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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
© 2011 ANSYS, Inc. May 14, 20123
• 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
© 2011 ANSYS, Inc. May 14, 20124
– 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
δ
δ
= ⋅
Bypass Transition
External 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!
© 2011 ANSYS, Inc. May 14, 20126
• 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
© 2011 ANSYS, Inc. May 14, 20127
• 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)
© 2011 ANSYS, Inc. May 14, 20128
– 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 (γ-ReΘ model)
Machinery: Non-local formulations
Algebraic Operations:• Find stagnation point
• Move downstream from boundary layer profile to boundary layer profile
• Compute ReΘ for each profile
• Obtain ReΘt from correlation using Tuand λ at boundary layer edge and
dyU
u
U
u∫
−=δ
θ0
1 µθρ
θU=Re
U
kTu
3/2=
© 2011 ANSYS, Inc. May 14, 20129
and λΘ at boundary layer edge and compare with ReΘ
• If ReΘ > ReΘt activate turbulence model
New Formulation (LCTM):• Avoid any algebraic formulation and
formulate conditions locally
• Use only transport equations (like in turbulence model)
8/5400Re −= Tutθ
tθθ ReRe ≥
Transition onset
Transition Onset Correlations
Transition onset is affected
by:− Free-stream turbulence
turbulence intensity (Tu=FSTI)
− Pressure gradients (λθ)
Right: Correlation of Abu-
dyU
u
U
u∫
−=δ
θ0
1µθρ
θU=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 Θ= λθ Tuft
Re tθ
ANSYS Model based on Intermittency
• Intermittency:
• Laminar flow:
• Turbulent flow
turb
lam turb
t
t tγ =
+
0γ =
© 2011 ANSYS, Inc. May 14, 201211
• Turbulent flow
• Transition
• Goal is transport equation for γ using exp.
correlations and local formulation
1γ =
0 1γ< <
Transport Equation for Reθt
2
500
Ut
ρµ=
( ) ( ) ( )
∂∂+
∂∂+=
∂∂
+∂
∂
j
ttt
jt
j
tjt
xxP
x
U
tθ
θθθθ µµσ
ρρ eR~eR
~eR
~
( )( )ttttt Ft
cP θθθθθρ −−= 0.1eR
~Re
© 2011 ANSYS, Inc. May 14, 201212
• The function Fonset
requires the critical Reynolds number from the
correlation
• Tu and λΘ are computed at the boundary layer edge – non-local
• Second transport equation required to transport information on ReΘt
into the boundary layer (by diffusion term)
• This second transport equation will be eliminated din future versions
of the mode.
),(Re Θ= λθ Tuft
Modification to SST Turbulence Model
( )
∂∂+
∂∂+−=
∂∂+
∂∂
jtk
jkkj
j x
k
xDPku
xk
tµσµρρ ~~
)()(
2SP tk µ= ωρβ kDk*=
© 2011 ANSYS, Inc. May 14, 201213
k kP Pγ=% ( )min max( ,0.1),1.0k kD Dγ=%
• The intermittency γ 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 (γ) Equation� Fraction of time of turbulent vs laminar flow� Transition onset controlled by relation between vorticity Reynolds
number and Reθt− 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
© 2011 ANSYS, Inc. May 14, 201214
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
γ-ReΘ Model
Flat Plate Results: dp/dx=0
T3A: FSTI = 3.5 % (~ 39000 hexahedra)
© 2011 ANSYS, Inc. May 14, 201215
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
© 2011 ANSYS, Inc. May 14, 201216
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 %
© 2011 ANSYS, Inc. May 14, 201217
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 %
© 2011 ANSYS, Inc. May 14, 201218
Aerospatial A Airfoil
• Transition on suction side due
to laminar separation
• Transition model predicts that
effect
• Important:
© 2011 ANSYS, Inc. May 14, 201219
• 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
© 2011 ANSYS, Inc. May 14, 201220
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 Experiment
Transition Model
Transition Model
Laminar separation bubble size f(Re, Tu)
© 2011 ANSYS, Inc. May 14, 201221
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
© 2011 ANSYS, Inc. May 14, 201223
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 γ-ReΘ-SST model predicts the total pressure ratio of the compressor much better then the SST and k-ε models
• k-ε model on the coarse mesh produces “correct” results due to error cancellation
© 2011 ANSYS, Inc. May 14, 201224 Mass Flow / Choke Mass Flow
To
talP
ress
ure
Rat
io
0.9 0.92 0.94 0.96 0.98 11.9
22.
12.
2
experimentSST Mesh1SST Mesh2SST Mesh3
Mass Flow / Choke Mass Flow
Tot
alP
ress
ure
Rat
io
0.9 0.92 0.94 0.96 0.98 11.9
22.
12.
2
experimentk-ε Mesh1k-ε Mesh2k-ε Mesh3
Mass Flow / Choke Mass Flow
To
talP
ress
ure
Rat
io
0.9 0.92 0.94 0.96 0.98 11.9
22.
12.
2
experimentSST+TM Mesh2SST+TM Mesh3SST SST-TMk-epsilon
0.4·106 nodes
1.5·106 nodes
4.5·106 nodes
11.5·106 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
© 2011 ANSYS, Inc. May 14, 201225
− Applicable to unstructured-grid massively parallelized codes• Onset prediction is completely automatically
− User must specify correct values of inlet k, ω• 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