6819900 turbulent flows case studies fluent
TRANSCRIPT
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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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Axisymmetric Afterbody
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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Axisymmetric Afterbody
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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Axisymmetric Afterbody
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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Axisymmetric Afterbody
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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Axisymmetric Afterbody
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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Results at x = 25 mm Section
-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
Innerjetmolefraction
exp
Xjet-SKE
Xjet-RKE
Xjet-RNG
Xjet-RSM
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Results at x = 51 mm Section
-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
Innerjetmolefraction
exp
Xjet-SKE
Xjet-RKEXjet-RNG
Xjet-RSM
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Results at x = 102 mm Section
-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
Radialvelocilyv(m/s)
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
Innerjetmolefraction
exp
Xjet-SKE
Xjet-RKE
Xjet-RNG
Xjet-RSM
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Results at x = 203 mm Section
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
Radialvelocilyv(m/s)
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
Innerjetmolefraction
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!