ignition modeling for controlling cyclic-variability
TRANSCRIPT
Ignition Modeling
for Controlling Cyclic-Variability
Guangfei Zhu and Chris Rutland
Engine Research Center
University of Wisconsin β Madison
LES4ICE
11-12 December 2018
UW-Madison, Engine Research Center
Introduction
β’ Can we control CCV using the ignition system?
β’ CCV Causes
β Flow (velocities, equivalence ratio, residuals, temperature, etc)
β Ignition conditions (spark energy, plasma characteristics, surface heat transfer, etc.)
β’ Stoichiometric combustion
β Primary cause: Velocity field (turbulence)
β’ Possible control
β Spark kernel transport by fluid
β’ Feedback through spark voltage
β Adjust spark energy during ignition event when needed
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CFD Model
β’ OpenFOAM
β’ Turbulence modeling
β Dynamic structure model
β’ Dynamic procedure for tensor coefficient
β Transport for subgrid kinetic energy: ππ ππ
β’ Combustion
β G-Equation model
β Improved swept volume calculations
β Improved re-initialization procedure
β’ Ignition modeling
β ATKIM based circuit model
β Lagrangian and Eulerian kernel growth model
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G-Equation Model
β’ G-Equation
β’ Eulerian phase of ignition kernel
β’ Fully developed flame
β π πππππ from Pitsch (2002)
β’ Improvements
β Swept volume approach
β Re-initialization scheme
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ππΊ
ππ‘+ π’ β βπΊ =
ππ’π β π πππππ βπΊ
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Reaction Rate: Swept Volume Approach
β’ Common approach:
β Velocity * area
β’ Swept Volume Approach
β Evaluate βburntβ volume
change: ππ = πππ+1 β ππ
π
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ππ =π ππ
π’ β πππ
βπ‘
ππππ’
ππ = π πππ’ β ππ
π π ππ΄πΉπππππ
n
n+1 πΊ = 0
n
n+1
πΊ = 0
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Swept Volume Calculation
π = πππΊ
=1
3 β β π πππΊ
=1
3 π΄ππ β π
ππ‘ππ
π=1
β’ Methodology: Perini, et. al. (2016) β’ Find intersection points of πΊ = 0
surface with CFD cell edges β’ Triangulate the πΊ surface β’ Triangulate enclosing cell surfaces β’ Find centroid, π, and normal, π, of
triangulated volume surfaces β’ Use divergence theorem to find
volume:
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Swept Volume Tests
β’ Constant volume combustion
β Fairweather et al. (2009)
β Methane, π = 0.9
β πππππ‘ = 360πΎ, π’β² = 2π/π
β’ TCC3 Engine at U. Michigan
β Volker Sickβs group
β Propane , π = 1.0
β 1300 rpm
β Ign. Timing: -18 CA
0 2 4 6 8 10 12
0
10
20
30
40
50
60
rad
ius (
mm
)
Time (ms)
Experiment
Swept-vol model
GM model
transition point
GM model:
uses π ππ΄πΉ
Flame Radius
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End of ignition
-60 -40 -20 0 20 40 600.0
0.5
1.0
1.5
2.0
2.5
pre
ssu
re (
MP
a)
CA (deg.)
Experiment
swept-vol
non-swept-vol
0
10
20
30
40
50
60
70
80
90
HR
R (
J/d
eg
)
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Re-Initialization of G-field
β’ Common approach
β Iterate: ππΊππ‘β²
= π ππ πΊ0 1 β βπΊ
β Difficulties
β’ Poorly behaved near πΊ = 0
β’ Need to βupwindβ
β’ Arbitrary cell shapes: βπΊ
β’ New scheme (Ngo & Choi, 2018)
β Triangulate πΊ = 0 surface
β Center: π₯π , mesh point: π₯π
β Normal component projection
β Distance ππ = π β (π₯π β π₯π)
β Check all triangulated surfaces for minimum distance
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Ignition Model
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Ignition Model: Major Components
β’ Electric circuit model (AKTIM based, Colin et al., 2001, 2011 )
β’ Initial kernel radius and temperature (Refael & Sher, 1985)
β’ Lagrangian kernel growth: spherical πππ
ππ‘= ππ +
ππ’
ππ ππππππ
β Plasma channel model for ππ
β While ππ < 1ππ
β’ Use wrinkling factor (Colin et al., 2007): ππππππ = Ξ ππΏ
β’ Eulerian kernel growth: switch to G-equation
β π πππππ = π πππππ,π‘πππ + πΌ π π + π πΏ β π πππππ,π‘πππ
β πΌ hyperbolic tangent transition function (Colin and Truffin, 2000)
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Ignition Validation
β’ Propane air, constant volume chambers (Nwagwe, 2000)
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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
5
10
15
20
25
Ra
diu
s (
mm
)
Time (ms)
Exp 1
Exp 2
Exp 3
sim_Cbd300
sim_Cbd150
sim_Cbd120
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40
2
4
6
8
10
12
14
16
18
En
erg
y d
ep
osit (
W)
Time (ms)
sim_Cbd300
sim_Cbd150
sim_Cbd120
u'=2.36 m/s
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00
5
10
15
20
25
30
35
Rad
ius (
mm
)
Time (ms)
Exp 1
Exp 2
sim_Cbd300
sim_Cbd120
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40
2
4
6
8
10
12
14
16
18
En
erg
y d
ep
osit (
W)
Time (ms)
sim_Cbd300
sim_Cbd120
u'=4.72 m/s
Calibration: πΆππ
πΈππ =πππ2
πΆππ2 ππ
Coefficient for initial
energy deposition
Used only to determine
initial kernel radius and
temperature
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Engine Test Cases: TCC3 Engine
β’ General Motors TCC3 Engine
β’ Volker Sickβs group at the U. of Michigan
β’ 30 stoichiometric cases
β’ Initial conditions: mapped from CONVERGE to OpenFOAM at IVC
β Proved by Seunghwan Keum at GM
β Consecutive cycles with combustion
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Bore Γ Stroke 92 Γ 86 mm
Compression Ratio 10:1
IVC, EVO (Β°ATDC) -110, 130
Fuel Propane (phi =1.0)
Ignition Timing -18 deg. ATDC
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Pressure and Heat Release Rates
β’ Multiple cycles β well bounded but less variation than data
β 300 cycles in experiments
β’ Average cycle matches well
β’ Data from TCC-III CFD Input Dataset online
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-60 -40 -20 0 20 40 60
0
500
1000
1500
2000
2500
Pre
ssu
re (
kP
a)
CA (deg)
Sim_Ave
Exp_Ave
0
10
20
30
40
50
60
70
HR
R (
J/d
eg
)
30 Cycles Average Cycle
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Ignition Model: 30 Cycles
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Spark Current
Gap Voltage
Experiments Model
Experiments Model
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Example Flow Fields
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Sim_01
Sim_14
Sim_18
velocity
4 CAD after ignition Flame marked by G=0 surface
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Burnt Probability and Velocity Fields
Experiments
β’ From Volker Sickβs group
β Zheng et al. 2018
β’ Silicon oil marks flame
β’ Velocity for only 1.1 m/s to 65 m/s
β’ 80 cycle average
Simulation
β’ 8 cycle averages
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Isolate 3 Cycles for More Analysis
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Peak Pressure CA 10
CA 50
βhighβ
βmediumβ
βlowβ
βhighβ
βmediumβ βlowβ
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Impact of π, π, ππ ππ , π
β’ Replace βmediumβ fields with βhighβ and βlowβ fields
β’ Largest impact: π next largest impact: ππ ππ
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CA 10 CA 50
π
ππ ππ
π
π
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Spark Kernel: Plasma Channel Length
β’ Spark kernel radius increases by ππ and ΞππΏ
β’ Location moves with local gas velocity
β Changes spark plasma channel length, πΏπ
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πΏπ Gas Velocity
0.0 0.5 1.0 1.5 2.0 2.52
3
4
5
6
7
8
Ve
locity M
ag
(m
/s)
Distance from Cathode (mm)
sim_01
sim_14
sim_18
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Plasma Channel Feedback
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ππ
ππ
πππ
πΈπ(π‘)
π ππππππ¦
πππ = πππ + πππ
+ 40.46 πΏπ ππ β0.32π0.51
Energy supplied πΈπ decreases in time: π ππ, πππ , π
Plasma channel: current ππ, voltage πππ
Spark channel length: πΏπ
Spark channel length
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Plasma Channel Feedback
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ππ
πΏπ
ππ
πππ
πΈπ(π‘)
π ππππππ¦
πππ = πππ + πππ
+ 40.46 πΏπ ππ β0.32π0.51
Concept motivated by comments from Ron Grover at GM Research
Energy supplied πΈπ decreases in time: π ππ, πππ , π
Plasma channel: current ππ, voltage πππ
Spark channel length: πΏπ
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-18 -16 -14 -12 -10 -8 -6 -4 -20
500
1000
1500
2000
2500
Vo
lta
ge
(V
)
CA (deg.)
High
Low
Medium
-18 -16 -14 -12 -100
1
2
3
4
Spark
Le
ng
th (
mm
)
CA (deg.)
High
Low
Median
Ignition Characteristics: 3 Cases
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Spark Length Voltage
-18 -16 -14 -12 -100
1
2
3
4
5
6
7
8
Rad
us (
mm
)
CA(deg.)
High
Low
Median
Spark Radius
βLowβ Cycle: Add 30 mJ at -17CA
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βLowβ Cycle: Add 30 mJ at -17CA
β’ Increases current
β’ Decreases voltage
β’ Potential impacts - increase:
β Plasma velocity, ππ
β Energy deposition
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-18 -16 -14 -12 -10 -8 -6 -4 -2 00.00
0.02
0.04
0.06
0.08
0.10
0.12
Cu
rre
nt
(A)
CA (deg.)
add30
orig
-18 -16 -14 -12 -10 -8 -6 -4 -2 00
500
1000
1500
2000
Vo
lta
ge
(V
)
CA (deg.)
add30
orig
-18 -17 -16 -15 -14 -13 -12 -11 -10 -90
2
4
6
8
10
12
14
16
18
20
Eff
ective
Sp
ark
Po
we
r (J
/de
g.)
CA (deg.)
add30
orig
Spark Power
Current
Voltage
πππ ~ππ β0.32
original
add 30 mJ
UW-Madison, Engine Research Center
-18 -16 -14 -12 -10 -8 -6 -4 -2 00.0
0.2
0.4
0.6
0.8
1.0
Sp
(m
/s)
CA (deg.)
add30
orig
Impact on Plasma Velocity: Minor
β’ Plasma velocity, ππ , is much lower than ππ
β’ ππ increases
β But impact is insignificant
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-18 -16 -14 -12 -100
1
2
3
4
5
6
Sp
alpha starts
to work
Sp a
nd S
T (
m/s
)
CA(deg.)
High
Low
Median
ST
Original
ππ
ππ
ππ
UW-Madison, Engine Research Center
ππ Decreased: Overall Impact is Negative
β’ Impact on energy addition:
β Insignificant
β’ Eventual decrease in ππ
β Expansion and lower Ksgs
β’ Overall impact:
β Negative - misfire
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-60 -40 -20 0 20 40 600
200
400
600
800
1000
1200
1400
1600
1800
Pre
ssu
re (
kP
a)
CA (deg)
orig
add30
0
10
20
30
40
50
60
70
HR
R (
J/d
eg
.)
-18 -16 -14 -12 -10 -8 -6 -4 -2 00
1
2
3
4
5
6
St
(m/s
)
CA (deg.)
add30
orig
ππ
original
add 30 mJ
UW-Madison, Engine Research Center
Summary β’ Combustion model
β G-equation based
β Swept volume approach
β Re-initialization method
β’ Ignition model AKTIM based
β Simple electric circuit
β Kernel growth; merges with G-equation
β’ Testing
β Constant volume ignition/flame propagation
β TCC3 engine; 30 cycles
β’ Possible CCV control
β Fluid moves flame kernel; changes plasma channel length; affects voltage
β Feedback: low voltage -> increase spark energy
β Current results: misfire
β But demonstrate that on-the-fly impact of ignition is possible
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Acknowledgements
β’ Work supported financially and technically by General Motors Research through the GM-UW Cooperative Research Laboratory
β GM Director: Paul Najt
β GM Technical Contacts: Ronald Grover, Seunghwan Keum
β’ Engine experimental results provided by Professor Volker Sick, University of Michigan through the GM LES Working Group.
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References
H. Pitsch, βA G-equation formulation for large-eddy simulation of premixed turbulent combustion,β Cent. Turbul. Res. Annu. Res. Briefs, vol. 4, 2002. Heinz Pitsch, H.,Steiner, H., Scalar Mixing and Dissipation Rate in Large-eddy Simulations of Non-premixed Turbulent Combustion, Proceedings of the Combustion
Institute, 28, 41-49, 2000. Perini, Federico, Youngchul Ra, Kenji Hiraoka, Kazutoshi Nomura, Akihiro Yuuki, Yuji Oda, Christopher Rutland, and Rolf Reitz. "An efficient level-set flame propagation
model for hybrid unstructured grids using the G-equation." SAE International Journal of Engines 9, no. 3 (2016): 1409-1424. Fairweather, M., M. P. Ormsby, C. G. W. Sheppard, and R. Woolley. "Turbulent burning rates of methane and methaneβhydrogen mixtures." Combustion and Flame
156, no. 4 (2009): 780-790. Ngo, Long Cu, and Hyoung Gwon Choi. "Efficient direct re-initialization approach of a level set method for unstructured meshes." Computers & Fluids 154 (2017): 167-
183. O. Colin and K. Truffin, βA spark ignition model for large eddy simulation based on an FSD transport equation (ISSIM-LES),β Proc. Combust. Inst., vol. 33, no. 2, pp. 3097β
3104, 2011 Colin, O., F. Ducros, D. Veynante, and Thierry Poinsot. "A thickened flame model for large eddy simulations of turbulent premixed combustion." Physics of fluids 12, no.
7 (2000): 1843-1863. J. M. Duclos and O. Colin, βArc and Kernel Tracking Ignition Model for 3D Spark Ignition Engine Calculations, 5th Int,β in Symp. on Diagnostics and Modeling of
Combustion in Internal Combustion Engines, COMODIA, 2001 Refael, S., and E. Sher. "A theoretical study of the ignition of a reactive medium by means of an electrical discharge." Combustion and flame 59, no. 1 (1985): 17-30. Nwagwe, I. K., H. G. Weller, G. R. Tabor, A. D. Gosman, M. Lawes, C. G. W. Sheppard, and R. Wooley. "Measurements and large eddy simulations of turbulent premixed
flame kernel growth." Proceedings of the Combustion Institute 28, no. 1 (2000): 59-65. T. Lucchini et al., βA comprehensive model to predict the initial stage of combustion in SI engines,β 2013. L. Fan and R. D. Reitz, βDevelopment of an ignition and combustion model for spark-ignition engines,β SAE Trans., pp. 1977β1989, 2000 W. Zeng, S. Keum, T.-W. Kuo, and V. Sick, βRole of large scale flow features on cycle-to-cycle variations of spark-ignited flame-initiation and its transition to turbulent
combustion,β Proc. Combust. Inst., 2018. TCC-III CFD Input Dataset, for dx.doi.org/10.1177/1468087417720558 Pope S., B., CEQ: A Fortran Libray to Compute Equilibrium Compositions Using Gibbs Function Continuation, http://eccentric.mae.cornell.edu/~pope/CEQ, 2003.
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Appendix-1
β’ Plasma channel equations
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ππΈπ (π‘)
ππ‘= βπ π ππ
2 π‘ β πππππ π‘
ππ =2πΈπ πΏπ
Three Cases
Global Averaged High (sim05) Medium (sim29) Low (sim09)
ksgs (π2/π 2) 4.027 4.279 3.159
T (K) 715.637 712.304 711.117
π 0.99747 0.99739 0.99739
π π =ππππ π‘ ππ (π‘)
4πππ2ππ’ βπ β βπ’π
1 +πΏπ»π
πππππ
3
πππ = πππ + πππ
+ 40.46 πΏπ ππ β0.32π0.51
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Appendix-2
β’ Combustion model equations
31
ππΊ
ππ‘+ π’ β βπΊ =
ππ’π β π πππππ βπΊ
Gu lder π πΏ = π π’π πππ’π0
πΌπ
π0
π½
1.0 β π β πΉ
π ππ πΏ
= 1 + βπ4π3
2
2π1π·π +
π4π32
2π1π·π
2
+ π4π32π·π
1 2 π’β²
π πΏ
Peters, N., Turbulent Combustion. Cambridge University Press, 2000.
RANS
π π β π πΏπ πΏ
= βπ32πΆπ£
2π1πππ‘,πΊ
β
ππΉ+
π32πΆπ£
2π1πππ‘,πΊ
β
ππΉ
2
+π32π·π‘π πΏππΉ
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Pitsch, H. "A G-equation formulation for large-eddy simulation of premixed turbulent
combustion." Center for Turbulence Research Annual Research Briefs 4 (2002).
LES
UW-Madison, Engine Research Center
β’ Energy source term
β’ Sub-grid kinetic energy transport
ππ = πππππ‘
= π πππ’ β ππ
π π ππ΄πΉπππππ
πππππ‘
=π ππ,π β ππ
βπ‘
ππππ’
ππ ππ ππ
ππ‘+
ππ π’π ππ ππ
ππ₯π= βπ π€πππππ β πΆπ
ππ ππ
π₯+
π
ππ₯ππ ππ ππ
πππ ππ
ππ₯π
Appendix-3