Insights into the Effects of Mechanism Reduction on the Performance

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Insights into the effects of mechanism reduction on the performance of ndecane and its ability to act as a single-component surrogate for jet fuels Mohsin Raza, Yebing Mao, Liang Yu, and Xingcai Lu Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.9b00971 • Publication Date (Web): 16 Jul 2019 Downloaded from pubs.acs.org on July 24, 2019

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Energy & Fuels

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Insights into the effects of mechanism reduction on the performance of n-decane and its

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ability to act as a single-component surrogate for jet fuels

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Mohsin Raza, Yebing Mao, Liang Yu, Xingcai Lu*

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Key Laboratory for Power Machinery and Engineering of M. O. E., Shanghai Jiao Tong

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University, Shanghai 200240, PR China

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Abstract

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In this study, a detailed chemical reaction mechanism of n-decane containing 1034 species and

9

4268 reactions has been reduced at three different reduction levels to study the effects of

10

subsequent mechanism reductions on the performance of n-decane. The detailed and reduced

11

mechanisms were then used to validate ignition delays, laminar flame speeds, flame species and

12

species in a jet-stirred reactor (JSR). The one-half reduced mechanism performed nearly the

13

same as the detailed mechanism in most of the cases. The one-fourth and one-eighth reduced

14

mechanisms performed fairly well as compared to the detailed mechanism in some cases. The

15

differences were further elaborated by sensitivity analyses of ignition delays and laminar flame

16

speeds at different conditions followed by reaction pathway analysis of the detailed and one-

17

eighth reduced mechanisms. These analyses indicated the absence or presence of certain reaction

18

classes in reduced mechanisms that shaped the particular behavior of the mechanisms. In order to

19

evaluate the capability of n-decane as a single-component surrogate for jet fuels, the

20

experimental data of real-life jet fuels were used to validate the ignition delays and laminar flame

21

speeds using the reaction mechanisms. Among all the tested fuels, the ignition delay of jet A was

22

reproduced fairly well by the detailed mechanism followed by jet S8 and jet RP-3 fuels with a

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noticeable discrepancy in the negative temperature coefficient (NTC) region. One-eight reduced

24

mechanism performed well in the NTC region. The laminar flame speeds of jet A and jet S8 1 ACS Paragon Plus Environment

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fuels were predicted quite well by a detailed mechanism with one-fourth reduced mechanism

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performing well at fuel-lean conditions. This strengthened the capability of n-decane as a single-

3

component surrogate for jet fuels.

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Keywords: n-decane oxidation, mechanism reduction, chemical analysis, jet fuel surrogate

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1. Introduction:

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n-decane is widely used as a representative component of straight-chain hydrocarbons in

7

surrogates of transportation fuels especially jet fuels. n-decane has remained the focus of several

8

experimental studies to investigate its combustion characteristics. There are several studies that

9

described these combustion parameters including ignition delay,1-3 laminar flame speeds,4-7

10

pyrolysis8,9 and oxidation in a jet-stirred reactor.10 All of these studies have paved the way for

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the formulation of detailed chemical kinetic mechanism to understand the n-decane combustion.

12

Ranzi et al.11 proposed a detailed kinetic model up to n-hexadecane that was generated

13

automatically using MAMOX++ program. Battin-Leclerc along with colleagues12-14 used a

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program, EXGAS, to develop different models for n-decane. Westbrook et al.15 presented a more

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comprehensive model describing the kinetics of C8-C16 n-alkanes which was validated using

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various experimental data. Sarathy et al.16 developed a kinetic model for 2-methylalkanes from

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C7-C20 that also updated the previously developed n-alkanes mechanisms by Westbrook et al.

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Malewicki et al.17 developed n-decane mechanism after performing pyrolysis and oxidation in a

19

shock tube at high pressures up to 74 atm. Chang et al.18 recently proposed a well-validated

20

skeletal mechanism for n-decane.

21

The use of single-component surrogates is limited to study, for example, the combustion

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efficiency. Multi-component surrogates, on the other hand, are more complex and can be used to

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investigate a wide range of combustion characteristics and can be adopted for numerical

2 ACS Paragon Plus Environment

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modeling.19 n-decane is regarded as a single-component surrogate for jet fuels and also a

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representative of straight chain alkanes in multi-component surrogates. Another reason is the

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average carbon number of n-decane that is closer to practical aviation fuels like Norpar 12®

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(C11.5H25).20 Dagaut et al.21 studied the combustion of kerosene using n-decane in a jet-stirred

5

reactor. Zhao et al.22 studied the decomposition of JP-8 jet fuel by taking n-decane as a reference

6

fuel.

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The computations are important to understand the combustion process and the reduced

8

mechanisms are a good trade-off to obtain a reasonable simulation efficiency.23 Some of the

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prominent methods of mechanism reduction include; the direct relation graph (DRG) method,24

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the direct relation graph with error propagation (DRGEP) method,25 the sensitivity and reaction

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pathways analysis,26 and the computational singular perturbation (CSP) method,27 etc. The

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reduction of large mechanisms is performed using one of these methods or a combination of

13

these methods to obtain a more simplified mechanism. In addition to mechanism reduction, in

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situ adaptive tabulation (ISAT) method is used to enhance the computational speed.28

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There are several studies about mechanism reduction but all of them have achieved a targeted

16

reduced mechanism. We have, therefore, explored how reducing a mechanism sequentially to

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different sizes impacts its performance in predicting e.g. ignition delays. Furthermore, the

18

sensitivity analyses and pathways analyses will give chemical insights to these differences. This

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will prove to be a starting point for the researchers to choose an appropriate mechanism size and

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know beforehand what effects with each reduction they should anticipate. In this work, therefore,

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we have analyzed the detailed kinetic mechanism of n-decane. In the first part of the study, we

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have reduced the mechanism at different levels using DRG and DRGEP reduction methods. In

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the second part, we have studied the underlying chemistry to analyze the impact on reaction


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pathways and which reaction classes dominate or diminish as the mechanism size decreases

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along with the sensitivity analysis. In the final part, n-decane is investigated as a single-

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component surrogate for jet fuels.

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2. Methodology:

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The detailed n-decane mechanism is taken from Sarathy et al.16 They presented an updated

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C8–C16 n-alkane mechanism presented previously by Westbrook et al.15 The detailed mechanism

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contains 1034 species and 4268 reactions. The mechanism was validated over various test

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conditions in15 but the validations were limited only to the detailed mechanism. We, thus,

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reduced the mechanism to different sizes and evaluated the performance of each reduced

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mechanism. The direct relation graph (DRG) method is well acquainted with reducing large

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mechanisms as it is based on a linear time scale algorithm and uses production rate analysis to

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reduce the mechanism. In this method, a graph is formed with nodes representing the species and

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there is an edge, for example, between the vertex of species A to species B. It implies that the

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production of species A would be accurate if species B is retained in the mechanism. The

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assumption to keep all the target species in the mechanism and the species strongly related to

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them might not be right all the time. This paved the way for an improved method called direct

17

relation graph method with error propagation (DRGEP) to help make a finer species selection

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than DRG. This method proposes that the effect of an error obtained from the change in species

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concentration or eliminating them completely decreases as it propagates down to the user-

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specified targets. Furthermore, these two methods when used together with sensitivity analysis

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can produce a more simplified reaction mechanism then being used alone.29,30 In a recent study

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by Qiu et al.,31 the use of these methods together was indicated as an optimal method of

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mechanism reduction.


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Energy & Fuels

Table 1. List of the reduced mechanisms along with the number of species and reactions

1

Mechanism size

Species

Reactions

Reduction Method

Detailed Mechanism

1034

4268

-

One-half (1/2)

524

2469

DRG

One-fourth (1/4)

259

1154

DRG+DRGEP

One-eighth (1/8)

126

457

DRG+DRGEP

2 3

The target temperature range was set at 600-1600 K to cover both low and high-temperature

4

regimes and a pressure of 50 bar. The ignition time and OH radical was selected as a target

5

species. The reduction did not involve the addition of reactions from other mechanisms or

6

revision of kinetic parameters and mechanisms are analyzed in the original reduced form. The

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error tolerance was kept within 0.2-0.95 as the mechanism was reduced step-wise to half, one-

8

fourth and one-eighth of the size of the detailed mechanism to achieve the target number of

9

species and reactions. The reduced mechanisms along with the number of species and reactions

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are summarized in Table 1.

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3. Mechanism validations

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3.1.

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Ignition delay time

Ignition delay is one of the important benchmarks to quantify the performance of the reaction

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mechanism. Therefore, in this study ignition delay was validated using constant volume and

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constant internal energy assumption in a closed homogeneous batch reactor model in the

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CHEMKIN Pro32 software. The constant volume model can be used conveniently to compare

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modeled and experimental pressure rise and pressure peaks during and after ignition.33 The

18

temperature onset to determine the occurrence of ignition was set as 400 K. The validations were


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performed at various equivalence ratios with varying pressures. The equivalence ratios were

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varied from 0.5-2.0 keeping in view the fuel stratification during engine operation. Furthermore,

3

the pressures were varied from 12 bar to 80 bar because the operation of engine covers a wide

4

pressure range.

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The experimental data of n-decane ignition delay are taken from Zhukov et al.,1 Shen et al.2

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and Pfahl et al.34 Zhukov et al. conducted ignition delay study of n-decane at high pressure of 80

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bar between 800 K and 1300 K. Shen et al. investigated the ignition delay time of n-decane in a

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heated shock tube at a temperature between 786-1396 K, equivalence ratios of 0.25, 0.5, 1.0 and

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pressures between 9 and 58 atm. Pfahl et al.34 investigated at a temperature range of 650-1300 K

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and pressures of 13 bar and 50 bar, respectively. The experiments were performed at equivalence

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ratios of 0.5, 1.0 and 2.0 for 13 bar and 0.67, 1.0, 2.0 for 50 bar. Figures 1-3 show the ignition

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delay calculated at equivalence ratios of 0.5-2.0 and pressures of 12 bar, 50 bar and 80 bar,

13

respectively. The ignition delay follows an S-shaped curve which indicates that the mechanism is

14

able to predict ignition delay in NTC region. In Fig. 1, the ignition delay is overpredicted with a

15

noticeable difference at low temperatures for a pressure of 50 bar. The mechanism, however, is

16

able to capture the ignition delay between 1000 and 1250 K. In Fig. 2, the mechanism performs

17

well at pressures of 12 bar and 40 bar especially between 900 K and 1250 K as compared to high

18

pressures of 50 bar and 80 bar. The performance of the mechanism, however, is more

19

satisfactory at low pressure, 12 bar, and stoichiometric conditions (Φ=1) as compared to fuel-

20

lean conditions (Φ=0.5). In Fig. 3, at fuel-rich conditions, the mechanism performs well at 50 bar

21

between 952 K and 833 K while there is a discrepancy at 80 bar under same temperature range.

22

As the equivalence ratio and pressure are increased, the ignition delay times become shorter. The

23

mechanism overestimates the ignition delay more noticeably at high pressures which suggest an


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improvement needed especially at fuel-lean and high-pressure conditions as indicated by

2

Westbrook et al.15 At low pressure, however, the mechanism performs well according to the

3

experimental results.

4

It can be observed that the detailed mechanism and one-half reduced mechanism show almost

5

the same performance. The next two subsequent reductions, however, make the performance

6

worse especially the one-eighth reduced mechanism. The deviation is more pronounced in the

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NTC region for the one-eighth reduced mechanism. Another noticeable feature here is the

8 9 10 11 12 13 14 15

Figure 1. Comparison of ignition delay times at equivalence ratio of 0.5 and pressures of 50 bar

16

and 80 bar. Experimental data are taken from1,2,34

l

17 18

increase in ignition delay times as the mechanism is reduced. This can be attributed to the OH

19

production rate which in the case of the detailed mechanism will be higher. As the production

20

rate is reduced in subsequent reductions, the reactivity will decrease leading to a longer ignition

21

delay time.

22 23

Sensitivity analysis was conducted to identify the reactions that have a pronounced effect on the ignition delay. It was conducted in a homogeneous, constant volume reactor model in the


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Figure 2. Comparison of ignition delay times at an equivalence ratio of 1.0 and pressures of 12,

3

40, 50 and 80 bar. Experimental data are taken from1,2,34

4 5

CHEMKIN Pro32 software. The analysis was performed on temperatures of 950 K and 1200 K,

6

at pressures of 10 bar and 50 bar and at an equivalence ratio of 1.0. For each condition, the top

7

fifteen sensitive reactions were identified and then the following equation was used to calculate

8

the sensitivity (Si) of each reaction;

9

𝑆𝑖 =

𝜏(2𝑘𝑖) ― 𝜏(𝑘𝑖) 𝜏(𝑘𝑖)

10

where ki is the rate constant of reaction i, τ(ki) and τ(2ki) are the ignition delay times calculated

11

with original and doubled rate constant. According to this equation, a reaction with positive

12

sensitivity will inhibit the ignition while a reaction with negative sensitivity will promote the

13

ignition. The results of the analysis are outlined in Figures 4, 5 and Figures S1, S2. In general,

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the sensitivity spectrum at all conditions shows that the ignition delay predictions can be adjusted

15

by changing the rate constants of fuel-specific reactions. Although there are reactions from


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Figure 3. Comparison of ignition delay times at an equivalence ratio of 2.0 and pressures of 12

9

bar and 50 bar. Experimental data are taken from34

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H2/C1-C3 chemistry, the fuel-specific reactions dominate the spectrum. The general trend of the

12

lower sensitivity of same reactions in detailed mechanism as compared to the reduced

13

mechanism is most probably due to the contribution of a large number of reactions in

14

determining the overall sensitivity of the detailed mechanism which reduces the contribution of

15

each individual reaction. Similarly, the sensitive reactions particular to the detailed mechanism

16

once removed during the reduction process are chosen from the reactions available in the

17

reduced mechanism. This makes some reactions sensitive only in the reduced mechanism. In Fig.

18

4, at 950 K and 10 bar, the fuel-specific reactions for both detailed and one-eighth reduced

19

mechanisms have the highest negative sensitivity i.e. capable to promote the ignition. The fuel

20

undergoes H-atom abstraction by reacting with HO2:

21

NC10H22 + HO2 = C10H21-x + H2O2

22

Another important feature here is the position of H-atom abstraction. If abstracted from the

23

second site in the fuel chain, it will have a more enhancing effect on ignition as compared to the

(R2871)


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Figure 4. Brute force sensitivity analysis conducted at 950 K and pressures of 10 bar.

12 13

abstraction from the fifth site in the fuel chain. The recombination reaction:

14

H2O2 (+M) = 2OH (+M)

15

also tends to promote the ignition because of the formation of more OH radicals in the reaction

16

pool. The fuel decomposition reaction:

17

C10H21-5 = C6H12-1 + PC4H9

18

shows highest positive sensitivity i.e. pronounced ignition inhibition. This reaction is followed

19

by other fuel decomposition reactions that tend to inhibit the ignition process. In case of detailed

20

mechanism, ignition is promoted by the reactions from C1-C3 sub-system:

21

CH3 + HO2 = CH3O + OH

(R109)

22

C3H5-A + HO2 = C3H5O + OH

(R499)

(R16)

(R3023)


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In the one-eighth reduced mechanism, however, the ignition process is enhanced by the

2

isomerization of O2QOOH:

3

C7H14OOH(x) = C10KET(y) + OH

4

The spectrum at 950 K and 50 bar is shown in Fig. S1. At higher pressure, the ignition is

5

totally governed by the fuel-specific reactions with detailed and one-eighth reduced mechanism

6

ignitions being controlled by different reactions belonging to the same class. This further stresses

7

the importance of the rate constants of fuel-specific reactions to improve the performance of

8

mechanism in ignition delay predictions. Another feature is the nature of reactions at higher

9

pressure; all the most sensitive reactions tend to promote the ignition process as seen in the

10

sensitivity spectrums of both detailed and one-eighth reduced mechanisms. The abstraction of H-

11

atom from fuel shows highest negative sensitivity in both mechanisms as observed at 10 bar

12

which is followed by O2 addition in decyl radical to form QOOH:

13

C10H21O2-x = C10OOH(y)

14

The two reactions, R16 and R499, also have a significant contribution in promoting ignition at a

15

higher pressure in the detailed mechanism. The addition of O2 to ethane:

16

C2H5 + O2 = CH3CHO + OH

17

tends to promote the ignition in the one-eighth mechanism at 50 bar which was not observed at

18

10 bar.

19

(R’116)

The sensitivities at a higher temperature of 1200 K and 10 bar are shown in Fig. S2. At this

20

temperature, in contrast with the sensitivities at 950 K, the reactions belonging to C1-C3 sub-

21

system dominates the spectrum and have a pronounced effect on promoting the ignition. The

22

reactions:

23

CH3 + HO2 = CH3O + OH

(R109)


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Figure 5. Brute force sensitivity analysis conducted at 1200 K and pressure of 50 bar.

13 14

H + O2 = H + OH

(R1)

15

have the highest negative sensitivities with R1 being the chain-branching reaction. Another

16

reaction of methyl radical:

17

CH3 + HO2 = CH4 + O2

18

shows the highest positive sensitivity in both detailed and one-eighth reduced mechanisms. The

19

graph shows that the tendency of methyl radical to inhibit the ignition is larger than the tendency

20

to promote the ignition in the one-eighth reduced mechanism. In their studies, Curran et al.35 and

21

Metcalfe et al.36 mentioned CH3 + HO2 reaction as very important for hydrocarbon combustion.

22

This reaction can either take the chain-branching pathway, R109, to promote the ignition or

23

chain termination pathway, R110, to inhibit the ignition. The fuel decomposition reactions also

(R110)


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tend to inhibit the ignition. Furthermore, at a higher temperature, the thermal decomposition of

2

fuel becomes more noticeable as compared to a lower temperature.

3

The reactions:

4

2CH3 (+M) = C2H6 (+M)

(R151)

5

HO2 + OH = H2O + O2

(R’13)

6

inhibit the ignition in the detailed and reduced mechanism, respectively. The effect of these two

7

particular reactions was not observed at a lower temperature.

8 9

The sensitivities at 1200 K and 50 bar are shown in Fig. 5. The reactions R1 and R109, as observed at 10 bar, show the highest negative sensitivities. The reactions R16 and R499, as

10

observed before, tend to promote ignition at all the conditions considered for the analysis. The

11

reaction of ethylene:

12

C2H4 + OH = C2H3 + H2O

13

shows highest negative sensitivity in the one-eighth reduced mechanism which was also

14

observed at 10 bar. This reaction indicates that ethyl radical has a noticeable effect on ignition

15

delay which becomes pronounced at higher pressure. The formation of decyl radicals by H-atom

16

abstraction also promote the ignition as in the case of 950 K. At low pressure and high

17

temperature, however, these reactions are not very dominant in the sensitivity spectrum as shown

18

in Fig. S2. The reactions inhibiting the ignition are same as observed at the low-pressure

19

condition. In order to improve the ignition delay prediction, the rate constants of fuel-specific

20

and the reactions that are observed particularly at high pressures should be reconsidered.

21

3.2. Laminar flame speed

22 23

(R’162)

Laminar flame speed is an important flame parameter considered while studying combustion and, therefore, employed for validation of kinetic models. The current data has been validated


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against experimental data taken from Zhao et al.5 and Hui et al.7 The experiments were

2

performed at unburned temperatures of 500K and 400K, respectively and at equivalence ratios

3

between 0.6 and 1.5. The validations were performed in the CHEMKIN Pro32 software using

4

Premixed Laminar Flame-speed Calculation model. The mechanism performance was first tested

5

at constant pressure and varying unburned gas temperatures followed by constant temperature

6

and varying pressures. The results are shown in Figure 6 and Figure 7, respectively. At constant

7

pressure, the mechanism performs quite well in predicting laminar flame speeds. A noticeable

8

difference of about 10cm/s is observed at the fuel-lean condition for both temperatures. The

9

flame speed increases with increasing temperature. The increase in pressure, however, decrease

10

the flame speed which is due to the widely known effect of upstream gas density. At the constant

11

temperature, the mechanism performs well at lower pressure but the flame speed decreases as the

12

pressure is increased to 2 atm.

13

The deviation is prominent between equivalence ratios of 0.85 and 1.15. The detailed

14

mechanism performs almost the same as one-half reduced mechanism, which is the same as

15

observed in case of ignition delay. The one-fourth reduced mechanism underpredicts the flame

16

speed and the effect becomes prominent at a higher temperature. The one-eighth reduced

17

mechanism shows a very distinctive behavior, unlike that observed in ignition delay, and shows

18

an increase in laminar flame speed. One possible reason for an increase in the flame speed is the

19

change in the balance of chain propagating and chain termination reactions that led to this

20

particular behavior. Furthermore, it must be noted here that the flame velocity is controlled by

21

kinetics at higher temperature regime which is in contrast with ignition delay that depends more

22

on the low-temperature regime. Figure 8 shows the distribution proportion of carbon species

23

ranging from C0-C10 in the detailed and one-eighth reduced mechanism to analyze the effect of


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species proportion in increasing or decreasing the flame speed. As the mechanism is reduced,

2

there is a considerable decrease in the proportion of C9 to C5 species. This corresponds to the

3

increase in the flame speed as the mechanism is reduced. Another noticeable trend is the increase

4

in the proportion of C10, C4 and C1 species. In the case of one-eight reduced mechanism, this

5

proportion reaches a higher level which tends to increase the laminar flame speed and as

6

indicated by Zhao et al.,5 flame speed is dominated by the kinetics of small-species. In terms of

7

kinetics, the flame speed is influenced by the radicals generated during the initial fuel oxidation.

8

If the radicals are resonantly stable or unable to disintegrate quickly to produce H-atoms, there

9

would be a decrease in the flame velocity. In addition to kinetics, transport properties of small

10

species also play a significant role in controlling the flame speed owing to their high diffusivity.

11

In order to further analyze the underlying chemistry at a higher pressure and the performance

12

of the one-eight reduced mechanism, a sensitivity analysis was performed at two 2 atm and at

13

the ambient temperature of 298 K at fuel-lean (∅=0.85), stoichiometric (∅=1.0) and fuel-rich

14

(∅=1.15) condition. Figure 9 and Figure 10 show the comparison of laminar flame speed

15

sensitivities at the aforementioned conditions for detailed and one-eighth reduced mechanisms.

16

In general, the flame speed in both mechanisms is largely influenced by a high-temperature

17

chain-branching reaction which shows the highest positive sensitivity:

18

H + O2 = O + OH

19

The other reactions that have noticeable positive coefficients are,

20

HCO + M = H + CO + M

(R26)

21

CO + OH = CO2 + H

(R24)

22

The second, formyl radical reaction, and third reactions are also chain reactions but they produce

23

H-atoms which are then consumed by the first reaction and thus also exhibit positive sensitivity.

(R1)


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Page 16 of 39

1 2 3 4 5 6 7 8

Figure 6. Comparison of laminar flames speeds at a pressure of 1 atm and unburned gas

9

temperatures of 400 K and 500 K, respectively. Experimental data are taken from5,7

10 11 12 13 14 15 16 17

Figure 7. Comparison of laminar flames speeds at an unburned gas temperature of 400 K and

18

pressures of 1 atm and 2 atm, respectively. Experimental data are taken from7

19 20

The recombination reaction:

21

H2O + (M) = H + OH + (M)

22

exhibits a large negative sensitivity because it contributes to chain termination. Another

23

important reaction inhibiting the flame speed is:

(R8)


Page 17 of 39 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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1 2 3 4 5 6 7 8

Figure 8. The proportion of carbon species distribution in detailed and reduced mechanisms

9 10

H + O2 (+M) = HO2 (+M)

(R9)

11

This reaction, in particular, competes with R1 at higher pressures. As indicated in,37,38 R1 is a

12

vital chain-branching reaction and the reaction competing with this reaction for H-atom

13

consumption will slow down the overall combustion process. This reaction, as shown in

14

sensitivity graphs, slows down the flame velocity above atmospheric pressures. This reduction

15

effect, below atmospheric pressure, is compensated by the rise in temperature and less reduction

16

in flame speed is observed. At pressure above 1 atm, however, the effect is more noticeable and a

17

sharp decrease in flame speed is observed. Another velocity promoting effect can be observed in

18

the interaction between methyl radical and OH which yield singlet methylene radical:

19

CH3 + OH = CH2(S) + H2O

20

The other reactions dominating sensitivity graphs involve species from C1 to C3 and most of

21

these reactions involve the consumption of H atoms. Furthermore, the reactions undergoing H-

22

atom abstraction also have a negative effect on the flame velocity. The fuel contribution can be

23

noticed only in one-eighth reduced mechanism:

(R75)


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1 2 3 4 5 6 7 8 9 10 11 12

Figure 9. Sensitivity analysis of laminar flame speeds using detailed mechanism at T=400K and

13

P=2atm and fuel-lean, stoichiometric, and fuel-rich conditions.

14 15

C10H21 = C6H12 + PC4H9

16

which can be related to the increased proportion of C10 species as shown in Fig. 10. The fuel,

17

overall, and the species larger than C4 have a negligible effect on the laminar flame speed as

18

evident from the sensitivity analysis. In order to improve the flame speed predictions, the C1-C4

19

chemistry needs further investigation.

20

3.3.

21

(R391)

Species in flame and Jet-Stirred Reactor (JSR)

Laminar flame species were also validated using all the reduced mechanisms. The

22

experimental data were taken from Douté et al.39 performed at an equivalence ratio of 1.7 and

23

pressure of 1 atm. The validation was performed in the CHEMKIN Pro32 software using


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1 2 3 4 5 6 7 8 9 10 11 12

Figure 10. Sensitivity analysis of laminar flame speeds using one-eighth reduced mechanism at

13

T=400K and P=2atm and fuel-lean, stoichiometric, and fuel-rich conditions

14 15

Premixed Burner model. The results can be seen in Figure 11(a), (b), and (c) for some selective

16

species including O2, H2, CO, CO2, H2O, and the fuel n-C10H22. The overall trend of fuel

17

consumption is predicted quite well with the exception of one-eighth reduced mechanism


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

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1 2 3 4 5 6 7 8

Figure 11. Species mole fractions in flame (a) nC10H22, CO (b) O2, H2 (c) H2O, CO2 measured at

9

an equivalence ratio of 1.7 and pressure of 1 atm. Experimental data are taken from39

10 11

that underpredicts the mole fraction with a noticeable error. The fuel is consumed at a distance of

12

about 2-3mm above the burner surface. The CO mole fraction is underestimated before 10mm

13

while its mole fraction estimate increases beyond that. The major source of CO production is

14

through the reaction,

15

HCO + M = H + CO + M

16

The increase in error as the mechanism is reduced is pronounced after 10mm where one-eighth

17

mechanism performing the least of all. The mole fraction of O2 is predicted well with a less

18

noticeable error in the performance of reduced mechanisms. The H2 mole fraction follows the

19

same trend as observed in case of CO mole fraction but the error becomes paramount as the

20

mechanism is reduced especially in case of the one-eighth reduced mechanism. H2O and CO2 are

21

also predicted reasonably with a noticeable under prediction in H2O whereby, the major source

22

of CO2 production is through the reaction,

23

CO + OH = CO2 + H

(R26)

(R24)


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The one-eighth reduced mechanism shows a higher mole fraction as compared to the detailed

2

mechanism. This could have increased the flame speed, Fig. 6 and Fig. 7, as the reaction

3

producing CO2 is among the top reactions promoting flame speed as shown in Fig. 10. The

4

overall performance of all the reduced mechanisms remain the same with a negligible error

5

observed in case of the one-eighth reduced mechanism. The mechanism, in general, performs

6

well in predicting the mole fractions of the species in flame.

7

The species mole fractions in a jet-stirred reactor (JSR) were validated for all the mechanisms

8

using a perfectly stirred reactor (PSR) model of the CHEMKIN Pro32 package. The experimental

9

data were taken Dagaut et al.10, 40 All the validations are shown in Fig. S3. Methane is produced

10

primarily by the reaction of methyl radical with H radical;

11

CH3 + H (+M) = CH4 (+M)

12

In the downstream, methane is consumed by reaction with OH and H radicals. The mole

13

fractions of methane are predicted quite well at lower temperatures while the discrepancy is

14

noticeable from 950 K onwards as shown in Fig. S3 (b). Ethyl radical is thermally decomposed

15

to form ethene and H radical, which is also the dominant production pathway of ethene;

16

C2H5 (+M) = C2H4 + H (+M)

17

Ethene is majorly consumed as it reacts with H radical to form vinyl radical;

18

C2H4 + H = C2H3 + H2

19

The mole fractions of ethene are underpredicted by a considerable error by the detailed

20

mechanism as shown in Fig S3 (c).

21

(R98)

(R163)

(R248)

The behavior of different reduced mechanisms is also different which was not observed

22

during flame species validations. The performance of one-half reduced mechanism is the same as

23

the detailed mechanism for all the species with a negligible error, which is the same as observed


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Page 22 of 39

1

in other validations. One-fourth reduced mechanism shows comparable performance as the

2

detailed mechanism except for CH4, CO2 and CO. It, however, reproduces the mole fraction of

3

CO2 fairly well as compared to the detailed mechanism. There are considerable increase and a

4

decrease of mole fractions of CH4 and CO, respectively in one-fourth reduced mechanism. The

5

one-eighth reduced mechanism performs worst for all the species except for ethene whose mole

6

fraction is reproduced quite well as compared to the detailed mechanism. Similarly, the mole

7 8

Figure 12. Reaction pathways of n-decane at 20% fuel conversion observed in the detailed

9

mechanism at an equivalence ratio of 1.0 and pressure of 10 atm. 680 K (plain), 790 K (italic)

10

and 950 K (bold). Dotted arrows show multi-step reactions leading to the production of OH.


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the fraction of CO is predicted fairly well only at a higher temperature. These results indicated

2

that reducing the mechanism can improve the performance in some aspects as the uncertainties in

3

the reduced mechanism are reduced as compared to the detailed mechanism.

4

4. Chemical kinetics

5

4.1.

Reaction pathways

6

The reaction pathways were analyzed at three different temperature conditions; 680 K (low

7

temperature), 790 K (intermediate temperature) and 950 K (high temperature). The analysis was

8

performed in CHEMKIN Pro32 software using 0-D homogeneous, constant volume reactor model

9

at a pressure of 10 atm and equivalence ratio of 1.0. The reaction pathways observed in the

10

detailed mechanism and one-eighth reduced mechanism are shown in Fig. 12 and Fig. 13,

11

respectively. The number on the arrows represents the percentage consumption of the reactant

12

through the corresponding pathway.

13

The fuel consumption starts with an H-atom abstraction (NC10H22 + X) by the attack of OH

14

radical (attack by other radicals like CH3, HO2 is limited) leading to the formation of decyl

15

radical. The pathways leading to propagation, termination or branching reactions and the low-

16

temperature chemistry is governed by this initial radical pool formed by H-atom abstraction from

17

any of the specific sites. This site-specific H-atom abstraction by the attack of OH radical is well

18

explained in the literature.41,42 The decyl radical then undergoes oxygen addition (R + O2 = RO2)

19

to form decylperoxy radical at all temperature conditions with a noticeable decrease in

20

consumption at 950 K. A small consumption at 680 K is also observed by addition of

21

decylperoxy radical to decyl radical (R + RO2 = RO + RO). At 790 K, decomposition of decyl

22

radical is observed, which belongs to a high-temperature class. Similarly, decyl radical


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1

isomerization is observed only at 950 K, which also belongs to the high-temperature reaction

2

class.

Page 24 of 39

3 4

Figure 13. Reaction pathways of n-decane at 20% fuel conversion observed in the one-eighth

5

reduced mechanism at an equivalence ratio of 1.0 and pressure of 10 atm. 680 K (plain), 790 K

6

(italic) and 950 K (bold). Dotted arrows show multi-step reactions leading to the production of

7

OH


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The decylperoxy radical is consumed preferably by isomerization to decylhydroperoxy radical

2

(ROO = QOOH) with the highest consumption observed at 790 K. This, the isomerization of

3

ROO radical via internal H-atom abstraction, is the most favored pathway for ROO radical

4

conversion. The consumption through concerted elimination (ROO = alkene + HO2) becomes

5

noticeable as the temperature is increased to 950 K. This pathway is chain-terminating because

6

of HO2 production and it is removed by H2O2 in the downstream. The ROO chain-termination

7

decreases the reactivity as the temperature is increased, which is usually termed as NTC

8

(negative temperature coefficient) region.43 The addition of decylhydroperoxy radical to

9

decylhydroperoxy radical (RO2 + RO2 = RO + RO + O2) can be observed only at low temperature

10

and this class diminishes as the temperature is increased to 950 K. At 680 K and 790 K,

11

decylperoxy radical is majorly consumed by the addition of oxygen to form peroxy

12

decylhydroperoxy radical (QOOH + O2 = O2QOOH) and this particular reaction class exists only

13

at low temperatures. The conversion of decylhydroperoxy radical to an alkene (QOOH = alkene

14

+ HO2) is observed only at intermediate temperature (790 K) and diminishes at a higher

15

Table 2. Reaction classes not observed in the one-eight reduced mechanism

16

Class No.*

Reaction class

Temperature regime

6

Alkenes + OH = alkenyl radical

High temperature

8

Alkenyl radical decomposition

High temperature

12

R + RO2 = RO + RO

Low temperature

16

RO2 = alkene + HO2

Low temperature

20

RO2 + RO2 = RO + RO + O2

Low temperature

24

QOOH = alkene + HO2

Low temperature

25

QOOH = alkene + carbonyl + OH

Low temperature

* The number of reaction class can be referred to 16


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Page 26 of 39

1

temperature. The conversion of decylhydroperoxy radical to cyclic ethers (QOOH = cyclic ether

2

+ OH) becomes dominant only at a higher temperature. The peroxy decylhydroperoxy radical

3

finally yields ketohydroperoxide (O2QOOH = KET + OH) which later converts to oxygenated

4

radical species by decomposition. The isomerization and dissociation of O2QOOH produce

5

several radicals that promote the chain branching, especially at low temperatures.

6

The reaction classes not observed in the reduced mechanism are illustrated in Table 2.

7

The removal of certain high and low-temperature reaction classes impacted the mechanism

8

performance. The effect of each reaction class can be quantified based on the percentage of

9

consumption through that particular class. Among low-temperature classes, highest fuel

10

consumption is through class 24 and removing this class will have a noticeable impact on

11

12

Figure 14. Brute force sensitivity analysis of ignition delay based on the reaction classes

13

observed in the detailed mechanism at 10 bar and different temperature conditions.

14 26 ACS Paragon Plus Environment

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performance as compared to the other classes. Similarly, among high-temperature reaction

2

classes, class 8 will impact mechanism performance. This further indicates that removing a

3

particular class will have a different effect under different validation conditions. A more

4

thorough analysis would be to find the implications of removing each particular reaction class

5

and compare the performance under different validation conditions.

6

4.2.

Class-wise sensitivity analysis

7

The analysis was performed at three different temperature conditions for both detailed and

8

one-eighth reduced mechanisms at low pressure (10 bar) and high pressure (50 bar). The bars

9

with the same color and different pattern indicate that this reaction is observed only at that

10

particular pressure and the corresponding temperature. The results of the analysis using detailed

11

and reduced mechanism at 10 bar are depicted in Fig. 14 and Fig. S4, respectively.

12

At 10 bar, as shown in Fig. 14 and Fig. S4, the abstraction of H-atom from the fuel is the

13

dominant reaction class at low temperatures showing the highest negative sensitivity (promote

14

reactivity). This behavior of this reaction class is explicable because it leads to the formation of

15

alkyl radicals. At 680 K, this reaction class also shows the highest positive sensitivity (inhibit

16

reactivity) which corresponds to different reactions from the same class. This indicates that the

17

behavior of reactions from this class also depends on the site of H-atom abstraction. In addition

18

to this, particularly at low temperature, the QOOH species is also important in promoting

19

reactivity which is evident from the behavior of reaction classes leading to the formation of

20

QOOH and isomerization of OOQOOH species. Similarly, decomposition of

21

carbonylhydroperoxide promotes the ignition only at low temperature. As the temperature is

22

increased to 1200 K, the high-temperature reaction classes dominate the spectrum with the

23

addition of OH to alkenes being the most sensitive reaction class promoting the ignition. Alkyl


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Page 28 of 39

1

radical decomposition also undergoes two pathways, corresponding to two different reactions, at

2

a higher temperature with one promoting the ignition while other inhibiting the ignition. In the

3

one-eighth reduced mechanism, however, only the pathway that promotes the reactivity is

4

retained. Furthermore, the addition of OH to alkenes promotes the ignition only in the one-eighth

5

reduced mechanism.

6

At 50 bar, as shown in Fig. 15 and Fig. S5, the pathway leading to the formation of

7

QOOH shows highest negative sensitivity followed by H-atom abstraction, which was observed

8

as the dominant class at low pressure (10 bar) at a temperature of 680 K. At 950 K, however, H-

9

atom abstraction shows the highest negative sensitivity as observed at 10 bar pressure. The

10

isomerization of OOQOOH also promotes the reactivity at 950 K, which was not observed at 10

11

bar pressure. The ignition at high temperature is promoted mainly by H-atom abstraction from

12

alkenes and addition of OH radical to alkenes. The H-atom abstraction at a higher temperature,

13

observed only at 50 bar, also tends to promote the reactivity. Alkyl radical decomposition and H-

14

atom abstraction from fuel tend to inhibit the reactivity. In the one-eighth reduced mechanism,

15

unimolecular fuel decomposition and the addition of O2 to an alkyl radical also promote the

16

ignition. These two classes were not observed in the detailed reaction mechanism.

17

5. n-decane as a surrogate for jet fuels

18

The capability of n-decane to act as a single-component surrogate was tested for various jet

19

fuels. There are many studies that include investigation of n-decane as a single-component

20

surrogate for kerosene. The capability of n-decane as a single-component surrogate, however,

21

has not been explored for all the jet fuels considering the different chemical compositions of jet

22

fuels available in the market today. We, therefore, used this mechanism to validate the ignition

23

delays of jet A, RP-3 and S8 fuels. In addition, the current validation results will only testify for


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Energy & Fuels

1

the mechanism under investigation. The other n-decane mechanisms might perform differently

2

for various jet fuels under similar conditions.

3

The ignition delay of jet A fuel at 20 atm predicted by mechanism is shown in Fig. 16 (a).

4

There is a considerable error at low temperature but at high temperature, the performance is quite

5

well. A closer look, however, indicates the good performance of one-eight reduced mechanism in

6

the NTC region, which can be attributed to the removal of chain-termination pathway in the

7 8 9 10 11 12 13 14 15 16 17 18

Figure 15. Brute force sensitivity analysis of ignition delay based on the reaction classes

19

observed in the one-eighth reduced mechanism at 50 bar and different temperature conditions.

20 21

the reduced mechanism as indicated in the reaction pathway analysis. The performance of the

22

current mechanism of n-decane in case of jet S8, as shown in Fig. 16 (b), is much better at both

23

high and low temperatures as compared to jet A fuel. This indicated that this mechanism can be


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Page 30 of 39

1

explored further as the potential single-component surrogate for this jet fuel. The ignition delay

2

of jet fuel RP-3, as shown in Fig. 16 (c), is better predicted by one-eighth reduced mechanism in

3

the NTC region but there is a noticeable discrepancy at lower temperatures. The validations of

4

laminar flame speeds are shown in Fig. 17. The validations of jet A and jet S8 were performed at

5

pressures of 1 atm and 2 atm and at an unburned gas temperature of 400 K. The laminar flame

6 7 8 9 10 11 12 13

Figure 16. Ignition delays validation of real-life jet fuels (a) Jet A (b) Jet S8 (c) Jet RP-3 with the

14

detailed and reduced mechanisms at the mentioned conditions. Experimental data are taken from

15

44-47

16 17


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speeds of jet A and jet S8 at 1 atm as predicted by the detailed mechanism are faster as compared

2

to the experimentally measured speeds as shown in Fig. 17 (a) and Fig. 17 (b), respectively. The

3

one-fourth reduced mechanism performs fairly well at fuel-rich conditions for both the fuels.

4

As the pressure is increased to 2 atm, the detailed mechanism performs quite well except

5

some discrepancy observed at fuel-lean conditions. The one-eighth reduced mechanism performs

6

fairly well at fuel-lean conditions. The flame speed of RP-3 fuel, shown in Fig. 17 (c), was

7 8 9 10 11 12 13 14

Figure 17. Validations of laminar flame speeds of real-life jet fuels at unburned gas temperature

15

of 400 K (a) Jet A (b) Jet S8 (c) Jet RP-3 with detailed and reduced mechanisms. Experimental

16

data are taken from48,49


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Page 32 of 39

1

validated at a pressure of 1 atm and unburned gas temperature of 400 K. The flame speed, as

2

depicted by the detailed mechanism, is slower at fuel-lean conditions and faster at fuel-rich

3

conditions with the exception of stoichiometric conditions where it performs fairly well. The

4

one-fourth reduced mechanism performs well at fuel-rich conditions as observed in Fig. 17 (a)

5

and Fig. 17 (b). The fair performance of reduced mechanisms is only under considered

6

conditions and it does not testify for a comprehensive enhanced performance as compared to the

7

detailed mechanism. The validations, in general, lie within an acceptable range.

8

6. Summary

9

In this study, a detailed mechanism of n-decane containing 1034 species and 4268 reactions

10

was reduced to different sizes; one-half, one-fourth and one-eighth of the size of the detailed

11

mechanism using DRG and DRGEP reduction methods. The performance of these mechanisms

12

was evaluated by validating ignition delays, laminar flame speeds, flame species, and species in

13

a JSR. The performance of one-half reduced mechanism was the same as the detailed mechanism

14

with a negligible discrepancy observed in most validations. The one-fourth and one-eighth

15

reduced mechanism performed worst of all in most cases. In some cases, however, their

16

performance was even better than the detailed mechanism.

17

The reaction pathways of detailed and one-eighth reduced mechanism indicated that the major

18

consumption pathways are the same in both mechanisms. The minor consumption pathways in

19

the detailed mechanism were removed in the one-eighth reduced mechanism. These classes were

20

responsible for the different behavior of reduced mechanism observed during validations.

21

Sensitivity analysis of reaction classes indicated the particular reaction classes that have an

22

impact on the overall reactivity of the system. The increase or decrease of sensitivity or presence

23

or absence of some reaction classes in the one-eighth reduced mechanism as compared to the


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detailed mechanism can be connected to the different behaviors of reduced mechanisms in the

2

considered cases.

3

The ignition delays and laminar flame speeds of jet A, S8 and RP-3 fuels were validated using

4

the detailed and reduced mechanisms. A noticeable discrepancy was observed at NTC region

5

which was fairly addressed by the one-eighth reduced mechanism. The flame speeds were

6

predicted quite well, especially at 2 atm, over an entire range of equivalence ratios. At fuel-rich

7

conditions, one-fourth reduced mechanism performed quite well.

8

Supporting Information

9

The supporting information associated with this article includes Figures S1-S5 and comparative

10

performance evaluation of 1/8th reduced mechanism (Fig. S6-S7) with mechanisms of Chang et

11

al. 22 and Qiu et al. 50

12

Acknowledgments

13

This work was supported by the Key Project of National Natural Science Foundation of China

14

(Grants 91641202, 51425602) and Program of Shanghai Academic Research Leader (No.

15

19XD1401800)

16 17 18 19 20 21 22 23


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1

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References

2

(1) Zhukov, V. P.; Sechenov, V. A.; Starikovskii, A. Y. Autoignition of n-decane at high

3

pressure. Combust. Flame 2008, 153 (1-2), 130-136.

4

(2) Shen, H. P. S.; Steinberg, J.; Vanderover, J.; Oehlschlaeger, M. A. A shock tube study of the

5

ignition of n-heptane, n-decane, n-dodecane, and n-tetradecane at elevated pressures. Energy

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Fuels 2009, 23 (5), 2482-2489

7

(3) Olchanski, E.; Burcat, A. Decane oxidation in a shock tube. Int. J. Chem. Kinet. 2006, 38 (12),

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703-713.

9

(4) Kumar, K.; Mittal, G.; Sung, C. J. Autoignition of n-decane under elevated pressure and low-

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to-intermediate temperature conditions. Combust. Flame 2009, 156 (6), 1278-1288.

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(5) Zhao, Z. W.; Li, J.; Kazakov, A.; Dryer, F. L.; Zeppieri, S. P. Burning velocities and a high-

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temperature skeletal kinetic model for n-decane. Combust. Sci. Technol. 2005, 177 (1), 89-106.

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(6) Kumar, K.; Sung, C. J. Laminar flame speeds and extinction limits of preheated n-

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decane/O2/N2 and n-dodecane/O2/N2 mixtures. Combust. Flame 2007, 151 (1-2), 209-224

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(7) Hui, X.; Sung, C. J. Laminar flame speeds of transportation-relevant hydrocarbons and jet

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fuels at elevated temperatures and pressures. Fuel 2013, 109, 191-200.

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(8) Zeppieri, S. P.; Klotz, S. D.; Dryer, F. L. Modeling concepts for larger carbon number

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alkanes: a partially reduced skeletal mechanism for n-decane oxidation and pyrolysis. Proc.

19

Combust. Inst. 2000, 28 (2), 1587-1595.

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(9) Jahangirian, S.; Dooley, S.; Haas, F.M.; Dryer, F. L. A detailed experimental and kinetic

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