overview of turbulence modeling - ansys...•streamline curvature and system rotation are typical...
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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
© 2011 ANSYS, Inc. October 23, 20123
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
© 2011 ANSYS, Inc. October 23, 20124
• 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
© 2011 ANSYS, Inc. October 23, 20125
• 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
© 2011 ANSYS, Inc. October 23, 20127
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
© 2011 ANSYS, Inc. October 23, 20128
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
© 2011 ANSYS, Inc. October 23, 20129
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:
© 2011 ANSYS, Inc. October 23, 201210
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
© 2011 ANSYS, Inc. October 23, 201211
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
© 2011 ANSYS, Inc. October 23, 201212
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
© 2011 ANSYS, Inc. October 23, 201213
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
© 2011 ANSYS, Inc. October 23, 201214
Stanford DiffuserFlow Topology
• Flow topology depends
strongly on turbulence
model
• Stress anisotropy
necessary to obtain
correct behaviour
X/H=16
© 2011 ANSYS, Inc. October 23, 201215
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
© 2011 ANSYS, Inc. October 23, 201216
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
© 2011 ANSYS, Inc. October 23, 201217
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
© 2011 ANSYS, Inc. October 23, 201218
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
© 2011 ANSYS, Inc. October 23, 201219
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
© 2011 ANSYS, Inc. October 23, 201220
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
© 2011 ANSYS, Inc. October 23, 201221
Wall Shear @ Rotor 1
SST - Transitionk-ω - Model SST - Model
© 2011 ANSYS, Inc. October 23, 201222
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
© 2011 ANSYS, Inc. October 23, 201224
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
© 2011 ANSYS, Inc. October 23, 201225
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
© 2011 ANSYS, Inc. October 23, 201226
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
© 2011 ANSYS, Inc. October 23, 201227
• 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
© 2011 ANSYS, Inc. October 23, 201228
• 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
© 2011 ANSYS, Inc. October 23, 201229
• 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
© 2011 ANSYS, Inc. October 23, 201230
• 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
© 2011 ANSYS, Inc. October 23, 201231
ELES: vortex structures
Q-criterion iso-surface colored by Velocity Magnitude
© 2011 ANSYS, Inc. October 23, 201232
Pressure Contours
URANS ELES
© 2011 ANSYS, Inc. October 23, 201233
U velocity Profiles
x= -163mm
x= -223mm
x= -163mm
x= -223mm
© 2011 ANSYS, Inc. October 23, 201234
U velocity Profiles
x= -3mm
x= -123mm
x= -3mm
x= -123mm
© 2011 ANSYS, Inc. October 23, 201235
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
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 122
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 123
Grid ~ 3 million nodes
SRS for Acoustics
© 2011 ANSYS, Inc. October 23, 201236
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
© 2011 ANSYS, Inc. October 23, 201237
DrivAer Validation Project:RANS & SRS Modeling
http://www.aer.mw.tum.de Courtesy by TU Munich, Inst. of Aerodynamics
© 2011 ANSYS, Inc. October 23, 201238
• 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
© 2011 ANSYS, Inc. October 23, 201239
SAS-SST Simulation: 10-15 days, 100 cores
© 2011 ANSYS, Inc. October 23, 201240
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
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