Modelling Laminar-Turbulent Transition Processes
2011 ANSYS, Inc. May 14, 20121
Gilles Eggenspieler, Ph. D.Senior Product Manager
What is Laminar-Turbulent Transition in Wall Boundary Layers?
Laminar boundary layer Layered flow without any (or low level) of disturbances
Only at moderate Reynolds numbers
Low wall shear stress and low heat transfer
Prone to separation under weak pressure gradients
Turbulent boundary layer:
2011 ANSYS, Inc. May 14, 20122
Chaotic three-dimensional unsteady disturbances present
At moderate to high Reynolds numbers
High wall shear stress and heat transfer
Much less prone to separation under pressure gradients
Laminar-Turbulent Transition: Disturbances inside or outside the laminar boundary layer
trigger instability
Small disturbances grow and eventually become dominant
Laminar boundary layer switches to turbulent state (Flat plate
transitional Reynolds numbers ~104 106)
Effects of Transition Wall shear stress
Higher wall shear for turbulent flows (more resistance in
pipe flow, higher drag for airfoils, )
Heat transfer Heat transfer is strongly dependent on state of boundary
layer
Much higher heat transfer in turbulent boundary layer
Separation behaviour
Laminar separation
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Separation behaviour Separation point/line can change drastically between
laminar and turbulent flows.
Turbulent flow much more robust than laminar flow. Stays
attached even at larger pressure gradients
Efficiency
Axial turbo machines perform different in laminar and
turbulent stage
Wind turbines have different characteristics
Small scale devices change characteristics depending on
flow regime
Turbulent separation
Natural Transition
Low freestream turbulence
( Tu~0-0.5%)
Typical Examples:
Wind Turbine blades
Fans of jet engines
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Fans of jet engines
Helicopter blades
Any aerodynamic body
moving in still air
Picture from White: Viscous Fluid Flow, McGraw Hill, 1991
23 100%
kTu
U
=
Bypass TransitionExternal disturbance leading to instability
Bypass transition ( Tu~ 0.5-
10%)
High freestream turbulence
forces the laminar
boundary layer into
transition far upstream of Turbulent spot
2011 ANSYS, Inc. May 14, 20125
Picture from:
S. Heiken, R. Demuth, Laurien, E.: Visualization of Bypass-Transition Simulations using Particles (ZAMM)
transition far upstream of
the natural transition
location
Typical Examples:
Turbomachinery flows
All flows in high freestream
turbulence environment
(internal flows)
Turbulent spot
Separation Induced Transition
Strong Inflexional Instability Produces Turbulence in the Boundary Layer
Most important transition mechanism in engineering flows!
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Laminar boundary layer separates and attaches as turbulent boundary layer
Transition takes place after a laminar separation of the boundary layer.
Leads to a very rapid growth of disturbances and to transition.
Can occur in any device with a pressure gradients in the laminar region.
If flow is computed fully turbulent, the separation is missed entirely.
Examples: fans, wind turbines, helicopter blades, axial turbomachines.
Transition Model Requirements
Compatible with modern CFD code:
Unknown application
Complex geometries
Unknown grid topology
Unstructured meshes
Parallel codes domain decomposition
Fully Turbulent
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Requirements:
Different transition mechanisms
Natural transition
Bypass transition
Robust
No excessive grid resolution
Laminar Flow
Transitional
Challenges Transition Modelling Combination of linear and non-linear physical processes
Linear process can be captured by linear stability analysis
Coupling of Navier-Stokes code with laminar boundary layer code and
stability analysis code very complex
Empirical criterion (en) required
Only applicable to simple and known geometries (airfoils)
Cannot capture all physical effects (no bypass transition)
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Cannot capture all physical effects (no bypass transition)
Not suitable for general-purpose CFD codes
RANS Models
Have failed historically to predict correct transition location
Low Reynolds number models have been tested for decades but proved
unsuitable
Local Correlation based Transition Models (LCTM)
Developed by ANSYS to resolve gap in CFD feature matrix (-Re model)
Machinery: Non-local formulations
Algebraic Operations: Find stagnation point Move downstream from boundary
layer profile to boundary layer profile Compute Re for each profile Obtain Ret from correlation using Tu
and at boundary layer edge and
dyUu
Uu
=
0
1
U
=Re
UkTu 3/2=
2011 ANSYS, Inc. May 14, 20129
and at boundary layer edge and compare with Re
If Re > Ret activate turbulence model
New Formulation (LCTM): Avoid any algebraic formulation and
formulate conditions locally Use only transport equations (like in
turbulence model)
8/5400Re = Tut
t ReRe
Transition onset
Transition Onset CorrelationsTransition onset is affected
by: Free-stream turbulence
turbulence intensity (Tu=FSTI)
Pressure gradients ()Right: Correlation of Abu-
dyUu
Uu
=
0
1
U
=Re
2011 ANSYS, Inc. May 14, 201210
Right: Correlation of Abu-
Ghannam and Shaw Low Tu late transition
(natural transition High Tu early transition
(bypass transition) Effect of pressure gradient
),(Re = Tuft
Re t
ANSYS Model based on Intermittency
Intermittency:
Laminar flow:
Turbulent flow
turb
lam turb
t
t t =
+
0 =
2011 ANSYS, Inc. May 14, 201211
Turbulent flow
Transition
Goal is transport equation for using exp. correlations and local formulation
1 =
0 1<
Transport Equation for Ret
2500
Ut
=
( ) ( ) ( )
+
+=
+
j
ttt
jt
j
tjtxx
Px
Ut
eR~eR~eR~
( )( )ttttt FtcP = 0.1eR~Re
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The function Fonset
requires the critical Reynolds number from the
correlation
Tu and are computed at the boundary layer edge non-local Second transport equation required to transport information on Ret
into the boundary layer (by diffusion term)
This second transport equation will be eliminated din future versions
of the mode.
),(Re = Tuft
Modification to SST Turbulence Model
( )
+
+=
+
jtk
jkkj
j x
kx
DPkux
kt
~~)()(
2SP tk = kDk *=
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k kP P=% ( )min max( ,0.1),1.0k kD D=% The intermittency is introduced into the source terms of the ST
turbulence model
At the critical Reynolds number the SST model is activated
Main effect is through production term Pk
Summary Transition Model Formulation 2 Transport Equations
Intermittency () Equation Fraction of time of turbulent vs laminar flow Transition onset controlled by relation between vorticity Reynolds
number and Ret Transition Onset Reynolds number Equation (will be removed
from future versions) Used to pass information about freestream conditions into b.l.
e.g. impinging wakes
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e.g. impinging wakes New Empirical Correlation
Similar to Abu-Ghannam and Shaw, improvements for Natural transition
Modification for Separation Induced Transition Forces rapid transition once laminar sep. occurs Locally Intermittency can be larger than one
-Re Model
Flat Plate Results: dp/dx=0T3A: FSTI = 3.5 % (~ 39000 hexahedra)
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Mesh guidelines: y+ < 1 wall normal expansion ratio ~1.1 good resolution of streamwise direction
T3B
FSTI = 6.5 %
T3A
FSTI = 3.5 %
Flat Plate Results: dp/dx=0
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T3A-
FSTI = 0.9 % Schubauer and
Klebanoff
FSTI = 0.18 %
T3C5
FSTI = 2.5 %
Flat Plate Results: dp/dx (variation in Re number)
T3C2
FSTI = 2.5 %
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T3C3
FSTI = 2.5 %
T3C4
FSTI = 2.5 %
Comparison CFX-Fluent
T3C2 (transition near suction peak)
FSTI = 2.5 %
T3C4 (separation induced transition)
FSTI = 2.5 %
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Aerospatial A Airfoil
Transition on suction side due
to laminar separation
Transition model predicts that
effect
Important:
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Important: The wall shear stress in the region
past transition is higher than in the fully turbulent simulation
The turbulent boundary layer can therefore overcome the adverse pressure gradient better
Less separation near trailing edge
McDonnell Douglas 30P-30N 3-Element Flap
Tu ContourRe = 9 millionMach = 0.2C = 0.5588 mAoA = 8
Exp. hot film transition location measured
Main lower transition:
CFX = 0.587
Exp. = 0.526
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Slat transition:
CFX = -0.056
Exp.= -0.057
Error: 0.1 %
measured as f(x/c)
Main upper transition:
CFX = 0.068
Exp. = 0.057
Error: 1.1 %
Error: 6.1 %Flap transition:
CFX = 0.909
Exp. = 0.931
Error: 2.2 %
Separation Induced Transition forLP-Turbine
Pratt and Whitney Pak-B LP
turbine blade
Transition Model
Experiment ExperimentTransition Model
Transition Model
Laminar separation bubble size f(Re, Tu)
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Increasing Rex
turbine blade
Rex= 50 000, 75 000 and
100 000
FSTI = 0.08, 2.25, 6.0
percent
Plateau indicates laminar
separation bubble
Model predicts that effect
Computations performed
by Suzen and Huang, Univ.
of Kentucky
Transition Model
Experiment
Test Cases: 3D RGW Compressor Cascade
Hub Vortex
Laminar Separation
2011 ANSYS, Inc. May 14, 201222
RGW Compressor (RWTH Aachen)
FSTI = 1.25 %
Rex = 430 000
Tip Vortex
Separation Bubble
Transition
Loss coefficient, (Yp) = 0.097
Yp = (poinlet
- pooutlet
)/pdynoutlet
Test Cases: 3D RGW Compressor Cascade
Flow
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Experimental Oil Flow
Yp = 0.097
Transition Model
Yp = 0.11
Fully Turbulent
Yp = 0.19
3D laminar separation bubble on suction side of blade
Fully turbulent simulation predicts incorrect flow topology
Transition model gets topology right
Strong improvement in loss coefficient Yp
Transitional flow has lower Yp!
Yp = (poinlet
- pooutlet
)/pdynoutlet
Examples of Validation Studies:NASA Rotor 37 test case
Computations are performed on a series of hex scalable meshes with 0.4, 1.5, 4.5 and 11.5 million nodes for single passage
The mesh with 4.5 million nodes provides for virtually grid-independent solution
The -Re-SST model predicts the total pressure ratio of the compressor much better then the SST and k- models
k- model on the coarse mesh produces correct results due to error cancellation
2011 ANSYS, Inc. May 14, 201224 Mass Flow / Choke Mass Flow
T
o
t
a
l
P
r
e
s
s
u
r
e
R
a
t
i
o
0.9 0.92 0.94 0.96 0.98 11.
9
2
2
.
1
2
.
2
experimentSST Mesh1SST Mesh2SST Mesh3
Mass Flow / Choke Mass Flow
T
o
t
a
l
P
r
e
s
s
u
r
e
R
a
t
i
o
0.9 0.92 0.94 0.96 0.98 11.
9
2
2
.
1
2
.
2
experimentk- Mesh1k- Mesh2k- Mesh3
Mass Flow / Choke Mass Flow
T
o
t
a
l
P
r
e
s
s
u
r
e
R
a
t
i
o
0.9 0.92 0.94 0.96 0.98 11.
9
2
2
.
1
2
.
2
experimentSST+TM Mesh2SST+TM Mesh3SST SST-TMk-epsilon
0.4106 nodes
1.5106 nodes
4.5106 nodes
11.5106 nodes
Total Pressure Ratio
Summary
The Local Correlation-based Transition Modelling (LCTM) concept closes a gap in the model offering of modern CFD codes
Formulation allows the combination of detailed experimental data (correlation) with transport equations for the intermittency.
Correlation based transition model has been developed Based strictly on local variables Applicable to unstructured-grid massively parallelized codes
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Applicable to unstructured-grid massively parallelized codes Onset prediction is completely automatically
User must specify correct values of inlet k, Validated for a wide range of 2-D and 3-D turbomachinery and
aeronautical test cases Computational effort is moderate. Model implemented in CFX and Fluent