Development of a Phenomenological Soot Model Coupled with a

Article pubs.acs.org/EF

Development of a Phenomenological Soot Model Coupled with a Skeletal PAH Mechanism for Practical Engine Simulation Bin Pang, Mao-Zhao Xie, Ming Jia,* and Yao-Dong Liu Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, P. R. China S Supporting Information *

ABSTRACT: A new chemical mechanism with 12 species and 26 reactions for formation of polycyclic aromatic hydrocarbons (PAHs) was developed and integrated into a skeletal mechanism for oxidation of primary reference fuel (PRF). Coupled with the new skeletal PRF-PAH mechanism, an improved phenomenological soot model was further constructed based on our previous work. By validating against the experimental data on the related PAHs in four premixed laminar flames of n-heptane/iso-octane and three counterflow diffusion flames of n-heptane, it is indicated that the major species concentrations were well reproduced by the model. Moreover, validations of the new soot model show that the soot yield, particle diameter, and number density were predicted with reasonable agreement with the experimental data in a rich n-heptane shock tube over wide temperature and pressure ranges. Compared with the soot model with acetylene as precursor species, the new model agrees better with the measurement, which proves the necessity of including PAHs chemistry for soot modeling. Finally, the model was applied to simulate the soot distributions in n-heptane sprays in the Sandia constant-volume combustion chamber under high EGR conditions, as well as the evolutions of PAH and soot concentrations in an engine fueled with n-heptane. It is also found that the experimental data was reasonably well reproduced by the model.

1. INTRODUCTION Recently, there has been growing concern about engine-relevant conditions for fuel efficiency and emission control. The increasingly stringent regulation on the size and number of particulate matter in engine exhaust has heightened the need for understanding of soot precursors and soot formation processes.1−3 Although there have been numerous publications on soot models over the last 30 years, the type of precursor species responsible for soot formation is still under debate. For example, Belardini et al.4 proposed a coupled soot formation and combustion model in 1996, assuming acetylene as the precursor species. They demonstrated that the reduced, kinetic soot model could reproduce, with satisfactory accuracy, the soot concentration in the combustion chamber, keeping the main features of diesel combustion. Therefore, C2H2 has been widely used as the precursor species in engine simulations. However, Vishwanathan and Reitz5,6 recently indicated that although present soot models applicable to internal combustion engines could be tuned to yield the total in-cylinder soot, the regimes of soot formation could not be accurately captured using only C2H2 as the precursor species for soot formation, particularly under low-temperature combustion conditions. The experimental observations of Idicheria and Pickett7 showed polycyclic aromatic hydrocarbons (PAHs) formation occurred far downstream in the lifted diesel flame and the soot formation/oxidation region was far downstream; thus, they led to the conclusion that PAH chemistry might play an important role not only for accurate soot mass predictions but also for accurate predictions of the soot distribution within the flame. Mechanisms that describe decomposition and oxidation have been developed for many hydrocarbons. Over the past decade © 2013 American Chemical Society

or so, detailed mechanisms have appeared that describe aromatics formation. A prominent example is the mechanism developed by Wang and Frenklach in 1997,8 which is a detailed kinetic model of aromatics formation in laminar premixed acetylene and ethylene flames. This model describes fuel pyrolysis and oxidation, benzene formation, and PAH mass growth and oxidation with 99 species and 527 reactions. Slavinskaya et al.9 proposed a reduced PAH formation mechanism which focuses on formation of the first aromatic ring from small aliphatic hydrocarbons and growth of PAHs. They indicated that the most important species for the first aromatic ring formation were C2H2, C2H3, C3H2, C3H3, C3H4, C4H2, i-C4H3, C4H4, i-C4H5, 1,3-C4H6, and c-C5H5. In 2009, Marchal et al.10 predicted formation of benzene and PAHs up to four rings from C2 fuels using a detailed kinetic mechanism for toluene reference fuel (TRF). Nevertheless, the detailed kinetic mechanism is too complex to be coupled with a multidimensional computational fluid dynamics (CFD) code for quantitative description of a reacting flow. In particular, application of the detailed PAH mechanism to simulation of engine combustion in connection with a multidimensional CFD model is still well beyond current computational capabilities, so most of the PAH mechanisms used in soot modeling are reduced ones. Recently, several soot phenomenological models coupled with reduced PAH mechanism have been developed.6,11−15 However, it is worth noting that the PAH mechanism in these models was not well validated by comparing against experimental data. Received: January 6, 2013 Revised: February 28, 2013 Published: February 28, 2013 1699

dx.doi.org/10.1021/ef400033f | Energy Fuels 2013, 27, 1699−1711

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Figure 1. Major reaction pathways for formation of large PAHs.

In this paper, first, a skeletal PAH mechanism including up to four fused aromatic rings (pyrene or A4) was developed and incorporated into a skeletal chemical mechanism for oxidation of primary reference fuel (PRF). Then, a phenomenological model of soot particle dynamics was constructed by integrating with the skeletal PAH mechanism. The new PAH mechanism was validated by comparing with experimental data of premixed laminar n-heptane and iso-octane flames. Several modifications and optimizations were made to improve the performance of the soot model. Finally, validations of the developed soot model were performed by comparing with experimental results in a shock tube, a constant-volume combustion chamber, and an engine fueled with n-heptane.

Moreover, the PRF mechanism does not include several important species, such as C3H3, C4H4, and C5H5, which play an important role in PAHs formation and growth processes. In order to couple the PRF combustion mechanism with the PAH mechanism, 4 species and 13 reactions relating formation of propargyl radicals (C3H3), C4H4, and C5H5 were quoted from ref 19. 2.2. PAH Kinetic Mechanism. By reviewing recent mechanisms for formation of PAHs up to 4 ring molecules, important pathways were identified and used to construct the initial skeletal PAH mechanism. In order to minimize the size of the reaction mechanism, further reduction efforts are concentrated on selecting the dominate pathways in premixed flame through the normalized rate of production (ROP) approach in which reactions with normalized ROP value less than the specified threshold value (around 0.2 used in this study) were removed. More about the normalized ROP approach has been description in ref 20. After establishment of the reaction pathways, it is still necessary to optimize the reaction rate parameters in order to match the experimental data in various reactors under wide operating conditions. Detailed optimization of the reaction rates can be summarized in three steps. (1) Using sensitivity analysis, the contribution of an individual reaction to formation of PAHs in premixed flame was identified. Reaction rate constants for the identified reactions were optimized in order to match the measured concentration of PAHs in premixed flame under wide operating conditions.21−23 During optimization of the reaction rate constants, it was found that if the predicted concentrations of PAHs show good agreement with the measured data in premixed flame the corresponding species concentrations can also be well reproduced in counterflow flame. (2) Further optimization on the reaction rate constants were performed by comparing with the predicted PAHs concentrations of the detailed mechanism18 in a shock tube in order to improve the abilities of the skeletal model to describe the soot formation process.

2. CHEMICAL KINETIC MECHANISMS FOR PRIMARY REFERENCE FUEL 2.1. Combustion Chemistry. A skeletal kinetic mechanism for PRF oxidation developed recently by the authors’ group16 was used as combustion chemistry of fuels in this work. It was constructed by combining newly constructed n-heptane and isooctane oxidation submechanisms. On the basis of the skeletal model target, the methodology used for model development considered the combustion mechanism as two parts: a comprehensive part describing reaction processes involving small radicals and molecules as the ‘core’, and a skeletal one which, in coupling with the ‘core’, controls the ignition characteristics. The PRF mechanism consists of 57 species and 176 reactions. Because the reactions of PRF pyrolysis were not included in the PRF mechanism, in order to validate soot formation under PRF pyrolysis conditions, 3 species and 4 reactions were added into the original PRF mechanism as follows C7H16 = C7H15 + H

(RG 1 ref 17)

C8H18 = C5H11 + C3H 7

(RG 2 ref 18)

C6H5CH 2 = C5H5 + C2H 2

(RG 3 modified)

C6H5CH 2 = C4 H4 + C3H3

(RG 4 modified) 1700


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Table 1. PAH Formation and Growth Mechanisms K = ATn exp(−E/RT) no.

reaction

3

A (cm /mol/s)

n −2.5

1692.0

18

0.0

2000.0

18

62

RP(1)

C3H3 + C3H3 = A1

5.56 × 10

RP(2)

C3H3 + C3H3 = A1 + H

4.40 × 108

19

E (cal/mol)

ref

RP(3)

A1 = A1 + H

1.29 × 10

−12.5

14 8085.6

18

RP(4)

A1 + H = A1− + H 2

2.50 × 1014

0.0

16 000.0

31

3.9

11 463.0 56 500.0

18

−

RP(5)

A1 + CH3 → A1 + CH4

4.42 × 101

RP(6)

A1 + C3H3 = C9H8 + H

6.26 × 109

2.6

RP(7)

A1 + O = C6H5O + H

13

2.20 × 10

0.0

4530.0

32

RP(8)

A1 + OH = C6H5OH + H

1.30 × 1013

0.0

10 600.0

32

29

33

−

RP(9)

A1 + C4 H4 = A2 + H

2.50 × 10

−4.4

26 400.0

RP(10)

2C5H5 = A2 + 2H

5.30 × 1011

0.0

4888.3

RP(11)

A1− + C2H 2 = A1C2H + H

2.50 × 1029

−4.4

26 400.0

10

RP(12)

A1C2H + H = A1C2H* + H 2

2.50 × 1014

0.0

16 000.0

10

RP(13)

A1C2H + OH = A1C2H* + H 2O

8

1.60 × 10

1.4

1450.0

10

RP(14)

A2 + H → A2−1 + H 2

2.20 × 107

1.9

9829.5

RP(15)

A2−1 + C4 H4 = A3 + H

2.50 × 1026

−4.4

26 400.0

33

A1C2H* + A1 = A3 + H

1.10 × 1024

−2.9

15 890.0

10

24

1.10 × 10

−2.9

15 890.0

10

1.10 × 1023

−2.9

15 890.0

10

RP(16) RP(17) RP(18)

−

−

A1 + A1C2H = A3 + H −

A1 + A1 = P2 + H

RP(19)

P2 + H = P2 + H 2

2.50 × 10

0.0

16 000.0

31

RP(20)

P2− + C2H 2 = A3 + H

4.60 × 106

2.0

7300.0

31

RP(21)

A3 + H → A3−4 + H 2

5.00 × 10

RP(22)

A3−4 + C2H 2 = A4 + H

1.40 × 1029

RP(23) RP(24) RP(25) RP(26)

−

14

8

1.9

9829.5

−3.4

17 800.0

33

C 9 H8 = C 9 H 7 + H

68

1.73 × 10

−15.2

11 6371.9

34

C9H 7 + C5H5 → A3 + 2H

6.39 × 1029

−4.0

35 205.5

34

C9H 7 + C9H 7 → A4 + C2H 2 + H 2

6.39 × 10

−4.0

35 205.5

35

A4 + CH3 → A4−1 + CH4

5.40 × 10°

3.9

11 771.0

29

(aliphatic or aromatic) and operating conditions (low or high pressure, temperature range).24−29 A detailed overview is given by Zhang et al.29 Several important intermediate species contribute to formation of the first ring, including C2H2, C3H3, n-C4H3, and n-C4H5. Recent investigations24−26,29 indicated that the combination of C3H3 radicals plays an important role for A1 formation in the C2H2 flame and propene (C3H6) flame, which has been reiterated in subsequent kinetic studies. Moreover, on the basis of detailed kinetic simulations, n-heptane flames produce a large number of C2 species (e.g., C2H2, C2H4) and subsequently C3 species27−29 and iso-octane flames produces lots of C3 species (e.g., C3H3, C3H5).29 Because PAHs formation reactions for PRF oxidation are the focus of this study, an oddcarbon-atom pathway via combination of C3H3 as RP(1−2), listed in Table 1, was introduced in this skeletal PAH mechanism for formation of A1. 2.2.2. Naphthalene (A2) Reactions. One of the most important pathways for formation of naphthalene (A2) is through self-combination of cyclopentadienyl radicals (C5H5)30 as RP(10) in Table 1. Other important pathways involved in formation of A2 from A1 through the H-abstraction-C2H2/ C4H4-addition (HACA) mechanism8 were also used. 2.2.3. Phenanthrene (A3) Reactions. Besides growth of A2 through the HACA mechanism as RP(15) in Table 1, two

(3) Steps 1 and 2 were repeated until the mechanism is capable of satisfactorily reproducing the concentrations of PAHs in both a premixed flame and a shock tube. It should be noted that the final kinetic parameters in the PAH mechanism do not completely match the values in the detailed mechanism and other classic models, since significant adjustments of the rate parameters have been made to match the experimental data. The final PAH mechanism includes 12 species and 26 reactions. Important pathways in the new mechanism are shown in Figure 1. PAH formation processes consist of the first ring formation and subsequent growth from A1 to A4, as listed in Table 1. It should be noted that the new skeletal PAH mechanism is primarily developed and validated for n-heptane, so more optimizations for the pathways in the PAH mechanism are still needed as it is applied to model the oxidation of other different fuels that produce minor levels of C2H2, including toluene and other aromatic fuels, and fuels with large fractions of cyclic paraffins (such as methyl cyclohexane). 2.2.1. Benzene (A1) Reactions. The primary focus of the mechanism is on formation of the first aromatic ring benzene (A1) from small aliphatic hydrocarbons. Recently, research has demonstrated that A1 formation reactions show extremely complex behavior, which strongly depends on the type of fuel 1701


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Figure 2. Schematic representation of the improved phenomenological soot model.

Table 2. Soot Reaction Mechanisms k = ATn exp(−E/RT) no.

reaction

3

A (cm /mol/s)

n

E (cal/mol)

5

reaction rate

ref

C2H 2 → 0.04C(PR)50 + H 2

4.0 × 10

0

3.974 × 10

RS1 = k1[C2H 2]

RS(2)

A3 → 0.28C(PR)50 + 5H 2

1.0 × 106

0

3.974 × 104

RS2 = k 2[A3]

RS(3)

A4 → 0.32C(PR)50 + 5H 2

5.0 × 109

0

3.974 × 104

RS3 = k 3[A4]

C(PR)50 → 0.5C(S)100

4.1 × 10

C(S)m + C2H 2 → C(S)m + 2 + H 2

4.05 × 10

RS(6)

C(S)m + A1 → C(S)m + 6 + 3H 2

1.03 × 10

RS(7)

nC(S)m → C(S)n * m

Kazakov−Foster model

37

RS(8)

C(S)m + O2 → C(S)m − 2 + 2CO

NSC model

38

RS(9)

C(S)m + 2OH → C(S)m − 2 + 2CO + H 2

Neoh et al. model

C(PR)50 + 25O2 → 50CO

1.0 × 109

RS(1)

RS(4) RS(5)

RS(10)

11 3 4

4

0

8.9415 × 10

RS4 = k4[C(PR)]

0

6.1597 × 10

RS5 = k5[C2H 2](A soot )1/2

0

6.1597 × 10

3 3 3

40

1/2

RS6 = k6[A1](A soot )

39 3.974 × 104

0

RS10 = k10[C(PR)][O2 ]

40

from soot precursor, particle surface growth by C2H2 and A1, particle coagulation, particle surface oxidation via oxygen (O2) and OH, and precursor oxidation. The new model retains the main features of the original one,36 but two major modifications were conducted including (1) PAHs (A3, A4) are used as precursor species and (2) particle surface growth by A1 is added in the new soot model. The reaction rate expressions for the global reactions (shown in Figure 2) are given in Table 2, in which soot precursor and soot particle are represented by C(PR) and C(S), respectively. The rates for reactions including soot precursor formation (RS(1), RS(2), RS(3)), particle inception (RS(4)), particle surface growth (RS(5), RS(6)), and soot precursor oxidation (RS(10)) were assumed to be in the form of a global Arrhenius expression. The reaction rate of particle coagulation (RS(7)) is given by

pathways for formation of phenanthrene (A3) from reaction between A1C2H and A1 were considered in this work (RP(16−17) in Table 1). Addition of C2H2 on a biphenyl radical (P2−) can also lead to formation of A3, RP(18−20), as shown in Table 1. In addition, by sensitivity and pathway analysis, it was revealed that addition of a bindenyl radical (C9H7) on C5H5 was an important pathway under shock-tube conditions, which is also considered in this study (RP(24) in Table 1). 2.2.4. Pyrene (A4) Reactions. There are two pathways for pyrene (A4) formation, i.e., growth of A2 through the HACA mechanism and self-combination of C9H7, shown as RP(22) and RP(25) in Table 1, respectively.

3. MODEL FOR SOOT PARTICLE DYNAMICS The submodel for soot particle dynamics was constructed based on our previously developed phenomenological soot model36 by introducing necessary improvements and optimizations. The schematic representation in Figure 2 shows the structure of the six-step phenomenological soot model developed in this study. The complex processes of soot formation and oxidation are divided into several main steps including soot precursor formation via C2H2, A3 and A4 conversion, particle inception

RS7 =

1 2 βN 2

(1)

where N is the soot number density and β is the collision frequency which was estimated by the Kazakov−Foster37 model by considering particle collision in both the free-molecular regime and the near-continuum regime. The particle oxidation 1702


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rate is determined using the O2-related oxidation model (RS(8)) of Nagle and Strickland-Constable (NSC)38 and the OH-related oxidation model (RS(9)) by Neoh et al.39 In accordance with the experimental data in a shock tube with a rich n-heptane mixture, the parameters in the particle inception reaction were improved in this study on the basis of the original soot model. In the current study, it is assumed that soot precursor and soot particle are composed of only carbon atoms, and their thermochemical properties are the same as those of graphite on an individual carbon basis. Following the suggestions from previous studies,12,37 the number of carbon atoms in C(PR) is taken to be 50 and the initial soot nucleus is a spherical ball containing 100 carbon atoms, which results in an approximately 1 nm size of the incipient soot particle at a density of 1.86 g/cm3. On the basis of the soot formation and oxidation processes described above, the net rates for the soot mass density YS and the soot number density N are written as dYS = MC(50·RS4 + 2·RS5 + 6·RS6 − RS8 − RS9) dt

(2)

N dN = A RS4 − RS7 dt 2

(3)

where NA is Avogadro’s number and MC is the molecular weight of a carbon atom.

4. VALIDATION OF THE PAH MECHANISM 4.1. Validation of Intermediate and PAHs Concentrations for Premixed Laminar n-Heptane and Iso-octane Flames. This section provides a comparison between the simulation results obtained using the new chemical mechanism and the experimental data on intermediate and PAHs concentrations for the premixed laminar flames listed in Table 3.

Figure 3. Mole fraction profiles in C7H16 premixed flame (flame A) as a function of height above the burner.

experimental and the modeled results show decreasing fuel and oxygen and a steep increase in combustion products (CO, CO2) in the main oxidation zone. As n-heptane and oxygen are consumed, CO and CO2 approach constant concentration values in the main oxidation region. Because PAHs were used as precursor species in the soot model, we are essentially interested in A1 formation and PAH growth. Besides, special attention was focused on two categories of species: C2 and C3 species. For C2 species, C2H2 and C2H4 play an important role in growth of PAHs and soot particles. For C3 species, C3H6 and C3H4 are potential precursor of propargyl radical, which is the main source of A1. As shown in Figure 3, the mole fractions of C2H4, C3H6, and A1 are predicted reasonably well as compared to the experimental data. In the main oxidation zone, C2H4 and C3H6 exhibit a rise-decay profile, as typical of reaction intermediates being mainly formed in the oxidation zone and rapidly destroyed at the end of the oxidation region. In addition, A1 concentration increases in the main oxidation zone and decreases at the beginning of postoxidation flame region. The premixed laminar flames of n-heptane and iso-octane (flames B and C in Table 1) were measured by Bakali et al.,21 which were stabilized at atmospheric pressure on a 4.1 cm diameter flat flame burner. Species were sampled and analyzed by gas chromatography and a quartz microprobe. Flame temperature was measured by thermocouples. Profiles of the mole fractions of small chemical species (smaller than PAHs) as a function of height above the burner formed in flames B and C are shown in Figures 4 and 5, respectively. Simulations were conducted with the new skeletal mechanism, and for comparison, a detailed mechanism was developed by Raj.18 It can be seen from

Table 3. Test Conditions of Premixed Laminar Flames at Atmospheric Pressure composition (mol %) flame

fuel

fuel

O2

N2 or Ar

cold gas velocity (cm/s)

ref

flame A flame B flame C flame D

C7H16 C7H16 C8H18 C7H16

5.7 3.98 4.23 5.33

28.3 23.01 27.80 29.70

66.00 (N2) 73.01 (N2) 67.97 (N2) 64.97 (Ar)

4.0 4.98 4.18 5.25

23 21 21 22

All of the flames were simulated by the Premixed Laminar Burner-stabilized Flame module in the CHEMKIN PRO package. The experimental temperature or modified temperature (in flame D) profiles were introduced as the input data in simulations. Anna et al.23 carried out an experiment on premixed n-heptane flame (flame A), which was stabilized at atmospheric pressure on a commercial sintered bronze burner. Oxidation and pyrolysis products were sampled and quantified by means of gas chromatographic analysis. Temperature profiles were measured with a fast-response thermocouple using a fast-insertion procedure. The concentration profiles of reactants and main products in flame A are plotted in Figure 3. The temperature profile in Figure 3a was used as input for simulations without considering the energy balance. The vertical dashed line in each figure, corresponding to the limit of the main oxidation zone, is identified by the peak in temperature profile. Both the 1703


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Figure 4. Mole fraction profiles in C7H16 premixed flame (flame B) as a function of height above the burner.

Figure 5. Mole fraction profiles in C8H18 premixed flame (flame C) as a function of height above the burner.

Figure 4 that both of the new skeletal and detailed mechanisms show not only qualitative but also quantitative agreement with the measurements for the mole fraction profiles of reactants (e.g., C7H16, O2), products (e.g., H2O, CO2), and C3 species (e.g., C3H6, C3H4). In contrast, the predicted peak concentration of C2H2 from the skeletal mechanism is lower than the measurement. It is because the C2 mechanism used in the combustion chemistry is a simplified one which omits some routes to form C2H2. The same level of agreement was obtained for the iso-octane flame (Figure 5) except for C3H6 which is underpredicted by the skeletal mechanism. It is worth noting that the predicted mole fractions of A1 from the skeletal mechanism show better agreement with the experimental data than those from the detailed mechanism in flames B (Figure 4) and C (Figure 5). This is mainly because the detailed mechanism includes PAH submechanisms to account for formation and growth from A4 to coronene (A7), which lead to more consumption of A1. It is found from Figure 5 (iso-octane flame C) that both of the new skeletal and detailed mechanisms cannot well reproduce the experimental mole fraction of A1. It is mainly because of the deficient C3 mechanism used in the

combustion chemistry without considering some routes to form enough C3 species (e.g., C3H3, C3H4, and C3H6), which play an important role for A1 formation in iso-octane flames.29 Furthermore, by comparing Figures 4 and 5, it is found that there is a large difference in the maximum A1 mole fraction between n-heptane flame and iso-octane flame: 6.5 × 10−5 in n-heptane flame and 2.6 × 10−4 in iso-octane flame. This is caused by the fact that formation of C3H3 and C3H4 rapidly occurs in iso-octane flame, while the n-heptane flame produces primarily C2 species and yields C3 species in subsequent steps,29which leads to slower reaction rates for formation of C3 species. Moreover, C3H3 is also formed from propyne (C3H4) by H and OH atom abstraction. Reaction of C3H3 from C3H4 occurs in n-heptane flame, but its importance is magnified in iso-octane flame.10 Therefore, a higher concentration of A1 was produced in iso-octane flame than in n-heptane flame. An n-heptane premixed laminar flame (flame D) has been studied by Inal and Senkan,22 where the experimental data of PAHs up to A4 are available. Samples were analyzed by gas chromatography and mass spectrometry. Flame D was simulated using the new skeletal mechanism to predict the profiles of large 1704


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experiment indicates that the peak points of A3 and A4, in the postoxidation region, locate at a larger height above the burner than those of A1 and A2, which is well reproduced by the model. 4.2. Validation of Intermediate and PAHs in Counterflow Flames of n-Heptane. The above results indicate that the chemical mechanism can predict reasonably well the PAH mole fractions in premixed flames, and the mechanism was further tested for counterflow diffusion flames in this section. Under the experimental conditions of ref 42, as shown in Table 4, numerical

PAHs. Radiation loss was considered in the simulation by introducing the modified input temperature based on the method of Tian et al.41 with the equation T(h) = Tb + ΔTmax[1 − exp(−kh)] − k′h, where Tb is the temperature of the burner, ΔTmax the maximum temperature difference between the burner and the exhaust, h is the height above the burner, k is the initial exponential slope of temperature rise with inverse length units, and k′ (units K/m) is the second slope which is a measure of energy loss for larger heights above the burner. Figures 6 and 7 show the profiles of C7H16, O2, and A1−A4,

Table 4. Operating Conditions for n-Heptane Counterflow Diffusion Flames flame

strain rate (s−1)

equivalence ratio

nozzle separation (cm)

flame E flame F flame G

50 50 150

6.1 2.5 4.1

1 2 1

investigation of the flame structure and emission characteristics was performed at different strain rates (aG) and equivalence ratios (φ) in the counterflow flames of n-heptane. For all tested cases, the fuel stream was introduced from the bottom nozzle and the oxidizer from the top nozzle. The oxidizer was pure air, while the fuel stream was a mixture of n-heptane and air with the desired values of equivalence ratio. Simulations of the counterflow diffusion flames were performed using the Opposed-flow Diffusion Flame module in the CHEMKIN PRO package with the method of solve gas energy equation. The multicomponent diffusion coefficient was taken into account for all simulations presented in this section. Detailed comparisons of simulations and measurements for the three flames listed in Table 4 are presented in Figures 8−10, which show the simulated and measured temperatures, axial velocities, and species mole fraction profiles. The vertical lines in each figure indicate (1) the nonpremixed reaction zone location that is identified by the peak in temperature profile and marked by the green dash-dotted line, (2) the stagnation plane that is established at the location where the simulated axial velocities (Vx) equal zero and marked by the dashed line, and (3) the rich premixed zone location that is identified by the peak in hydrogen profile and marked by the red dash-dotted line. From a general observation, the three counterflow flames are characterized by a double flame structure: a rich premixed zone and a nonpremixed reaction zone.42 Pyrolysis and partial oxidation of n-heptane occurs at the rich premixed zone located on the fuel side. In addition, the products of partial oxidation (CO, H2) and intermediate hydrocarbon species are transported and consumed in the nonpremixed reaction zone located on the oxidizer side where they turn to produce CO2 and H2O. The flame structure becomes visually more distinct as strain rate decreases by increasing the nozzle separation distance. The double flame structure is reproduced by the skeletal mechanism in flames E and F but not so evident in flame G. The discrepancies between prediction and measurement are also observed in the study with a detailed mechanism.42 The reasons for the discrepancy could be the deficiencies of the chemical mechanism and the assumption of one-dimensional counterflow flame. Furthermore, Sung et al.43 indicated that in counterflow premixed flames the heat release rate is characterized by a single sharp maximum, and for diffusion flames, the heat release rate profile exhibits an additional, secondary peak, which indicated the strong diffusion effect of the diffusion flame structure. Hence,

Figure 6. Mole fraction profiles of C7H16 and O2 in C7H16 premixed flame (flame D) as a function of height above the burner.

Figure 7. Mole fraction profiles of PAHs in C7H16 premixed flame (flame D) as a function of height above the burner.

respectively. The dashed vertical line in each figure is identified by the limit of the main oxidation zone. According to the experimental investigation of Inal and Senkan,22 the measured mole fraction data within a few millimeters above the burner surface may be considered questionable due to the possible sampling probe-burner surface interactions. Thus, only the comparison at large heights above the burner may be meaningful.18 It is seen from Figure 6 that the mole fractions of C7H16 and O2 are well reproduced by the model. Moreover, the mole fractions of A1−A4, predicted using the new skeletal mechanism, are in reasonable agreement with the experimental data as indicated in Figure 7. The mole fraction of A1 increases in the main oxidation zone and decreases at the beginning of the postoxidation flame region, but the predicted location of the peak point in the A1 profile slightly advances more than the experiment. The 1705


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Figure 8. Predicted (lines) and measured (symbols) profiles for flame E.

Figure 9. Predicted (lines) and measured (symbols) profiles for flame F.

locations of the peaks for temperatures and other intermediate species are also observed from Figures 8−10. In the present study, particular attention was focused on prediction of A1 profiles. In spite of their relatively low concentrations, the predicted and measured A1 profiles exhibit good agreement for all three flames as shown in Figures 8−10. Both measurements and predictions indicate that the A1 concentration decreases as the level of partial premixing and strain rate are increased.

refinement of the diffusion coefficients of species in the mechanism could be helpful for improvement of the simulation results. The temperatures and major species mole fraction profiles of simulations and experiments are in relatively good agreement. It can be seen from Figures 8−10 that the model is able to qualitatively predict the measured reactants (e.g., C7H16, O2) and products (e.g., H2, CO), although the consumption rates of fuel and oxidizers (which leads to the shift of concentration profiles to the fuel side) are overpredicted. Similar discrepancies between experiment and simulation on the 1706


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Figure 10. Predicted (lines) and measured (symbols) profiles for flame G.

5. VALIDATION OF THE SOOT MODEL 5.1. Validation of Soot Yield for n-Heptane Oxidation in a Shock Tube. The phenomenological soot model coupled with the new skeletal PAH mechanism was used to simulate soot yield obtained by Kellerer et al.44 for n-heptane oxidation in a shock tube in this section. Simulations were performed under constant-volume homogeneous adiabatic conditions behind the reflected shock wave. In this study, our previous soot model36 with acetylene as precursor species (similar to the model developed by Tao et al.40) was compared with the model developed in this study. Comparisons between measurements and predictions for evolution of the particle diameter, particle number density, and soot yield are shown in Figure 11, in which soot yield is defined as the carbon present as soot referred to the total carbon available. It can be seen that the trends are well reproduced by the model. Following a large number of small soot particles being formed at the beginning of the particle inception period, the particle number density significantly decreases and the particle diameter quickly increases owing to particle coagulation and then the soot mass steadily grows. Compared with our previous soot model with C2H2 as the precursor species,36 the new model agrees better with measurement on evolutions of soot particle diameter, number density, and soot yield. This is mainly because a large number of C2H2 were produced in n-heptane oxidation. Formation of soot rapidly occurs in the previous soot model using only C2H2 as precursor species and surface growth species, whereas using the new soot model that coupled with the PAH mechanism, more C2H2 is consumed to form PAHs in subsequent steps, which leads to slower reaction rates for soot precursor formation and particle surface growth. Therefore, the predicted history of soot yield with the new model shows increasing consistence with the measurement than that from the soot model with C2H2 as precursor species. Overall, the skeletal PAH formation mechanism introduced in the new soot model provides more accurate predictions for soot modeling.

Figure 11. Comparison of experimental44 and modeling results for the soot particle diameter, number density, and soot yield in a n-heptane shock tube.

From the comparisons between measurements and predictions shown in Figure 12 for soot yield at 1.5 ms after the reflected shock arrival, it can be seen that the predicted trends agree reasonably well with experiments. The trend of higher soot yield with increased pressure is well reproduced by the model. The dependence of the soot yield on the temperature is also predicted by the simulation, which indicates that soot formation dominates over soot oxidation and leads to increased soot yields 1707


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extinction coefficient,50 which would result in certain deviations. Figure 13 compares the soot volume fraction distributions between the model and the experimental data. It can be found that the soot predictions for all cases agree reasonably well with the measurements. Both predictions and experiments show that there is substantial reduction in the soot emissions with the decreased O2 concentration. It can also be clearly seen that when O2 concentration is decreased, the center of the high soot concentration zone gradually moves away from the injector. In the new soot model, both C2H2 and PAHs play important roles in soot formation and growth. The predicted temperature, equivalence ratio, and C2H2 and PAHs concentration distributions for O2 = 15% are shown in Figure 14 to give clear explainations of formation and oxidation of soot. The black contours represent the soot volume fraction distribution. It can be seen that high soot concentration is located in the temperature range of 1700−2000 K. At high temperature (T > 2100 K), soot oxidation plays a more dominant role and leads to decreased soot yields, whereas at low temperature (T < 1600 K) only a small quantity of soot precursor species (PAHs) is formed and leads to low soot concentrations. In addition to the temperature, simulation results suggest that the equivalence ratio (φ) also strongly affects the soot formation process. As can be seen from Figure 14, most of the soot is formed inside the fuel jet, where φ > 1.6, and complete combustion of fuel leads to no soot formation outside. It can also be seen from Figure 14 that PAHs and soot are located in the center and downstream regions of the fuel jet, respectively. Because PAHs and C2H2 could be easily converted to soot precursor in the high soot region under the conditions of 1700 K < T < 2000 K and φ > 1.6, higher PAH concentrations appear just upstream of the peak soot concentration. By providing accurate information on the soot precursor from the skeletal PAH mechanism, the soot model is able to reliably capture the soot formation behavior. 5.3. Validations of PAHs and Soot Evolutions in an Engine Fueled with C7H16. The in-cylinder PAHs and soot evolutions of a direct-injection diesel engine fueled with C7H16 were simulated using the phenomenological soot model coupled with the skeletal PAH mechanism in this section. Fundamental physical dimensions and operating conditions of the engine and a set of fuel-spray parameters are listed in Table 7. Computational models used in this section are the same as those in section 5.2, for which the details can be found in Table 6. A 72° sector of the combustion chamber was modeled in this study, and the computational mesh is shown in Figure 15. The predicted pressure and heat release rate for the tested operating condition are shown in Figure 16. It is seen that model predictions are in good agreement with experimental data,51 which indicates that the n-heptane mechanism used in this study is capable of reproducing the fuel oxidation process in engines. Comparisons of the evolutions of PAHs (A2, A3, and A4) and soot between simulation and experiment are shown in Figures 17 and 18, respectively. It can be seen the overall trends of A2, A3, A4, and soot are well reproduced by the model. At the end of the combustion process, oxygen content decreases and the residual fuel in the cylinder converts to a large number of small aliphatic hydrocarbons due to incomplete combustion. Thus, the PAH mass quickly increases and reaches the maximum value around the top dead center. Then the PAH mass decreases, and the trend is toward a constant level after 15 °CA because of formation of soot at the high-temperature fuel-rich conditions.

Figure 12. Comparisons between measured44 and predicted soot yield at different temperatures and pressures.

at temperatures lower than a critical value, while soot oxidation plays a more dominant role when the temperature exceeds the critical temperature. 5.2. Validations Soot Distributions in a Sandia Constant-Volume Combustion Chamber. Soot formation in fuel jets injected into an optically accessible constant-volume combustion vessel under simulated quiescent n-heptane engine conditions was investigated by Sandia National Laboratories. Detailed experimental data are well documented in the Engine Combustion Network Web site. In this section, experimental results with focus on the influence of ambient O2 on soot emissions were used to validate the phenomenological soot model and discuss the soot source in n-heptane combustion conditions. Detailed experimental conditions are listed in Table 5. The experimental vessel has a cubic combustion Table 5. Conditions for the Sandia Constant-Volume Combustion Chamber ambient temperature ambient density fuel type fuel temperature injection rate profile orifice diameter O2 concentration

1000 K 30.0 kg/m3 n-heptane 373 K top hat 100 mm 15%, 12%, 10%

chamber 108 mm in size on each side. A single orifice was mounted at the center of a metal side port for injecting n-heptane fuel directly into the chamber. Simulations were conducted using a two-dimensional axisymmetric mesh 100 mm in diameter and 100 mm in length. Computational fluid dynamics (CFD) code KIVA-3 V was used for the simulations. The improved physical and chemistry submodels in KIVA-3 V are shown in Table 6. Table 6. Computational Models turbulent model break-up model collision model spray−wall interaction model heat transfer from the wall combustion model

RNG k-epsilon model45 KH-RT model46 Nordin47 model Han et al.48 model Han-Reitz49 model CHEMKIN

In the experiments, soot volume fraction was obtained by converting the extinction data with an empirical optical 1708


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Figure 13. Comparison of model predicted soot volume fraction (ppm) distributions with experiments for ambient density of 30.0 kg/m3.

Table 7. Engine Specifications and Operating Conditions squish (mm) bore (mm) stroke (mm) compression ratio swirl ratio nozzle hole diameter (mm) nozzle hole number

0.172 102 118 17.5 1.83 0.2 5

engine speed (r/min) injection pressure (MPa) SOI (°ATDC) injection duration (°CA) fuel/air ratio fuel fuel temperature(K)

1000 60 −30.0 3.6 0.133 C7H16 373

Figure 15. Computational mesh for a direct-injection diesel engine.

Figure 14. Predicted temperature, equivalence ratio, C2H2, and PAHs mole fractions for O2 = 15% at 3.2 ms after SOI.

Figure 16. Comparison of experimental51 and modeling results for the pressure and heat release rate.

discrepancy between simulation and experimental results, which need further in-depth exploration, including the uncertainties in the measured PAH mass with the gas chromatography and mass

However, it is worth noting that the magnitude of PAHs and soot are still underestimated by the model compared to measurements. There are diverse factors that might cause the 1709


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Figure 17. Comparison of PAHs mass curves between simulated and measured results.51

Figure 18. Comparison of soot mass curves between simulated and measured results.51

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spectra analysis in the experiment and further improvement of the PAH mechanism. Furthermore, the PAH mechanism is a skeletal one which possibly omits some routes to form PAH under the complicated engine-relevant conditions, although it was validated by comparing with the experimental data in premixed and counterflow flames. In order to cover a wide operating range, further improvement and optimization of the reaction rate constants and the pathways in the PAH mechanism still need to be done.

2. Using the improved phenomenological soot model coupled with the skeletal PAH chemistry, the soot yield, particle diameter, and number density were predicted with reasonable agreement with the rich n-heptane shock-tube experiments over wide temperature and pressure ranges. 3. The phenomenological soot model has gained significant improvements in the performance by incorporating the PAH chemistry into the model. 4. The soot volume fraction distributions in the Sandia constant-volume combustion chamber were simulated by the new soot model. The predicted soot distributions under various ambient oxygen concentrations agree well with the experimental results 5. Compared with experiments in a direct-injection engine fueled with C7H16, it is indicated that the evolutions of PAHs and soot are reasonably well reproduced.

ASSOCIATED CONTENT

S Supporting Information *

Skeletal mechanism (chem.txt), thermodata (therm.txt), and transport data (tran.txt) files. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: +86-411-8470-6302. Fax +86-411-8470-8460. E-mail: [email protected].

6. CONCLUSIONS A new skeletal PAH formation mechanism was constructed and integrated into a PRF oxidation mechanism in this study. The mechanism was validated by comparing the predicted major species and PAH concentrations with measurements in laminar premixed flames and counterflow flames. Furthermore, the new skeletal PAH mechanism was coupled with a phenomenological soot model using A3 and A4 as the soot precursor species and modeling the soot surface growth by C2H2 and A1. The new soot model was validated by comparing the soot yield, number density, and particle diameter with the experimental measurements in a constant-volume combustion chamber and a diesel engine. Major technical accomplishment can be summarized as follows. 1. The new skeletal PAH mechanism is capable of describing the formation process of PAHs beyond A1 and up to A4. Predictions of mole fraction profiles for PAHs match reasonably well with the measured results in four premixed laminar flames of n-heptane/iso-octane and three counterflow diffusion flames of n-heptane.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grant Nos. 51176020 and 51176021) and General Motors Global R&D (Grant No. GM024705-NV584). We also really appreciate Prof. Song at Tianjin University for providing experimental data in the engines.

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Development of a Phenomenological Soot Model Coupled with a

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