DES/LES Methods in Tau K.Weinman (contributions …tau.dlr.de/fileadmin/documents/meetings/2008/pdf/3rd-day-theory/... · The Renolds Stress tensor is defined as jij j ikk j ii i

Keith Weinman: 1

TAU SCHOOL 25-29 Feb. 2008TAU SCHOOL 25-29 Feb. 2008

DES/LES Methods in Tau

K.Weinman

(contributions from D.Schwamborn, V.Togiti,

H.Luedeke, A.Soda)

Keith Weinman: 2


RANS/URANS performs well in attached boundary layers up to separation. Most of the flow overan aircraft comprises regions of attached boundary layers.

Something better is required to capture the unsteady physics in separated flows, tip vortices, wingbody junctions.

MOTIVATION – External Aerodynamics

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MOTIVATION – resolve turbulence physics?

Relevant time, length, and velocity scales range from

(L)argest scales in flow for typical airfoil (in absence of any external forcing of scales)

,

,

/

l cu U

c Uτ∞

∞

==

=

∞

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(S)mallest scales in flow

( )( )( )

1/ 43

1/ 4

1/ 2

Kolmogorov length scale: /

Kolmogorov vel. scale:

Kolmogorov time scale: /

u

η ν ε

νε

τ ν ε

≡

≡

≡

Separation of scales so that small scales << largestscales. Small scales can be assumed to be statisticallyindependend of large scales. Small scales depend on on energy fed from large scales (ε) and kinematicviscosity (ν) (Friedlander et al. 1962, Tennekes et al 1972)

/ 1R uη ν= =→Viscosity dominatesat small scales

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Requirements to resolve smallest scales

3/ 4 1/ 2/ , /l R t Rη τ≡ ≡

2u≈Energy contained in large scales

Energy transfer rate in large scales

Dissipation of energy:

leads to following ratios:

3d flow: O(R9/4) nodes required for full spatial res.,

and computational work is O(R11/4) ~ O(R3)

/u l≈3 /u lε ≈

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The Reynolds Averaged NS Equation

2 1

The Reynolds decomposition is given by

The Renolds Stress tensor is defined as

j i j j

i k k j

i i i

i j i j i j

U U U U pt x x x x

U U u

u u U U U U

νρ

∂ ∂ ∂ ∂+ = −

∂ ∂ ∂ ∂ ∂

′= +

′ ′ = −

The Reynolds operator represents a form of low-passfiltering (due to averaging operation on finite interval) without any correction for the filtered out contributions.

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DNS/LES Methods

In DNS U(x,t) is resolved at lengthscales O(η).

In LES, a low-pass filter operation is made so thatthe resulting filtered velocity field U(x,t) isresolved on a relatively coarse mesh.

( , ) ( , ) ( , )

( , ) 1

( , ) ( , ) ( , )

U x t G r x U x r t dr

G r x dr

u x t U x t U x t

= −

=

= −

∫∫

G(r,x) is the filter function

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The Filtered NS Equation

2 1

The residual stress tensor is defined as

which has same form as Reynolds Stress tensor

j i j j

i k k j

Rij i j i j

i j i j i j

U U U U pt x x x x

U U U U

u u U U U U

νρ

τ

∂ ∂ ∂ ∂+ = −

∂ ∂ ∂ ∂ ∂

= −

= −

The Subgrid scale model computes the residual stress tensor – the form of filtered NS is similar to that of RANS, but mathematical properties are different.

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Some terminology (Pope, p560)

Filter and grid are toocoarse to resolve 80% of energy

VLESVery-large eddy simulation

80% of energy resolvedbut not in near-wallregion.

LES-NWMLarge-eddy simulation withnear-wall modelling

Filter and grid sufficientto resolve 80% of energyeverywhere

LES-NWRLarge-eddy simulation withnear-wall resolution

Turbulent motions of all scale are fully resolved

DNSDirect numerical simulation

ResolutionAcronymModel

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Provide a conservativeestimate for a ``clean´´ wingwith no separation withReynolds number (rootchord) ~ 107 (Spalart,1997)

Cost Estimate for Clean Wing

AssumptionsTrue LES (>80% resolved energy)

∆x,y,z= δ(z)/No

Hybrid grid

~1022~1016DNS~107

~108

~1011

Nodes

~1015LES-NWM

~1013RANS

~1020LES-NWR

Comp.UnitsMethod

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Cost Estimate for Clean Wing

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RANS is cheap but may not reproduce correct physics!

Full LES is slightly cheaper than DNS but much tooexpensive!

Wall model LES is less expensive but limited to flowswhere the wall model is accurate.

HYBRID Models to bridge between LES and RANS?Zonal methods: Stochastic Turbulence, Overlap regionsNon-Zonal methods: DES, TTRANS, SAS, OES

Conclusions on how to proceed

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Detached Eddy Simulation

The DES method (suitable for all Eddy viscosity models.

Choose length scale: d* = min(dRANS, CDES∆)

RANS: dRANS < CDES∆

LES: dRANS > CDES∆

At equilibrium (Production=Destruction) the eddy viscosity model reduces to a Smagorinsky type eddy viscosity model in the LES mode of DES.

* 22) ( )( T SMAG

L

D

E

E

D S

S

ES

C d C SS υ⇒ ∆⇐14243 14243

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Modeled Stress Depletion (MSD): d* = min(dRANS, CDES∆)

Natural DES:

∆ >> δ so that DES scale is on RANS branch

Ambiguous DES:

∆ ~ δ but grid notfine enough to support resolvedvelocity within BL.

LES Limit:

∆ much smaller thanδ. Model acts as a SGS model in bulk of BL and RANS-likeclose to wall

DES inconsistency: near wall/thin shear regions

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Solutions to Modeled Stress Depletion

Ψ(νT/ν)CDES∆DES

-OES, SAS, TRANS. Potential, but control between LES and RANS not well understood

Modified RANS

Delay onsett of LES mode in DES

DDES+other schemes

- Not a robust solution, especially in unstructuredmeshes.

Aspect ratio control

- Not possible to define zonesapriori – ignore!

Zonal control

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GRID DESIGN IS CRITICALPLEASE READ: ``Young persons guide to Detached-Eddy Simulation Grids´´, P.Spalart

NASA/CR-2001-211032

A proper DES meshis the mostimportantingredientfor successin a DES calculation!

You getpeanuts forpeanuts!!!

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An example of incorrect DES!!

∆=C/32, C=0.65 ∆=d*, C=CCOARSE*R

∆ < d* for regionsoutside curve Match on all grids (∆=Rd*)!

FILTER WIDTH A FILTER WIDTH B

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Grid Generated Turbulence (Comte-Bellot (1971)

(1) Generation of velocity field

5/3( ) ~E κ κ −

11214e-76464

3261e-061632

2165.27e-06416

T(secs)100 outer100 inner

Time/pt/it.PN

(2) Create TAU restart file•copy field to TAU restart file

• correct Thermodynamicquantities in field.

• run code with frozen velocityfield to generate consistentviscosity field (2-400 iterationsbefore residual change lessthan machine ε

Computational Performance on Enigma(3v ) No MG for turbulence

5/3( ) ~E κ κ −

Choose initial velocityfield for

DNS/ILES or

LES/DES

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Grid Generated Turbulence (Comte-Bellot (1971)

Since we can only computewith two periodicboundaries, it is useful to examine the differencewhich arises between 2 periodic + 4 symmetryboundaries and the proper fully periodic cube. Computation provided byStrelets et al., NTS; St Petersburg, Russia as partof FLOWMANIA project.

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( ) ( 2 ) ( 4 )1 2

1 1ˆ ˆ ˆ ( (...) (...2

) )2f L RF F F DG D Gα= + + +

Smooth regionsShocks/Discontinuities(2)

2 1( )j jD f fε += −

(4)4 1( ( ) ( ))j jD L f L fε += −

The JST dissipation operator.

Dissipation control is IMPORTANT

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Comparison against Comte Bellot, Central + JST+ Mod. Diss

• reason for deviation for N=16 from k2 not yet understood.

• Cdes = 0.65 but for thisproblem we are in DNS range(SGS low) – ILES?.

• N = 32 gives best result butstill searching for the best form of scaling function/parametercombination.

• Results show that TAU cando DNS!!! --- IF DISSIPATION HANDLED PROPLRLY.

• (0.5, 84, 0.8, 0.001, 0.001)

• decay of K(t) - add.constraint.

DIT. Calibration for LES/DES

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Skew Symmetric 0.5((uiuj),j + ujui,j)Convective ujui,j

Divergence (uiuj),j

Rotational uj(ui,j - uj,i) + 0.5(ujuj),•Aliasing occurs when inner productsare made in physical space - High frequency components produce higherfreq. components that cannotPreservation of symmetries in discreteN.S. ensure conservation of energyand stabilty.

• will allways occur on a finite grid.

• Frequencies beyond cut-off arealiased to resolved wave numbers.

• Aliasing errors prevent conservationof energy.

•See Verstappen et al, JCP, 2003

Influence of Numerics (aliasing)

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Mod JST + MDSpectral resolutionimproved.

No high κ fall-offobserved.

Additional memorybut no siginificantcomputationalexpense.

Std. JST + MDSpectral resolutionbetter than scalardissipation model

high κ fall-off issignificant.

Grid Generated Turbulence (DNS-ILES??)

Std. JSThigh κ fall-off issignificant. No significant energyretained at high wave numbers –Completedestruction of energy cascade.

Keith Weinman: 24


• We assume that a LES/RANS switch cannot switch ideally betweenRANS and LES in a perfect fashion.

• For stability we would like numerical viscosity to be higher in regions where LES is not used.

• Similarly, we would like to use a scheme with lower numericalviscosity where LES is to be calculation.

One solution is to use a hybrid differencing, or a weighting betweenRANS and LES modes in regions where the switch cannot performoptimally. In following F is the invisicid flux vector, uds means upwinddifference scheme (more dissipative), cds means a central scheme withlow dissipation, and σ is a weighting factor.

Hybrid Differencíng for DES/LES

( )1 cds upwF F Fσ σ= − +For choice of weighting factor see eg.

Travin et al. ``Physical and numerical upgrades in Detached-Eddy simulation of Complexturbulent flows´´, Advances in LES of Complex Flows, Kluwer Academic publishers, 2002

Keith Weinman: 25


NACA0021 60 deg. AoA (K.Weinman)

• NACA0021 at an angle of attack of 60 degrees

• Re = 270,000• Time resolved

experimental force coefficient data (Swalwell et al. 2004)

Keith Weinman: 26


Std JST+MD. NACA0021 at 60 degs. AoA

•Rapid break up of structure apparent.

•Pressure in vortex core larger than thatobtained with modified scheme.

• Resolved structure is coarse.

Mod JST+MD. NACA0021 at 60 degs. AoA

•Improved resolution + reduced break-up.

•Integral values show slight change.

•Lower presure in vortex core.

•Farfield retains structure (better induced lift?).

NACA0021: Modifying JST Dissipation

Keith Weinman: 27


Arianne Launcher (Lüdeke)

Averaged pressure ratio at inner nozzle wall

Validation with wind tunnel data

Averaged pressure distribution RMS values of pressure distribution

Study aiming at fluidStudy aiming at fluid--structure coupling to structure coupling to understand buffeting effects in nozzle area understand buffeting effects in nozzle area of rocket and boostersof rocket and boostersRANSRANS-- external to nozzle areaexternal to nozzle areaDES DES -- flow in the nozzle areaflow in the nozzle area

Keith Weinman: 28

TAU SCHOOL 25-29 Feb. 2008TAU SCHOOL 25-29 Feb. 2008 Base Flow (Togiti)

M∞ : 2.46ρ∞ : 0.7579 Kg/m3

p∞ : 3.14 104 N/m2

T∞ : 145 KRe : 45 ·106 1/mR : 31.75 mmU∞ : 593.8 m/sec

Keith Weinman: 29


AHMED BODY (Schwamborn)

Brief description:Flow around a car body with two

slant angles (25o and 35o)Re = 768,000 (based on a body

height of 288 mm and a reference velocity of 40 m/s)

Challenging because of the sensitivity of the case to the prediction of separation as the flow structure radically changes with the separation

Pre-stall

Post-stall

Separated flow behind the slant in the pre-stall and the post-stall regimes.Courtesy of H. Lienhart, University of Erlangen-Nurenberg.

(taken from Deliverable D3.1.18b p. 56)

Keith Weinman: 30


25o case

Velocity profiles at x = -243 mm (DLR - IMFT - NUMECA)Velocity profiles at x = -163 mm (DLR - IMFT - NUMECA)

AHMED BODY (Schwamborn, Temmerman)

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Delta Wing(H.Luedeke)

• Validation for XLES und DES

• Unstructured grid (6x106)

• DES,XLES (∆t=10µs)

• Comparison againstExperiments

• Minimium y+ < 0.5

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M219 Cavity (Leicher (EADS))

- Unstr. EADS Grid

•Tau SADES M∞ = 0.85 & 1.35

•Tau XLES M∞ = 0.85

XLES XLES

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Parameter Settings for TAU (2007)

Turbulence --------------------------------------:

Turbulence model version: SAO+DES

DES/LES switches ----------------------------:SA DES constant: 0.65DES grid protection: 0Low Reynolds number corrections (0/1/2): 0Forced Les branch (0/1):1Set RANS distance: -1Miles active (0/1):

Dual time ----------------------------------------:Unsteady time stepping: dual, global

Moving grid ------------------------------------:Type of grid movement: static

DES/LES switches -----------------------------:SA DES constant: 0.65XLES constant: 0.05SST DES constant: 0.78 0.62

Turbulence---------------------------------------:SAS correction (0/1): 0

k-w models--------------------------------------:TRANS coefficient: 1.5

Turbulent SAS Correction --------------------:SAS flow correction model: sstSmoothing eps for sas flow correction: 0.3Effective Smagorinsky model coefficient for SAS: 0.215Number of smoothing steps for sas correction: 0

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TAU Tips for DES

1. Current implementations work well for flows with stronggeometry driven separation ie. Bluff body flows

2. We still have work to do for boundary layer driven instabilitiesin the flow!!!

Keith Weinman: 35


TAU Tips for DES

1. Make certain grid is designed for DES/LES!!!

2. It is not necessary to restart from a stationary solution! This canbe counterproductive. Alternatively start from a LES solutionfor DES if you feel you really need a restart solution.

3. Does time step resolves critical frequencies?

4. Analyse flow at intermediate stages of computation!!

5. Check max and min eddy viscosity during run! These can oftenshow if problems will occur.

6. CHECK YOUR PARAMETER FILE - TWICE!!

7. ASK QUESTIONS!

Documents

DES/LES Methods in Tau K.Weinman (contributions …tau.dlr.de/fileadmin/documents/meetings/2008/pdf/3rd-day-theory/... · The Renolds Stress tensor is defined as jij j ikk j ii i