ignition modeling for controlling cyclic-variability

Ignition Modeling

for Controlling Cyclic-Variability

Guangfei Zhu and Chris Rutland

Engine Research Center

University of Wisconsin – Madison

LES4ICE

11-12 December 2018

UW-Madison, Engine Research Center

Introduction

• Can we control CCV using the ignition system?

• CCV Causes

– Flow (velocities, equivalence ratio, residuals, temperature, etc)

– Ignition conditions (spark energy, plasma characteristics, surface heat transfer, etc.)

• Stoichiometric combustion

– Primary cause: Velocity field (turbulence)

• Possible control

– Spark kernel transport by fluid

• Feedback through spark voltage

– Adjust spark energy during ignition event when needed

2


CFD Model

• OpenFOAM

• Turbulence modeling

– Dynamic structure model

• Dynamic procedure for tensor coefficient

– Transport for subgrid kinetic energy: 𝑘𝑠𝑔𝑠

• Combustion

– G-Equation model

– Improved swept volume calculations

– Improved re-initialization procedure

• Ignition modeling

– ATKIM based circuit model

– Lagrangian and Eulerian kernel growth model

3


G-Equation Model

• G-Equation

• Eulerian phase of ignition kernel

• Fully developed flame

– 𝑠𝑓𝑙𝑎𝑚𝑒 from Pitsch (2002)

• Improvements

– Swept volume approach

– Re-initialization scheme

4

𝜕𝐺

𝜕𝑡+ 𝑢 ∙ ∇𝐺 =

𝜌𝑢𝜌 ∙ 𝑠𝑓𝑙𝑎𝑚𝑒 ∇𝐺


Reaction Rate: Swept Volume Approach

• Common approach:

– Velocity * area

• Swept Volume Approach

– Evaluate ‘burnt’ volume

change: 𝑉𝑆 = 𝑉𝑏𝑛+1 − 𝑉𝑏

𝑛

5

𝜔𝑖 =𝜌 𝑌𝑖

𝑢 − 𝑌𝑖𝑏

∆𝑡

𝑉𝑆𝑉𝑢

𝜔𝑖 = 𝜌 𝑌𝑖𝑢 − 𝑌𝑖

𝑏 𝑠𝑇𝐴𝐹𝑉𝑐𝑒𝑙𝑙

n

n+1 𝐺 = 0

n

n+1

𝐺 = 0


Swept Volume Calculation

𝑉 = 𝑑𝑉𝛺

=1

3 ∇ ∙ 𝑓 𝑑𝑉𝛺

=1

3 𝐴𝑖𝑓 ∙ 𝑛

𝑛𝑡𝑟𝑖

𝑖=1

• Methodology: Perini, et. al. (2016) • Find intersection points of 𝐺 = 0

surface with CFD cell edges • Triangulate the 𝐺 surface • Triangulate enclosing cell surfaces • Find centroid, 𝑓, and normal, 𝑛, of

triangulated volume surfaces • Use divergence theorem to find

volume:

6


Swept Volume Tests

• Constant volume combustion

– Fairweather et al. (2009)

– Methane, 𝜙 = 0.9

– 𝑇𝑖𝑛𝑖𝑡 = 360𝐾, 𝑢′ = 2𝑚/𝑠

• TCC3 Engine at U. Michigan

– Volker Sick’s group

– Propane , 𝜙 = 1.0

– 1300 rpm

– 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 𝑠𝑇𝐴𝐹

Flame Radius

7

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

)


Re-Initialization of G-field

• Common approach

– Iterate: 𝜕𝐺𝜕𝑡′

= 𝑠𝑔𝑛 𝐺0 1 − ∇𝐺

– Difficulties

• Poorly behaved near 𝐺 = 0

• Need to ‘upwind’

• Arbitrary cell shapes: ∇𝐺

• New scheme (Ngo & Choi, 2018)

– Triangulate 𝐺 = 0 surface

– Center: 𝑥𝑐 , mesh point: 𝑥𝑛

– Normal component projection

– Distance 𝑑𝑓 = 𝑛 ∗ (𝑥𝑛 − 𝑥𝑐)

– Check all triangulated surfaces for minimum distance

8


Ignition Model

9


Ignition Model: Major Components

• Electric circuit model (AKTIM based, Colin et al., 2001, 2011 )

• Initial kernel radius and temperature (Refael & Sher, 1985)

• Lagrangian kernel growth: spherical 𝑑𝑟𝑘

𝑑𝑡= 𝑆𝑃 +

𝜌𝑢

𝜌𝑏 𝑆𝑓𝑙𝑎𝑚𝑒

– Plasma channel model for 𝑆𝑃

– While 𝑟𝑘 < 1𝑚𝑚

• Use wrinkling factor (Colin et al., 2007): 𝑆𝑓𝑙𝑎𝑚𝑒 = Ξ 𝑆𝐿

• Eulerian kernel growth: switch to G-equation

– 𝑠𝑓𝑙𝑎𝑚𝑒 = 𝑠𝑓𝑙𝑎𝑚𝑒,𝑡𝑟𝑎𝑛 + 𝛼 𝑠𝑇 + 𝑠𝐿 − 𝑠𝑓𝑙𝑎𝑚𝑒,𝑡𝑟𝑎𝑛

– 𝛼 hyperbolic tangent transition function (Colin and Truffin, 2000)

10


Ignition Validation

• Propane air, constant volume chambers (Nwagwe, 2000)

11

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: 𝐶𝑏𝑑

𝐸𝑏𝑑 =𝑉𝑏𝑑2

𝐶𝑏𝑑2 𝑑𝑔

Coefficient for initial

energy deposition

Used only to determine

initial kernel radius and

temperature


Engine Test Cases: TCC3 Engine

• General Motors TCC3 Engine

• Volker Sick’s group at the U. of Michigan

• 30 stoichiometric cases

• Initial conditions: mapped from CONVERGE to OpenFOAM at IVC

– Proved by Seunghwan Keum at GM

– Consecutive cycles with combustion

12

Bore × Stroke 92 × 86 mm

Compression Ratio 10:1

IVC, EVO (°ATDC) -110, 130

Fuel Propane (phi =1.0)

Ignition Timing -18 deg. ATDC


Pressure and Heat Release Rates

• Multiple cycles – well bounded but less variation than data

– 300 cycles in experiments

• Average cycle matches well

• Data from TCC-III CFD Input Dataset online

13

-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


Ignition Model: 30 Cycles

14

Spark Current

Gap Voltage

Experiments Model

Experiments Model


Example Flow Fields

15

Sim_01

Sim_14

Sim_18

velocity

4 CAD after ignition Flame marked by G=0 surface


Burnt Probability and Velocity Fields

Experiments

• From Volker Sick’s group

– Zheng et al. 2018

• Silicon oil marks flame

• Velocity for only 1.1 m/s to 65 m/s

• 80 cycle average

Simulation

• 8 cycle averages

16


Isolate 3 Cycles for More Analysis

17

Peak Pressure CA 10

CA 50

“high”

“medium”

“low”

“high”

“medium” “low”


Impact of 𝑈, 𝜙, 𝑘𝑠𝑔𝑠, 𝑇

• Replace “medium” fields with “high” and “low” fields

• Largest impact: 𝑈 next largest impact: 𝑘𝑠𝑔𝑠

18

CA 10 CA 50

𝑇

𝑘𝑠𝑔𝑠

𝑈

𝜙


Spark Kernel: Plasma Channel Length

• Spark kernel radius increases by 𝑆𝑃 and Ξ𝑆𝐿

• Location moves with local gas velocity

– Changes spark plasma channel length, 𝐿𝑠

19

𝐿𝑠 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


Plasma Channel Feedback

20

𝑆𝑃

𝑖𝑠

𝑉𝑖𝑒

𝐸𝑆(𝑡)

𝜔 𝑒𝑛𝑒𝑟𝑔𝑦

𝑉𝑖𝑒 = 𝑉𝑐𝑓 + 𝑉𝑎𝑓

+ 40.46 𝐿𝑠 𝑖𝑠−0.32𝑝0.51

Energy supplied 𝐸𝑆 decreases in time: 𝑓 𝑖𝑆, 𝑉𝑖𝑒 , 𝑅

Plasma channel: current 𝑖𝑆, voltage 𝑉𝑖𝑒

Spark channel length: 𝐿𝑠

Spark channel length


Plasma Channel Feedback

21

𝑆𝑃

𝐿𝑠

𝑖𝑠

𝑉𝑖𝑒

𝐸𝑆(𝑡)

𝜔 𝑒𝑛𝑒𝑟𝑔𝑦


+ 40.46 𝐿𝑠 𝑖𝑠−0.32𝑝0.51

Concept motivated by comments from Ron Grover at GM Research

Energy supplied 𝐸𝑆 decreases in time: 𝑓 𝑖𝑆, 𝑉𝑖𝑒 , 𝑅

Plasma channel: current 𝑖𝑆, voltage 𝑉𝑖𝑒

Spark channel length: 𝐿𝑠


-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

22

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

‘Low’ Cycle: Add 30 mJ at -17CA


‘Low’ Cycle: Add 30 mJ at -17CA

• Increases current

• Decreases voltage

• Potential impacts - increase:

– Plasma velocity, 𝑆𝑃

– Energy deposition

23

-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

𝑉𝑖𝑒 ~𝑖𝑠−0.32

original

add 30 mJ


-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

• Plasma velocity, 𝑆𝑃 , is much lower than 𝑆𝑇

• 𝑆𝑃 increases

– But impact is insignificant

24

-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

𝑆𝑃

𝑆𝑃

𝑆𝑇


𝑆𝑇 Decreased: Overall Impact is Negative

• Impact on energy addition:

– Insignificant

• Eventual decrease in 𝑆𝑇

– Expansion and lower Ksgs

• Overall impact:

– Negative - misfire

25

-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

𝑆𝑇

original

add 30 mJ


Summary • Combustion model

– G-equation based

– Swept volume approach

– Re-initialization method

• Ignition model AKTIM based

– Simple electric circuit

– Kernel growth; merges with G-equation

• Testing

– Constant volume ignition/flame propagation

– TCC3 engine; 30 cycles

• Possible CCV control

– Fluid moves flame kernel; changes plasma channel length; affects voltage

– Feedback: low voltage -> increase spark energy

– Current results: misfire

– But demonstrate that on-the-fly impact of ignition is possible

26


Acknowledgements

• Work supported financially and technically by General Motors Research through the GM-UW Cooperative Research Laboratory

– GM Director: Paul Najt

– GM Technical Contacts: Ronald Grover, Seunghwan Keum

• Engine experimental results provided by Professor Volker Sick, University of Michigan through the GM LES Working Group.

27

UW-Madison, Engine Research Center 28


References

H. Pitsch, “A G-equation formulation for large-eddy simulation of premixed turbulent combustion,” 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 methane–hydrogen 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, “A spark ignition model for large eddy simulation based on an FSD transport equation (ISSIM-LES),” Proc. Combust. Inst., vol. 33, no. 2, pp. 3097–

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, “Arc and Kernel Tracking Ignition Model for 3D Spark Ignition Engine Calculations, 5th Int,” 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., “A comprehensive model to predict the initial stage of combustion in SI engines,” 2013. L. Fan and R. D. Reitz, “Development of an ignition and combustion model for spark-ignition engines,” SAE Trans., pp. 1977–1989, 2000 W. Zeng, S. Keum, T.-W. Kuo, and V. Sick, “Role of large scale flow features on cycle-to-cycle variations of spark-ignited flame-initiation and its transition to turbulent

combustion,” 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.

http://eccentric.mae.cornell.edu/~pope/CEQ


Appendix-1

• Plasma channel equations

30

𝑑𝐸𝑠(𝑡)

𝑑𝑡= −𝑅𝑠𝑖𝑠

2 𝑡 − 𝑉𝑖𝑒𝑖𝑠 𝑡

𝑖𝑠 =2𝐸𝑠𝐿𝑆

Three Cases

Global Averaged High (sim05) Medium (sim29) Low (sim09)

ksgs (𝑚2/𝑠2) 4.027 4.279 3.159

T (K) 715.637 712.304 711.117

𝜙 0.99747 0.99739 0.99739

𝑠𝑝 =𝜂𝑉𝑖𝑒 𝑡 𝑖𝑠(𝑡)

4𝜋𝑟𝑘2𝜌𝑢 ℎ𝑏 − ℎ𝑢𝑏

1 +𝐿𝐻𝑉

𝑐𝑝𝑇𝑎𝑑

3


+ 40.46 𝐿𝑠 𝑖𝑠−0.32𝑝0.51


Appendix-2

• Combustion model equations

31

𝜕𝐺

𝜕𝑡+ 𝑢 ∙ ∇𝐺 =

𝜌𝑢𝜌 ∙ 𝑠𝑓𝑙𝑎𝑚𝑒 ∇𝐺

Gu lder 𝑠𝐿 = 𝑠𝑢𝑜 𝜙𝑇𝑢𝑇0

𝛼𝑝

𝑝0

𝛽

1.0 − 𝑓 ∙ 𝐹

𝑠𝑇𝑠𝐿

= 1 + −𝑎4𝑏3

2

2𝑏1𝐷𝑎 +

𝑎4𝑏32

2𝑏1𝐷𝑎

2

+ 𝑎4𝑏32𝐷𝑎

1 2 𝑢′

𝑠𝐿

Peters, N., Turbulent Combustion. Cambridge University Press, 2000.

RANS

𝑠𝑇 − 𝑠𝐿𝑠𝐿

= −𝑏32𝐶𝑣

2𝑏1𝑆𝑐𝑡,𝐺

∆

𝑙𝐹+

𝑏32𝐶𝑣

2𝑏1𝑆𝑐𝑡,𝐺

∆

𝑙𝐹

2

+𝑏32𝐷𝑡𝑠𝐿𝑙𝐹

12

Pitsch, H. "A G-equation formulation for large-eddy simulation of premixed turbulent

combustion." Center for Turbulence Research Annual Research Briefs 4 (2002).

LES


• Energy source term

• Sub-grid kinetic energy transport

𝜔𝑖 = 𝑑𝜌𝑖𝑑𝑡

= 𝜌 𝑌𝑖𝑢 − 𝑌𝑖

𝑏 𝑠𝑇𝐴𝐹𝑉𝑐𝑒𝑙𝑙

𝑑𝜌𝑖𝑑𝑡

=𝜌 𝑌𝑖,𝑏 − 𝑌𝑖

∆𝑡

𝑉𝑆𝑉𝑢

𝜕𝜌 𝑘𝑠𝑔𝑠

𝜕𝑡+

𝜕𝜌 𝑢𝑗 𝑘𝑠𝑔𝑠

𝜕𝑥𝑗= −𝜌 𝛤𝑖𝑗𝑆𝑖𝑗 − 𝐶𝑒

𝑘𝑠𝑔𝑠

𝛥+

𝜕

𝜕𝑥𝑗𝜌 𝜈𝑠𝑔𝑠

𝜕𝑘𝑠𝑔𝑠

𝜕𝑥𝑗

Appendix-3

ignition modeling for controlling cyclic-variability

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