overview of turbulence modeling - ansys...•streamline curvature and system rotation are typical...

Overview of Turbulence Modeling

Paul Galpin

ANSYS Inc.

© 2011 ANSYS, Inc. October 23, 20122

Mixing /combustion

Turbulence Modelling Challenges

Flow Separation

Vortical Flows

Flow Reattachment

Corner Vortices

Transition

Unsteady Effects


Turbulent Flow Simulation Methods

RANS

(Reynolds Averaged Navier-Stokes Simulations)

SRS

(Scale Resolving Simulations)

DNS

(Direct Numerical Simulation)

• Numerically solving the full unsteady Navier-Stokes equations

• No modeling is required

• A research tool only– far too much information for industrial applications

• Not available in ANSYS CFD

• Includes Large Eddy Simulation (LES)

• The motion of the largest eddies is directly resolved in the calculation, in at least a portion of the domain, but eddies smaller than the mesh are modeled

• Inherently unsteady method

• Solve Reynolds-averaged Navier-Stokes equations (time-average)

• Steady state solutions are possible

• All turbulence is modeled. Larger eddies are not resolved

• RANS turbulence models are the only modeling approach for steady state simulation of turbulent flows

• This is the most widely used approach for industrial flows


• RANS models are (or will be) mostly for wall boundary layers

– y+-insensitive wall treatment

– Accurate separation prediction

– Swirl flow (Curvature correction)

– Corner flows

– Laminar-turbulent transition

• For free shear flows use Scale-Resolving Simulation (SRS)

– SAS model

– DDES models

– Zonal/embedded models

– LES/WMLES

– Synthetic turbulence

Key Elements in Turbulence Modelling


• RANS

– Advantages: For many applications, steady state solutions are preferable, and for many applications a good RANS model with a good quality grid will provide all the required accuracy

– Disadvantages: For some flows, challenges associated with RANS modeling can limit the level of accuracy that it is possible to attain

• SRS

– Advantages: Potential for improved accuracy when the resolution of the largest eddies is important or when unsteady data is needed

– Disadvantages: computationally expensive• Higher grid resolution required

• Unsteady simulation with small time steps generates long run times and large volumes of data

Comparison of SRS and RANS

RANS Modeling


Integration Platform w-equation

w-equation

2-equation models

• k-w, BSL, SST

Higher order models

• EARSM – w

• SMC - w

Extensions•Stagnation point•Curvature correction•Rough walls•Reattachment correction

Wall Treatment• Automatic wall treatment

Transition Model• g-ReQ model

Unsteady models

• SST-SAS

• SST-DES


ANSYS Models

Example: Solids suspension in an tall, unbaffled tank. Reynolds stress model together with Eulerian granular multiphase model

Courtesy of the University of Bologna

• It is not enough just to provide many choices

• More importantly, for the models that are available, emphasis is placed on

– Correct implementation• Models should be well understood and tested

– Accurate and validated for some class(es) of applications

– Robust performance on all mesh topologies

– Interoperability with other physical models, e.g. multiphase, dynamic mesh, ….

– Wall treatment


Near Wall the w-equation reduces to an elliptic equation:

k- w Near WallElliptic Relaxation

2

log

2

2

1;

6vis

u

yC

u

y

w

w

2( )( )

( )j t

k

j j j

UP

t x k x xw

w w w w w

22

2

jx

w w

• Information about the wall presence is transmitted by the Poisson equation + boundary conditions (no damping required)

• Log layer:

• Sublayer:


Engine installation drag

AIAA Drag Prediction Workshop 2003

WB WBPN

Wide range of results

Mainly specialized aeronautics codes

Drag prediction is difficult!!

Cd - Drag

Cl –

Lift

Cd - Drag Cd - Drag

Part of this work was supported by research grants from the European Union under the FLOMANIA project


Engine installation drag

ANSYS ResultsDrag Polar

WB WBPN

Grid refinement

Accurate prediction of lift and drag

Improved results under grid refinement

Web-page for AIAA Drag Prediction workshop

Cd - Drag

Cd - Drag

Cl –

Lift


Corner Flows

Early separation of linear Eddy

Viscosity Models in corners observed

Can be caused by lack of anisotropy in

the stress formulation(differences in

normal stresses near wall)

Anisotropy is cause of secondary flows

into the corner

Reynolds Stress Model (RSM) could

account for this – but is often not

robust enough for complex flows

Explicit Algebraic RSM (EARSM) offer

an attractive alternative with reduced

numerical effort and increased

robustness

¼ of cross section of square duct. Secondary flow into corner


WJ-EARSM-BSL –Wallin-Johansson

2

3ij i ij ijj

u u k a

1 1, 2 2, 3 3, 4 4, 6 6,ij ij ij ij ij ija T T T T T

1, 2, 3, 4,

6,

1 1; ; ;

3 3

2;

3

ij ij ij ik kj S ij ij ik kj ij ij ik kj ik kj

ij ik kl lj ik kl lj ij ij

T S T S S II T II T S S

T S S IV II S

1 2 3 4 6

1 1

2 1, 0, , , ,

N IV N

Q NQ Q Q

kP

CN4

91

1 1 1 1

91.2; 1 , 1.8

4A C C C

Non-linearity due to Pk

Linear part of Stress-Strain relation


Stanford DiffuserFlow Topology

• Flow topology depends

strongly on turbulence

model

• Stress anisotropy

necessary to obtain

correct behaviour

X/H=16


Streamline Curvature

• Streamline curvature and system rotation are typical for many turbulent flows of practical interest

• However, conventional eddy viscosity models often fail to capture important flow features in such flows

• This is partially due to the fact that linear eddy viscosity models do not have any sensitivity to curvature or system rotation effects


j

t

j

r

t

k

j

j

xxCdDf

P

x

U

t

w

ww

w

ww )()()(

1

Rotation/Curvature function for the SST turbulence model

• The only difference between the modified, or SST-CC,

model accounting for the Rotation/Curvature effects and

the “pure” SST model is multiplier fr1 in production terms

0.0,25.1,minmax1 rotationr ff

jk

t

j

rk

j

j

x

k

xkfP

x

kU

t

k)(

)()( *

1

w


Cross Flow & Axial Velocities

Cross Flow Velocity

Z[m

]

0 0.2 0.4 0.6 0.8 10.2

0.4

0.6

0.8

1

1.2

Exp.

SST

SST-RC

Plane 1, X/C = 0.24 18 Jul 2007

Axial Velocity/U_inlet

Z[m

]

0.8 1 1.2 1.4 1.6 1.80.2

0.4

0.6

0.8

1

Exp.

SST

SST-RC

Plane 1, X/C = 0.24 18 Jul 2007

Cross Flow Velocity

Z[m

]

0 0.2 0.4 0.6 0.8 10.2

0.4

0.6

0.8

1

1.2

Exp.

SST

SST-RC

Plane 1, X/C = 0.67 18 Jul 2007

Axial Velocity/U_inlet

Z[m

]

0.8 1 1.2 1.4 1.6 1.80.2

0.4

0.6

0.8

1

Exp.

SST

SST-RC

Plane 1, X/C = 0.67 18 Jul 2007

SST

SST-CC


Tangential Velocity

Line 1

Line 2

Line 3

Line 4

Line 5

z

x [m]

Ta

ng

en

tio

na

lV

elo

city

[m/s

]

-0.02 -0.01 0 0.01 0.02-6

-4

-2

0

2

4

6

Exp 1

Exp 2

SST

SST-CC

RSM-SSG

Line 1, Z = - 20 mm 03 Jul 2007

x [m]

Ta

ng

en

tio

na

lV

elo

city

[m/s

]

-0.01 0 0.01-6

-4

-2

0

2

4

6

Exp 1

Exp 2

SST

SST-CC

RSM-SSG

Line 3, Z = - 53 mm 03 Jul 2007

x [m]

Ta

ng

en

tio

na

lV

elo

city

[m/s

]

-0.005 0 0.005-6

-4

-2

0

2

4

6

Exp 1

Exp 2

SST

SST-CC

RSM-SSG

Line 5, Z = - 117 mm 03 Jul 2007

x [m]

Ta

ng

en

tio

na

lV

elo

city

[m/s

]

-0.02 -0.01 0 0.01 0.02-6

-4

-2

0

2

4

6

Exp 1

Exp 2

SST

SST-CC

RSM-SSG

Line 2, Z = - 32 mm 03 Jul 2007


Transition Model

• Compatible with modern CFD code:

– Unknown application

– Complex geometries

– Unknown grid topology

– Unstructured meshes (no search directions)

– Parallel codes – domain decomposition

• Requirements:

– Absolutely no search algorithms

– Absolutely no integration along lines

– Local formulation

– Different transition mechanisms

– Robust

– No excessive grid resolution

Laminar Flow

Transitional

Fully Turbulent


Intermittency Equation g

j t

j j f j

UP E

t x x xg g

gg g

0.5

1 (1 )length onsetP F S Fg g g

Fonset transition onset when:

Fonset linked to exp. transition correlations

t ReRe


Wall Shear @ Rotor 1

SST - Transitionk-ω - Model SST - Model


Cost of Transition Model

• Eurocopter configuration

• 6 million nodes

• Max y+ = 1

• 16 CPU’s

• Total Additional CPU: 17%

Discretization 12%

Linear Solution 5%

Fully Turbulent

Transitional

Drag reduced 5

% compared to

fully turbulent

Drag

Lift

SRS Modeling


Motivation for Scale-Resolving Simulation (SRS)

• Accuracy Improvements Flows with large separation zones (stalled

airfoils/wings, flow past buildings, flows with

swirl instabilities, etc.)

• Enriched Information Acoustics - Information on acoustic

spectrum not reliable from RANS

Vortex cavitation – low pressure inside

vortex causes cavitation – resolution of

vortex required

Combustion

Fluid-Structure Interaction (FSI) – unsteady

forces determine frequency response


SRS by SAS Model

• Model based in introduction of von

Karman Length Scale (LvK) into scale

equation (w-equation)

• Model based on theory of Rotta using an

exact definition of the turbulent length

scale SAS automatically detects attached flows (RANS)

and unstable separated flows (LES)

Least problematic hybrid RANS-LES model as no

explicit grid dependency in RANS portion

Requires sufficiently strong flow instability to

convert to LES mode

• Suitable for numerous technical flows Flows past bluff bodies

Combustion chambers

Jet in crossflow

…

URANS

SAS


SAS 2-Equation Model (KSKL)

• With:

Lk

22

1 2 32

1''

j tk t

j

UP L U k

t x k y y

2 2'

' ; '' ;''

i i i ivK

j j j j k k

U U U U UU U L

x x x x x x U

Relevant terms can also be transformed and included in other RANS models (SST):

3/ 23/ 4j t

k

j j k j

U kk k kP c

t x L x x

1/ 4

t c


• Types of highly unstable flows:– Flows with strong swirl instabilities

– Bluff body flows, jet in crossflow

– Massively separated flows

• Physics– Resolved turbulence is generated quickly by flow instability

– Resolved turbulence is not dependent on details of turbulence in upstream RANS region (the RANS model can determine the separation point but from there ‘new’ turbulence is generated)

• Models– SAS: Most easy to use as it converts quickly into LES mode, and

automatically covers the boundary layers in RANS. Has RANS fallback solution in regions not resolved by LES standards (Dt, Dx)

– DDES: Similar to SAS, but requires LES resolution for all free shear flows (Dt, Dx) (jets etc.)

– ELES: Not really required as RANS model can cover boundary layers. Often difficult to place interfaces for synthetic turbulence.

Globally Unstable Flows

Green-recommended, Red=not recommended


• Types of moderately unstable flows:– Jet flows, Mixing layers …

• Physics– Flow instability is weak – RANS/SAS models stay steady state.

– Can typically be covered with reasonable accuracy by RANS models.

– DDES and LES models go unsteady due to the low eddy-viscosity provided by the models. Only works on fine LES quality grids and time steps. Otherwise undefined behavior.

• Models– SAS: Stays in RANS mode. Covers upstream boundary layers in

RANS mode. Can be triggered into SRS mode by RANS-LES interface.

– DDES: Can be triggered to go into LES mode by fine grid and small Dt. Careful grid generation required. Covers upstream boundary layers in RANS mode.

– ELES: LES mode on fine grid and small Dt. Careful grid generation required. Upstream boundary layer (pipe flow) in expensive LES mode. Alternative – ELES with synthetic turbulence RANS-LES interface.

Locally Unstable Flows

Green-recommended, Red=not recommended

BL Turbulence

ML Turbulencey

x

z


• One SRS model for entire domain• SAS, DDES ideally suited

• Steady boundary conditions• Wall b.l. treated in RANS mode

• Separated zones in SRS mode

• Globally unstable flow required• Requires strong flow instability• Generates unsteady resolved

turbulence

• Easiest SRS model to set up & run

Global SRS Approaches

URANS

Global SRS Model

Courtesy: ETH Zurich


• Zone with high accuracy demand within a larger RANS domain

• LES zone coupled to RANS zone with synthetic turbulence at interfaces

• LES zone requires suitable (WM)LES methods

• Integrated or sequential zonal approaches also

• Arbitrarily large computational savings

Zonal SRS Approaches

Courtesy: Benjamin Duda, Airbus Toulouse


ELES: vortex structures

Q-criterion iso-surface colored by Velocity Magnitude


Pressure Contours

URANS ELES


U velocity Profiles

x= -163mm

x= -223mm

x= -163mm

x= -223mm


U velocity Profiles

x= -3mm

x= -123mm

x= -3mm

x= -123mm


Sensors downstream the mirror

10 100 1000Frequency [Hz]

0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

SP

L [

dB

]

Freestream Velocity = 140 km/h

Experimental data

SAS model

Sensor 121


0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

SP

L [

dB

]


Experimental data

SAS model

Sensor 122


0

10

20

30

40

50

60

70

80

90

100

110

120

130

140

SP

L [

dB

]


Experimental data

SAS model

Sensor 123

Grid ~ 3 million nodes

SRS for Acoustics


SRS for IC Engine Flows

Intake

ValveExp. RANS DES SAS

3 mm 1 0.95 0.985 0.996

9 mm 1 0.988 - 0.99

Mass flow Rates

Courtesy VW AG Wolfsburg: O. Imberdis, M. Hartmann, H. Bensler, L. Kapitza

VOLKSWAGEN AG, Research and Development, Wolfsburg, Germany

D. Thevenin University of Magdeburg


DrivAer Validation Project:RANS & SRS Modeling

http://www.aer.mw.tum.de Courtesy by TU Munich, Inst. of Aerodynamics

http://www.aer.mw.tum.de/


• Comparison of the pressure distribution on the

symmetry plane with CFX & Fluent on Mesh3

ANSYS CFX, SST, steady-state, 1ms ANSYS Fluent, SST, steady-state, 1ms

RANS SimulationsComparison of ANSYS CFX & Fluent


SAS-SST Simulation: 10-15 days, 100 cores


Summary

• RANS modelling key to industrial CFD Grid quality is key issue

• Transition modelling important for many applications External aeordynamics

Turbomachinery

Wind turbines

…

• SRS is making its way into industrial CFD Different types of model recommended for different types of

applications

• Currently favored methods within ANSYS: SAS – globally unstable flows DDES – globally and locally unstable flows

ELES/WMLES marginally unstable flows

overview of turbulence modeling - ansys...•streamline curvature and system rotation are typical...

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