PPT

Transcript PPT

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

Lionel Temmerman Anne Dejoan Sylvain Lardeau Chen Wang Ning Li Fabrizio Tessicini Yong-Jun Jang Ken-ichi Abe Kemo Hanjalic Collaborators

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 Reverse flow 3 Y/H 2 1 0 0 1 2 AL model with k w equation (Separation : X/H = 0.26, Reattachment : X/H = 4.7) RANS 3 4 5 6 7 8 X/H 9

Dynamics of Separated Flow Steady Unsteady Separation

Dynamics of Separated Flow Steady Reattachment Recovery Attached

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 u

i j

 

  

U



x

 

U



x

  

2 3

k



;

U



};

x

 Wrongly implies that eigenvalues of stress and strain tensors aligned Wrong even in thin-shear flow: Channel flow

2 

2  2 3

Which is wrong

The Argument for Resolving Anisotropy Exact equations imply complex stress-strain linkage 

 



x k j k



U i



x k P ij

Analogous linkage between scalar fluxes and production     

u u i k



x k i

 

U i



x k



P ui

 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

Dt

j C ij



AdvectiveTransport

=

  

u u

i k



U



x

k j

+ u u

j k



U



x

k P ij



Production



Diffusion



Dissipation

   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

Homogeneous Straining Axisymmetric expansion

Homogeneous Straining Homogeneous shear and plain strain

Channel flow Near-Wall Shear

Explicit Algebraic Reynolds-Stress Modelling Arise from the explicit inversion of

Du u

i j

Dt

C ij



AdvectiveTransport

 2 3

D k D t



=

  

u u

i k



U



x

k j

+ u u

j k



U



x

 

P ij



Production



Diffus o

0 

D issipation

Transport of anisotropy (and shear stress) ignored Redistribution model linear in stress tensor Lead to algebraic equations of the form

u u i j

 Most recent variant: Wallin & Johansson (2000)

, 

 Recent modification (Wallin & Johansson (2002/3)): approximation of anisotropy transport by reference to streamline oriented frame of reference

Non-linear EVM   

k j

Constitutive equation  

S ij

a



2



s

2 3 

     3 1

(

s

(

w

2   1 3 1 3 2

s I



{

} )

  1 2

s s

  2

{

}

  3

(

w s



sw

2  2

(

ws



{

}

  



sw

)

 2 3

{ } )

  4

(

ws

2  2

s w

)

Quadratic Quasi-cubic 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

0.4

Near wall, resolution requirement rise with

2 Near-wall resolution can have strong effect on separation process Sensitivity to subgrid-scale modelling At high

, increasing reliance on approximate near-wall treatments  Wall functions  Hybrid RANS-LES strategies  DES  Immersed boundary method  Zonal schemes Achilles heal of LES Spectral content of inlet conditions

Realism of LES – Channel Constriction Effects of Resolution – no-slip condition x=2h x=6h Re=21900 Distance of nodes closest to wall

4 5 0 1 2 3

Sensitivity of Reattachment to Separation

Abe, Jang and Leschziner

0 10

x/H

20 30

Δx reat =7 Δx sep 0.4

0.05

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 Effect of the mesh • Mesh 1: 320 x 64 x 32 = 6.6 • 10 5 cells • Mesh 2: 768 x 128 x 64 =

6.3 • 10 6

cells • Mesh 3: 640 x 96 x 64 = 3.9 • 10 6 cells • Mesh 4: 1280 x 96 x 64 =

7.8 • 10 6

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)

Mid Coarse Grid Tau w vector

Y 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

1.2

1 0.8

0.6

New Experimental Information Flow visualisation vs. LDV x/H  0.18

separation in oilflow x/H  0.7

attachment in oilflow

0.3 Uref

-2 -1.8

-1.6

-1.4

-1.2

-1 -0.8

-0.6

-0.4

-0.2

TKE contour, velocity vector and streamline y L = 145 micron, y + = 8 based on 2D Utau TKE/Uref 2

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

Uref

0 0 x/H  0.5

2.0

x/H

1.5

2 attachment in oilflow 0.4

0.2

0 0 Large bump#3 0.2

0.4

0.6

Separation in CCLDV data 0.8

1 x/H  1.5

separation in oilflow 1.2

1.4

x/H

1.6

1.8

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   

k j

Constitutive equation  

S ij

a



2



s

2 3 

     3 1

(

s

(

w

2   1 3 1 3 2

s I



{

} )

  1 2

s s

  2

{

}

  3

(

w s



sw

2  2

(

ws



{

}

  



sw

)

 2 3

{ } )

  4

(

ws

2  2

s w

)

Quadratic Quasi-cubic 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) 

,   Thus, addition of near-wall-anisotropy term, calibrated by reference to channel-flow DNS 

d

time scales and viscous-damping function

a

 1

a

 2

a



a

ij w

a

d

 

C f

d w

(

R

)

 

d d

i j

N N N

k i k

N

  

l



x



3 d d

k k

  

f l

 

S

,





, invariants



l d

2C-Limit Non-Linear EVM Performance of AJL model in channel flow (  and  reference to DNS variants) by

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 W-velocity Q-criterion Pressure

X/H 9 3 Y/H 2 1 0 0 1 0 0 3 Y/H 1 2 3 4 5 6 7 Cubic k  (Craft, Launder & Suga, 1996) (CLS) (Separation : X/H = 0.26, Reattachment : X/H = 5.9) 8 1 2 3 4 5 6 7 8 1 X/H 9 0 0 3 Y/H 1 2 3 4 5 6 7 Abe k w (Separation : X/H = 0.31, Reattachment : X/H = 4.90) 8 Abe et al 2 X/H 9 1 X/H 9 0 0 1 2 3 4 5 6 7 8 X/H 9

Velocity Profiles (x/h=2.0) LS AL WJ   CLS AJL w  w LES (x/h=6.0) LS AL WJ   CLS AJL w  w LES -0.2

0 0.2

0.4

U/U b 0.6

0.8

1 -0.2

0 0.2

0.4

U/U b 0.6

0.8

Shear-Stress Profiles 3 (x/h=2.0) 2.5

2 LS AL WJ   CLS AJL w  w LES 1.5

1 0.5

0 -0.04

-0.02

uv/U 2 b 0 (x/h=6.0) LS AL WJ   CLS AJL w  w LES 0.02

-0.04

-0.02

uv/U 2 b 0 0.02

A-priori Study – modelled vs. simulated stresses 3 2.5

2 1.5

1 0.5

0 Symbols : a-priori analysis Lines : LS 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 * * ** ** * *

0.02

** * * * * * L ** * **

(X/H=2.0) 0.04

с с с 2/3k L uu(=2/3k+L) uu-2/3k (actual LES) 0.06

0.08

0.1

2/3k, mean strain and normal stress Linear EVM

L L L L L L L L L L L L L L L L L

(X/H=2.0) LS model a-priori analysis uu-2/3k (actual LES) uu

L L L L L L L L L L L L L L

0 0.01

0.02

(L=)Linear term of uu/U b 2

(X/H=2.0) LS model a-priori analysis 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

-0.04 -0.03 -0.02 -0.01

uv/U b 2

L L L

0 uv 0.01

0.02

3 2.5

2 1.5

1 0.5

0 Symbols : a-priori analysis Lines : Abe-w model Quadratic 2c limit EVM 0

L L L ** ** * *

(X/H=2.0)

** ** ** ** ** L L L L L ** ** ** ** * L ** **

с с с 2/3k L+Q uu(=2/3k+L+Q) uu-2/3k (actual LES)

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) Abe-w model a-priori analysis

(linear) 0 0.01

0.02

(L=)Linear term of uu/U b 2 0.03

Abe,Jang &Leschziner, 2003

(X/H=2.0) Abe-w model a-priori analysis (quadr) 0 0.01

0.02

(Q=)Quadratic term of uu/U b 2 0.03

A-priori Study – modelled vs. simulated stresses 3 2.5

2 1.5

1 0.5

0 Symbols : a-priori analysis Lines : LS model 0

L L ** L ** ** ** L L L L L ** ** L L L L L L * ** L L L L * ** ** ** ** ** * * * * *

0.02

** * L ** * * * * **

(X/H=2.0) 0.04

с с с 2/3k L uu(=2/3k+L) uu-2/3k (actual LES) 0.06

0.08

0.1

2/3k, mean strain and normal stress Linear EVM

L L L L L

(X/H=2.0) 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

0 0.01

0.02

(L=)Linear term of uu/U b 2

(X/H=2.0) LS model a-priori analysis 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

-0.04 -0.03 -0.02 -0.01

uv/U b 2

L L

0 uv 0.01

3 2.5

2 1.5

1 0.5

0 Symbols : a-priori analysis Lines : CLS model 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 * * ** **

0.02

** * ** * * * L

(X/H=2.0) 0.04

с с с 2/3k L+Q+C uu(=2/3k+L+Q+C) uu-2/3k (actual LES) 0.06

0.08

0.1

2/3k, mean strain and normal stress Cubic EVM Craft, Launder & Suga, 2003 (X/H=2.0) CLS model a-priori analysis

(linear) 0 0.01

0.02

(L=)Linear term of uu/U b 2 0.03

(X/H=2.0) CLS model a-priori analysis

(quadr) 0 0.01

0.02

(Q=)Quadratic term of uu/U b 2 0.03

0.02

(X/H=2.0) CLS model a-priori analysis

(‘cubic’) 0 0.01

0.02

(C=)Cubic term of uu/U b 2 0.03

A-priori Study – modelled vs. simulated stresses 3 2.5

2 1.5

1 0.5

0 Symbols : a-priori analysis Lines : LS model 0

L L ** L ** ** ** ** ** ** ** ** L L L L L ** ** ** ** * L ** **

(X/H=2.0) с с с 2/3k L uu(=2/3k+L) uu-2/3k (actual LES)

L L L L L * * L L * * * * * * * * *

0.02

0.04

0.06

0.08

0.1

2/3k, mean strain and normal stress Linear EVM

L L L L L

(X/H=2.0) LS model a-priori analysis uu-2/3k (actual LES)

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/U b 2

(X/H=2.0) LS model a-priori analysis Actual LES

L L L L L L L L L L L L L L L L L L L L

-0.04 -0.03 -0.02 -0.01

uv/U b 2

L L L

0.01

0.02

3 2.5

2 1.5

1 0.5

0 Explicit ASM Wallin &Johansson, 2000 Symbols : a-priori analysis Lines : WJ-LS model 0

L L ** L ** ** ** ** ** ** L L L L ** L L L L L L * * * * * L ** L * * L ** L L L * * L * * * *

0.02

* * ** * L

(X/H=2.0) 0.04

с с с 2/3k L+Q uu(=2/3k+L+Q) uu-2/3k (actual LES) 0.06

0.08

2/3k, mean strain and normal stress 0.1

(X/H=2.0) WJ-LS model a-priori analysis

(linear) 0 0.01

0.02

2 (L=)Linear term of uu/U b 0.03

(X/H=2.0) WJ-LS model a-priori analysis

(quadr.) 0 0.01

0.02

2 (Q=)Quadratic term of uu/U b 0.03

3D-Hill - Motivation Efforts to predict flow around 3d hill with anisotropy-resolving closures Y Z X -4 -2 0

x/H

2 4 6 4 2

z/H

8 6 LDA Experiments by Simpson et al (2002) 0 0 1 2 3

Re

=130,000, boundary-layer thickness = 0.5x

h

Computations with up to 170x135x140 (=3.3 M) nodes Several NLEVMs and RSTMs

Topology – Experiment vs. NLEVM Computation

Mid Coarse Grid Tau w vector

Y 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

0.4

0.2

0 -0.2

-0.4

-0.6

-0.8

-1 -1.2

-2 -1 0 1 2

x/H

AJL AL-

 w

SSG WJ-

w 

Exp.

4 5 6 0.05

0.04

0.03

0.02

0 0.5

1 1.5

z/H

AJL-

AL WJ-



SSG-

 w

Exp., z>0 Exp., z<0

2.5

Corrected Experimental Information 1.2

1 0.8

0.6

0.4

0.2

0 0

0.3 Uref

0.2

0.4

0.6

0.8

x/H

1.2

1.4

1.6

1.8

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, 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

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 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 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

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

Time evolution Wall Jet  Grid: 420x208x96

Resolution indicators Wall Jet

Q-structure criterion Wall Jet

Log law & Equilibrium Wall Jet

Wall Jet Shear-strain / stress dislocation

Stress diffusion and budgets Wall Jet

Wall Jet Comparison of stresses: AJL NLEVM / SSG RSTM / LES

Wall Jet Comparison of budgets: SSG RSTM / LES   

x k

  

C u u d k l

  2 2 

x l

  

Wall Jet Comparison of budgets: SSG RSTM / LES   

x k

  

C u u d k l

  1 2 

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)

Dk l Dt



  

k l



2  2 

k y

2 In laminar region, shear production assumed = 0; rise in k attributed to k- diffusion by pressure fluctuation (pressure diffusion) Model proposed:

P



C

U

 2   

 /



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

T3A

New transition-specific model

T3B

T3A

New transition-specific model

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:

-

h

x

,

y

Downstream the step

: 0

x

h; -h

y

h

Spanwise direction homogeneous,

L

=4

/3

Reynolds number:

Re=U c h /



=3700

Strouhal number

St=f

h / U

= 0.2

Optimum frequency

Separation Control - Effect on Recirculation Length

0.0

0.2

Exp.

x r,o

=

5.5

h x r

=

3.8

h x r

LES

x r,o

=

5.5

h x r,o

=

6.5

h x r

=

4.6

AJL 

x r,o

=

h x r

=

5.5

Skin Friction Coefficient

LES

Separation Control – Effect on Shear Stress

LS model

LES

Separation Control – Effect on Shear Stress

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, 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

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,

=2.2x10

4 , 0.6M nodes

LES / Wall-Functions Hydrofoil trailing edge,

=2x10 6 , 384x64x24 grid

Methodology Hybrid RANS-LES Interface conditions Target  Velocity

RANS

U

int  Turbulent viscosity 

LES

U

int 

RANS t

, int  

LES t

, int  Turbulence energy

RANS k

mod, int 

k LES

mod, int Superimposed RANS layer

Hybrid RANS-LES Implementation 

RANS

mod  

LES

mod 

RANS

mod  0.5

or 

RANS

mod  2

 ,int  

LES

mod,int  0.5

l k RANS

,int

< . > : spatial average in the homogeneous directions.

 Alternative: instantaneous value 

0.09

 

 ,int 

0.09

       

int   int 

model at interface Hybrid RANS-LES

 across RANS layer

RANS model Hybrid RANS-LES



Hybrid RANS-LES Channel flow, Re=42200

64



64



32



int  135 -

 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

 RANS model,

Re

 =2000

Hybrid RANS-LES Velocity in channel flow, 2-eq. RANS model,

Re

 =2000, average and instantaneous input of



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=4x10 5 against reference of 4.6x10

Hybrid RANS-LES 2d-hill flow,

Re

=21500, variations of



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

Methodology Low-Re solution In sublayer Two-Layer Model

Two-Layer Model Methodology  Near-wall control volume divided into subgrid volumes  Transport equations solve across the subgrid for:  Mean-flow parameters:

 Wall-normal

-velocity from continuity within subgrid

Two-Layer Model Methodology  Wall-parallel pressure gradient (

) calculated from main-grid and assumed constant across subgrid  

wall

calculated from subgrid

, solution   

wall

applied to main-grid as in standard wall-function treatments 



 



 

dP dx

  

     

 



 

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=2.2x10

6  512x128x24 nodes  Comparison with highly-resolved  LES by Wang, 1536x96x48 nodes Sub-layer thickness

  40

Streamwise velocity pressure

Two-Layer Model Streamwise-velocity contours Wall model

Two-Layer Model Velocity magnitude

B C D E F G X/h

|U|/U_e Full LES Wall model (dynamic SGS)

Turbulence energy Two-Layer Model Full LES Wall model (dynamic SGS)

Two-Layer Model Streamwise velocity in wake Full LES Wall model (dynamic SGS)

Skin friction Two-Layer Model 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