6819900 Turbulent Flows Case Studies FLUENT

7/30/2019 6819900 Turbulent Flows Case Studies FLUENT

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Turbulent Flow Case Studies

Brian Bell, Fluent Inc.


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Motivation

How do I know which turbulence model and nearwall modeling approach to choose for a given

application?

Understanding of how turbulence modeling issuesaffect turbulence model selection and performance

Observation and comparison of behavior of turbulence

models for flows in similar applications Results will be presented from a variety of flows to help with

this point


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Outline Turbulence Model Selection

Turbulence Model Comparisons (1) Flows of low to moderate complexity

Analysis of Differences Between Turbulence

Models Treatment of Reynolds Stresses

Near-wall modeling

Turbulence Model Comparisons (2) Flows of increasing complexity

Advanced Applications

Large Eddy Simulation (LES) and Detached EddySimulation (DES)


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Turbulence Model Selection

Elements of Turbulent Flows Overview of Computational Approaches

Opportunities and Challenges Turbulence Modeling Choices


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Elements of Turbulent FlowsFeature Space

Thin B.L. flows

Rotating & swirlingflows

Crossflow/Secondary

flows

Rapidly strained flows

Transitional flows &re-laminarization

Separated &recirculating flows

Large-scale unsteady structure

Thick BL, mildly

separated flows

Streamwise

vortices

Free shear flows

(BL, mixing layer,

wakes, jets


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Overview of Computational Approaches Direct Numerical Simulation (DNS)

Theoretically all turbulent flows can be simulated by numerically solving thefull Navier-Stokes equations. The whole spectrum of scales is resolved and

no modeling is required. But the cost is too prohibitive! Not practical for industrial flows - DNS is not

available in Fluent.

Large Eddy Simulation (LES)

Solves the spatially averaged (filtered) N-S equations. Large eddies aredirectly resolved, but eddies smaller than the mesh sizes are modeled.

Less expensive than DNS, but the amount of computational resources andefforts are still too large for most practical applications.

Reynolds-Averaged Navier-Stokes (RANS) Equations Models

Solve ensemble-averaged Navier-Stokes equations

All turbulence scales are modeled in RANS.

The most widely used approach for calculating industrial flows.

There is not yet a single turbulence model that can reliably predict allturbulent flows found in industrial applications with sufficient accuracy.


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Turbulence Scales and Prediction Methods


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Turbulence Modeling - Opportunities Ever-increasing computing power in terms of memory and speed

Numerical error can be made smaller than ever. Use of several million cells is a norm these days. Tens of

million cells are not uncommon.

We see more and more unsteady RANS (URANS)simulations , LES

Mesh flexibility allows us to model complex configurations that

could not be modeled previously. We have a unique opportunity likely to become the first witness

to how different turbulence models work for real-world

problems.


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Turbulence Modeling - Challenges There are many other factors affecting CFD predictions.

Choice of solution domain, boundary conditions, numerical error, etc.

User error

Yet turbulence modeling is a pacing item for the fidelity of CFD predictions.

Higher expectation for the fidelity predictions as CFD technology is

matured

Widely varying requirement on accuracy.

No breakthrough in turbulence modeling for industrial flows.

Theres no single, dominantly superior, universally reliableengineering turbulence model yet.

There are so many models with so many tweaks ...

All this puts a considerable burden on CFD vendors who have to meet the

widely varying needs.


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FLUENT Suite of Turbulence Models

Core Turbulence Models

Near-wall options

Customization

Auxiliary Models

Spalart-Allmaras one-equation model Standard k- model Renomalization-Group (RNG) k- model Realizable k- model Wilcox k- model Menters (SST) k- model Gibson & Launders RSM

Speziale, Sarkar, and Gatzkis RSM

Detached Eddy Simulation (DES)

Subgrid-scale models for LES v2f model

z Standard wall functions

z Non-equilibrium wall functions

z

Enhanced wall treatment

Buoyancy effects Compressibility effects

Low Re effects

Pressure gradient effects

z Turbulent viscosity

z Source terms

z Turbulence transport equations


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Turbulence Model Selection

Many factors affect turbulence modelselection

Flow Physics

Computational Resources

Accuracy Requirements

Turnaround Time

Etc.


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Turbulence Model Comparisons

Part 1: Flows of low to moderatecomplexity

Channel flow

Mild adverse pressure gradient, separation and

recirculation

Free shear flows Low Re flows


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Channel Flow

Comparison with DNS data of Moser et al. (1999)for Re = 395 (Re = 28,600)

DNS data available on webhttp://www.tam.uiuc.edu/Faculty/Moser/channel

Calculations performed with k-e, k-w, RSM, V2Fand low-Re models on fine near-wall mesh withenhanced wall treatment (y+ 1)

Why channel flow?

Relatively easy to run many cases and compare modelresults for 2D flow without complexity


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Results for k- Models

y+

u+ k+

y+

2

w

t

u

kk;

yuy;

u;

u

uu ==+== ++ Results normalized by:

RNG-DV: RNG model with differential viscosity option enabled

This does not appear to have noticeable effect for this flow

Models predict similar velocity profiles, peak tke values


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Results for k- and V2F Models

All models predict similar velocity profiles

SKO and V2F predict TKE better than k- models for this flow

SST model calculations performed without transitional flows

option. Would this have helped with TKE?

y+

u+ k+

y+


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RSM Results

y+

u+ k+

y+

Calculations performed with default pressure strain term (GL) and quadratic pressure strain term

(SSG) using wall boundary conditions obtained from the k-equation and from the individual Reynolds

stresses (BC)

The wall boundary condition treatment does not appear to have much effect for this flow

The quadratic pressure strain model is not intended for use in the viscous sublayer.

Results from V2F and k- model appear to be more accurate for this flow


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Results for Low-Re Models

y+

u+ k+

y+

Calculations performed with Lam Bremhorst and Launder-Sharma low Re k-

modelsThe Lam Bremhorst model appears slightly more accurate than the other

variations of k- models shown in a previous slide

The Launder-Sharma model does not appear to have been calibrated for this typeof flow


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Are Results Grid-Independent?

Results shown for RSM and V2F. Similar agreement seen for standard k-

and standard k- models

y+

u

+

k

+

y+

y+

u+ k+

y+


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What About Triangular Cells?

Standard k- model: For quadrilateral cellsand boundary layer mesh, y+ = 1. For

triangular cells, 0.35 < y+ < 0.7.With sufficient mesh resolution, results are

nearly identical for quad and tri meshes

y+

u+ k+

y+


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2d Backstep Experiments conducted at NASA Ames (Driver and

Seegmiller, 1985);ReH

= 3.74 x 104, = 0 deg. The flow features re-circulation, reattachment, and re-

developing BL.

Computed using SKE, RNG, RKE, and k-models on a

fine mesh.


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Std. k- Real. k- SST k- Wilcox k- Measured

xr/H 5.8 6.6 6.6 7.3 6.4

Predicted reattachment lengthsSkin Friction Coefficient


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The 2-D back-step of Driver and Seegmiller was computed

using five different near-wall mesh resolutions with thestandard wall functions (SWF) and the enhanced wall

treatment (EWT).

2D Backstep: Mesh (y+) Dependency


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Symmetric Diffuser Measured by Reneau et al.(1967)

Flow goes from attached to stalled asincluded angle, , increases


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Flow Near End of Diverging Section

RSM, 2 = 12

SKO, 2 = 12SKO, 2 = 16

RSM, 2 = 16


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Pressure Recovery Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15 20 25

2

Cp2-Cp1

Reneau et al. (1967)

SKO

SST

RSM

SKE

RKE

RNG

SA

SKO (w/o transitional flows option)


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Summary

Standard k-omega model results mostclosely match data

Quality of standard k-omega results

decreases without transitional flows optionsactive

Results are similar for different models forsmall included angle, but differ significantlyafter stall begins


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Measured by Obi (1993), Bruice and

Eaton (1997) - ERCOFTAC test case) Incompressible, moderately high-Re flow

(ReH= 20,000 at the inlet channel) with

separation

Computed using various k-models and

k-models on a fine near-wall mesh (y+< 1)

Asymmetric Planar Diffuser


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Comparison with Data

Y(m)

Y(m)


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Skin-friction predictions

Asymmetric Planar Diffuser


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2-D Hill Measured by Baskaran et al. (JFM, Vol. 182, 1987)

High-Re (ReL = 1.33 x 106/m) incompressible BL

subjected to pressure gradient, streamline curvature

The main interests are the skin-friction, static pressure, and

extent of the BL separation (x=1.1 m).

Computed using SA, SKE, RKE, and k-models.


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Results from 2D HillPressure distribution

The k- models predict the

Cpplateau very closely.

Skin-friction distribution

The k- models give an earlier

and larger separation than othermodels.


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Axisymmetric Bump

Measured by Bachalo and Johnson (1986).

Transonic BL flow with a standing shock and a pocket of

BL separation behind the shock.

Ma = 0.875, Rec

= 13.6 x 106 at freestream.

Computed using S-A, SKE, RKE, KO, SST models.


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Axisymmetric Bump (2)Wall pressure predictions


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RAE 2822 Airfoil RAE2822 Transonic airfoil

Measured by Cox (1981) (Case 9 in Stanforddatabase)

The corrected = 2.79 deg., Ma = 0.73, Re = 6.5x 106

Computed using SA, SKE, RKE, and k-models

on a wall function (coarse) mesh


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RAE 2822 AirfoilCp Predictions


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RAE 2822CfPredictions


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RAE 2822 Airfoil SummaryForces and moment predictions

(= 2.79, Re = 6.5 x 106, Ma = 0.73)

The shock location predicted by the k-models is slightly

upstream of the measured one and the prediction by othermodels.

The two k-models give a slightly lower lift coefficient,

but their results are almost identical.

Flow S-A SKE RKE SST k- Wilcox k- Exp.

CL 0.811 0.835 0.820 0.772 0.774 0.803

CD 0.0180 0.0198 0.0189 0.0172 0.0172 0.0168

CM -0.1093 -0.1063 -0.1092 -0.1068 -0.1072 -0.099


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Axisymmetric Underwater Body Experiments conducted (Huang et al., 1976) at DTNSRDC

High-Re (ReL= 5.9 x 106), incompressible BL flow with a separation

at around x/L = 0.92, and reattachment at x/L = 0.97.

SKE, RNG, RKE, SA, SKO, SST, RSM and Low Re models tried.

Different near-wall treatments tried.

Modified hull form


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Axisymmetric Afterbody

Spalart-Allmaras

model (fine mesh)

Std. k- model +2-layer (fine mesh)No separation

on afterbody


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Model Separates?

Std k- nRNG k- nReal. k- yRSM y

S-A y

Cp

Pressure coefficient oncoarse mesh (y+ ~ 40)using wall functions

Position (m)


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Cp

Pressure coefficient on

fine mesh (y+ ~ 0.5)

using two-layer model

Model Separates?

Std k- nRNG k- nReal. k- y?RSM y

S-A y


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Axisymmetric Underwater Body Pressure (Cp) predictions

Static pressure in the separatedregion is over-predicted by k-models.

Skin-friction predictions

The experiment shows the flowseparates at x/L = 0.92 andreattaches at x/L = 0.97

k-models gives too large aseparation.


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Spalart-Allmaras gives consistent results on both meshes

Separation not predicted by Standard k- on either mesh

RSM separates on both meshes

Cp on body somewhat overpredicted on coarse mesh

Wall reflection term, or quadratic pressure-strainterm, necessary to obtain coarse mesh separation

Subtle separation illustrates effect of near-wall treatment

Realizable k- has smaller separation bubble on finemesh

Difficult to get grid-independent solutions using wall

functions --- would a low-Re formulation work?


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Cp

Position (m)

Model Separates?

V2F y

Abid n

Launder-Sharma n

Yang-Shih n

Abe-Kondo-Nagano nChang-Hsieh-Chen n

Pressure coefficient on

fine mesh using Low-Re

models


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Low-Re models using dampingfunctions do not predict the separation

Durbins V2F (4-equation) modelpredicts separation


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Low-Re Backstep

Re = 5,100

Comparison with DNS data of Le and Moin

(1994) Comparison of Standard k- + 2-layer, Yang-Shih

low-Re model and V2F low-Re model


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Low-Re Backstep

Cp Cfx

Pressure coefficient and x-component of skin friction

2-layer model less accurate than V2F and Yang-Shih


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XVelocity X

Velocity

XVelocity

XVelocity

X/h = 1 X/h = 3

X/h = 5 X/h = 7

Low-Re Backstep


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X/h = 1

X/h = 3

X/h = 5 X/h = 7

YVelocity Y

Velocity

YVelocity

YVelocity

Low-Re Backstep


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Low-Re Backstep

Contours of Rey < 200

For 2-layer model where Rey

< 200, and t

areprescribed algebraically. Much of the flow is inthis region

2-layer model is not always a good substitute for alow-Re model


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Measured by Graziani (1980) -

P&W Aircraft Group in UTC

The local heat transfer rate was

measured.

A 2-D model of the original (3d-

D) configuration at the mid-span The suction side flow undergoes a

laminar-to-turbulent transition.

Several near-wall models and

low-Re models were tested

Two-layer zonal model

k- models with and without

the transitional flow option

2D Turbine Blade


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The k-models with the transitional flow

option give much better results than other modelson the suction side.

Results for 2D Turbine Blade


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Ota & Kan 151x75 quad mesh

Impinging Flow Over a Blunt Plate


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Standard k- model Reynolds-Stress model(exact)

Contours of TKE production

Blunt Plate The standard k- model gives spuriously large turbulent

kinetic energy on the front face, underpredicting the size of

the recirculation.


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Results: Blunt Plate Skin Friction

Standard k-

Realizable k-

Experimentally observed

reattachment point is at x/d = 4.7

Predicted separation bubble


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Compressible Mixing LayerA

B

STREAM A

Total Pressure: 487 kPa

Static Pressure: 36 kPa

Total Temperature: 360 K

Mach Number: 2.35

k: 74 m/s

: 62,300 m/s

STREAM B

Total Pressure: 38 kPa

Static Pressure: 36 kPa

Total Temperature: 290 K

Mach Number: 0.36

k: 226 m/s

: 332,000 m/s

300 mm

72 mm

Comparison with experimental data of Goebel and Dutton (1991)

x=

50mm

x=100

mm

x=150

mm

x=175

mm


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Velocity Predictions

X= 50mm

X= 100mm

X= 150mm

X= 175mm


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TKE PredictionsX= 50mm

X= 100mm

X= 150mm

X= 175mm


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Conclusions from Mixing Layer

RNG and Realizable k-epsilon models more

accurately predict velocity profiles in mixing layer

RNG and Realizable k-epsilon models reasonably

accurate in predicting tke in low-speed layer, butoverpredict tke in high-speed layer

RSM and standard k-epsilon results very similar in

this case


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Confined Swirling Coaxial Jet

InnerJet

Swirler

Computational

DomainSwirling OuterJet

An axisymmetric representation of the geometry [Roback, R. and Johnson, B.V., 1983]

Calculations performed on fine mesh with y+ ~ 1

Velocity and turbulence

profiles specified at inlet to

computational domain

X=5mm X=25mm X=51mm X=102mm X=203mm

Inner injector

Annular injector


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Velocity and Stream Function


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Results at x = 5 mm Section

-0.5

0

0.5

1

1.5

2

2.5

0 0.2 0.4 0.6 0.8 1

y/R0

Axialvelocilyu

(m/s)

exp

u-SKE

u-RKE

u-RNG

u-RSM

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

y/R0

Swirlvelocilyw

(m/s)

expw-SKE

w-RKEw-RNGw-RSM

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 0.2 0.4 0.6 0.8 1

y/R0

Radialvelocily

v(m/s)

exp

v-SKE

v-RKEv-RNG

v-RSM

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

y/R0

Innerjetmolefraction

exp

Xjet-SKE

Xjet-RKE

Xjet-RNG

Xjet-RSM


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-1

-0.5

0

0.5

1

1.5

2

0 0.2 0.4 0.6 0.8 1

y/R0

Axialvelocilyu

(m/s)

exp

u-SKE

u-RKEu-RNG

u-RSM

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

y/R0

Radialvelocily

v(m/s)

exp

v-SKE

v-RKE

v-RNG

v-RSM

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.2 0.4 0.6 0.8 1

y/R0

Swirlvelocilyw

(m/s)

exp

w-SKE

w-RKEw-RNG

w-RSM

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

y/R0


exp

Xjet-SKE

Xjet-RKE

Xjet-RNG

Xjet-RSM


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-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

y/R0

Axialvelocilyu(m/s)

exp

u-SKE

u-RKEu-RNG

u-RSM

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 0.2 0.4 0.6 0.8 1

y/R0

Radialvelocilyv(m/s)

exp

v-SKE

v-RKEv-RNG

v-RSM

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1

y/R0

Swirlvelocilyw

(m/s)

exp

w-SKE

w-RKEw-RNG

w-RSM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

y/R0


exp

Xjet-SKE

Xjet-RKEXjet-RNG

Xjet-RSM


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-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

y/R0

Axialvelocilyu(m/s)

exp

u-SKE

u-RKEu-RNG

u-RSM

-0.2

-0.15

-0.1

-0.05

0

0.05

0 0.2 0.4 0.6 0.8 1

y/R0


exp

v-SKE

v-RKEv-RNG

v-RSM

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

y/R0

Swirlvelocil

yw

(m/s)

exp

w-SKE

w-RKEw-RNG

w-RSM

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.2 0.4 0.6 0.8 1

y/R0


exp

Xjet-SKE

Xjet-RKE

Xjet-RNG

Xjet-RSM


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.2 0.4 0.6 0.8 1

y/R0

Axialvelocilyu(m/s)

expu-SKE

u-RKEu-RNGu-RSM

-0.16

-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0 0.2 0.4 0.6 0.8 1

y/R0


exp

v-SKE

v-RKE

v-RNG

v-RSM

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1

y/R0

Swirlvelocilyw

(m/s)

exp

w-SKE

w-RKE

w-RNG

w-RSM

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.2 0.4 0.6 0.8 1

y/R0


exp

Xjet-SKE

Xjet-RKE

Xjet-RNG

Xjet-RSM


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Conclusions

Johnson-Roback test case was run using the k- turbulencemodels and the Reynolds Stress model (RSM)

Velocities (axial, radial and swirl) showed good agreement

with data

RNG k- model performed the best in predicting velocities andmixing

Mixing results were poor downstream (x > 25 mm)

A possible cause for this behavior is the presence of large,unsteady flow structures that cannot be captured in a RANS

framework.


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Analysis of Differences BetweenTurbulence Models

Treatment of Reynolds stresses

Treatment of terms in model equations

Treatment of wall boundary conditions Near-wall modeling


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RANS Equations Reynolds AveragedNavier-Stokes equations:

How to model the Reynolds Stresses, Rij = ? 1. Boussinesq hypothesis

Isotropic eddy viscosity based on dimensional analysis

2. Reynolds stress transport equations

No assumption of isotropy, but more computationally

expensive and requires additional modeling

j

ji

j

i

jik

ik

i

x

uu

x

U

xx

p

x

UU

t

U

+

+

=

+

jiuu


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Modeling t Oh well, focus attention on modeling t anyways.

Basic approach made through dimensional arguments Units oft = t/are [m

2/s]

Typically one needs 2 out of the 3 scales:

velocity - length - time

Models classified in terms of number of transport

equations solved, e.g.,

zero-equation

one-equation

two-equation


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K- Model of Wilcox (1998) Originally conceived by Kolmogorov (1942) - The firsttwo-equation model

Based on Kolmogorov-Prandtl relation:

Turbulent viscosity

The dependency of* uponReTwas designed to

recover the correct asymptotic values in the limitingcases.

k

kkkk t

where

,, l

k

t *=

kR

R

R

Tk

ii

kT

kT

==

==+

+=

Re,6

125

9,

3,

Re1

Re *0

*

0*

bulent)(fully turas1* TRe

1

k

specific dissipation rate

(SDR)

Eddy turn-over frequency


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TKE Equation for k- Model444 3444 21

43421321

kofDiffusion

kofratenDissipatio

kofproduction

+

+

=jk

t

jj

iij

x

k

xkf

x

U

Dt

Dk

*

*

( )

( )

( )0.2

8,Re1

Re154

100

9

2

31

4

4

*

**

=

=+

+=

+=

k

T

T

i

ti

RR

R

MF

( )

44 344 21

parameterdiffusion-cross

jj

k

k

k

k

k

tt

tttt

tt

t

xx

kf

RTaMa

k

M

MMMM

MMMF

=

>++

=

===

>

=

3

2

2

02

2

0

2

0

2

0

1,

04001

6801

01

,4

1

,

2

0

*

Note the dependence uponReT ,Mt, and k.

Dilatation dissipation is accounted for viaMtterm. Improves high-Mach

number free shear and boundary layer flow predictions - reduces spreading rates

The cross-diffusion parameter (k) is designed to improve free shear flow predictions.

Transitional Flows option controls allReTTerms, Shear Flow Corrections option

controls cross-diffusion, parameter, Compressibility Effects option controlsMtterms.


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SDR Equation for k- Model

+

+

=j

t

jj

iij

xxf

x

U

kDt

D

2

( ) ( )

=

+

=

=

+

+=

+=

====++

=

i

j

j

iij

i

j

j

iij

kijkij

ti

i

i

T

T

x

U

x

U

x

U

x

US

SfMF

RR

R

2

1,

2

1

,801

701,

2

31

0.2,95.2,9

1,

25

13,

Re1

Re

3*

*

00

*

Note the dependence uponReT ,Mt , and .

Vortex-stretching parameter () designed to remedy the plane/round-jet anomaly

Transitional Flows option controls allReTTerms, Shear Flow Corrections option

controls vortex stretching parameter, Compressibility Effects option controlsMt terms


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Faults in the Boussinesq Assumption Boussinesq:Rij = 2tSij

Is simple linear relationship sufficient? Rij is strongly dependent on flow conditions and history Rij changes at rates not entirely related to mean flow

processes

Rij is not strictly aligned with Sij for flows with: sudden changes in mean strain rate

extra rates of strain (e.g., rapid dilatation, strongstreamline curvature)

rotating fluids

stress-induced secondary flows

Modifications to two-equation models cannot be

generalized for arbitrary flows.


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Reynolds Stress Transport Equations

k

ijk

ijijij

ij

x

JP

Dt

DR

++=

Generation

+

k

ikj

k

j

kiijx

Uuu

x

UuuP

+

i

j

j

iij

x

u

x

up

k

j

k

iij

x

u

x

u

2

Pressure-Strain

Redistribution

Dissipation

Turbulent

Diffusion

(modeled)

(related to )

(modeled)

(computed)

(incompressible flow w/o body

forces)

Reynolds Stress

Transport Eqns.

434214342144 344 21

)( jik

kjiikjjkiijk uux

uuuupupJ

++

Pressure/velocity

fluctuations

Turbulent

transport

Molecular

transport


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Importance of Near-Wall Turbulence

Walls are main source of vorticity and turbulence.

Accurate near-wall modeling is important for mostengineering applications.

Successful prediction of frictional drag for externalflows, or pressure drop for internal flows, depends onfidelity of local wall shear predictions.

Pressure drag for bluff bodies is dependent upon extent

of separation. Thermal performance of heat exchangers is determined

by wall heat transfer whose prediction depends uponnear-wall effects.


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Near-Wall Modeling Issues (1) k- and RSM models are valid in the turbulent

core region and through the log layer.

Some of the modeled terms in these equations are basedon isotropic behavior.

Isotropic diffusion (t/)

Isotropic dissipation Pressure-strain redistribution

Some model parameters based on experiments of isotropicturbulence.

Near-wall flows are anisotropic due to presence ofwalls.

Special near-wall treatments are necessary since

equations cannot be integrated down to wall.


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Near wall modeling issues (2) K-, Spalart-Allmaras and V2F models require no

special near-wall treatment. Designed to predict correct behavior when integrated to

the wall (first grid point in viscous sublayer)

FLUENTs implementation of these models issufficiently robust for use on coarse meshes (first gridpoint in log-law region)

Low Reynolds number variations of standard k-models use damping functions to attempt toreproduce correct near wall behavior


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Flow Behavior in Near-Wall Region

Velocity profile exhibits layer structure identifiedfrom dimensional analysis

Inner layer

viscous forces rule, U = f(, w, , y) Outer layer

dependent upon mean flow Overlap layer

log-law applies

kU/u

kproduction and dissipation are nearlyequal in overlap layer

turbulent equilibrium

dissipation >> production in sublayer

region


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The goal of near wall modeling is to reproduce flow behavior illustrated on previousslide. Two choices are available in FLUENT

Wall Functions

In general, wall functions are a collection or set of laws that serve as boundary conditions formomentum, energy, and species as well as for turbulence quantities.

The Standard and Non-equilibrium Wall Function optionsrefer to specific sets designed for highRe flows.

The viscosity affected, near-wall region is not resolved.

Near-wall mesh is relatively coarse.

Cell center information bridged by empirically-basedwallfunctions.

Enhanced Wall Treatment or Low-Re Option

This near-wall model combines the use ofenhancedwallfunctions and a two-layer model.

Used for low-Re flows or flows with complex near-wallphenomena.

Generally requires a very fine near-wall mesh capable ofresolving the near-wall region.

Turbulence models are modified for inner layer.

EWT is only option available for k- models, TKE b.c. same as k- model, value in wall-adjacent cell determined by distance from wall and friction velocity.

Near-Wall Modeling Options

inner

layer

outerlayer


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Turbulence Model Comparisons

Part 2: Flows of increasing complexity

Streamline curvature

Rotation

Swirl

Impinging flows

Secondary flows Three dimensional effects


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Comparison with experimental data of Monson et al. (1990)

2D U-Bend


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Streamwise Velocity Comparisons

r*

U/Uref

= 90

= 0

U/Uref

r*r*

U/Uref

= 180


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Cp Cp

S/H S/H

Inner

WallOuter

Wall

Pressure Coefficients


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Standard k-Spalart-Allmaras

RNG k- RSM

Stream Function Contours


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Lessons from 2-D U-Bend

Only the RSM correctly predicts theeffects of streamline curvature

Standard k- does not predict anyseparation

RNG k-predicts slight separation

Both RSM and Spalart-Allmaras predictsignificant separation


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Turbulent Vortex Breakdown

Comparison with experimental data of

Sarpkaya (1999) 2D axisymmetric calculation

Simulation courtesy of R. Spall, Utah State

University


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Axial

Velocity

r/r0

x/r0 = 5

Axial

Velocity

r/r0

x/r0 = 8.3

Comparisons of Axial Velocity Profiles


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Comparisons of Swirl Velocity Profiles

Swirl

Velocity

r/r0

x/r0 = 5

Swirl

Velocity

r/r0

x/r0 = 8.3


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Turbulent Vortex Breakdown Summary

k- model cannot predict vortex breakdown in high strain rates, turbulent kinetic energy

increases and increases turbulent viscosity

RNG k- model is better (additional strain-rateterm and an ad hoc swirl correction reduce the

turbulent viscosity) but not acceptable

RSM results show significant improvement

for this and many other swirling flow cases


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Non-dimensional

Parameters RatioH/D

ReynoldsRe

Pr

Calculation of:

h(x)=/(Tp-T0) Nu=h(x)L/f

T0

Tp or

Example: Impinging Jet


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Modeling Challenge

Ex: Standard k- model (SKE): Overestimates Nusselt number (30% - 80%) in the vicinity of the

stagnation point.

Single peak in Nusselt number for H/D < 3

Simulation SKE: H/D=2, Re=70000

Heat transfer calculation

Nu*=Nu/Re0.7Exp: Baughn, Shimizu (1989)


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Modeling Challenge: Complex Flow

Free jet turbulence ,stagnation point, boundary layer, strong

streamline curvature, transition ? ...

Free jet

Stagnation zone

Boundary layer & transition

Wall Jet

?

Impinging Jet Flow Characteristics


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Turbulence intensity and

Nusselt Number (Lytle and Webb (1991)) The second peak in the Nusselt number corresponds to the increase

in turbulence intensity

Laminar/Turbulent transition follows the relaminarization of the

flow after impact => k-model is the model of choice

Effect of Transition


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Modification of TKE production term

Production based on S Production based on :

k- model

Effect of Modified Production Term


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Results: H/D=2, RE=23 000

SKE

RNG

KWW

SKE

RNG

KWW

Nu*

Results from Two-Equation Models

TKE*


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Results: H/D=2, RE=23 000Comparison of k- and V2F models

Nu* TKE*

V2F

KWW

V2F

KWW


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In the vicinity (r


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Conclusions:

H/D=6 (not shown):

Two-equation models give similar results (heat transfer coefficientover predicted by 20%).

The results obtained with the V2F model are still superior to the

results from the two-equation models.

Computational expense:

Two-equation models: Grid independence achieved with 10,000 cells,

acceptable results with 6,000 cells V2F: 30% - 40% more expensive for similar mesh. 30,000 cells

needed for grid independent results.

Impinging Jet: Conclusions (2)


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Flow configuration:

Johnston et al. (1972)

ReH = 11,500

Ro = 0.21

Flow in a Rotating Channel Represents flows through

rotating internal passages

(e.g. turbomachineryapplications)

Rotation affects mean axial

momentum equationthrough turbulent stresses.

Rotation makes mean axialvelocity asymmetrical.

Computations are carriedout using SKE, RNG, RKEand RSM models are with

the standard wallfunctions.


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Flow in a Cyclone 40,000 cell hexahedral

mesh High-order upwind

scheme was used.

Computed using SKE,RNG, RKE and RSM

models with the

standard wall functions Represents highly

swirling flows (Wmax =

1.8 Uin

)

0.97 m

0.1 m

0.2 m

Uin = 20 m/s

0.12 m


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Velocity Profiles in Cyclone Tangential velocity profile at 0.41 m below the vortex finder


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Flow in a Triangular Duct Duct flows exhibit secondary flows caused byanisotropy of Reynolds stresses

Solved using RSM, SST and RNG with swirland differential viscosity options.

Periodic flow with Re = 9870. 14,772 hex

cells, fine near wall mesh (y+ < 3).


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Streamwise Velocity Contours

Similar streamwise velocity profiles

predicted by all models

RNGSST RSM


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Transverse Velocity Components

Only the Reynolds stress model predicts flow in

plane normal to streamwise direction

RNGSST RSM


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Secondary Flow Details

Recirculating secondary flow patterns

caused by anisotropy of Reynolds stresses

RSMSST & RNG RSM


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Measured by Prof. Simpsons group at VPI

Incompressible (Ma = 0.15), high-Re (Re = 4.2 x 106) flow

The most salient features are the cross-flow (open) separation,

stream-wise vortices, and vortex-lift (nonlinear).

Computed using SA, SKE, RKE, k-, and RSM models.

6:1 Prolate Spheroid at Incidence


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6:1 Prolate Spheroid at Incidence


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Flow in a Transition Duct Fully developed inlet profiles, 64,240 hexahedral cells,

Re = 3.9x105.

Calculated with k-, k- and RSM with non-equilibrium wallfunctions (30 < y+ < 70)

Measurements by Davis and Gessner (1992) taken at centerline and

locations shown below

Station 5

Station 6

Inlet

Outlet


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All models predict similar transverse velocity pattern atstation 6

Secondary flow induced by transition from circular to

rectangular duct in this case

Velocity Vectors at Station 6

RSMSSTSKOSKE


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Pressure and Skin-Friction Coefficients

Station 5Station 5

Station 6 Station 6


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Centerline Pressure Coefficient


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Transition Duct Summary All models considered predict skin friction

and pressure coefficients qualitatively

Except for standard k- model, all models

considered here predict similar results. Experimental velocity contours (not shown)

suggest that velocity field predicted by SKE

is slightly less accurate than the othermodels.


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Example: Ship Hull Flow Experiments: KRISOs 300K VLCC (1998)

Complex, highReL (4.6 106) 3D Flow

Thick 3D boundary layer in moderate pressure gradient Streamline curvature

Crossflow

Free vortex-sheet formation

(open separation)

Streamwise vortices embedded

in TBL and wake

Simulation

Wall Functions used to manage mesh size.

y+ 30 - 80

Hex mesh ~200,000 cells Contours of axial velocity compared with simulations.


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Contour Plots of Axial Velocity

SKO and RSM models capture characteristic shape at propeller plane.

SA RKE RNG

SKE SKO RSM


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0.4860.482

0.537 0.539 0.538

0.5830.561 0.56 0.557

0.3

0.35

0.4

0.45

0.5

0.55

0.6

S-A

SKE

RNG

RKE

KO-SST

KO-Wilc

ox

RSM-GL

RSM-SS

GExp.

w

4.0514.216 4.145 4.149 4.2 4.258 4.048 4.06 4.056

0

0.5

11.5

2

2.53

3.5

44.5

S-A

SKE

RNG

RKE

KO-SST

KO-Wilc

ox

RSM-GL

R

SM-SSG Ex

p.

1000xCT,CF,CVP

CT

CF

CVP

Wake Fraction and Drag Though SKO (and SST)

were able to resolve salient

features in propeller plane,not all aspects of flow

could be accurately

captured.

Eddy viscosity model RSM models accurately

capture all aspects of the

flow.

Complex industrial flowsprovide new challenges to

turbulence models.

dAU

u

Aw

PAP

=

0

11


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Advanced Applications

Large Eddy Simulation (LES) and Detached

Eddy Simulation (DES)

Theory

Applications


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Large Eddy Simulation (LES) Recall: Two methods can be used to eliminate the need to resolve

small scales.

Reynolds Averaging Approach

Periodic and quasi-periodic unsteady flows

Filtering (LES)

Transport equations are filtered such that only larger eddies need beresolved.

Difficult to model large eddies since they are

anisotropic

subject to history effects

dependent upon flow configuration, boundary conditions, etc.

Smaller eddies are modeled.

Typically isotropic and so more amenable to modeling.

Deterministic unsteadiness of large eddy motions can be resolved.


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In finite-volume schemes, the cell size in a mesh can determine the

filter width. e.g., in 1-D,

more or less information is filtered as is varied. In general,

where the subgrid scale (SGS) velocity,

( ) ( ) VdxtuV

txuV ii

rrrrr ,;,1, where Vis the volume of cell

ui

xi

uiui

=

+

+

x

xi

ii dudx

dxuxu)(

2

1

2

)()(

iii uuu =

Resolvable-scale filtered velocity

Filtering


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The governing equations for LES are obtained by filtering

(space-averaging) Navier-Stokes equations:

The SGS stresses consist of terms that must be modeled:

j

ij

j

i

jij

jii

i

i

xx

u

xx

p

x

uu

t

u

x

u

+

=

+

=

1)(

0

jijiij uuuu

jijijijiji uuuuuuuuuu +++=

LES - Governing Equations


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The subgrid-scale stress is modeled by;

The subgrid-scale eddy viscosity is modeled by: Smagorinskys subgrid-scale model

RNG-based subgrid-scale model

+

=

i

j

j

iijijijkkij

x

u

x

uSS2

1;23

1

( ) ijijS SSC 22

( ) ijijRNGSeffs

eff SSCCH 2,12

3/1

3

2

++

Smagorinsky constant Cs

varied from flow to flow

SGS Stress Modeling


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Iso-surface of instantaneous

vorticity magnitude colored by

velocity angle

LES Example: Dump Combustor A 3-D model of a lean premixed combustor studied by Gould (1987) at

Purdue University Non-reacting (cold) flow was simulated with a 170K cell hexahedral

mesh using second-order temporal and spatial discretization schemes.


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Simulation done for:

Computed usingRNG-based subgrid-

scale model

Mean axial velocity at x/h = 5

( )150Re10Re 5 = d

LES Example: Dump Combustor Mean axial velocity

prediction at x/h = 5;


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LES Example: Dump Combustor RMS velocities predictions at x/h = 10;


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Detached Eddy Simulation (DES) Hybrid RANS/LES Modeling Approach

DES approach combines an unsteady RANS version of the Spalart-Allmaras model with a filtered version of the same model

A practical and computationally efficient alternative to LES for predictingflow around high-Reynolds-number, high-lift airfoils

To enable DES

1. Activate S-A model in viscous panel

2. In TUI, enter

/define/models/viscous/turbulence-expert/detached-eddy-

simulation? yes


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DES: Calculation of Turbulent/SGS Viscosity Recall that for S-A model, the distance from the wall, d, plays a major

role in the terms for production and destruction of turbulent viscosity

This creates two separate regions in the flow calculation

Near walls, the flow calculation reduces to unsteady RANS with

the S-A model In the high-Re turbulent core region, where large turbulence scales

play a dominant role, DES recovers LES with a one-equation

model for the sub-grid scale viscosity

( ) direction-zoryin x,dimensioncellmaximum,65.0C,Cd,mind~such thatd

~e,lengthscalnewabymodelA-Sin theeverywherereplacedisdDES,In

desdes ===

LES Region

RANS Region

dd~

=

= DESCd~


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DES Example: Airfoil at High Incidence

Angle of attack 13.3, Re = 2.1x106

360 x 64 x 16 mesh (368,640 cells) Affordable for real engineering applications

Cell count decreased by order of magnitude compared with

successful LES simulation of same airfoil


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DES Example: Results

Instantaneous x-vorticity contours Time-averaged velocity vectors at trailing edge


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DES Example: Airfoil Grid

Grid Detail Instantaneous y+ values


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DES (3)

Pres

sureandskinf

rictioncoeffici

ents

Tim

e-averagedand

rmsvelocity

prof

ilesinthewake


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Conclusions For flows with strong streamline curvature,

rotation, swirl or three-dimensional boundarylayers, RSM results are generally more accurate.

For less complex flows there does not appear to be

a demonstrable advantage to using RSM. SKO,

SST, RNG and RKE demonstrate satisfactory

results for a wide range of flows. Check comparisons between models to see which is

best for your particular application


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Conclusions The standard k- model was seen to be less

accurate than the other models considered here fora wide variety of different flows

Ensure proper near wall grid resolution and near

wall treatment. If possible, avoid placing the first cell in the buffer

layer

Beware of using a turbulence model for a flowoutside its range of applicability

If in doubt, check with support engineer first.


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Acknowledgements The following individuals in Fluent Inc.

contributed material shown in this training

session

Davor Cokljat, Yi Dai, Sung-Eun Kim, FabriceMathey, Carl-Henning Rexroth, Shin Rhee,

Amish Thaker, Xuelei Zhu.

May also be other unknown contributors.

M Th k t ALL h h l d!

6819900 Turbulent Flows Case Studies FLUENT

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Transcript of 6819900 Turbulent Flows Case Studies FLUENT