Large 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

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


Effects of near-wall treatment (WFs) on 0.6M mesh


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


High-lift aerofoil

Effect of the spanwise extent


Effect of the mesh

Streamwise velocity at x/c = 0.96

Prediction of the friction coefficient


• 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


(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


(x/h=2.0)

uv/Ub2

-0.04 -0.02 0 0.02


(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)


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


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 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


0 0.01 0.02 0.03

CLS modela-priori analysis

(X/H=2.0)


0 0.01 0.02 0.03


(X/H=2.0)

(C=)Cubic term of uu/Ub2

0 0.01 0.02 0.03


(X/H=2.0)*******************************************

LL


LL

LLLLL

LL

LL

LL

LL

LLLL


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


*******************************************

LL


LL

LLLL

LLL

LLLL

LL

LLL


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)



LL

LL

LLLLLLLLLLLLLLLLLL

LL

LL

LL L

LL

LLL

LL

LLL

LLL L


0 0.01 0.02


(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


(X/H=2.0)


Linear EVM

Cubic EVM Craft, Launder & Suga, 2003

uu uv

uu (linear) uu

(quadr)

uu (‘cubic’)

*************************** ****************

LL


LL

LLLLL

LL

LL

LL

LL

LLLL


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



0 0.01 0.02 0.03

WJ-LS modela-priori analysis

(X/H=2.0)


0 0.01 0.02 0.03

WJ-LS modela-priori analysis

(X/H=2.0)

*******************************************

LL


LL

LLLL

LL

LLLL

LL

LLLL


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)



LL

LL

LLLLLLLLLLLLLLLLLL

LL

LL

LL

LL

LL

LL

LL

LL

LL

LL

L


0 0.01 0.02


(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


(X/H=2.0)


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


Time-space representation of shape factor (unsteady transition)


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



VKI blade test case, TUFS = 1%

Displacement thickness Momentum thickness Shape factor

Turbulence energy profiles along the suction side of the blade


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



Streamline



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


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


2d hill flow, Re=2.2x104, 0.6M nodes


Hydrofoil trailing edge, Re=2x106, 384x64x24 grid


Methodology

Target

Velocity

Turbulent viscosity

Turbulence energy

SuperimposedRANS layer

Interface conditions

LESRANS UU intint LESt

RANSt int,int,

LESRANS kk intmod,intmod,


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


Typical variation of mean in channel flow , 1-eq. RANS model

C

at interface across RANS layer


Variations of mean and instantaneous in channel flow, 1-eq. RANS model

C


512 128 128

326464

Channel flow, Re=42200

17 - 135int jy


Channel flow, Re=42200

Resolved

Modelled

DES


Channel flow, Re=42200, velocity and shear stress distributions for two interface positions


Variations of mean and instantaneous in channel flow, 2-eq.

RANS model, Re=2000

C


Velocity in channel flow, 2-eq. RANS model, Re=2000, average and instantaneous input of C


Structure (streamwise vorticity) in channel flow, 2-eq. RANS

model, Re=2000

Interface y+=610Interface y+=120


2d-hill flow, Re=21500, interface conditions

Grid: 112x64x56=4x105

against reference of 4.6x106


2d-hill flow, Re=21500, variations of C


2d-hill flow, Re=21500, variations of velocity and shear stress


2d-hill flow, Re=21500, variations of velocity and shear stress


2d-hill flow, Re=21500, variations of velocity against log-law


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


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


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


pressureStreamwise velocity


Trailing-edge separation from hydrofoil; Re=2.2x106

512x128x24 nodesComparison with highly-resolved LES by Wang, 1536x96x48 nodes Sub-layer thickness

40y


Streamwise-velocity contours

Wall model

B C D E F G

X/h

|U|/U_e

Full LESWall model (dynamic SGS)


Velocity magnitude



Turbulence energy



Streamwise velocity in wake



Skin friction


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

Documents

Large 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