Advanced Turbulence Modeling
for engine applications
Chan Hee Son
University of Wisconsin, Engine Research Center
Advisor: Professor Christopher J. Rutland
Sponsor: General Motors
GM
Collaborative Research Lab
UW
1
Motivation

Linear k-e model
 widely used, but compromise between expense and accuracy
 Inherently unable to account for secondary flows
 Poor predictions for separated or curved streamline flows

Non-linear models
 Able to predict secondary flow of the second kind
 Numerical instability leads to excessive computational expense
 Wallin-Johansson's explicit Algebraic Reynolds Stress Model as a
representative case

v2-f model
 Two turbulence scales are used
 More accurate representation of the physics (eddy viscosity)
close to the wall
 Very good performance in flow separation regions
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Collaborative Research Lab
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2
Model formulation

Turbulence governing equations of v2 - f

  
 t k  U  k      T  k   P  e
k  


T  
e
e2
 t e  U  e       e   Ce 1 P  Ce 2
e  
k
k

Ce 1  1.3 
0.25
1  

d
 
8
l
Ce 2  1.9


 
e
 t v2  U   v2      T   v2   kf  v2
k 
k


 2  v2 
k 
3
P
2 2

f  L  f  Cf1
 Cf 2
T
k
C f 1  0.4, C f 2  0.3
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Collaborative Research Lab
P  Production
Ce 1  1.44, Ce 2  1.92
1
 k3
3 2



l 2  max  2 , C2   
e
 e  

d  wall distance
1


2
k



T  max  ,6   
e  e  


 T  C v2T
L  CL l
C  0.19 CL  0.3 C  70
UW
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Sandia National Lab Optical engine

Specifications
Bore – 79.5mm, Stroke – 85.0 mm
 CR = 18.7
 1500 RPM
 RS = 1.5 ~ 3.5
 Cold flow (no spray or combustion)


Measurement locations
3 clusters of 5 points located in a vertical plane bisecting the
exhaust valves
 The 3 center points are at r= 13.6 mm with all neighboring
measurement points being 1mm away.

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Collaborative Research Lab
UW
4
Radial and tangential velocities @ 5 ATDC with
swirl ratio 3.5
v2-f
W-J
Radial Vel. Rs=3.5 5ATDC
Tangential Vel. Rs=3.5 5ATDC
0.000
-0.005
Z(m)
k-e
2
v -f
W-J
exp
-0.010
-0.015
-1.0
-0.5
0.0
0.5
1.0
0
1
2
Vel(m/s)
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Collaborative Research Lab
3
4
5
6
Vel(m/s)
UW
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TKE history for case with swirl ratio = 3.5
1.2
exp
1.6
k-e
1.2
TKE/Sp
2
0.8
0.8
0.4
0.4
0.0
0.0
3.0
1.2
W-J
z=4
z=8
z=12
2
v -f
2.5
0.8
TKE/Sp
2
2.0
1.5
0.4
1.0
0.5
0.0
-60
-40
-20
0
20
40
60
0.0
-60
-40
-20
CAD
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Collaborative Research Lab
0
20
40
60
CAD
UW
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Conclusion

For the Sandia National lab optical engine simulation, W-J
eARSM does not show any improvement for the mean flow.
Even the k-e model is better.
 Potential reason: the W-J ARSM is originally derived for 2D flow. 3D
version is quartic order. Thus, too complex for practical use.

Increased levels of turbulence is predicted by the WJ model.
 At swirl ratio 2.5 and 3.5, TKE prediction over time is very similar to k-e
model in trend, but about 50% higher in turbulence level.
 This is not due to the ability of this model to capture turbulence
anisotropy, as the trend is almost exactly the same as k-e. At high swirl
anisotropy increases.

GM
The v2-f model consistently shows improved results. Still it fails
to catch the trends of the experimental turbulent kinetic energy
results.
Collaborative Research Lab
UW
7