effects of split injection, oxygen enriched air, and heavy egr rate on soot emissions in a diesel engine

15Figure 4 Comparison of net acetylene mass between Lee model and Fusco model in case of single injection without EGR.. 21 Figure 5 Comparison of net soot mass between Lee model and Fusc

Effects of Split Injection, Oxygen Enriched Air, and Heavy EGR Rate on Soot Emissions

in a Diesel Engine

Nguyen Le Duy Khai

The Graduate School Sungkyunkwan University Department of Mechanical Engineering

Effects of Split Injection, Oxygen Enriched Air, and Heavy EGR Rate on Soot Emissions

in a Diesel Engine

Nguyen Le Duy Khai

A Dissertation Submitted to the Department of Mechanical Engineering

and the Graduate School of Sungkyunkwan University

in partial fulfillment of the requirements for the degree of Doctor of Philosophy

June 2009

Approved by Professor Nakwon Sung Major Advisor

Chapter 3 Results and Discussion

3.3 Effects of oxygen enriched air (OEA) and split injection 57

3.4 Effects of heavy EGR, OEA, and split injection 78

List of Tables

Table 2 Rate of change of mass fraction of species 20

Table 4 Computational test conditions 23 Table 5 Mass of species in the intake air 79

List of Figures

Figure 1 Schematic diagram of flame in diesel engine (Dec, 1995) 6Figure 2 Schematic diagram of the soot model 12Figure 3 Saturation vapor pressure of carbon as function of temperature 15Figure 4 Comparison of net acetylene mass between Lee model and Fusco

model in case of single injection without EGR

21

Figure 5 Comparison of net soot mass between Lee model and Fusco model

in case of single injection without EGR

22

Figure 6 Schemes of split injection and single injection 24Figure 7 The computational meshes at 3oBTDC 24Figure 8 Comparison of calculated and measured cylinder pressure and heat

release rate in case of single injection without EGR

26

Figure 9 Comparison of calculated and measured cylinder pressure in case of

split injection

27

Figure 10 Comparison of soot and NOx emissions between calculation and

experiment of single injection with different injection timing

28

Figure 11 Comparison of NOx and soot emissions with various amount of fuel

injected during the first pulse of split injection without EGR

29

Figure 12 Distributions of temperature and soot on the cutting plane at

4oATDC in case of single injection without EGR

30

Figure 13 Variation in heat release rate 31

Figure 14 Variation in average gas temperature 32Figure 15 Variations in mass of precursor formation, conversion into soot

particles, oxidation, and net precursor

33

Figure 17 Variation in gas mass fraction with φ = 1.2-2.0 35Figure 18 Variations in acetylene formation, oxidation, consumption, and net

Figure 29 Variations in rich mixture (φ = 1.2-2.0) mass fraction 47

Figure 31 Variations in acetylene formation, oxidation and consumption 49

Figure 33 Variations in soot formation and oxidation 50Figure 34 Distributions of temperature and soot formation rate at 90oATDC 51Figure 35 Reaction rate of soot oxidation at 20o, 50o and 90oATDC 52

Figure 38 Diesel emissions of various schemes 55

Figure 41 Variations in average gas temperature 58Figure 42 Distribution of equivalence ratio, temperature, and precursor

formation rate at 10oATDC

Figure 46 Variations in acetylene formation, oxidation, and consumption 62Figure 47 Reaction rate of acetylene formation, oxidation, and consumption 64Figure 48 Reaction rate of acetylene consumption at 30oATDC 65

Figure 49 Variations in mass of net acetylene 65Figure 50 Variations in soot formation and oxidation 66Figure 51 Reaction rate of soot formation and soot oxidation at 90oATDC 67

Figure 54 Variations in average gas temperature 69

Figure 58 Reaction rates of acetylene formation, oxidation, and growth with

soot

74

Figure 59 Variations in soot formation and oxidation 74Figure 60 Distributions of soot formation rate and oxidation rate at 90oATDC 75

Figure 62 Trend of diesel emissions with various oxygen concentrations 77Figure 63 Effect of EGR ratio on soot emissions in case of single injection 78

Figure 67 Distributions of temperature at 20oATDC 83Figure 68 Variations in rich-mixture mass percentage 83Figure 69 Variations in precursor formation and net precursor 84

Figure 70 Variations in acetylene formation, oxidation and consumption 84

Figure 72 Variations in reaction rate of acetylene formation and growth with

soot

87

Figure 73 Variations in soot formation and oxidation 88Figure 74 Reaction rate of soot formation and oxidation at 90oATDC 89

Figure 77 Diesel emissions with different schemes 91

be raised in the future As the number of diesel engines increases, reducing their emissions has become more important Nitrogen oxides (NOx) and soot emissions in diesel engines are the most challenging to reduce Nitrogen oxides are efficiently controlled in the combustion process by exhaust gas recirculation (EGR) However, a decrease in NOx is usually accompanied by an increase in soot An aftertreatment device such as a diesel particulate filter is needed to control soot emissions, however using this device requires additional cost, including equipment cost, operation cost, and maintenance cost A strategy to reduce NOx and soot simultaneously without after treatment devices is necessary; for example, a combination of split injection with oxygen enriched air (OEA) and EGR

Split injection has been used as a method to reduce soot emissions in diesel engines

In 1990, Schulte et al [1] showed the possibility of applying split injection with an electronic unit injector Split injection became more practical later with the development

of a common rail injection system [2-4] Many studies have been done to examine the effects of split injection on engine emissions By varying the amount of fuel in the first injection, Nehmer and Reitz [5] found that soot emissions decrease when more fuel is injected in the firstinjection Tow et al [6] evaluated the effect of dwell period on diesel emissions They reported that a long dwell period is effective for significant reduction in soot emissions For example, when a 10crank angle degree dwell is used in split injection scheme 48.10.52, in which 48% fuel injected in the first pulse and 52% fuel injected in the second pulse, soot emissions are reduced by a factor of three without increase in NOx emissions Han et al [7] numerically studied a mechanism of reduction

of soot emissions of split injection and found that the optimum split injection scheme was 75.8.25 in their study cases With this scheme, soot emissions are reduced by a factor of four while NOx emissions increase slightly in comparison with single injection Other researchers [8-10] using two-color imaging optics to observe the soot emission process in diesel engines also confirmed the benefit of split injection in reducing soot emissions There is some reasons lead to the reduction of soot emissions with split injection Tow et al [6] and Kong et al [11] pointed that the second injection of fuel enhances the fuel/air mixing and thus improves the oxidation of soot from the first injection Han et al [7] showed that the second injected fuel is entered into a relatively fuel-lean and high temperature region which is left over from the combustion of the first injection The fuel injected by the second injection is quickly burned, and thus it does not contribute significantly to soot production In general, split injection reduces soot emissions, however, split injection can cause an increasing in soot emissions if the injection timing is too retarded or the injection dwell is not optimized [8, 9]

The concept of using oxygen enriched air in diesel engines has been studied for years The use of OEA has advantages such as reduction of soot emissions, carbon monoxide (CO), and unburned hydrocarbons [12-15] However, the increase in NOx emissions and lack of practical on-board oxygen enrichment devices prevented any applications of this concept In recent years, however, there has been progress in the development of oxygen enrichment devices such as a permeable oxygen membrane [16, 17] A compact membrane module developed by Argonne National Laboratory can increase the concentration of oxygen to 23-25% in volume and can be incorporated into a vehicle design [16] As this technology is developed, oxygen enriched air becomes more attractive as a method to reduce soot emissions

The effects of EGR on the reduction of NOx emissions in diesel engines have been confirmed a long time ago, and it is an indispensable technology for modern diesel engines Because the EGR affects diesel combustion through the dilution of the inlet charge air with carbon dioxide (CO2) and water vapor (H2O), the local flame temperature is decreased, and thus NOx formation is decreased [18-23] However, the lower temperature results in increased soot emissions To avoid this drawback, many researchers suggested that EGR ratio should be restricted Kim and Sung [23] showed in their study that the optimum EGR ratio is 10% at the full load and 15% at the part load Wagner et al [24] reported that soot emissions start to increase significantly at EGR ratio of 30%, and a steep increase is observed once the EGR ratio reaches about 45% Uchida et al [25] suggested the EGR ratio of 20% should be used, since at this ratio NOx emissions are reduced by 50% without penalty of soot emissions Whereas EGR

decreases NOx emissions and increases soot emissions, the OEA technology has reverse effects If EGR is used together with OEA, a higher EGR ratio can be applied to reduce NOx emissions without a penalty on soot emissions

It is of interest to examine the effects of a combination of these technologies on diesel emissions Taking the benefits of EGR for reducing NOx emissions and split injection for reducing soot emissions, Pierpont et al [26] examined the possibility of a combined use of EGR and split injection They reported that this combination is effective in reducing both soot and NOx, especially during a high load (75%) when EGR causes a significant increase in soot emissions In the study of Montgomery and Reitz [27], NOx and soot emissions as well as fuel consumption can be reduced over the entire engine operating map with the use of multiple injection and EGR They showed that at a 1600 rev/min and 75% load running condition, NOx and soot emissions could be further reduced by using 10% EGR with a quadruple injection Other researches confirmed that NOx and soot emissions are reduced simultaneously with the combined use of split injection and EGR [28-30] and they tried to optimize the operating parameters to receive the full benefits of this combination [31-34]

In this study, a simulated method is applied to investigate the effects of the combination of split injection, OEA, and EGR on soot emissions in a DI diesel engine The level of reduction of emissions is dependent on many variables: engine load, injection pressure, injection timing, OEA concentration, EGR ratio and split injection parameters such as the ratio of fuel injected in fist pulse to second pulse, the dwell angle, and the profile of injected velocity Due to the complexity of the problem, optimization

is not a main target of this study The research presented herein focuses only on the effects of each technology on the production of intermediate species during the combustion process, and how these changes affect the final emissions The purpose is to understand the mechanism of soot formation and oxidation, to get details of spatial distribution and time evolution of quantities which are relevant to soot production, and

to evaluate their influence on soot production during the combustion At the beginning, the split injection scheme of 75.8.25 is used with an EGR rate of 20% Other schemes such as 50.8.50 and 25.8.75 are also considered to evaluate the effect of different injection schemes on diesel emissions Then, a combination of split injection 75.8.25 with the oxygen concentration in the intake air increased to 22% in volume is tested After that, the concentration of oxygen is increased to 23% in volume to evaluate the effects of higher oxygen concentration Finally, a high OEA concentration of 23% with

a heavy EGR ratio of 30% and split injection is used, and the result is compared with the previous tests

Chapter 2 Soot Model

The formation of soot in a diesel engine has been studied for many years In 1997, Dec [35] presented a schematic diagram of flame in a diesel engine based on a series of his previous experimental researches [36-38] The diagram of Dec is shown in Figure 1

It reveals the evolution of a diesel fuel jet from the start of injection until the end of injection It also gives a mechanism for soot formation, soot oxidation and a distribution

of soot in a diesel flame Following Dec [35], soot appears throughout a jet section rather than only in the shell around the jet periphery as the old description Small soot particles are formed initially at the zone of fuel-rich premixed flame near the tip of the liquid jet After formation, these soot particles move downstream During

cross-Figure 1 Schematic diagram of flame in diesel engine (Dec, 1995)

movement, they grow in size and volume fraction, and the soot concentration reaches the highest level at the head vortex Soot particles also move outward, and they are oxidized at the diffusion flame zone located around the jet periphery which has enough oxygen and high temperature The soot model of Dec [35] is verified successfully by other researchers later [39, 40] Although the experimental model of Dec [35] illustrates the spatial distribution of soot quite well, it is limited within a short period of combustion process, just from start of injection to end of injection

Experimental methods are important but they are expensive to perform, and sometimes are impossible Whenever the operating conditions need to be changed to explore their effects, a complicated system configuration needs to be set up Moreover, the observation of soot distribution in the burnout phase of combustion, which is from the end of fuel injection to the end of combustion, is difficult because the soot concentration becomes too low to be detected during this period, and the distribution of soot particles may be shifted out of the field of view Another approach to study soot emissions is a modeling method The availability of a high performance computing hardware nowadays makes modeling to be an essential analysis tool in engine research and development Modeling has an ability to study a system where experiments are difficult or impossible to perform In addition, modeling can explore unlimited level of detail of results, and it reduces time and cost significantly Modeling method is especially convenient to perform parametric studies and optimal studies In the literature,

a variety of soot models with different level of complexity were proposed and applied to modeling of diesel combustion Among them, the two-step soot model of Hiroyasu et al [41] and the eight-step soot model of Fusco et al [42] are the most popular

The two-step soot model of Hiroyasu et al [41] includes two reaction steps, one for

soot formation and one for soot oxidation The rates of soot formation and soot

oxidation are expressed in Arrhenius form as shown in Eqs (1) and (2) The net rate of

change in soot mass, Eq (3), is the difference between the rates of soot formation and

In the above equations, m , sf m , and so m are the formed, oxidized, and the net soot s

mass respectively, m is the fuel vapor mass, fv P is the pressure in bar, and X O2 is the

mole fraction of oxygen Hiroyasu et al [41] suggested the activation energies of 12500

cal/mole for E and 14000 cal/mole for f E o The pre-exponential factors, A and f ,

are adjustable to match the corresponding measured data of soot emissions for each

experimental case

o A

In 1994, Patterson et al [43] pointed out that the Hiroyasu model gives a relatively

low peak of soot concentration in a cylinder They modified the Hiroyasu soot model by

replacing the soot oxidation reaction by the Nagle and Strickland-Constable (NSC) soot

oxidation model [44] In the NSC model, soot oxidation occurs by two mechanisms involving the more reactive type A sites and the less reactive type B sites on the soot surface The reaction rate is given by Eq (4),

2

2 2

11

where P O2 is the partial pressure of oxygen, and x is the fraction of the surface A

occupied by type A sites,

1 2

A

B O

k x

The rate of soot mass oxidation is

where MW is the carbon molecular weight, C ρs is the soot density, and is the soot

diameter Due to the simplicity and computational efficiency, the two-step soot model

of Hiroyasu and its modified versions are used commonly in diesel engine simulations

[7, 8, 22, 23, 28, 32, 33, 45, 46] One of its drawbacks is that the Hiroyasu soot model

cannot be applied reliably to other systems except those for which it was calibrated

Moreover, it cannot provide detail information regarding the soot formation process in a

cylinder

p d

In 1994, Fusco et al [42] proposed an eight-step phenomenological soot model In

their model, the soot production does not link directly to fuel but through two

intermediate species, precursor and acetylene Soot is formed through a series of

processes such as fuel pyrolysis to precursor and acetylene, particle inception, surface

growth of particles with acetylene, soot coagulation and soot oxidation In 1998,

Kazakov and Foster [47] modified the Fusco’s model They counted the effect of

turbulent mixing on oxidation process by using the harmonic mean of the kinetic

oxidation rate and the mixing oxidation rates for the final oxidation rates of precursor,

acetylene and soot particles Because the eight-step model of Fusco offers a better

physical description of soot formation and it shares similar advantages of the two-step

model of Hiroyasu, the Fusco soot model and its modified version have been developed and applied widely in simulation of diesel combustion recently [48-52]

In this study, the soot model of Kazakov and Foster [47] is modified and is used to simulate the soot production The computation is performed by the modified version of KIVA-3V code [53], which was developed at Los Alamos National Laboratory, USA The turbulent flows are modeled using the Renormalization Group (RNG) k-ε turbulence model proposed by Han and Reitz [54] The spray model is a wave breakup model developed by Reitz [55] In this spray model, the breakup mechanisms of Rayleigh-Taylor and Kelvin-Helmoltz instabilities are implemented Diesel combustion modeling is divided into two regimes: ignition and combustion The ignition process is modeled using the Shell model developed by Halstead and Quinn [56] for low temperature chemistry If the cell temperature reaches the specified temperature (was set

at 1100K), the laminar and turbulent characteristic time combustion model of Kong et al [45] is activated for describing high temperature chemistry The extended Zeldovich mechanism described by Heywood [57] is implemented for calculating NOx formation The multi-step Foster soot model [47] is used to calculate soot formation, and the NSC model [44] is used to calculate soot oxidation

A schematic diagram of the eight-step soot model of Foster is shown in Figure 2 Under high temperature during combustion, precursor and acetylene are generated simultaneously from fuel pyrolysis For calculation, the precursor, , is assumed to be C

PR

50, and the fuel is n-tetradecane (C14H30) due to its similar carbon/hydrogen ratio to diesel fuel The global chemical reactions are as follows:

Figure 2 Schematic diagram of the soot model

C14H30 Æ 7C2H2 + 8H2 (12)

and their reaction rates are

12 1

1200.7 10 * exp F

490.9 10 * exp F

A portion of precursors was converted into soot particles,

In this study, the solidification of carbon molecules presented by Lee et al [58] is used

for the inception of soot particles instead of the chemical reaction suggested in the

Foster model After formation, the partial pressure of precursors in the product increases

gradually When the partial pressure of gaseous precursors in the mixture exceeds the

saturation pressure of carbon, , at the given temperature, T , the phase change of

gaseous precursors into solid particles is occurred The saturation pressure of carbon is

obtained by applying the Clapeyron relation,

SAT P

2

IG

dP h dT

The necessary data for calculation P SAT are listed in Table 1 Integrating the Clapeyron

equation between the triple point, TP , and the state of product, the saturation pressure

of carbon is found,

exp IG SAT TP

Table 1 Data for carbon

Parameter Value

Enthalpy of fusion, hIF 104.6 (kJ/kg) Enthalpy of vaporization, hFG 355.8 (kJ/kg) Normal melting point, TNMP 3773 (K) Normal boiling point, TNBP 5000 (K)

TP T

Figure 3 Saturation vapor pressure of carbon as function of temperature

The reaction rate of the inception of soot particles from precursors is

4 4

124.2 10 * exp F

Leung et al [59] suggested that the growth rate being proportional to provides a

better result as compared to the traditional expression proportional to The total soot

surface area per unit volume, , is calculated from

1/ 2

S

S S

The coagulation constant β is determined from harmonic mean of free-molecular

collision frequency, βfm, and near continuum collision frequency, βnc,

C2H2 + O2 Æ 2CO + H2 (35)

The original chemical reaction of oxidation of precursor, Eq (34), suggested by Fusco

et al [42] is used instead of the following reaction used by Lee et al [58],

PR + O2 + 24H2 Æ 2CO + 24C2H2 (37)

Pay attention that the presence of H2 in Eq (37) results in the formation of acetylene in

the right hand side part The formed acetylene, in turn, affects directly the mass of soot

as shown below The Arrhenius form is used for calculation of oxidation of precursor

PR O

⎡

To consider the effect of turbulent mixing in oxidation, the global oxidation rates of precursors, soot particles and acetylene are calculated as the harmonic mean of the above kinetic rate, k i kin, and the turbulent mixing rate,k i mix,

i r

hydrogen concentration does not impact on soot production, the change in acetylene concentration affects directly the mass of soot Figure 4 shows the variations of mass of net acetylene of single injection with two models used, Fusco model and Lee model The difference is found in the peak of acetylene with the higher value in Lee model

Table 2 Rate of change of mass fraction of species

In this study (Fusco [42] model) Lee et al [58] model

1 2

F dY

Figure 5 shows the variations of net soot mass Because soot formation is affected by acetylene concentration in the cylinder, an increase by 6% in peak acetylene in Lee model results in an increase by 15% in peak net soot, and an increase in 58% in soot emissions compared to Fusco model Compared to experimental data, soot emission with Fusco model shows better agreement In case of split injection, preliminary tests used Lee model also result in significantly higher soot emissions The Fusco model therefore is selected in this study

This soot model is incorporated into the KIVA-3V code The specifications of the engine and the conditions for calculation are listed in Tables 3 and 4, respectively Two injection schemes, single injection and split injection, both with EGR ratio of 20%

Figure 4 Comparison of net acetylene mass between Lee model and Fusco model

in case of single injection without EGR

Figure 5 Comparison of net soot mass between Lee model and Fusco model

in case of single injection without EGR

are considered in this study For split injection, the scheme of 75% of total fuel injected

in the first pulse, followed by an 8oCA dwell and 25% of total fuel injected in the second pulse is chosen Figure 6 illustrates the profiles of fuel injection and injection timing of two schemes The amount of injected fuel and the total duration of injection (excluding the dwell) of the split injection are kept as the same as that of the single injection

Figure 7 shows the computational meshes of the combustion chamber at 3oBTDC It represents one-sixth of the engine combustion chamber for computational efficiency because the injector has six holes, and the combustion chamber is axisymmetric There are 20 cells in the radial direction, 30 cells in the azimuthal direction and 26 cells in the

Table 3 Engine specifications

Engine type single cylinder, direct injection Piston geometry Mexican hat

Bore x stroke 137.2 x 165.1 (mm)

Compression ratio 15.1 : 1 Intake valve close 147o BTDC Exhaust valve open 134o ATDC Injector type Common rail injector

Start of injection 6o BTDC Duration of injection 21oCA (for single injection) Initial temperature 319 (K)

Initial pressure 200 (kPa)

Figure 6 Schemes of split injection and single injection

Figure 7 The computational meshes at 3oBTDC

axial direction The computation is started from IVC and is ended at EVO timing It takes approximately three hours to calculate one case with a Pentium 4 PC

Chapter 3 Results and Discussion

3.1 General results

The calibration of ignition, combustion, and spray atomization submodels was performed to reproduce the experimental pressure and the heat release rate in a cylinder The experimental results of Chan et al [28] for single injection and split injection are used as reference data Results of this calibration for single injection without EGR are presented in Figure 8 As shown in Figure 8(a), there is a good agreement for cylinder pressure between the experimental measurement and the modeling result In Figure 8(b), the heat release rate of modeling is little retarded compared to experimental measurement, however the shape of two curves is closed Figure 9 compares the experimental pressure and the modeling pressure in case of split injection with scheme

of 50.8.50 Two cases are checked: without EGR and with 10% EGR Although there is

a slight discrepancy during the expansion stroke, the ignition delay and the peak of pressure are similar The agreement between experiment and modeling curves is quite good and acceptable

The soot model is also calibrated against the experimental data Kazakov and Foster [47] pointed out that the most sensitive parameters affecting prediction of soot mass are the rate of acetylene formation, , and the rate of soot oxidation, It is reasonable

to adopt some simple but consistent criterion for comparison of model predictions and

2

r

8

mix r

(a) Pressure

(b) Heat release rate

Figure 8 Comparison of calculated and measured cylinder pressure and heat release rate

in case of single injection without EGR

(a) Split injection 50.8.50 without EGR

(b) Split injection 50.8.50 with 10% EGR

Figure 9 Comparison of calculated and measured cylinder pressure

in case of split injection

the experimental measurements In this study, the pre-exponential factor of acetylene formation reaction,A , is adjusted to 0.9 x 102 8 to achieve better agreement of soot mass with experimental data of Chan et al [28] The value of in soot oxidation rate is 10, the same as that was used in the study of Kazakov and Foster [47] After adjusted, these values are unchanged throughout this study Figure 10 compares the soot and NOx emissions of single injection between modeling and experiment data with two different injection timings: 6

8

C

oBTDC and 9oBTDC There is a good agreement between modeling results and experimental measurements The predicted trend is similar to the experimental value, with the decrease in NOx and increase in soot with fuel injection retard

Figure 10 Comparison of soot and NOx emissions between calculation and experiment

of single injection with different injection timing

Figure 11 Comparison of NOx and soot emissions with various amount of fuel injected

during the first pulse of split injection without EGR

Figure 11 shows the variations in NOx and soot with different schemes of split injection: 25.8.75, 50.8.50, and 75.8.25 Likewise, the computations are able to predict the increase of NOx and the decrease of soot when more fuel is injected in the first injection, as reported in the literature [5, 7] Thus the model is dependable for prediction

of the soot and NOx emissions

Figure 12 shows distributions of temperature and soot in case of single injection without EGR on the cross section at 4oATDC, the moment when the mixing controlled combustion phase has just started The stoichiometric zone is marked by the curve of φ

= 1 on the figure A flame has a typical structure of mixing controlled combustion flame with a higher temperature zone along the periphery and a relatively colder and fuel-rich zone inside The symmetry of the flame around the injection axis is not maintained due

(a) Cutting plane

Figure 12 Distributions of temperature and soot on the cutting plane at 4oATDC

in case of single injection without EGR

to swirl effects The edge of the flame is swept clockwise, resulting in a vortex of high temperature in the downside of the flame and a relatively lower temperature in the upside of the flame Soot exists throughout the flame with the highest concentration at the vortex The overall structure of the modeling flame agrees well with the conceptual model of Dec [35]

To illustrate the general results of modeling, the single injection with 20% EGR ratio

is used from now on In this study, the EGR ratio is defined by Eq (51), where is

the intake air volume without EGR, and is the intake air volume with EGR,

old V

new V

Figure 13 shows the variation in heat release rate during the combustion process The

curve has a typical shape of diesel combustion with four distinguishable stages: the

ignition delay period (a), the premixed combustion phase (b), the mixing controlled

Figure 13 Variation in heat release rate