Effect of fuel and engine operational characteristics on the heat loss from combustion chamber...

International Communications in Heat and Mass Transfer 33 (2006) 122–134

www.elsevier.com/locate/ichmt

Effect of fuel and engine operational characteristics on the heat loss

from combustion chamber surfaces of SI enginesB

Ali Jafari *, Siamak Kazemzadeh Hannani

Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran

Available online 8 September 2005

Abstract

Understanding of engine heat transfer is important because of its influence on engine efficiency, exhaust emissions and

component thermal stresses. In this paper, the effect of various parameters such as compression ratio, equivalence ratio, spark

timing, engine speed, inlet mixture temperature and swirl ratio as well as fuel type on the heat transfer through the chamber

walls of a spark ignition (SI) engine is studied. For this purpose, a proper tool is developed which uses a KIVA

multidimensional combustion modeling program and a finite-element heat conduction (FEHC) code iteratively. Also, an

improved temperature wall function is used for the KIVA program. It was found that this iterative scheme and the new wall

function can improve the predictions considerably. A parametric study shows that this methodology is efficient in predicting

the engine heat transfer and the effects of changes in the fuel type and engine operational parameters on the engine thermal

behavior.

D 2005 Elsevier Ltd. All rights reserved.

Keywords: SI engine; Multidimensional modeling; Heat transfer; FEM; CNG

1. Introduction

In the design of internal combustion engines (ICEs), the accurate estimation of heat transfer is of vital importance.

Heat transfer affects the performance, efficiency and emissions from the engine. In regions having high heat flux

values, thermal stresses must be kept below levels that may cause failure (i.e., temperatures must be kept below about

400 8C for cast iron and 300 8C for aluminum alloys). The gas-side surface temperature of the cylinder wall must be

less than 180 8C to prevent deterioration of the lubricating oil film. Also, spark plug and valves must be kept cool

enough to avoid knock and pre-ignition problems [1].

Due to the crucial role of heat transfer in the design of engines, nearly all computer programs for simulation of

ICEs include a heat transfer model. In this study, KIVA-II computer program is used for the fluid flow and

combustion modeling of fuel mixture which determines the gas temperature and local heat fluxes in the chamber

walls.

0735-1933/$ - s

doi:10.1016/j.ich

B Communicat

* Correspondin

M5S 3G8.

E-mail addre

ee front matter D 2005 Elsevier Ltd. All rights reserved.

eatmasstransfer.2005.08.008

ed W.J. Minkowycz.

g author. Present address: Department of Mechanical & Industrial Engineering, University of Toronto, Toronto, ON, Canada,

ss: [email protected] (A. Jafari).

AssumedConstant

Wall Temp.

LocalHeatFlux

Values

PredictedTime-averagedWall Surface

Temp.

KIVA-IICode

FEHCCode

Fig. 1. Flowchart of the iteration procedure for KIVA and FEHC codes.

A. Jafari, S.K. Hannani / International Communications in Heat and Mass Transfer 33 (2006) 122–134 123

Generally, the combustion chamber of an ICE is formed by the cylinder wall, head, and piston, and the temperature

may vary considerably within each of these engine parts. But in the KIVA code, the temperature of each surface is

assumed to be constant [2]. This is not consistent with the actual situation occurring on the surfaces of the combustion

chamber [3].

In order to obtain the temperature distribution on the chamber surfaces, a computational method is used in this

work to calculate the temperature distribution using heat conduction equations. By specifying accurate boundary

conditions, a temperature distribution (instead of an assumed wall temperature) is obtained. This approach results in a

more accurate simulation of engine combustion and heat transfer. Since NOx and some other emissions tend to form

in the regions near the wall, more accurate prediction of the wall surface temperature is expected to have a significant

effect on predicting emission levels.

To obtain the temperature distribution in engine components, a 2-D axisymmetric finite-element heat

conduction (FEHC) code is developed. In the engine geometry, some boundary points have specified tempera-

tures and others have specified heat flux valves. Wall heat flux boundary conditions are obtained from KIVA

code. To calculate a pseudo-steady-state surface temperature distribution, KIVA and FEHC are run in an

iterative sequence. First, a modified version of KIVA, which accounts for a non-uniform temperature distribu-

tion, is run with the uniform temperature profile specified in the input file. Next, the FEHC code generates a

new surface temperature profile, based on the heat flux data from KIVA, which will be used as a refined

boundary condition for the next iteration. This iterative process continues until the temperature profile no longer

fluctuates. Using this method, the pseudo-steady-state temperature distribution is determined. Also, the KIVA

simulation results for pressure, temperature and species inside the cylinder become more accurate, since more

Table 1

Main engine specifications

Number of cylinders 4

Bore 88 mm

Stroke 66.6 mm

Compression ratio 7.8

Displacement volume 1.6 L

Squish clearance 3.6 mm

Intake valve closure 868 ABDCExhaust valve opening 668 BBDC

Engine speed 3000 rpm

Fuel Iso-octane

Equivalence ratio (/) 1.2

Spark timing 408 BTDC

Swirl ratio 0.2

Intake mixture temperature at IVC 350 K

(1)

(3)

(2)

(5)

(4)

3

171

7

8

5

6

9

2

10

14

11

4

12

15 1618

13

Fig. 2. Different regions and boundary surfaces (vertical and horizontal scales are different).

A. Jafari, S.K. Hannani / International Communications in Heat and Mass Transfer 33 (2006) 122–134124

appropriate temperature boundary conditions have been used. The flowchart of the iteration procedure is shown

in Fig. 1.

2. Problem formulation

In this section, due to relevance of this study to the heat transfer in ICEs, only the governing equations for the fluid

flow and heat transfer are briefly discussed and the temperature wall functions are introduced. A comprehensive

discussion about all the equations, models and the method of solution in KIVA code can be found in Ref. [2].

2.1. Governing equations for fluid flow and heat transfer

The equations of motion for the fluid phase can be used to solve for both laminar and turbulent flows. The mass,

momentum and energy equations for the two cases differ primarily in the form and magnitude of the transport

0 25 50 75 100x (mm)

0

20

40

60

80

100

120

140

y (m

m)

Fig. 3. The mesh used for the FEHC code (one out of every two grid points are shown, vertical and horizontal scales are different).

0 20 40x

140

160

180

y

468.35456.06443.78431.50419.22406.94394.66382.38370.10357.82345.54

Temp.(K)

Fig. 4. Pseudo-steady-state temperature distribution in combustion chamber components.


coefficients (e.g., viscosity, thermal conductivity and species diffusivity), which are much larger in the turbulent case.

The continuity equation for species m is

Bqm

Btþjd qm uð Þð Þ ¼ jd qmDmj

qqm

�� þ qqc

m þ qqddkl

�ð1Þ

where qm is the mass density of species m, q the total mass density and u the fluid velocity. Diffusion according to

Fick’s Law is being assumed, with a single coefficient D. The terms q˙sub mc and qd represent source terms due to

chemistry and the spray and d is the Dirac delta function.

The momentum equation for the fluid mixture is

B quð ÞBt

þjd ðuuÞ ¼ � 1

a2jp� Aoj

2

3qk

�þjd r þ Fs þ qg

�ð2Þ

The dimensionless quantity a is used in conjunction with the pressure gradient scaling (PGS) method, which enhances

computational efficiency in low Mach number flows, where the pressure is nearly uniform. The quantity Ao is zero in

laminar calculations and unity when one of the turbulence models is used. FS is the rate of momentum gain per unit

volume due to the spray. When one of the turbulence models is being used (Ao=1), two additional transport equations

have to be solved, for the kinetic energy k and its dissipation rate e.

0 10 20 30 40x (mm)

385

390

395

400

405

410

415

420

425

430

435

440

445

450

Tem

p. (

K)

Iter 1Iter 2Iter 3Original Input

Fig. 5. Temperature distribution in the cylinder head.

0 10 20 30 40 50s (mm)

350

360

370

380

390

400

410

420

430

440

450

460

Tem

p. (

K)


Fig. 6. Temperature distribution in piston (s is the coordinate along the piston profile).


The internal energy equation is

B qIð ÞBt

þjd ðuIÞ ¼ � pjd uþ 1� Aoð Þr : ju�jd Jþ Aoqe þ QQc þ QQs ð3Þ

where I is the specific internal energy, exclusive of chemical energy and J is the sum of contributions due to heat

conduction and enthalpy diffusion. Qc and Qs are source terms due to chemical heat release and spray interaction.

2.2. Heat conduction formulation

To obtain the temperature distribution in the engine components, one needs to solve the following equation:

qsCB Tð ÞBt

�jd ðKsjTÞ ¼ 0 ð4Þ

where T is the temperature, and qs, Cp, and Ks are the density, specific heat and thermal conductivity of the solid.

2.3. Improved temperature wall function

KIVA program uses the temperature wall function (TWF) for calculation of heat transfer. This function was

derived with the assumptions of a steady and incompressible flow, no source terms (terms that account for pressure

0 50 100 150y (mm)

340

350

360

370

380

390

400

410

Tem

p.

(K)


Fig. 7. Temperature distribution in the cylinder wall.

-50 0 50 100

CA (deg)

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

Old TWFImproved TWF

Fig. 8. Variation of heat loss vs. crank angle for the two TWFs.


work and chemical heat release) and the validity of the Reynolds analogy. The formula for the temperature wall

function in KIVA is as follows [2]:

Tþ ¼ uþPrl ð5Þwhere Prl is the laminar Prandtl number. The velocity wall function formulation is

uþ ¼1

jln yþð Þ þ B yþN11:6

yþ yþb11:6

(ð6Þ

where j =0.4327, B =5.5, y+=(yu*)/m and u*=sw/q [2]. Here sw is the wall shear stress and m is the kinematic

viscosity. The model mentioned above predicts much lower heat fluxes in different cases compared to experimental

results [7,8]. In an actual engine, the gas density is known to vary widely due to piston motion and combustion.

Chemical heat release and the general transient nature of the flow may also invalidate the Reynolds analogy.

Therefore, Han and Reitz [7], proposed a new temperature wall function taking to account the pressure work and

chemical heat release. The final expression for temperature wall function is

Tþ ¼ 2:1ln yþð Þ þ 2:1Gþyþ þ 33:4Gþ þ 2:5 ð7Þwhere G+=Gm/( qwu*), G = Qgen is the time-averaged volumetric heat generation from combustion, and qw is the heat

flux through the wall.

3. Simulation conditions

The engine studied is a specific four-cylinder gasoline engine. The main engine specifications and operational

conditions are given in Table 1. The piston and cylinder block are made of aluminum alloy and cast iron, respectively.

-50 0 50 100CA (deg)

5

10

15

20

25

30

35

40

P (

bar

)

Old TWFImproved TWF 16 18 20

40

40.5

41

Fig. 9. Variation of pressure vs. crank angle for the two TWFs.

0

500

1000

1500

2000

T (

K)

17 18 19 202110

2120

2130

2140

2150

-50 0 50 100CA (deg)

Old TWFImproved TWF

Fig. 10. Variation of temperature vs. crank angle for the two TWFs.


Here, the notations BDC and TDC, and IVC refer to bottom dead center, top dead center, and intake valve closure,

respectively. For these operational characteristics, the maximum pressure has been predicted about 40.5 bar that is

close to its experimental value, i.e., 41 bar. Also, the predicted BSFC (brake-specific fuel consumption) of 238.52 g/

kW h is in good agreement with the experimental value of 245 g/kW h [4].

3.1. FEHC solution domain

The engine geometry consisting cylinder wall, head and piston is shown in Fig. 2. For simplicity, it is assumed that

the engine geometry is axisymmetric. The engine geometry is divided into the following five regions that are shown

in Fig. 2 as numbers in parentheses: region (1) including the cylinder head, region (2) for the cylinder wall and

regions (3), (4), and (5) forming the piston.

The boundary is divided into 18 different surfaces, as shown in Fig. 2, such that each surface has its own boundary

condition (BC). For example, surfaces 1 and 2 have constant flux BCs ( qW=0) due to symmetry, surfaces 13, 14, 15,

16, 17 and 18 (in the combustion chamber) have specified heat flux BCs that are obtained from KIVA predictions.

The specified temperature boundary conditions for other surfaces are as follows: Tw=355 K for surfaces 3 and 4,

Tw=335 K for surfaces 5, 6 and 7, and Tw=345 K for surfaces 8, 9, 10, 11 and 12.

It should be noted that when the piston moves up or down, points below the piston on the cylinder wall

dynamically change their BC from a specified heat flux to a specified temperature. A total number of 5000

quadrilateral elements, as shown in Fig. 3, are used in this study.

For determining the time-averaged temperature distribution, the computed heat fluxes of boundary elements should

be averaged in one complete cycle, i.e., 7208 crank angle (CA). It is noteworthy that since the KIVA-II program does

0

1

2

3

4

5

6

7

CO

(*1

0-3 g

r)

-50 0 50 100CA (deg)

Old TWFImproved TWF

Fig. 11. Variation of CO emission vs. crank angle for the two TWFs.

0

0.1

0.2

0.3

0.4

0.5

NO

x (*

10-3

gr)

-50 0 50 100CA (deg)

Old TWFImproved TWF

Fig. 12. Variation of NOx emission vs. crank angle for the two TWFs.


not include any port or valve motion, only the period between the intake valve closure (IVC) and the exhaust valve

opening (EVO) can be simulated. Therefore, to average the heat flux data over the entire cycle, from �3608 ATDC to

IVC, the program uses the same values at IVC and from EVO to +3608 ATDC, the program uses the heat flux values

from EVO. These values are good approximations since they are three orders of magnitude smaller than those near

TDC. For the simulation of combustion in the cylinder, a grid similar to that of FEHC is used in the KIVA code with

the number of grids in the vertical direction inside the chamber walls changing in order to produce an accurate

solution in the different piston positions.

4. Results and discussion

Here, the results of the combined solution of combustion, heat generation from the combustion and heat conduction inside the

chamber walls are presented. The temperature distribution in the chamber walls and temperature, pressure, heat loss to the walls,

and emissions for different temperature wall functions, and under different operating conditions are studied.

4.1. The computed temperature distributions

The pseudo-steady-state temperature distributions on the combustion chamber surfaces are shown in Figs. 4–7. In the first

iteration, the uniform temperature of 400 K is used as the original input for KIVA program. The KIVA and FEHC codes yielded a

bconvergedQ quasi-steady temperature profile after three iterations. For the cylinder head, the third and final temperature

distribution, as shown in Fig. 5, are 10–45 K lower than the original constant temperature profile. There is a temperature

difference of 50 K for the cylinder wall. For the piston, also, a similar condition can be observed (in Fig. 6, s is the coordinate along

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

CR=7.8CR=8.5

-50 0 50 100CA (deg)

Fig. 13. Effect of compression ratio on the heat loss.

=1.2 =1.0φφ

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 14. Effect of equivalence ratio on the heat loss.


the piston profile). The maximum temperature difference between the high-temperature region (piston crown) and the low-

temperature region (bowl valley) is about 100 K. Fig. 7 shows that the first, second and third temperature distributions on the

cylinder wall surface are the same as the coolant temperature adjacent to the wall for the majority of locations on the surface. But,

there is a 60 K increase in the temperature in the region near the cylinder head. This shows that combustion and heat transfer within

the cylinder does not have much influence on the temperature distribution on the wall surface, except for a narrow region near the

cylinder head.

The maximum piston temperature (468 K) is located on the lip where the bowl and piston face come together. According to the

computations, the gas temperature in the region where the bowl and face meet is slightly lower compared to the inner bowl region.

However, material in the lip/face region is subjected to a concentrated heat flux from two sides since it is heated from two different

surfaces, the bowl and face. This is to be contrasted with the nearly one-dimensional heating of the material in the bowl and on the

surface of the piston elsewhere in the domain.

Fig. 4 shows that the temperature of the head in the edge of the piston bowl is also higher than the rest of the head. According to

the temperature computations near TDC, a plume of high-temperature gas located close to the bowl wall is turned upward by the

bowl geometry where it strikes the head [5]. Although the highest heat flux levels are in the bowl region, this is only true during the

ignition period. For the steady-state analysis, the heat flux is averaged over a 7208 operating cycle for each boundary element.

Thus, the highest daveragedT heat fluxes are located near the bowl lip.

The present FEHC code (in an iterative sequence with KIVA) can provide an accurate and consistent method for

obtaining the temperature distributions within engine components, and these results would also be useful for structural

analysis and mechanical design of the engine components. In addition, combustion chamber wall temperatures have been

shown to significantly influence engine NOx emissions [5,6] and thus the accurate prediction of wall temperature is of special

importance.

Best Timing (-40)Retarded (-30)

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 15. Heat loss for different spark timing.

2000 rpm2500 rpm3000 rpm

0

10

20

30

40

50

60

70

80

90

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 16. Heat loss for different engine speeds.


4.2. Effect of improved temperature wall function

According to the literature [7,8], the original heat transfer model of KIVA predicts much lower heat fluxes in different cases

compared to experimental results. But in the model of Han and Reitz [7], pressure work and chemical heat release has been taken

into account. Using this new temperature wall function, the predicted heat fluxes increased significantly (Fig. 8). However, it

should be noted that this increase in heat flux prediction has a negligible effect on the bulk gas temperature and pressure (Figs. 9

and 10). However, as shown in Figs. 11 and 12, it has an important effect on CO and NOx predictions.

4.3. Parametric study

In this section is a parametric study of different operational characteristics on the heat loss from the engine.

4.3.1. Effect of compression ratioCylinder gas properties change with increasing compression ratio (CR). By increasing the compression ratio, the cylinder gas

pressures and peak burned gas temperatures increase. This causes gas motion to increase resulting in faster combustion. Also, the

surface/volume ratio close to TDC increases by compression ratio. Therefore, increasing the compression ratio in a spark ignition

(SI) engine decreases the total heat flux to the coolant (Fig. 13).

4.3.2. Effect of equivalence ratio (/)The maximum heat flux occurs at the equivalence ratio for maximum power, i.e., / =1.1 [4], and decreases as the mixture is

diluted or enriched from this value. Although as a fraction of the fuel’s chemical energy, the heat transfer decreases, heat loss to the

chamber walls increases when equivalence ratio increases from 1.0 to 1.2 (Fig. 14).

Tempi=350Tempi=380

0

10

20

30

40

50

60

70

80

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 17. Effect of inlet mixture temperature on the heat loss.

Swirl=0.2Swirl=0.5

0

10

20

30

40

50

60

70

80

90

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 18. Effect of swirl ratio on the heat loss.


4.3.3. Effect of spark timingRetarding the spark timing from its best timing (�40 BTDC in this case) causes lower mixture temperature and bulk pressure in

the cylinder and thus decreasing the heat flux to chamber walls. The burnt gas temperatures are decreased as timing is retarded

because combustion occurs later when the cylinder volume is larger (Fig. 15).

4.3.4. Effect of engine speedChanging the engine speed has the greatest effect on the heat flux to the walls. Increasing the engine speed alone leads to a

longer combustion period in terms of crank angle history, causing an increase in the overlap of the burning time with the

expansion stroke. Thus, increasing the engine speed causes a decrease in the heat loss per cycle but increases the heat loss per unit

time (Fig. 16).

4.3.5. Effect of inlet mixture temperature and swirl ratioIt is obvious that the heat flux to the chamber walls increases with increasing inlet temperature from 350 K to 380 K [1] as

shown in Fig. 17. Also, increasing swirl results in higher gas velocities and better mixing and, therefore, higher heat fluxes to the

chamber walls (Fig. 18).

4.3.6. Effect of the fuelConversion of engine fuel from gasoline to natural gas reduces the emissions from SI engines while it may lower the engine

power if the engine characteristics (such as compression ratio, spark timing, IVC and EVO) are not changed [9]. One parameter that

can be modified is the compression ratio. Natural gas has a higher octane number and thus higher resistance to knock than gasoline

and can operate at higher compression ratios. The increase in compression ratio gives higher torque and thermal efficiency,

compensating, to some extent, for the loss in power resulting from the decrease in fuel energy density and volumetric efficiency

with the use of natural gas. Thus, here, we also investigate replacement of SI engine fuel by compressed natural gas (CNG).

CR=7.8CR=8.5

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 19. Effect of compression ratio (for CNG fuel) on the heat loss.


In this study, the fuel type also has been investigated in addition to the effect of engine variables. Since methane is the major

component of natural gas, thus, methane is used as fuel for this investigation. Therefore, the iso-octane has been replaced with

methane and the effect of various parameters has been studied. According to the results, the CO and NOx emissions reduced for the

CNG-fueled engine without any special change in the engine characteristics [4]. Also, the effect of changing engine parameters

φ=1.0φ=1.2

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 20. Effect of equivalence ratio (for CNG fuel) on the heat loss.

Best Timing (-40)Retarded (-30)

0

10

20

30

40

50

60

70

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 21. Effect of spark timing (for CNG fuel) on the heat loss.

2000 rpm2500 rpm3000 rpm

0

10

20

30

40

50

60

70

80

90

Hea

t L

oss

(J)

-50 0 50 100CA (deg)

Fig. 22. Effect of engine speed (for CNG fuel) on the heat loss.


(compression ratio, equivalence ratio, timing and engine speed) on the heat loss is similar to that of gasoline-fueled engine as can

be seen in Figs. 19–22. However, the heat loss in the CNG-fuelled engine is slightly less than that of gasoline-fuelled engines.

5. Conclusion

In this study, a finite-element heat conduction (FEHC) code is developed for the determination of temperature

distribution in engine components, and using it in an iterative sequence with KIVA multidimensional reacting flow

modeling program, an SI engine is simulated. This is done to obtain a more realistic temperature distribution on the

surface and inside the combustion chamber components. This accurate temperature distribution can be used for stress

analysis in engine parts or as the proper boundary condition for engine simulation. As the main results, by modifying

temperature wall function, the predicted heat fluxes improved significantly. The maximum temperature is on the

piston lip where the bowl and piston face come together. The temperature in the cylinder head close to the edge of the

piston bowl is also higher than the rest of the head.

The effects of different operational characteristics are also investigated. According to engine parametric study, an

increase in compression ratio from 7.8 to 8.5 decreases heat loss to the chamber walls and the cooling system. Also,

reducing equivalence ratio from 1.2 to 1.0 results in a decrease in the heat loss. Retarding the spark timing also

reduces the heat loss. Moreover, increasing the inlet mixture temperature and swirl ratio can increase the heat loss to

the chamber walls. Changing fuel from gasoline to natural gas can result in a decrease in engine emissions and heat

loss. By changing operational characteristics in the gas-fueled engine, similar trends as in the gasoline engine are

observed.

References

[1] J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill, 1988.

[2] A.A. Amsden, P.J. O’Rourke, T.D. Butler, KIVA-II: A Computer Program for Chemically Reactive Flows with Sprays, Los Alamos National

Lab., 1989 LA-11560-MS.

[3] G. Borman, K. Nishiwaki, Internal combustion engine heat transfer, Progress in Energy and Combustion Science 13 (1987) 1–46.

[4] A. Jafari, Heat Transfer Analysis of Internal Combustion Engines, M.S. Thesis, Dept. of Mechanical Eng., Sharif University of Technology,

Tehran, Iran, 2000.

[5] J.F. Wiedenhoefer, Finite Element Modeling of I.C. Engine Component Temperatures, M.S. Thesis, University of Wisconsin–Madison, 1999.

[6] R. Stone, Introduction to Internal Combustion Engines, MacMillan, 1992.

[7] Z. Han, R.D. Reitz, A temperature wall function formulation for variable-density turbulent flow with application to engine convective heat

transfer modelling, International Journal of Heat and Mass Transfer 40 (3) (1997) 613–625.

[8] R.D. Reitz, Assessment of Wall Heat Transfer Models for Premixed-Charge Engine Combustion Computations, SAE Paper 910267 (1991).

[9] D. Yossefi, M.R. Belmont, S.J. Ashcroft, M. Abraham, R.W.F. Thurley, S.J. Maskell, Early stages of combustion in internal combustion engines

using linked CFD and chemical kinetics computations and its application to natural gas burning engines, Combustion Science and Technology

130 (1997) 171–200.

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