n-Heptane Fuel Blends under

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Ignition characteristics of methane/n-heptane fuel blends under engine-like conditions Haiqiao Wei, Jiayue Qi, Lei Zhou, Wanhui Zhao, and Gequn Shu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b04128 • Publication Date (Web): 18 Apr 2018 Downloaded from http://pubs.acs.org on April 18, 2018

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Ignition characteristics of methane/n-heptane fuel blends under engine-like conditions Haiqiao Wei*, Jiayue Qi, Lei Zhou*, Wanhui Zhao, Gequn Shu State Key Laboratory of Engines, Tianjin University, Tianjin 300072, China

*Corresponding author: Lei Zhou, Haiqiao Wei Address: 92 Weijin Road, Nankai District, Tianjin, P. R. China Tel.: +86-22-27402609 Email: [email protected] (L. Zhou) [email protected] (H. Wei)

Abstract

There is significant interest in using pilot fuel as a source of ignition for enhancing the performance of natural gas engine. In this work, ignition of methane/n-heptane fuel blends is numerically studied based on the condition after the compression in dual-fuel engine. The Chemkin-Pro is used to model ignition in a closed homogenous reactor. Compared with the calculated IDs based on four mechanisms (Liu 44, Sk 88, GRI 3.0, Detailed Zhang), the Liu 44 mechanism yields the closest agreement with experimental data both for CH4/air mixtures and C7H16/air mixtures, which is adopted in this investigation. Results show that the initial temperature and equivalence ratio have great influence on the ID in all research conditions. While the effects of pressure and blend ratio depend on the special condition, such effects are great at high equivalence ratio but small at low equivalence ratio. It is interesting that the ignition delay map can be divided into four different zones, which can derive from the

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coupling effect of methane concentration and equivalence ratio. Specially, the negative temperature coefficient (NTC) can also be observed for dual fuel. And the sensitivity analysis indicates that the effect of C7H16 addition on the total reaction rate is high in the NTC regime. The rate of production and consumption analysis shows the main production and consumption path of the important radicals. Such analysis also shows that initial temperature and equivalence ratio have great influences not only on the reaction rates but also on the reaction temperature region. These studies can provide theoretical basis for the study on ignition control of dual fuel engine. Keywords: Dual fuel; Ignition delay (ID); Sensitivity analysis; Negative temperature coefficient (NTC); Methane

1 Introduction

With the growing number of vehicle, the shortage of fossil energy and increasingly environmental pollution, there is worldwide interest in the use of renewable and environmentally fuels for automobile engines. In this regard, natural gas can be used for its rich resources, widespread distribution infrastructure, low cost, and clean-burning qualities 1-3. Furthermore, the use of natural gas is not prone to knock due to its high methane number, so it can achieve high efficiency with relatively high compression ratio

4. 5

. However, it suffers

from poor ignition characteristics due to the high auto-ignition temperature and low cetane number compared with diesel fuel

6-9

. Previous studies found that the addition of small

amount of higher alkanes such as ethane, propane and butane can lower the IDs of methane-oxygen mixtures in shock tubes

10. 11

. Therefore, the dual fuel engine, in which the


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pilot diesel ignition is used to trigger high-temperature ignition, is applied to ensure reliable combustion initiation. The ignition stability plays an important role in this kind of engine because longer IDs will lead to unacceptable rates of pressure rise followed by knock

9. 12

.

Therefore, there is considerable interest in investigating the ignition characteristics of methane-diesel fuel blend. The present work has a new contribution to providing the fundamental understanding of the ignition features of this dual fuel. In recent years, a number of studies of gas engines with pilot ignition have been focused on combustion, emissions and engine performance characteristics

13. 14

. However, the studies

on the ignition characteristics and chemistry for methane/n-heptane mixtures are limited. Some experimental studies have been done using rapid compression machines, shock tube 15, constant volume configuration and single cylinder four stroke direct injection engines

16

. It

was found that the auto-ignition of methane is promoted by addition of n-heptane, however, in other word, the ignition of n-heptane is delayed by the presence of methane in the ambient gas 17. 18

. Schlatter et al.

18

conducted an experimental study in a rapid compression expansion

machine and found that lower ambient temperatures or dilution of the ambient oxidizer caused longer IDs, which resulted in a higher heat release due to more methane/air entrained and mixed with the pilot injection. They also investigated the effect of nozzle geometry, methane equivalence ratio, EGR (exhaust gas recirculation) dilution of the premixed charge and ambient temperature on the ignition in literatures

19. 20

. Polk et al.

16

studied the effect of

equivalence ratio, pilot fuel quantity, gaseous fuel percent energy substitution (PES) and brake mean effective pressure (BMEP) at a constant engine speed (1800 rev/min) using a four-cylinder direct injection diesel engine. However, the types of data obtained from the


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experiments were still limited by the measurement techniques. For simulation studies, a reduced mechanism

21

of CH4/C7H16 including 41 species and 109 reactions has been

developed by Keyvan Bahlouli et al. Maghbouli et al. 22 performed a numerical investigation in a natural gas-diesel dual fuel engine using CFD model, and found a shorter ID and peak pressure increment caused by increasing pilot fuel amount. Demosthenous et al.

17. 23

conducted a direct numerical simulation in a constant volume configuration, finding that ignition was localized and occurred at rich mixture fractions, and the methane oxidation behavior followed roughly an auto-ignition regime and a canonical premixed flame for large and small amounts of n-heptane respectively. Wang

24

found that the ID was a function of

pressure and an exponential function of temperature. Available literatures have mostly studied the effects of many factors on the IDs, but the deep mechanism of ignition characteristic for methane/n-heptane fuel blend needs further study. Since n-heptane (C7H16) is an important surrogate for diesel fuel, its oxidation chemistry has been extensively researched, and the NTC behavior in auto-ignition has been observed and studied in homogenous systems such as the shock tube and computational reactors27.

28

25

, rapid compression machine

26

. The view that the peroxy-chemistry pathways in the

low-to-intermediate temperature regimes lead to the NTC behavior is widely accepted 26. 29. In addition, the NTC behavior of CH4/C7H16 mixture has been found in some conditions

30

,

while the fundamental investigations on the effect of temperature, pressure, equivalence ratio and fuel blend on the NTC behavior of the CH4/C7H16 mixtures are limited. Therefore, the objective of this work is to understand the effects of temperature, pressure, equivalence ratio and fuel blend on the ignition process. As the effect of one factor varies with


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the working conditions, the effect sensitivities of various factors on the ignition delay time at different conditions are discussed in detail to provide theoretical basis for the study on ignition control of dual fuel engine. In present work, a study on the IDs using the closed homogenous reactor model in CHEMKIN is first conducted. The NTC behavior of fuel blend with various CH4 mass fractions is analyzed. Then, the sensitivity analysis is employed to examine the effect of main elementary reactions on ignition process. Finally, the rate of production and consumption of key species, including CH4, C7H15 and C7ket, are performed, explaining the process of CH4/C7H16 fuel blend ignition. The present study is organized as follows. The physical-numerical model is shown and validated in Section 2. The effects of different factors on the ID, the sensitivity analysis and rate of production and consumption are discussed in Section 3.1, 3.2 and 3.3 respectively. Finally, the present work and the main conclusions are summarized in Section 4. Nomenclature Notation P T ∅ 𝜏1 𝜏2

pressure temperature equivalence ratio first stage ignition delay of C7H16 second stage ignition delay of C7H16

Abbreviation IDs NTC ROP EGR

ignition delay times negative temperature coefficient reaction rate of production exhaust gas recirculation

2 Numerical model

The physical model is based on the 0-D homogeneous, isobaric, adiabatic system with equations of mass, energy, and species. The IDs are calculated using the closed homogenous reactor model in Chemkin-Pro 18.0 software package constants of the ith reaction are 𝑘𝑓𝑖 = 𝐴𝑖 𝑇𝛽𝑖 exp(

−𝐸𝑖 𝑅𝑐 𝑇

31

. The forward and reverse rate

) and 𝑘𝑟𝑖 =


𝑘𝑓𝑖 𝐾𝑐𝑖

, respectively, where 𝐴𝑖

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is pre-exponential factor, 𝛽𝑖 is the temperature exponent, 𝐸𝑖 is the activation energy, 𝑅𝑐 is gas constants, T presents the temperature and 𝐾𝑐𝑖 is the equilibrium constants. More details can be found in Ref. 31. A set of specified initial conditions, including the initial temperature, pressure, equivalence ratio and reactant mixture composition, have been performed in present work. The IDs are calculated based on two distinct definitions. One is the time when the mixture temperature increases by 400 K over one-time step during simulations, and the other is the time when a max rate of increase of OH radical occurs. These two ways of definitions yield basically the same ID time. For validation, the IDs are computed using four different mechanisms and are compared with experimental ignition data for n-heptane/air mixtures and CH4/air mixtures, respectively. The mechanisms include (I) the Liu 44

32

, (ii) Sk 88

33

, (iii)

GRI 3.0 34, and (iv) Zhang detailed n-C7H16 mechanism 35. Figure 1 shows a comparison of simulated IDs for CH4/air mixtures and the experimental data from Burke et al.36 at different initial pressures and equivalence ratios. The simulated IDs are obtained by three available mechanisms (Liu 44, Sk 88, GRI 3.0). The Liu 44 and Sk 88 mechanisms have good predictions in IDs and are able to capture the experimentally observed effects of pressure, temperature and equivalence ratio on the IDs, while GRI mechanism gives a slightly low value at high temperature and a slightly high value at low temperature.


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Fig. 1 Measured and simulated ignition delay times for CH4 with different pressures and equivalence ratios, (a) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟑, (b) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (c) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (d) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (e) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (f) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟐. 𝟎 A further validation study is performed to predict the IDs for heptane/air mixture at different initial pressures and equivalence ratios. Fig. 2 compares the predicted IDs, using three available mechanisms (Liu 44, Sk 88, Detailed Zhang), with the experimental data of Shiling Liu et al.

32

. The IDs calculated by the Sk 88 mechanism are slightly high in high

temperature and are lower than experimental data in the NTC area at ∅ = 0.5. The Liu 44 and n-heptane detail mechanisms also have slightly lower predictions in the NTC regime at


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∅ = 0.5. Overall, the Liu 44 and n-heptane detail mechanisms provide reasonable agreement with measurements. 1000

EXP Liu44 Sk88 Detailed Zhang

100

10

1

0.1

n-heptane 13.5bar =0.5

0.01 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Ignition delay times (ms)


1000


100

10

1

0.1

n-heptane 42bar =0.5

0.01

1.6

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1000/T (1/K)

1000/T (1/K) EXP Liu44 Sk88 Detailed Zhang

100

10

1

0.1


0.01 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6


1000

1000


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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100

10

1

0.1


0.01 0.8

0.9

1000/T (1/K)

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1000/T (1/K)

Fig. 2 Measured and simulated ignition delay times for C7H16 with different pressures and equivalence ratios, (a) 𝟏𝟑. 𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (b) 𝟒𝟐𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (c) 𝟏𝟑. 𝟓𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (d) 𝟒𝟐𝐛𝐚𝐫, ∅ = 𝟏. 𝟎 Based on the comparison above, the Liu 44 mechanism is able to reasonably predict both the IDs of C7H16/air mixture and the IDs of CH4/air mixture. Furthermore, the Liu 44 mechanism has successfully been validated and used in the CH4/C7H16 mixture combustion in previous studies 23. Therefore, the Liu 44 mechanism is employed to characterize the effect of different initial conditions on the ignition of C7H16/CH4 mixture fuel as follows. As shown in Table 1, the calculation conditions are set up based on the dual fuel micro-ignition engine, in which a small amount of diesel fuel is injected during the


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compression stroke, to act as a source of ignition for the methane–air mixture. And the amount of pilot fuel is between 10% and 20% or even less of the total fuel 13. 37. Therefore, the mass fraction of C7H16 and CH4 is set from 0% to 30% and 100% to 70% respectively. The initial temperature and pressure are set based on the condition after the compression in dual-fuel engine 14. 38. Table 1 Calculation settings Variable

Range

Mass fraction of C7H16

0%-30%

Mass fraction of CH4

100%-70%

Equivalence ratio

0.2-3.0

Temperature

800 K-1200 K

Pressure

40 bar-80 bar

3 Results and discussion

3.1 Ignition process of methane/n-heptane-air mixtures

3.1.1 The effect of single variable

Many experiments have shown the existence of the auto-ignition negative temperature coefficient (NTC) behavior for n-heptane. NTC behavior means that the ignition delay time increases with the increase of temperature changing from low to medium. The plot of IDs as a function of temperature for CH4/C7H16 also performs NTC behavior as shown in Fig. 3a, and the IDs of dual fuel are between those of CH4 and C7H16. As the amount of C7H16 in the blend


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increases from 10% to 30%, the ID decreases and the NTC behavior becomes more pronounced. This is because that as the amount of C7H16 increases, the heat released from the C7H16 reaction increases and the ignition delay period is shortened. Fig. 3b shows that, with pressure increasing, the IDs decrease and the turning point of the ignition delay moves towards higher temperature, which is also be seen in previous literatures 28. Fig. 3c shows that with equivalence ratio increasing, the NTC behavior can be seen at ∅ = 3.0 and IDs decrease. This is because that the ignition in the NTC regime of C7H16 consists of two stages and ID is the sum of the first and second stage ignition delays, i.e. 𝜏1 and 𝜏2 respectively39. The heat release rate at the first stage increases with increasing ∅ due to, causing shorter 𝜏2 at the second stage and thereby shorter IDs of dual fuel 27. 100% CH4

1000

90% CH4/ 10% C7H16

Ignition delay times(ms)


80% CH4/ 20% C7H16 70% CH4/ 30% C7H16

100

10

100% C7H16

 50bar

1

100

10

40bar 50bar 60bar 70bar 80bar

upper turnover lower turnover =1.0 90%CH4/ 10%C7H16

1

0.1 0.8

0.9

1.0

1.1

1.2

1.3

1.4

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1000/T (1/K)

1000/T (1/K) 1000


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 46

100

     

10

50bar 90%CH4/ 10%C7H16

1

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1000/T (1/K)

Fig. 3 Measured ignition delay times with different CH4/C7H16 blends (a), different pressures (b), different equivalence ratios (c)


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50bar fuel:


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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90% CH4/ 10% C7H16 80% CH4/ 20% C7H16

100

70% CH4/ 30% C7H16

800K 10

1000K 1

1200K 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Equivalence ratio

Fig. 4 Measured ignition delay times at initial temperatures of 800 K, 1000 K, 1200 K, and different CH4/C7H16 blend ratios with 70% CH4, 80% CH4 and 90% CH4 in mass fraction Figure 4 presents the effects of CH4 mass fraction, equivalence ratio and initial temperature on the ignition of n-heptane/methane mixtures at initial pressure of 50 bar. Different from above, results are shown in terms of the plot of ID as a function of equivalence ratio, and meanwhile, several new trends are discovered. As the temperature increases, the distances between the curves with different blend ratios decrease, indicating that the effect of blend ratio decreases. This is because that as the initial temperature is very high, it provides part of energy for the ignition of methane and the dependence on n-heptane releasing heat is reduced. The distances between the curves are smaller at low equivalence ratio than those at high equivalence ratio, which means that the effect of C7H16 fraction on ignition increases with equivalence ratio increasing. In addition, there is overlap area at 800 K and 1000 K, which presents that when equivalence ratio is greater than 2.0, the ID under the conditions of 1000 K and 98% CH4 is greater than that under the conditions of 800 K and 90% CH4. The result also indicates that in this respect, both the initial temperature and little heptane concentration can control the ignition process of methane fuel with equivalent effect.


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3.1.2 The effect of multi-variables

As mentioned above, the effect sensitivity of various factors on the IDs at different working conditions is studied. Then, the effects of different factors on ID and NTC behavior of the fuel blend under different CH4 fractions is discussed below. X and Y axis represent two variables and the color represents the IDs. =1.0,50bar

IDs (ms) 74.60

CH4 Mass Fraction

0.95

65.28 55.95

0.90

46.63 0.85

37.30 27.98

0.80

NTC

18.65

0.75

9.325

0.70 800 850 900 950 1000 1050 1100 1150 1200

0.000

Temperature (K)

Fig. 5 Measured ignition delay time versus the CH4 mass fraction and temperature

75 70

=1.0,70%CH4,30%C7H16

IDs (ms) 4.540

NTC

65

IDs (ms) 9.100

4.002

75

8.005

3.465

70

6.910

65

5.815

2.928

60

(b) 80 =1.0,80%CH4,20%C7H16

2.390

Pressure (bar)

80

60

4.720

NTC

55

55

1.852

50

1.315

50

2.530

45

0.7775

45

1.435

40 800

0.2400

40 800

850

900

950 1000 1050 1100 1150 1200

Temperature (K)

(c)

Pressure (bar)

(a)

Pressure (bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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80

=1.0,90%CH4,10%C7H16

3.625

0.3400 850

900

950 1000 1050 1100 1150 1200

Temperature (K) IDs (ms) 24.30

75

21.29

70

18.28

65

15.26

60

12.25

55

9.238

50

6.225

45

3.213

40 800

0.2000 850

900

950 1000 1050 1100 1150 1200

Temperature (K)


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Fig. 6 Measured ignition delay time versus the pressure and temperature, (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction, (c) 90% CH4 mass fraction Figure 5 shows the effect of temperature and fuel blend on the IDs. With CH4 mass fraction of 70%-80%, the NTC behavior of C7H16/CH4 mixture is obviously observed in the temperature range of 860-950 K. Furthermore, the ID is influenced by both temperature and CH4 mass fraction in the low temperature conditions from 800 K to 1000 K, where the heptane concentration has the significant effect on the ignition of C7H16/CH4 mixture, even with the very few mass fraction of heptane. However, in the high temperature region, the heptane concentration has a little influence on the ignition process because the reaction time of C7H16 low temperature reaction becomes short at high temperature. Another reason is that the ignition of CH4 can obtain some heat from the high temperature condition and is less restricted by the heat release from heptane combustion. Therefore, the IDs are short and the influence of blend ratio becomes small at high temperature. As shown in Fig. 6a, b, c, the NTC behavior is clearly observed with 70% CH4 and 80% CH4. With 70% CH4 fraction, the ID is influenced by both pressure and temperature in the temperature range of 800-1000 K. However, it is mainly influenced by temperature when the temperature is above 1100 K, as the ignition delay time changes significantly with temperature but slightly with pressure. The result with 80% CH4 is similar with that with 70% CH4, but the critical temperature point shifts to low temperature. As the CH4 mass fraction is up to 90%, the effect of C7H16 decreases and the NTC behavior gradually disappears.


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(a) 1200

IDs (ms)

50bar,70%CH4,30%C7H16

IDs (ms)

50bar,80%CH4,20%C7H16

21.20

(b) 1200

1150

18.58

1150

31.03

1100

15.95

1100

26.65

1050

13.33

1050

22.28

1000

10.70

1000

17.90

950

8.075

950

13.53

900

5.450

900

9.150

850

2.825

850

4.775

800

0.2000 0.5

1.0

1.5

2.0

2.5

Temperature (K)

Temperature (K)

3.0

35.40

0.4000

800 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Equivalence Ratio

IDs (ms)

(c)1200 50bar,90%CH4,10%C7H16

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 46

66.40

1150

58.18

1100

49.95

1050

41.73

1000

33.50

950

25.28

900

17.05

850

8.825 0.6000

800 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig. 7 Measured ignition delay time versus the temperature and equivalence ratio, (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction, (c) 90% CH4 mass fraction Figure 7 shows that both temperature and equivalence ratio have great influence on the IDs. It can be seen that the IDs change significantly with these two factors, which can also be observed in previous studies

16. 19

. However, the present result shows that both temperature

and equivalence ratio have profound effect on the IDs, especially at low temperature and low equivalence ratio. As shown in Fig. 7c, at high temperature and rich equivalence ratio, the sensitivities of ignition delay time on temperature and equivalence ratio decline. Furthermore, as the amount of CH4 increases and C7H16 decreases, the total ignition delay time increases, because the oxidation of CH4 is slower than that of C7H16. This can be proved by the longer IDs for CH4/air than that for C7H16 under similar conditions as discussed in Fig. 3a.


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IDs (ms)

1000K,50bar

29.60 0.95

CH4 Mass Fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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26.03 22.45

0.90

3

18.88

1 4

15.30

2 0.85

11.73

0.80

8.150 0.75

4.575 1.000

0.70 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig.8 Measured ignition delay time versus the CH4 mass fraction and equivalence ratio Figure 8 shows the ignition delay time versus the methane concentration and equivalence ratio. It can be found that the figure is divided into four regions, i.e. (1) significant effect by only-equivalence ratio; (2) effect by both methane mass fraction and equivalence ratio; (3) significant effect by only methane mass fraction; (4) less effect by both methane mass fraction and equivalence ratio. In detail, in the two regions on the left, with equivalence ratio of less than 1.0, the ID is mainly affected by equivalence ratio for CH4 fraction below 86% and it is influenced by both equivalence ratio and CH4 fraction when the proportion of CH4 is greater than 86%. This indicates that adding a small amount of C7H16 in the lean methane-air mixture can significantly promote the methane ignition. As the addition of C7H16 increases, the effect of equivalent ratio is more significant. In the two regions on the right with equivalence ratio of more than 1.0, the ID is mainly influenced by CH4 fraction: it varies greatly with the CH4 mass fraction while varies slightly with equivalence ratio. Hence, the effect of blend ratio is dominated in the rich fuel mixture. Only in the region with larger heptane concentration and richer fuel, the ignition process is not sensitive to the blend ratio and equivalence ratio. Figure 9 shows that the ID is mainly influenced by equivalence ratio for equivalence


Energy & Fuels

ratio below 1.0, and the influence of pressure is obvious with the equivalence ratio of more than 1.0. It can be seen that the evolutions of ignition delay time demonstrate the similar trends at different blend ratios of methane and heptane. Besides, the effect of pressure increases with the proportion of CH4 increasing. IDs (ms)

1000K,70%CH4,30%C7H16

IDs (ms)

1000K,80%CH4,20%C7H16

19.70

(b) 80

75

17.31

75

20.33

70

14.91

70

17.55

65

12.52

65

14.78

60

10.13

60

12.00

55

7.731

55

9.225

50

5.338

50

6.450

45

2.944

45

3.675

0.5500

40

80

40 0.5

1.0

1.5

2.0

2.5

Pressure (bar)

(a)

Pressure (bar)

23.10

0.9000 0.5

3.0

(c)

80

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Equivalence Ratio

Pressure (bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 46

IDs (ms)

1000K,90%CH4,10%C7H16

27.90

75

24.66

70

21.43

65

18.19

60

14.95

55

11.71

50

8.475

45

5.238 2.000

40 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig. 9 Measured ignition delay time versus the pressure and equivalence ratio (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction and (c) 90% CH4 mass fraction To summarize the results so far, the NTC behavior of the fuel blend becomes stronger and the NTC temperature region expands as the fraction of C7H16 components increases. As for the wide ranges (T=800-1200 K, P=40-80 bar, ∅=0.2-3.0 and the mass fraction of CH4 from 70% to 98%), the temperature and equivalence ratio exert great influence on the IDs all


Page 17 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

the time, while the effect of pressure and blend ratio on the IDs depends on the condition. The effects of pressure and CH4 mass fraction are small when the temperature is higher than 1100 K, and the effects are great when equivalence ratio is greater than 1.0, but small with equivalence ratio of lower than 1.0. As for the large CH4 fraction and lean fuel condition (70%-98% CH4 mass fraction, 0.2-1.0 fraction) relevant to the natural gas engine with diesel micro pilot method, the effect of pressure and CH4 mass fraction decreases with the proportion of CH4 increasing because the NTC behavior is weakened.

3.2 Sensitivity analysis

A sensitivity study is performed to identify the dominate reactions associated with the ignition of CH4/C7h16 mixture under the conditions of 70% and 90% CH4 concentration, ∅ = 0.5 and 1.0, at six different initial temperatures of 850 K, 900 K and 950 K, which corresponds to the temperature of the NTC regime, and 800 K, 1000 K and 1200 K, which are set to investigate the effect of initial temperature. The normalized sensitivity coefficient is defined as 15, S

 (2ki )   (0.5ki ) 1.5 (ki )

where τ is ignition delay of the fuel blend and k i is the specific rate coefficient. A positive value indicates an inhibition effect on total reaction and a negative value indicates a promotion effect. As the temperature change can directly reflect the ignition process, the top 18 greatest sensitivity value reactions based on the temperature sensitivity analysis have been chosen which are also important in previous sensitivity analysis

26. 28. 40

. These 18 reactions

along with their kinetic parameters are listed in Table 2. The reactions can be divided into


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 46

three parts: Reactions R13-14 are important reactions for CH4; Reactions R36-53 are important for both the combustion of CH4 and C7H16; and Reactions R91-108 are relevant to the combustion of C7H16. Table.2 Important reactions for the ignition of mixture based on previous studies26. 28. 40 ＃

Reactions

A

b

E

13

ho2+ohh2o+o2

6.000e+13

0.000

0.00

14

2ho2h2o2+o2

2.500e+11

0.000

-1242.83

36

ch2o+ohhco+h2o

3.400e+09

1.200

-454.11

37

ch2o+ho2hco+h2o2

3.000e+12

0.000

13073.61

41

ch3+o2=>ch2o+oh

3.300e+11

0.000

8938.81

42

ch3+ho2ch3o+oh

1.800e+13

0.000

0.00

43

ch3+ho2ch4+o2

3.600e+12

0.000

0.00

45

2ch3(+m)c2h6(+m)

1.813e+13

0.000

0.00

53

ch4+ohh2o+ch3

1.600e+07

1.830

2772.47

91

pxc7h15=>pxc5h11+c2h4

2.500e+13

0.000

28824.09

92

sxc7h15=>pxc4h9+c3h6

1.600e+13

0.000

28322.18

93

sxc7h15=>pxc6h12+ch3

4.000e+13

0.000

33030.59

100

c7h16+oh=>sxc7h15+h2o

5.200e+09

1.300

693.12

102

c7h16+ho2=>sxc7h15+h2o2

1.340e+13

0.000

17017.21

105

pxc7h15+o2pc7h15o2

2.000e+12

0.000

0.00

106

sxc7h15+o2pc7h15o2

2.000e+12

0.000

0.00


Page 19 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

107

pc7h15o2=>pheoohx2

6.000e+11

0.000

20458.89

108

pheoohx2+o2=>soo7ooh1

5.000e+11

0.000

0.00

Figure 10 shows the normalized sensitivity of ignition delay in various conditions. It can be seen in Fig. 10a, b, c, that the sensitivity coefficients to R91-108 (reactions associated with C7H16 ignition) decrease significantly as the temperature increases from 800 to 1200 K, which indicates that both inhibition and promotion effects are weakened. Therefore, the effects of relevant reactions of C7H16 on the total reaction rate decrease with temperature increasing. The sensitivity coefficients of reactions important for both CH4 and C7H16 are greater than those of reactions associated with C7H16, so the ignition of mixture fuel is mainly dominated by these reactions. R42 (ch3+ho2ch3o+oh) and R43 (ch3+ho2ch4+o2) are a pair of reactions competing for ho2 radical, the sensitivity coefficient of the reaction R43 is larger than R42 at T=800 K, which leads to an inhibition contribution to the total reaction. While the sensitivity coefficient of R43 decreases to an approximate valve to R42 at T=1200 K, leading to a comparable contribution to the total reaction. The sensitivity of reactions associated with C7H16 ignition decrease with the proportion of CH4 increasing, meaning that the effect of n-C7H16 reactions on the total reaction rate decreases. R106 R105 R107 R108 R93 R92 R91 R102 R100 R53 R45 R43 R42 R41 R37 R36 R14 R13

90%ch4 70%ch4 800K 50bar =0.5

(a)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

Normalized sensitivity

0.4

0.6

(b)

0.8 -0.8

90%ch4 70%ch4 1000K 50bar =0.5

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6



(c)

0.8 -0.8

90%ch4 70%ch4 1200K 50bar =0.5

-0.6

-0.4

-0.2

0.0

0.2


0.4

0.6

0.8

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R106 R105 R107 R108 R93 R92 R91 R102 R100 R53 R45 R43 R42 R41 R37 R36 R14 R13

(d)

-0.8

(e)

90%ch4 70%ch4 800K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8 -0.8

-0.6

90%ch4 70%ch4 850K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2


-0.4

-0.2

0.0

0.2

0.4

0.6

0.8 -0.8

90%ch4 70%ch4 1200K 50bar =1.0

-0.6


(g)

-0.8

(f)

90%ch4 70%ch4 1000K 50bar =1.0

Normalized sensitivity R106 R105 R107 R108 R93 R92 R91 R102 R100 R53 R45 R43 R42 R41 R37 R36 R14 R13

Page 20 of 46

0.4

0.6

90%ch4 70%ch4 900K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

-0.2

0.0

0.2

0.4

0.6

0.8


(h)

0.8 -0.8

-0.4

0.4

0.6


(i)

0.8 -0.8

90%ch4 70%ch4 950K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8


Fig. 10 Normalized sensitivity of ignition delay, (a) 800 K, ∅ = 𝟎. 𝟓, (b) 1000 K, ∅ = 𝟎. 𝟓 , (c) 1200 K, ∅ = 𝟎. 𝟓, (d) 800 K, ∅ = 𝟏. 𝟎, (e) 1000 K, ∅ = 𝟏. 𝟎, (f) 1200 K, ∅ = 𝟏. 𝟎 (g) 850 K,∅ = 𝟏. 𝟎, (h) 900 K,∅ = 𝟏. 𝟎, and (i) 950 K, ∅ = 𝟏. 𝟎 Figures 10a, b, c and d, e, f depict the effect of equivalence ratio on the sensitivity coefficient at 800 K, 1000 K and 1200 K. It can be noted that sensitivity coefficient to most of the reactions increases as the equivalence ratio is increased, but the sensitivity coefficient to R53 (ch4+ohh2o+ch3) decreases appreciably with increasing equivalence ratio, thus weakening the promotion effect. This is because that CH4 is mainly consumed by R53 at low equivalence ratio as discussed in the following section. The effect of reaction R36 (ch2o+ohhco+h2o) changes from inhibition to promotion as the equivalence ratio is increased from 0.5 to 1.0 at T=1200 K as shown in Fig. 10c, f. The effects also change from inhibition to promotion as the temperature increasing from 800 K to 1200 K as shown in Fig. 10d, e, f. As shown in Figs. 10g, h, i, these three different initial temperatures of 850 K, 900 K and


Page 21 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

950 K correspond to approximately the beginning temperature, the middle temperature and the end temperature of the NTC regime, respectively. It can be noted that the sensitivity coefficients of the reactions associated with C7H16 ignition increase significantly when the initial temperatures are in the NTC regime, indicating that the effect of C7H16 reactions on the total reaction rate is increased. In the NTC regime, however, the sensitivity coefficients to these reactions slightly change with the initial temperature, i.e. the effect of initial temperature on the sensitivity coefficient is small. This is consistent with the results that the ID is changed little in the NTC regime under these conditions.

3.3 Rate of production (ROP) analysis

The reaction rate of production (ROP) is the important information to understand the mechanism of mixture fuel ignition and oxidation. Radicals like ch4 and ch2o are main intermediate products for the ignition of methane

15

, and sxc7h15, pc7h15o2, pheoohx2 and

oc7ooh are main intermediate radicals for the reaction of n-heptane 28. In addition, ho2 and oh are the most important radicals which connect the reaction paths of n-heptane and methane 41. In Fig. 11, as the CH4 mass fraction varies from 70% to 90%, the reaction rates of intermediate species of ch4, ch2o, ho2 and oh have no apparent change in the high temperature region (1500-2500 K), while they change significantly in the low temperature region (800-1200 K). Therefore, the increase of C7H16 mass fraction has significant influence on the CH4 low temperature reaction rates, while such increase on the CH4 high temperature reaction rates is small. In addition, the consumption of methane occurs mainly in the high temperature region. In Fig. 12, the ROPs of sxc7h15, pc7h15o2, pheoohx2 and oc7ooh (or


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C7KET) change appreciably with the CH4 mass fraction and the reactions occur mainly in the low temperature region (800-1100 K). It means that the low temperature reaction of CH4 and C7H16 occurs firstly to release a lot of heat, and then triggers the CH4.

Fig. 11 Rates of production and consumption of (a) ch4, (b) ch2o, (c) ho2 and (d) oh with various CH4 mass fractions


Page 22 of 46

Page 23 of 46

6

(a)

sxc7h15

c7h16+oh=>sxc7h15+h2o 2

0

sxc7h15=>pxc6h12+ch3 -2

800K 

sxc7h15=>pxc4h9+c3h6 sxc7h15+o2pc7h15o2

70% CH4

-4

-6 800

80% CH4

900

950

4

sxc7h15+o2pc7h15o2

2

total

0

pxc7h15+o2pc7h15o2 pc7h15o2=>pheoohx2

-2

1000 1050 1100 1150 1200

800

90% CH4 850

900

Temprature (K)

2

(c)

pheoohx2

pc7h15o2=>pheoohx2

0

total

800K  70% CH4

-2


80% CH4

-4 800

4

90% CH4 850

900

950

950

1000 1050 1100 1150 1200

Temprature (K)

ROP (mole10-3/cm3-sec)


4

800K  70% CH4

80% CH4

-4

90% CH4 850

pc7h15o2

(b) ROP (mole10-3/cm3-sec)


4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1000 1050 1100 1150 1200

(d)

oc7ooh

px2heooh=>oc7ooh+oh

2

0

total -2

oc7ooh=>px2hepoo+oh -4

800K  70% CH4 80% CH4 90% CH4

-6 800

850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temprature (K)

Fig. 12 Rates of production and consumption of (a) sxc7h15, (b) pc7h15o2, (c) pheoohx2 and (d) oc7ooh with various CH4 mass fractions, 800 K, ∅ = 𝟏. 𝟎 Figure 12 shows that reaction rates of sxc7h15, pc7h15o2 and pheoohx2 increase significantly as the proportion of C7H16 increases. While the total reaction rate of sxc7h15, pc7h15o2 and pheoohx2 are always small, indicating that the rates of production and consumption are basically consistent. With the increase of the proportion of C7H16, the heat release rate of C7H16 combustion increases, which leads to the earlier ignition of methane and then the shorter ignition delay. The total reaction rate of oc7ooh increases noticeably as the proportion of C7H16 increases, and it products oc7ooh at 800-1300 K and consumes oc7ooh at 830-880 K at these conditions.


Energy & Fuels

20

ch4

ch3+h(+m)ch4(+m)

0 -20

ch4+hh2+ch3

-40

ch4+ohh2o+ch3

-60 -80

800K 

-100

70% CH4

-120

80% CH4



(a)

total

90% CH4

-140 800

1000

2.0

sxc7h15 1.5 1.0


0.5 0.0


-0.5


-1.0

sxc7h15+o2pc7h15o2 -1.5

1200

1400

1600

90% CH4

800

1800

(c) 40

850

900

ch2o

0

total

-40 -60

ch2o+ohhco+h2o 800K 

-80

70% CH4

-100

80% CH4

-120 800

90% CH4 1000

1000 1050 1100 1150 1200

(d) 2.5 (c) ROP (mole10-3/cm3-sec)

ch2o+hhco+h2

-20

950

Temperature(K)

ch3+och2o+h

20

oc7ooh

2.0 1.5 1.0

px2heooh=>oc7ooh+oh

0.5 0.0

total -0.5

oc7ooh=>px2hepoo+oh

-1.0

1400

1600

1800

800K  70% CH4 80% CH4 90% CH4

-1.5 1200

800K  70% CH4 80% CH4

-2.0

Temperature(K)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 46

800

850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temperature(K)

Fig. 13 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh with various CH4 mass fractions, 800 K, ∅ = 𝟎. 𝟓 To clarify the effect of equivalence ratio on the ROP, the rates of production and consumption of four important species are calculated at ∅ = 0.5: ch4, ch2o, the main intermediate products for the ignition of methane

15

; sxc7h15, which is a radical after

n-heptane dehydrogenation and is important for both low and high temperature reactions, and oc7ooh, a key radical of C7H16 low temperature combustion path

42

. Comparing Fig. 12 and

Fig. 13, it can be noted that the reaction rates of these radicals decrease with equivalence ratio decreasing due to the lean fuel. The ROP profile of R53 (ch4+ohh2o+ch3) exhibits a transition to that of total as the equivalence ratio decreases, implying that CH4 is mainly consumed by R53 for the fuel lean condition. CH2O is also mainly consumed by reacting with


Page 25 of 46

OH radical for the lean fuel condition. Furthermore, in such condition, the reactions of CH4, CH2O, sxc7h15 and oc7ooh take place in a relative low temperature region compared with that in the rich fuel condition due to the lower heat release rate. ch4

(b) 1.0 ROP (mole10-3/cm3-sec)


(a) 5000 ch3+h(+m)ch4(+m) 0

ch4+hh2+ch3

-5000

-10000

ch4+ohh2o+ch3 90%CH4 

-15000

800K 1000K 1200K

total

-20000 1000 1200 1400 1600 1800 2000 2200 2400 2600

sxc7h15

0.8 0.6


0.4 0.2 0.0

90%CH4

-0.2 -0.4 -0.6 -0.8

sxc7h15+o2pc7h15o2 600

800

ch3+och2o+h

ch2o

5000

total

0

ch2o+hhco+h2 -5000 90% CH4



-10000

1000

1200

1400

1600

1800

Temperature(K)

ch2o+ohhco+h2o

800K 1000K 1200K

(c) (d) ROP (mole10-3/cm3-sec )

(c) 10000

 800K 1000K 1200K

sxc7h15=>pxc6h12+ch3 sxc7h15=>pxc4h9+c3h6

Temperature(K)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

0.4

oc7ooh 0.3

px2heooh=>oc7ooh+oh

0.2 0.1

total

0.0 -0.1

oc7ooh=>px2hepoo+oh

-0.2 -0.3

-15000 1000 1200 1400 1600 1800 2000 2200 2400 2600

-0.4 800

90%CH4  800K 1000K 1200K

900 1000 1100 1200 1300 1400 1500 1600

Temperature(K)

Temprature (K)

Fig. 14 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh at various temperatures, 90% CH4, ∅ = 𝟏. 𝟎 Figure 14 shows the effect of initial temperature on the ROP of CH4, CH2O, sxc7h15 and oc7ooh. It can be seen that temperature has great influence on the ROP of these species as all the reactions have noticeable change with temperature increasing. The reaction rates of CH4 and CH2O increase with temperature increasing, and the maximum reaction rates occur at a higher temperature. The reaction rate of oc7ooh, a key radical of C7H16 low temperature


Energy & Fuels

combustion path, decreases significantly, which implies that the reaction rates of the n-heptane low-temperature reactions decrease as the temperature increases. The reaction rates of R92 and R93 have significant increase, exceeding that of R106. Therefore, sxc7h15 is mainly consumed by pyrolysis (R92 and R93) at high temperature. This conclusion has been discussed by Zhang et al.

26

using C7H16, and it is still applicable for CH4/C7H16 mixture. In

addition, the initial temperature has obvious influence on the reaction temperature regions of ch4, sxc7h15 and oc7ooh. sxc7h15=>pxc4h9+c3h6

(R92)


(R93)

sxc7h15+o2pc7h15o2

(R106)

In general, the initial temperature and equivalence ratio have great influence not only on the reaction rates but also on the reaction temperature region of all these species. The effect of ∅ on the reaction temperature region of CH4 is greater than that of initial temperature, while the initial temperature has more influence on the sxc7h15 and oc7ooh reaction area than ∅, which indicates that the initial temperature and equivalence ratio have relatively large influence on the ignition of C7H16 and the combustion of CH4, respectively. 4000 2000

ch4

(b)

ch3+h(+m)ch4(+m) 0 -2000

ch4+hh2+ch3

-4000

90%CH4

ch4+ohh2o+ch3

-6000  -8000

-10000

850K 900K 950K

total

1000 1200 1400 1600 1800 2000 2200 2400 2600


(a) ROP (mole10-3/cm3-sec)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 46

sxc7h15

0.6 0.4


0.2 0.0

sxc7h15=>pxc6h12+ch3 90%CH4 sxc7h15=>pxc4h9+c3h6  sxc7h15+o2pc7h15o2 850K 900K 950K

-0.2 -0.4 -0.6 -0.8 800

900

Temperature(K)


1000

1100

1200

1300

Temperature(K)

1400

1500

Page 27 of 46

6000

(c)

ch2o

ch3+och2o+h 4000 2000

total

0 -2000 -4000

90% CH4 

-6000

(c) 0.6 (d) ROP (mole10-3/cm3-sec)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

ch2o+hhco+h2

ch2o+ohhco+h2o 850K 800K 950K

oc7ooh

0.4

px2heooh=>oc7ooh+oh

0.2

total

0.0

90%CH4

-0.2

oc7ooh=>px2hepoo+oh -0.4 -0.6 850

1000 1200 1400 1600 1800 2000 2200 2400 2600

900

950

1000

1050

1100

 850K 900K 950K 1150

1200

Temperature(K)

Temprature (K)

Fig. 15 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh in the NTC regime Figure 15 shows ROP characteristics in the NTC regime. Three different initial temperatures of 850 K, 900 K and 950 K correspond to the NTC regime as discussed above. The reaction rates of sxc7h15 and oc7ooh decrease with the increasing temperature, resulting in increasing of IDs with temperature increasing in the NTC regime. While the reaction rates of CH4 and CH2O increase with temperature increasing. The reaction rate of R106 (sxc7h15+o2pc7h15o2)

decreases

but

is

still

larger

than

that

of

R92

(sxc7h15=>pxc4h9+c3h6), indicating that sxc7h15 is mainly consumed by reacting with oxygen in this condition.

4. Conclusions

A numerical study has been conducted to examine the effects of temperature, pressure, equivalence ratio and blend ratio on IDs of methane/n-heptane mixtures. Furthermore, the sensitivity analyses of various factors on the IDs in different conditions are studied to provide theoretical basis for the study on ignition control of dual fuel engine. Beside, the simulations


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

are carried out based on the software CHEMKIN-PRO with a closed homogenous reactor. The parameters include temperature in the range of 800-1200 K, pressure in the range of 40-80 bar, and equivalence ratio in the range of 0.2-3.0. Main conclusions are summarized as follows. (1) The NTC behavior is performed for the CH4/C7H16 mixture fuel, and it becomes stronger as the fraction of C7H16 components increases and the equivalence ratio increases. In the NTC regime, the sensitivity coefficients of reactions associated with C7H16 increase, indicating that the effect of C7H16 reactions on the total reaction rate is relatively high in that regime. And the reaction rates of sxc7h15 and oc7ooh decrease with increasing temperature, resulting in the decreasing of IDs with temperature increasing in the NTC regime. (2) Temperature and equivalence ratio have great influence on the IDs over the wide range of present conditions. The present result shows that both temperature and equivalence ratio have profound effect on the IDs, especially at low temperature and low equivalence ratio. However, the effect of pressure and blend ratio depends on the condition. The effects of pressure and CH4 mass fraction are small when temperature is higher than 1100 K, and such effects are great when the equivalence ratio is greater than 1.0, but small with equivalence ratio of lower than 1.0. It is interesting that the ignition delay region can be divided into four different zones, derived from the coupling effect of methane concentration and equivalence ratio. From the perspective of dual fuel engine, these results can be used as a reference to improve the ignition and combustion of natural gas engine using C7H16 (or diesel) as the


Page 28 of 46

Page 29 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

pilot fuel. (3) A sensitivity study is performed to examine the effect of main elementary reactions on ignition. At high temperature, the sensitivity coefficients of R91-108 (reactions associated with C7H16 ignition) are small, so the effects of reactions associated with C7H16 are small due to the fast reaction of it. The ignition is mainly controlled by the reactions associated with CH4 as the sensitivity coefficient of them is high, because CH4 takes up most of the fuel. The sensitivity to R53 (ch4+ohh2o+ch3) increases as the equivalence ratio is decreased, because CH4 is mainly consumed by this reaction at low equivalence ratio. (4) The study on rates of production and consumption indicates that the methane is ignited by the combustion of C7H16. Initial temperature and equivalence ratio have great influence not only on the production and consumption rates but also on the reaction temperature region, which well explains the result above that the temperature and equivalence ratio have the greatest influence on the IDs.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 91741119, 91641203, 51606133) and Marine Low-Speed Engine Project (Phase I)


Energy & Fuels

Appendix: Effect of n-heptane with large mole fraction on the ROP

5000

ch3+h(+m)ch4(+m)

2000 1000 0

-2000 -3000

ch4+hh2+ch3 800K ch4+ohh2o+ch3  70% mole CH4

-4000 -5000

80% mole CH4

total

90% mole CH4

ch3+och2o+h

ch2o

3000 2000 1000

total

0 -1000

800K ch2o+hhco+h2

-2000  -3000

70% mole CH4

-4000

80% mole CH4 90% mole CH4

ch2o+ohhco+h2o

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

-5000 1000 1200 1400 1600 1800 2000 2200 2400 2600

Temprature (K)

Temprature (K)

(c) 30 20

sxc7h15 c7h16+oh=>sxc7h15+h2o

-3

10 0

-10 -20

sxc7h15=>pxc6h12+ch3 800K 


70% mole CH4

-30


-40 800

(c) (d) ROP (mole10 /cm3-sec)


3000

-1000

(b) 4000

ch4

4000


(a)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 46

1000

1200

1400

1600

40

oc7ooh 20

px2heooh=>oc7ooh+oh

0

total -20

800K  70% mole CH4


80% mole CH4

-60 800

90% mole CH4 850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temprature (K)

Fig. A1 Rates of production and consumption of (a) ch4, (b) ch3, (c) sxc7h15 and (d) oc7ooh with various CH4 mole fractions, 800 K, ∅ = 𝟏. 𝟎 With 70%, 80% and 90% CH4 mass fractions, the ROPs of ch4 and ch2o have no apparent change based on CH4 mass fraction. This is because that the amount of C7H16 addition is too little to significantly affect the oxidation of CH4 in the high temperature region. The molar mass of C7H16 is large and that of CH4 is small, so, by the calculation method of mass fraction, the amount of C7H16 addition is too little. It indicates that under the condition of C7H16 micro ignition (the mass fraction of pilot fuel is between 10% and 20% or even less), the effect of C7H16 quantity on combustion of CH4 in the high temperature region is small.


Page 31 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

To further elucidate the effect of n-heptane addition on methane oxidation, the ROPs of ch4, ch2o, sxc7h15 and oc7ooh are investigated at 70%, 80% and 90% CH4 mole fractions, respectively.

In

Fig.

1c,

Reactions

R110

(px2heooh=>oc7ooh+oh)

and

R111

(oc7ooh=>px2hepoo+oh) are promoted with the increase of n-heptane addition, producing more OH radicals. Subsequently, the more OH increases the reaction rates of R53 (ch4+ohh2o+ch3) and R36 (ch2o+ohhco+h2o) at the temperature range of 800-1300 K as shown in Fig. A1a and 1b, promoting the methane oxidation. Interestingly, during the high temperature, the reaction rates of methane decrease with the increase of n-heptane, meaning that the addition of n-heptane does not promote the high temperature reactions of methane. Therefore, the enhanced oxidation of CH4 by C7H16 addition is realized by the increase of OH radical production, which is supported by Zang et al.

41

. However, it only

affects the low temperature reactions of methane.

Reference

(1) Reitz, R. D. Combust. Flame. 2013, 160, 1-8. (2) Abdelaal, M. M. and Hegab, A. H. Energ Convers Manage. 2012, 64, 301-312. (3) Papagiannakis, R. G. and Hountalas, D. T. Energ Convers Manage. 2004, 45, 2971-2987. (4) Fu, J. Q.; Shu, J.; Zhou, F., et al. Appl. Therm. Eng. 2017, 113, 1208-1218. (5) Papagiannakis, R. G.; Rakopoulos, C. D.; Hountalas, D. T., et al. Fuel. 2010, 89, 1397-1406. (6) Akansu, S. O.; Dulger, Z.; Kahraman, N., et al. Int. J. Hydrogen Energy. 2004, 29, 1527-1539. (7) Chandra, R.; Vijay, V. K.; Subbarao, P. M. V., et al. Appl. Energy. 2011, 88, 3969-3977. (8) Korakianitis, T.; Namasivayam, A. M. and Crookes, R. J. Prog Energ Combust. 2011, 37, 89-112.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(9) Nwafor, O. M. I. Renew Energ. 2007, 32, 2361-2368. (10) Crossley, R. W.; Dorko, E. A.; Scheller, K. et al. Combust. Flame. 1972, 19(3), 373-378 (11) Lifshitz, A.; Scheller, K.; Burcat, A., et al. Combust. Flame. 1971, 16(3), 311-321. (12) Nwafor, O. M. I. Sadhana-Acad P Eng S. 2002, 27, 375-382. (13) Sahoo, B. B.; Sahoo, N. and Saha, U. K. Renew Sust Energ Rev. 2009, 13, 1151-1184. (14) Wei, L. J. and Geng, P. Fuel Process Technol. 2016, 142, 264-278. (15) Zhang, Y. J.; Huang, Z. H.; Wei, L. J., et al. Combust. Flame. 2012, 159, 918-931. (16) Polk, A. C.; Gibson, C. M.; Shoemaker, N. T., et al. J Energy Resour Technol. 2013, 135, 032202. (17) Demosthenous, E.; Borghesi, G.; Mastorakos, E., et al. 2014, DOI: 10.2514/6.2014-1020. (18) Schlatter, S.; Schneider, B.; Wright, Y. M., et al. Fuel. 2016, 179, 339-352. (19) Schlatter, S.; Schneider, B.; Wright, Y. M., et al. SAE technical paper. 2013, DOI: 10.4271/2013-24-0112. (20) Schlatter, S.; Schneider, B.; Wright, Y., et al. SAE technical paper. 2012, DOI: 10.4271/2012-01-0825. (21) Bahlouli, K.; Atikol, U.; Khoshbakhti Saray, R., et al. Energ Convers Manage. 2014, 79, 85-96. (22) Maghbouli, A.; Saray, R. K.; Shafee, S., et al. Fuel. 2013, 106, 98-105. (23) Demosthenous, E.; Borghesi, G.; Mastorakos, E., et al. Combust. Flame. 2016, 163, 122-137. (24) Wang, Z. and Abraham, J. Proc Combust Inst. 2015, 35, 1041-1048. (25) Campbell, M. F.; Wang, S. K.; Goldenstein, C. S., et al. Proc Combust Inst. 2015, 35, 231-239. (26) Zhang, P.; Ji, W.; He, T., et al. Combust. Flame. 2016, 167, 14-23. (27) Zhao, P. and Law, C. K. Combust. Flame. 2013, 160, 2352-2358. (28) Ji, W.; Zhao, P.; He, T., et al. Combust. Flame. 2016, 164, 294-302. (29) Curran, H. J.; Gaffuri, P.; Pitz, W. J., et al. Combust. Flame. 1998, 114, 149-177.


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Energy & Fuels

(30) Aggarwal, S. K.; Awomolo, O. and Akber, K. Int. J. Hydrogen Energy. 2011, 36, 15392-15402. (31) ANSYS CHEMKIN-PRO 18.0, ANSYS Reaction Design: San Diego, 2017. (32) Liu, S. L.; Hewson, J. C.; Chen, J. H., et al. Combust. Flame. 2004, 137, 320-339. (33) Yoo, C. S.; Lu, T. F.; Chen, J. H., et al. Combust. Flame. 2011, 158, 1727-1741. (34) Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.; Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S., Jr.; et al. GRI-mech 3.0; http://www.me.berkeley.edu/gri-mech/. (35) Zhang, K.; Banyon, C.; Bugler, J., et al. Combust. Flame. 2016, 172, 116-135. (36) Burke, U.; Somers, K. P.; O'Toole, P., et al. Combust. Flame. 2015, 162, 315-330. (37) Papagiannakis, R. G.; Hountalas, D. T. and Rakopoulos, C. D. Energ Convers Manage. 2007, 48, 2951-2961. (38) Yousefi, A.; Birouk, M. and Guo, H. Fuel. 2017, 203, 642-657. (39) Ji, W.; Zhao, P.; Zhang, P., et al. Proc Combust Inst. 2017, 36, 343-353. (40) Hu, E.; Li, X.; Meng, X., et al. Fuel. 2015, 158, 1-10. (41) Zang, R.; Yao, C.; Yin, Z., et al. Energy Fuels. 2016, 30, 8630-8637. (42) Zhang, P.; Ji, W. Q.; He, T. J., et al. Combust. Flame. 2016, 167, 14-23.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

All Graphics

Fig. 1 Measured and simulated ignition delay times for CH4 with different pressures and equivalence ratios, (a) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟑, (b) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (c) 𝟐𝟓𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (d) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (e) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (f) 𝟏𝟎𝐛𝐚𝐫, ∅ = 𝟐. 𝟎


Page 34 of 46

Page 35 of 46

1000


100

10

1

0.1


0.01 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5



1000


100

10

1

0.1


0.01

1.6

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1000/T (1/K)

1000/T (1/K) EXP Liu44 Sk88 Detailed Zhang

100

10

1

0.1


0.01 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6


1000

1000


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels


100

10

1

0.1


0.01 0.8

0.9

1000/T (1/K)

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1000/T (1/K)

Fig. 2 Measured and simulated ignition delay times for C7H16 with different pressures and equivalence ratios, (a) 𝟏𝟑. 𝟓𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (b) 𝟒𝟐𝐛𝐚𝐫, ∅ = 𝟎. 𝟓, (c) 𝟏𝟑. 𝟓𝐛𝐚𝐫, ∅ = 𝟏. 𝟎, (d) 𝟒𝟐𝐛𝐚𝐫, ∅ = 𝟏. 𝟎


Energy & Fuels

100% CH4

1000

80% CH4/ 20% C7H16 70% CH4/ 30% C7H16

100

10

40bar 50bar 60bar 70bar 80bar

90% CH4/ 10% C7H16



100% C7H16

 50bar

1

100

upper turnover

10

lower turnover =1.0 90%CH4/ 10%C7H16

1

0.1 0.8

0.9

1.0

1.1

1.2

1.3

1.4

0.8

0.9

1.0

1000


1.1

1.2

1.3

1.4

1000/T (1/K)

1000/T (1/K)      

100

10

50bar 90%CH4/ 10%C7H16

1

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1000/T (1/K)

Fig. 3 Measured ignition delay times with different CH4/C7H16 blends (a), different pressures (b), different equivalence ratios (c) 50bar fuel:


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 46

90% CH4/ 10% C7H16 80% CH4/ 20% C7H16

100

70% CH4/ 30% C7H16

800K 10

1000K 1

1200K 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Equivalence ratio

Fig. 4 Measured ignition delay times at initial temperatures of 800 K, 1000 K, 1200 K, and different CH4/C7H16 blend ratios with 70% CH4, 80% CH4 and 90% CH4 in mass fraction


Page 37 of 46

=1.0,50bar

IDs (ms) 74.60

CH4 Mass Fraction

0.95

65.28 55.95

0.90

46.63 0.85

37.30 27.98

0.80

NTC

18.65

0.75

9.325

0.70 800 850 900 950 1000 1050 1100 1150 1200

0.000

Temperature (K)

Fig. 5 Measured ignition delay time versus the CH4 mass fraction and temperature 80

=1.0,70%CH4,30%C7H16

IDs (ms) 4.540

75 70

NTC

65

IDs (ms) 9.100

4.002

75

8.005

3.465

70

6.910

65

5.815

2.928

60

(b) 80 =1.0,80%CH4,20%C7H16

2.390

Pressure (bar)

(a)

Pressure (bar)

60

4.720

NTC

55

55

1.852

50

1.315

50

2.530

45

0.7775

45

1.435

40 800

0.2400

40 800

850

900

950 1000 1050 1100 1150 1200

Temperature (K)

(c)

Pressure (bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

80

=1.0,90%CH4,10%C7H16

3.625

0.3400 850

900

950 1000 1050 1100 1150 1200

Temperature (K) IDs (ms) 24.30

75

21.29

70

18.28

65

15.26

60

12.25

55

9.238

50

6.225

45

3.213

40 800

0.2000 850

900

950 1000 1050 1100 1150 1200

Temperature (K)

Fig. 6 Measured ignition delay time versus the pressure and temperature, (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction, (c) 90% CH4 mass fraction


Energy & Fuels

(a) 1200

IDs (ms)

50bar,70%CH4,30%C7H16

IDs (ms)

50bar,80%CH4,20%C7H16

21.20

(b) 1200

1150

18.58

1150

31.03

1100

15.95

1100

26.65

1050

13.33

1050

22.28

1000

10.70

1000

17.90

950

8.075

950

13.53

900

5.450

900

9.150

850

2.825

850

4.775

800

0.2000 0.5

1.0

1.5

2.0

2.5

Temperature (K)

Temperature (K)

35.40

0.4000

800

3.0

0.5

1.0

2.0

2.5

3.0

IDs (ms)

(c)1200 50bar,90%CH4,10%C7H16

Temperature (K)

1.5

Equivalence Ratio

Equivalence Ratio

66.40

1150

58.18

1100

49.95

1050

41.73

1000

33.50

950

25.28

900

17.05

850

8.825 0.6000

800 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig. 7 Measured ignition delay time versus the temperature and equivalence ratio, (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction, (c) 90% CH4 mass fraction IDs (ms)

1000K,50bar

29.60 0.95

CH4 Mass Fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 46

26.03 22.45

0.90

3

18.88

1 4

15.30

2 0.85

11.73

0.80

8.150 0.75

4.575 1.000

0.70 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig.8 Measured ignition delay time versus the CH4 mass fraction and equivalence ratio


(a)

80

IDs (ms)

1000K,70%CH4,30%C7H16

75 70

Pressure (bar)

IDs (ms)

1000K,80%CH4,20%C7H16

19.70

(b) 80

17.31

75

20.33

14.91

70

17.55

65

14.78

60

12.00

55

9.225

23.10

65

12.52

60

10.13

55

7.731

50

5.338

50

6.450

45

2.944

45

3.675

0.5500

40

40 0.5

1.0

1.5

2.0

2.5

0.9000 0.5

3.0

(c)

80

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Equivalence Ratio

Pressure (bar)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Pressure (bar)

Page 39 of 46

IDs (ms)

1000K,90%CH4,10%C7H16

27.90

75

24.66

70

21.43

65

18.19

60

14.95

55

11.71

50

8.475

45

5.238 2.000

40 0.5

1.0

1.5

2.0

2.5

3.0

Equivalence Ratio

Fig. 9 Measured ignition delay time versus the pressure and equivalence ratio (a) 70% CH4 mass fraction, (b) 80% CH4 mass fraction and (c) 90% CH4 mass fraction


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

R106 R105 R107 R108 R93 R92 R91 R102 R100 R53 R45 R43 R42 R41 R37 R36 R14 R13

90%ch4 70%ch4 800K 50bar =0.5

(a)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

(b)

0.8 -0.8

0.6

(d)

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8 -0.8

90%ch4 70%ch4 850K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4


0.0

0.2

0.4

0.6

0.8 -0.8

-0.6

-0.4

-0.2

0.0

0.2

0.6

0.4

0.6

0.8 -0.8

90%ch4 70%ch4 900K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.0

0.2

0.4

0.6

90%ch4 70%ch4 1200K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.4

0.6


(i)

0.8

0.8 -0.8

90%ch4 70%ch4 950K 50bar =1.0

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6


Fig. 10 Normalized sensitivity of ignition delay, (a) 800 K, ∅ = 𝟎. 𝟓, (b) 1000 K, ∅ = 𝟎. 𝟓 , (c) 1200 K, ∅ = 𝟎. 𝟓, (d) 800 K, ∅ = 𝟏. 𝟎, (e) 1000 K, ∅ = 𝟏. 𝟎, (f) 1200 K, ∅ = 𝟏. 𝟎

0.8


(h)

0.8 -0.8

-0.2

(f)

90%ch4 70%ch4 1000K 50bar =1.0

-0.6

-0.4



(g)

-0.8

-0.2

(e)


-0.4

90%ch4 70%ch4 1200K 50bar =0.5

Normalized sensitivity 90%ch4 70%ch4 800K 50bar =1.0

-0.6

(c)

90%ch4 70%ch4 1000K 50bar =0.5


Page 40 of 46

(g) 850 K,∅ = 𝟏. 𝟎, (h) 900 K,∅ = 𝟏. 𝟎, and (i) 950 K, ∅ = 𝟏. 𝟎


0.8

Page 41 of 46 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Fig. 11 Rates of production and consumption of (a) ch4, (b) ch2o, (c) ho2 and (d) oh with various CH4 mass fractions


Energy & Fuels

6

(a)

sxc7h15

c7h16+oh=>sxc7h15+h2o 2

0

sxc7h15=>pxc6h12+ch3 -2


70% CH4

-4

-6 800

800K  80% CH4

900

950

4

sxc7h15+o2pc7h15o2

2

total

0

pxc7h15+o2pc7h15o2 -2

pc7h15o2=>pheoohx2

1000 1050 1100 1150 1200

800

90% CH4 850

900

Temprature (K)

2

(c)

pheoohx2

pc7h15o2=>pheoohx2

0

total -2


800

800K  70% CH4 80% CH4

-4

4

90% CH4 850

900

950

950

1000 1050 1100 1150 1200

Temprature (K)



4

800K  70% CH4

80% CH4

-4

90% CH4 850

pc7h15o2



4


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 42 of 46

1000 1050 1100 1150 1200

(d)

oc7ooh

px2heooh=>oc7ooh+oh

2

0

total -2


800K  70% CH4 80% CH4 90% CH4

-6 800

850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temprature (K)

Fig. 12 Rates of production and consumption of (a) sxc7h15, (b) pc7h15o2, (c) pheoohx2 and (d) oc7ooh with various CH4 mass fractions, 800 K, ∅ = 𝟏. 𝟎


Page 43 of 46

20

ch4

ch3+h(+m)ch4(+m)

0 -20

ch4+hh2+ch3

-40

ch4+ohh2o+ch3

-60

800K 

-80 -100

70% CH4

-120

80% CH4



(a)

total

90% CH4

-140 800

1000

2.0

sxc7h15 1.5 1.0


0.5 0.0


-0.5


-1.0

sxc7h15+o2pc7h15o2 -1.5

1200

1400

1600

90% CH4

800

1800

(c) 40

850

900

ch2o

0

total

-40 -60

ch2o+ohhco+h2o 800K 

-80

70% CH4

-100

80% CH4

-120 800

90% CH4 1000

1000 1050 1100 1150 1200

(d) 2.5 (c) ROP (mole10-3/cm3-sec)

ch2o+hhco+h2

-20

950

Temperature(K)

ch3+och2o+h

20

oc7ooh

2.0 1.5 1.0

px2heooh=>oc7ooh+oh

0.5 0.0

total -0.5 -1.0

oc7ooh=>px2hepoo+oh

1400

1600

1800

800

800K  70% CH4 80% CH4 90% CH4

-1.5 1200

800K  70% CH4 80% CH4

-2.0

Temperature(K)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temperature(K)

Fig. 13 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh with various CH4 mass fractions, 800 K, ∅ = 𝟎. 𝟓


Energy & Fuels

ch4 ch3+h(+m)ch4(+m)

0

ch4+hh2+ch3

-5000

-10000

ch4+ohh2o+ch3 90%CH4 

-15000

800K 1000K 1200K

(b) 1.0 ROP (mole10-3/cm3-sec)


(a) 5000

total

-20000 1000 1200 1400 1600 1800 2000 2200 2400 2600

sxc7h15

0.8 0.6


0.4 0.2 0.0

90%CH4

-0.2 -0.4 -0.6 -0.8

sxc7h15+o2pc7h15o2 600

800

ch3+och2o+h

ch2o

5000

total

0

ch2o+hhco+h2 -5000 90% CH4

-10000



1000

1200

1400

1600

1800

Temperature(K)

ch2o+ohhco+h2o

800K 1000K 1200K

(c) (d) ROP (mole10-3/cm3-sec )

(c) 10000

 800K 1000K 1200K

sxc7h15=>pxc6h12+ch3 sxc7h15=>pxc4h9+c3h6

Temperature(K)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 46

0.4

oc7ooh 0.3

px2heooh=>oc7ooh+oh

0.2 0.1

total

0.0 -0.1

oc7ooh=>px2hepoo+oh

-0.2 -0.3

-15000 1000 1200 1400 1600 1800 2000 2200 2400 2600

-0.4 800

90%CH4  800K 1000K 1200K

900 1000 1100 1200 1300 1400 1500 1600

Temprature (K)

Temperature(K)

Fig. 14 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh at various temperatures, 90% CH4, ∅ = 𝟏. 𝟎


(a)

4000 2000


ch4 ch3+h(+m)ch4(+m) 0 -2000

ch4+hh2+ch3

-4000

90%CH4

ch4+ohh2o+ch3

-6000 

850K 900K 950K

-8000 -10000

total

sxc7h15

0.6 0.4


0.2 0.0

sxc7h15=>pxc6h12+ch3 90%CH4 sxc7h15=>pxc4h9+c3h6  sxc7h15+o2pc7h15o2 850K 900K 950K

-0.2 -0.4 -0.6 -0.8 800

1000 1200 1400 1600 1800 2000 2200 2400 2600

900

ch2o

ch3+och2o+h 4000 2000

total

0 -2000 -4000 -6000

90% CH4 

ch2o+hhco+h2

ch2o+ohhco+h2o 850K 800K 950K

1100

1200

1300

(c) 0.6 (d) ROP (mole10-3/cm3-sec)

6000

(c)

1000

1400

1500

Temperature(K)

Temperature(K)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels


Page 45 of 46

1000 1200 1400 1600 1800 2000 2200 2400 2600

oc7ooh

0.4

px2heooh=>oc7ooh+oh

0.2

total

0.0

90%CH4

-0.2

oc7ooh=>px2hepoo+oh -0.4 -0.6 850

900

Temprature (K)

950

1000

1050

1100

 850K 900K 950K 1150

1200

Temperature(K)

Fig. 15 Rates of production and consumption of (a) ch4, (b) sxc7h15, (c) ch2o and (d) oc7ooh in the NTC regime


Energy & Fuels

5000

ch3+h(+m)ch4(+m)

2000 1000 0

-2000 -3000 -4000 -5000

ch4+hh2+ch3 800K ch4+ohh2o+ch3  70% mole CH4 80% mole CH4

total

90% mole CH4

ch3+och2o+h

ch2o

3000 2000 1000

total

0 -1000

800K ch2o+hhco+h2

-2000  -3000

70% mole CH4

-4000


ch2o+ohhco+h2o

800 1000 1200 1400 1600 1800 2000 2200 2400 2600

-5000 1000 1200 1400 1600 1800 2000 2200 2400 2600

Temprature (K)

Temprature (K)

(c) 30 20

sxc7h15 c7h16+oh=>sxc7h15+h2o

-3

10 0

-10 -20

sxc7h15=>pxc6h12+ch3 800K 


70% mole CH4

-30


-40 800

(c) (d) ROP (mole10 /cm3-sec)


3000

-1000

(b) 4000

ch4

4000


(a)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 46 of 46

1000

1200

1400

1600

40

oc7ooh 20

px2heooh=>oc7ooh+oh

0

total -20

800K  70% mole CH4


80% mole CH4

-60 800

90% mole CH4 850

Temprature (K)

900

950

1000 1050 1100 1150 1200

Temprature (K)

Fig. A1 Rates of production and consumption of (a) ch4, (b) ch3, (c) sxc7h15 and (d) oc7ooh with various CH4 mole fractions, 800 K, ∅ = 𝟏. 𝟎


n-Heptane Fuel Blends under

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