Two-Layer ModelTwo-Layer Model
Skin friction
Concluding RemarksConcluding 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
Recommended