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University of Wisconsin Engine Research Center

Modeling Combustion in Spark-Ignition Engines Using

G-equation Model with Detailed ChemistryLong Liang & Prof. Rolf D. Reitz

Acknowledgement: Ford Motor Company

PFI/DI-SI Engine

• CO Oxidation, H2-O2 reactions

• Pollutant formation

• G-equation description of combustion

• Laminar and turbulent flame speeds

• Primary heat release

• “Low” temperature chemistry

• Location / Intensity tracking

• Wall quenching

• Lean/rich mixture stratification

Objective: Develop an accurate, robust, versatile G-equation combustion model for PFI/DI SI engine simulations by incorporating detailed chemistry.

Platform: KIVA3V-G Code + Detailed Chemistry Solver.

General ApproachGeneral Approach

Turbulent Flame Propagation

Post-flame Chemistry

Knocking Combustion

Flame Quenching

G-equation ModelG-equation Model

0( ) | | | |uf ve r te x T t

Gv v G S G D G

t

22 2 2 2( ) ( ) 2 ( )u

f vertex t t s

Gv v G D G D G c G

t k

1/ 21/ 2 22 224 3 4 3

4 30 4 1 1

1 1 exp2 2

ignT

L m F F l F

t t a b a bS l l u la b

S I C b l b l S l

Premixed Flame Partially Premixed Flame

CO2, H2O,NO…

End-gas Flame Post-flameZone Front Zone

AutoIgnition

n

G > 0G < 0

G(x,t) = 0

Φ ≈ const

Φ ≈ 1

Φ > 1

Φ < 1

CO2, H2O, CO, NO…

O2, O, NO …

Fuel Droplets

Diffusion

Diffusion


CH4, CO, H, H2 …

Transport equations of Favre means of scalar G

and its variance

Turbulent flame speedconsidering kernel

flame evolution

Typical flame structuresobserved in SI engines.

The flame front is numerically tracked by G(x,t)=0 iso-surface.

Reduced PRF mechanism used in engine simulations(Tanaka et al., Combust. Flame, 133, 2003)

Chemical ProcessesChemical Processes

The low-temperature chemistry in the end-gas and the post-flame chemistry

are modeled using detailed chemical kinetics

The primary heat release and species conversion are based on the assumption that the burnt mixture within the turbulent flame brush tends to local and instantaneous chemical equilibrium.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.50.01

0.1

1

10

100

Igni

tion

Del

ay T

ime

(m

s)

1000(K) / T0

100% iC8H18 90% iC8H18 / 10% nC7H16 80% iC8H18 / 20% nC7H16 60% iC8H18 / 40% nC7H16 100% nC7H16

Vb

Vu

Mean Flame Front

Burnt

Unburnt

Calculated ignition delay time of PRF fuel

Mercury Marine two-stroke gasoline DI engine

Modeling a Two-Stroke GDI EngineModeling a Two-Stroke GDI Engine

In-cylinder species distributions at CA = 755 ATDC

Flame propagation and temperature contours.Start of injection = 635 ATDC

Spark timing = 679 ATDC

Fuel O2 OH CO NO

Ford DISI engine

Modeling a Ford DISI EngineModeling a Ford DISI Engine

Injection Ignition Flame propagation

Pressure and heat release rateEnd of injection = -72 ATDC

Spark timing = -20, -24, -28, -32 ATDC

-80-60 -40-20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

Hea

t Rel

ease

Rat

e (J

/Deg

)-20 O ATDC

-80-60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

-24 O ATDC

Hea

t Rel

ease

Rat

e (J

/Deg

)

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

-28 O ATDC

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

Hea

t Rel

ease

Rat

e (J

/Deg

)

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

-32 O ATDC

Hea

t Rel

ease

Rat

e (J

/Deg

) Knock onset due to end-gas auto-ignition(The dark interface is the deflagrating flame front)

Knocking Combustion ModelingKnocking Combustion Modeling

In-cylinder pressure fluctuation

-60 -50 -40 -30 -20 -10 0 10 200

2

4

6

8

10

12

Pre

ssu

re (

MP

a)

CA (ATDC)

Average Position1 Position2 Position3

Boosted stoichiometric combustion ( manifold pressure = 150 kPa )

1

2

3

Numerical transducers

PFI/DI-SI Engine

•CO Oxidation, H2-O2 reactions

•Pollutant formation

•G-equation description of combustion

•Laminar and turbulent flame speeds

•Primary heat release

•“Low” temperature chemistry

•Location / Intensity tracking

•Wall quenching

•Lean/rich mixture stratification

Objective: Develop an accurate, robust, versatile G-equation combustion model for PFI/DI SI engine simulations by incorporating detailedchemistry.

Platform: KIVA3V-G Code + Detailed Chemistry Solver.

General ApproachGeneral Approach

Turbulent Flame Propagation

Post-flame Chemistry

Knocking Combustion

Flame Quenching

G-equation ModelG-equation Model

0( ) | | | |uf vertex T t

Gv v G S G D G

t

22 2 2 2( ) ( ) 2 ( )u

f vertex t t s

Gv v G D G D G c G

t k

1/ 21/ 2 22 224 3 4 3

4 30 4 1 1

1 1 exp2 2

ignT

L m F F l F

t t a b a bS l l u la b

S I C b l b l S l

Premixed Flame Partially Premixed Flame

CO2, H2O,NO…


AutoIgnition

n

G > 0G < 0

G(x,t) = 0

Φ≈const

Φ≈1

Φ> 1

Φ< 1

CO2, H2O, CO, NO…

O2, O, NO …

Fuel Droplets

Diffusion

Diffusion


CH4, CO, H, H2…

Transport equations of Favre means of scalar G

and its variance

Turbulent flame speedconsidering kernel

flame evolution

Typical flame structuresobserved in SI engines.

The flame front is numerically tracked by G(x,t)=0 iso-surface.

Reduced PRF mechanism used in engine simulations(Tanaka et al., Combust. Flame, 133, 2003)

Chemical ProcessesChemical Processes

The low-temperature chemistry in the end-gas and the post-flame chemistry

are modeled using detailed chemical kinetics

The primary heat release and species conversion are based on the assumption that the burnt mixture within the turbulent flame brush tends to local and instantaneous chemical equilibrium.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.50.01

0.1

1

10

100

Igni

tion

Del

ay T

ime

(ms)

1000(K) / T0

100% iC8H18 90% iC8H18 / 10% nC7H16 80% iC8H18 / 20% nC7H16 60% iC8H18 / 40% nC7H16 100% nC7H16

Vb

Vu

Mean Flame Front

Burnt

Unburnt

Calculated ignition delay time of PRF fuel

Mercury Marine two-stroke gasoline DI engine

Modeling a Two-Stroke GDI EngineModeling a Two-Stroke GDI Engine

In-cylinder species distributions at CA = 755 ATDC

Flame propagation and temperature contours.Start of injection = 635 ATDC

Spark timing = 679 ATDC

Fuel O2 OH CO NO

Ford DISI engine

Modeling a Ford DISI EngineModeling a Ford DISI Engine

Injection Ignition Flame propagation

Pressure and heat release rateEnd of injection = -72 ATDC

Spark timing = -20, -24, -28, -32 ATDC

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

Hea

t Rel

ease

Rat

e (J

/Deg

)-20 O ATDC

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

-24 O ATDC

Hea

t Rel

ease

Rat

e (J

/Deg

)

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

-28 O ATDC

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

Hea

t Rel

ease

Rat

e (J

/Deg

)

-80 -60 -40 -20 0 20 40 60 80-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0

5

10

15

20

25

Pre

ssur

e (M

Pa)

CA (OATDC)

EXPT SIMU

-32 O ATDC

Hea

t Rel

ease

Rat

e (J

/Deg

)

Knock onset due to end-gas auto-ignition(The dark interface is the deflagrating flame front)

Knocking Combustion ModelingKnocking Combustion Modeling

In-cylinder pressure fluctuation

-60 -50 -40 -30 -20 -10 0 10 200

2

4

6

8

10

12

Pre

ssur

e (M

Pa)

CA (ATDC)

Average Position1 Position2 Position3

Boosted stoichiometric combustion ( manifold pressure = 150 kPa )

1

2

3

Numerical transducers