Application of a Decoupling Methodology for Development of Skeletal

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Application of a Decoupling Methodology for Development of Skeletal Oxidation Mechanisms for Heavy n‑Alkanes from n‑Octane to n‑Hexadecane Yachao Chang, Ming Jia,* Yaodong Liu, Yaopeng Li, Maozhao Xie, and Hongchao Yin Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, School of Energy and Power Engineering, Dalian University of Technology, P. R. China S Supporting Information *

ABSTRACT: A series of skeletal mechanisms was developed based on a decoupling methodology to describe the oxidation of nalkanes from n-octane to n-hexadecane. In the decoupling methodology, a fuel oxidation mechanism is divided into two parts: one is an extremely simplified model for species with a carbon atom number larger than two to simulate the ignition characteristics of n-alkane; the other is a detailed mechanism for H2/CO/C1 to predict the concentrations of small molecules, laminar flame speed, and extinction strain rate. The new skeletal mechanism includes only 36 species and 128 reactions for each n-alkane from n-octane to n-hexadecane. The mechanism was extensively validated against the experimental data in a shock tube, jet-stirred reactor, flow reactor, counterflow flame, and premixed laminar flame. Good agreements on ignition delay, the concentrations of major species, laminar flame speed, and extinction strain rate between the predictions and measurements were obtained over wide ranges of temperature, pressure, and equivalence ratio, which demonstrates the capability of the decoupling methodology to build skeletal oxidation mechanisms for n-alkanes. Due to the compact size of the new skeletal mechanism, it can be easily integrated into the computational fluid dynamics (CFD) simulation. Shen et al.14 at elevated pressures in a heated shock tube. More recently, Ji et al.15 measured the laminar flame speeds and extinction strain rates of premixed C5−C 12 n-alkane flames at atmospheric pressure in the counterflow configuration. The experimental results were also simulated by the Jet Surrogate Fuel (JetSurF) kinetic model, 16 and good agreements between the predictions and measurements on the laminar flame speed and extinction strain rate were achieved. A reliable kinetic model is crucial to assessing the characteristics of ignition, combustion, and pollutants of hydrocarbon fuels. Westbrook et al.17 developed a detailed mechanism to describe the pyrolysis and oxidation of n-alkanes from n-octane to n-hexadecane by organizing the large number of elementary reactions into 25 reaction classes. The mechanism was validated over wide ranges of temperature, pressure, and equivalence ratio in various reactors, whereas most of the validations were concerned with n-decane. For nnonane, n-dodecane, and n-hexadecane, the mechanism was only validated in a jet-stirred reactor and flow reactor for the concentrations of major species. And no comparisons between predictions and experimental data were performed for other nalkanes. A semidetailed kinetic model was developed by Ranzi et al.18 by using the MAMOX++ program to describe the pyrolysis, partial oxidation, and combustion of n-decane, n-dodecane, and n-hexadecane. The mechanism was compared with the experimental data including the ignition delay in the shock tube, the concentrations of species in the jet-stirred reactor and

1. INTRODUCTION The understanding of the combustion characteristics of practical fuels (gasoline, diesel, kerosene, etc.) is important to improve internal combustion engine efficiency and minimize its pollutant emissions. The chemical kinetics of fuel has become more and more important for the development of engines in recent years. In order to reduce the nitrogen oxides (NOx) and soot emissions in diesel engines, it is necessary to deeply understand the evolution histories of major species under wide equivalence ratio and temperature ranges. Whereas, for spark ignition (SI) engines, detailed flame propagation and extinction phenomena need to be concerned. Especially, for the advanced compression ignition combustion strategies, such as homogeneous charge compression ignition (HCCI) and premixed charge compression ignition (PCCI), the autoignition of fuel plays a crucial role in engine performance and emissions. However, the practical fuels often consist of hundreds, even thousands, of compounds. It is difficult to simulate the combustion of practical fuels in the internal combustion engine for current computational resources. Thus, the simplified “surrogate fuels” including a small number of pure compounds are often used to model the physical and chemical characteristics of practical fuels. Higher molecular weight n-alkanes are major components for all practical fuels and are primary components of surrogate fuel for practical fuels.1−8 In recent decades, many investigations have been carried out on the oxidation of n-alkanes from n-octane to n-hexadecane. Dagaut et al. studied the oxidation of n-nonane,9 n-decane,10,11 n-undecane,12 n-dodecane,12 and n-hexadecane13 in a jet-stirred reactor. Detailed mechanisms were also built to simulate the experimental results. The ignition delays of n-heptane, ndecane, n-dodecane, and n-tetradecane were investigated by © XXXX American Chemical Society

Received: March 15, 2013 Revised: May 30, 2013

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dx.doi.org/10.1021/ef400460d | Energy Fuels XXXX, XXX, XXX−XXX

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flow reactor, and the laminar flame speed in the premixed flame and counterflow diffusion flame, as well as the ignition and combustion of n-alkane droplets under microgravity conditions. It was indicated that the model predictions show good agreement with the experimental results under wide-range conditions. However, the above-mentioned detailed mechanisms typically contain a large number of species and reactions. It is difficult to integrate the detailed mechanisms into multidimensional simulation with current computer capability. To solve this problem, many researchers19−22 have tried to develop skeletal and reduced models. You et al.19 developed a simplified model including 115 species and 861 reactions to describe the pyrolysis and oxidation of n-dodecane at temperatures above 850 K. The simplified model was divided into two parts including an extremely simplified model for C5−C12 and a detailed mechanism for H2/CO/C1−C4. The model predictions show good agreement with the results from the detailed mechanism. It should be noted that most of the skeletal and reduced mechanisms for heavy n-alkanes include only high-temperature oxidation reactions. To the best of our knowledge, only the reduced mechanism developed by Bikas and Peters21 could well predict the n-decane oxidation at low temperatures and in the negative temperature coefficient (NTC) region. In this paper, based on a decoupling methodology, a new skeletal mechanism was developed to describe the ignition and oxidation of nalkanes from n-octane to n-hexadecane covering both low- and high-temperature regimes.

reactions. The overall reaction pathway for the oxidation of large n-alkanes developed in this study is shown in Figure 1.

Figure 1. Overall reaction pathway diagram describing the oxidation of large n-alkanes from low to high temperatures.

The reactions for Cn−C4 were built up based on the work from Cox and Cole,30 Hu and Keck,31 and Tanaka et al.32 for the oxidation of heavy n-alkanes. The first two important reaction classes to be defined are the initiation reactions and the H-abstraction reactions.18 According the work of Nehse et al.,33 the low-temperature oxidation of aliphatic fuel RH is initiated by the reaction with oxygen (O2) to produce the corresponding alkyl radicals R and HO2 (eq R1). The flow rate analysis shows that the consumption of heavy n-alkanes is essentially due to the reactions of H-abstraction by the free radicals OH (eq R2) and H (eq R3) at relatively high temperatures.21,34 Different alkyl radicals are formed depending on the structure of the heavy n-alkane molecule. On the basis of the assumption that each of the n-alkyl radicals with more than three carbon atoms is in isomeric partial equilibrium,22,27 only one alkyl is included in the model in order to reduce the number of species. For example, the n-dodecyl formed in the reactions R1−R3 includes six isomerides because of the different molecule structure, and only one n-dodecyl was considered in this study following the assumption. The rate constants of reactions R1, R2, and R3 are modified to take account of the influence of the removal of other alkyl radicals.

2. MODEL DEVELOPMENT The skeletal mechanism was built upon a decoupling methodology, which has been introduced in detail in our previous studies.23−25 Only a brief review of the methodology is provided here. In the decoupling methodology, the skeletal mechanism for the oxidation of heavy alkanes is divided into two parts: an extremely simplified model for C2−Cn (n is the number of carbon atom in a fuel molecule) and a detailed mechanism for H2/CO/C1. The reasons for the employment of the detailed H2/CO/C1 mechanism are that the laminar flame speed and extinction strain rate of large n-alkanes are dominated by the reactions involving C0−C1,15,26,27 and most of the heat releases during large hydrocarbon oxidation are from the oxidation of carbon monoxide (CO) to carbon dioxide (CO2).28 Moreover, the emissions of large n-alkane oxidation, such as small hydrocarbons, CO, and CO2 should be described in detail in order to accurately predict the concentrations of related species. Our previous studies indicate23−25,29 that a skeletal mechanism for C2−Cn is capable of reproducing the ignition delay and fuel consumption during the oxidation of heavy alkanes reasonably well. Thus a skeletal C2−Cn was coupled with a detailed H2/CO/C1 mechanism to describe the oxidation of heavy n-alkanes from n-octane to n-hexadecane in this study. Due to the compact size of the skeletal model for C2−Cn and limited species involved in the detailed H2/CO/C1 mechanism, the number of species in the final n-alkane oxidation model could be dramatically reduced. Overall, the skeletal mechanism being constructed based on the decoupling methodology is capable of predicting the ignition delay, heat release rate, the concentrations of major species, laminar flame speed, and extinction strain rate under wide operating conditions with a small number of species and

RH + O2 ⇔ R + HO2

(R1)

RH + OH ⇔ R + H 2O

(R2)

RH + H ⇔ R + H 2

(R3)

At low temperatures, the alkyl radicals react with O2 to produce the alkylperoxy radical (RO2) via reaction R4 or react with O2 by H-atom abstraction to produce fuel olefin and HO2 following reaction R10. In order to keep the compact size of the model, the successive reactions concerned with the fuel olefin are lumped into reaction R11. With the increase in temperature, reaction R4 processes toward the reverse direction, which leads to an inverse temperature dependence of the reaction. R + O2 ⇔ RO2

B

(R4)

R + O2 ⇔ fuel olefin + HO2

(R10)

fuel olefin ⇒ C0 − C3 species

(R11)


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Figure 2. The ignition delay time of the n-alkane/air mixture in a shock tube at φ = 0.5 and various pressures: (a) n-dodecane and (b) n-tetradecane. (Symbols are the experimental data;14,43,44 lines are simulation results of the present model.)

parameters can be summarized into four steps: (1) The reaction rate constants for reactions R1−R12 are first estimated by referencing the values in the corresponding reaction classes from the detailed mechanism.17 (2) Sensitivity analysis is conducted to identify the reactions dominating the ignition delay time, and the rate constants of the identified reactions are modified to fit the experimental data of ignition delay time in the shock tube. (3) The mechanism obtained by step 2 continues to be optimized to match the measured concentrations of major species in the jet-stirred reactor by using path flux analysis. (4) The final mechanism is obtained by repeating steps 2 and 3 until the final mechanism is capable of satisfactorily predicting the ignition delay in the shock tube and the major species concentrations in the jet-stirred reactor simultaneously. Since a detailed H2/CO/C1 mechanism is used in this study, the concentrations of primary small molecules, laminar flame speed, and extinction strain rate can be reproduced reasonably well for the oxidation of heavy n-alkanes without adjusting the kinetic parameters. A more detailed description of the optimization process can be found in ref 25.

The RO2 radicals then undergo isomerization to produce the corresponding alkylhydroperoxy radicals (QOOH) via reaction R5. Subsequently, the QOOH radicals react with O2 to form O2QOOH in a chain-branching step via reaction R6. Furthermore, the O2QOOH radicals form ketohydroperoxide (Cnket) and OH by internal H-atom abstraction isomerization via reaction R7. RO2 ⇔ QOOH

(R5)

QOOH + O2 ⇔ O2 QOOH

(R6)

O2 QOOH ⇔ Cnket + OH

(R7)

The subsequent decomposition of ketohydroperoxide produces C5H11CO, OH, formaldehyde (CH2O), and olefin in reaction R8. The C5H11CO then reacts with O2 to form C3H7, C2H3, CO, and HO2 via reaction R9. Cnket ⇒ C5H11CO + OH + CH 2O + olefin

(R8)

C5H11CO + O2 ⇒ C3H 7 + C2H3 + CO + HO2

(R9)

At high temperatures, the thermal decomposition reactions become important. In order to minimize the size of the model, the pyrolyses of alkyl formed in reactions R1, R2, and R3 are grouped simply into the following lumped reaction R12: R ⇒ C2 − C3 alkyl and olefin

3. MODEL VALIDATIONS A set of comparisons were carried out against different experimental data to validate the performance of the skeletal mechanism. Since the validation results for the n-decane oxidation have been presented in detail in ref 25, only the predictions for the newly published experimental data concerned with the n-decane oxidation are given in this section. All the simulations in this study were performed by the CHEMKIN PRO software.40 3.1. Validation of Ignition Delay of n-Alkane/Air Mixture in Shock Tube. The ignition properties of fuel are important in combustion configurations involving low temperature combustion (LTC), especially for advanced compression ignition engines, in which the ignition timing determines the engine combustion and emission characteristics.41,42 Thus, the ignition delay time was first used to validate the performance of the mechanism. In recent decades, many researchers have studied the ignition delay of large n-alkanes behind the reflected shock wave over low to high temperatures, pressures (p) up to 80 atm, and equivalence ratios (φ) from lean to rich mixture. Shen et al.14 studied the ignition delay of n-heptane, n-decane, n-dodecane,

(R12)

Furthermore, a skeletal C2−C3 mechanism from Patel et al.35 is chosen as the transition between the large molecules and the H2/CO/C1 base model because of its compact size and reliable performance.29,36 The detailed H2/CO/C1 mechanism is built upon the detailed methanol oxidation mechanism which was developed by Li et al.37 and updated by Klippenstein et al.38 Finally, the whole skeletal mechanism is completed including 36 species and 128 reactions for each n-alkane from n-octane to n-hexadecane. The thermal and transport properties for the species with a carbon atom number more than three are taken from the database of Lawrence Livermore National Laboratory (LLNL),17,39 while the corresponding properties for the H2/ CO/C1−C3 species are determined on the basis of the work of Li et al.37 and Patel et al.35 After establishment of the pathway of the skeletal mechanism, estimation and optimization of the kinetic parameters are needed to improve the performance of the mechanism. The major optimization process of the kinetic C


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Figure 3. The ignition delay time of the n-alkane/air mixture in a shock tube at φ = 1.0 and various pressures: (a) n-decane, (b) n-dodecane, (c) ntetradecane, and (d) n-hexadecane. (Symbols are experimental data;14,43−47 lines are simulation results of the present model.)

Figure 4. Chemical species concentrations in the shock tube for n-decane diluted in argon at (a) 103.8 ppm n-decane, φ = 0.57, p = 51.8−67.4 atm, and τ = 1.52−1.90 ms and (b) 95 ppm n-decane, φ = 1.96, p = 54.9−67.9 atm, and τ = 1.28−1.88 ms. (Symbols are experimental data from Malewicki and Brezinsky;48 lines are simulation results of the present model.)

and n-tetradecane at φ = 0.25, 0.5, and 1.0 for 9−58 atm and 786−1396 K in a heated shock tube. Vasu et al.43 measured the ignition delay time of n-dodecane/air using a heated, highpressure shock tube at temperatures (T) of 727−1422 K, pressures of 15−34 atm, and equivalence ratios of 0.5 and 1.0. Haylett et al.44 used an aerosol shock tube to measure the ignition delay of n-decane and n-dodecane at different

equivalence ratios and low pressures. The ignition delay of ndecane/air was also investigated by Pfahl et al., 45 Zhukov et al., 46 etc. at pressures of 8−80 atm, equivalence ratios of 0.5−2, and temperatures of 650−1500 K. However, for n-hexadecane, only one series of experiments was carried out by Assad et al.47 at high temperatures and stoichiometric ratios. D


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Figure 5. Chemical species concentrations in the shock tube for n-dodecane diluted in argon at (a) 68.0 ppm n-dodecane, φ = 0.46, p = 20.0−32.4 atm, and τ = 1.46−3.47 ms and (b) 75.9 ppm n-dodecane, φ = 2.05, p = 43.0−61.2 atm, and τ = 1.18−2.47 ms. (Symbols are experimental data from Malewicki and Brezinsky;48 lines are simulation results of the present model.)

Figure 6. Chemical species concentrations in JSR for n-alkane diluted in nitrogen at a pressure of 1 atm and a residence time of 70 ms for φ = 0.5: (a) 1000 ppm n-nonane and (b) 300 ppm hexadecane. (Symbols are experimental data;9,13 lines are simulation results of the present model.)

for n-decane and n-dodecane oxidation are shown in Figures 4 and 5, respectively. It can be seen that similar evolutions of species concentrations are exhibited for n-decane and n-dodecane in both the experiment and simulation. Overall, the agreement between the measurement and the prediction on species concentrations is satisfactory, although the decays of fuels and oxygen are underestimated at temperatures above 1100 and 1200 K, respectively. By using the analysis of rate of production for oxygen, it is revealed that the reactions related to small molecules of H2/CO/C1−C3 significantly affect the consumption of oxygen. Thus, further optimization of the C2−C3 submechanism and the detailed H2/CO/C1 mechanism could improve the accuracy for the predictions of oxygen evolution. As shown in Figures 4a and 5a, CO begins to form at 1200 K and reaches the peak at about 1250 K for the fuel-lean mixture. The behavior of CO is well reproduced by the model, while the predicted peak shifts toward higher temperature than that of the measurement. For the fuel-rich mixture, the concentration of CO is accurately predicted at temperatures below 1400 K but is underestimated at higher temperatures. The final production, CO2, is also well estimated for the fuel-rich mixture and is slightly underestimated for the fuel-lean mixture for both fuels. The validation of acetylene (C2H2) concentration is considered in this study, because C2H2 is recognized as an important

The comparisons of ignition delay of a large n-alkane/air mixture between the simulations using the skeletal mechanism and the experimental results at various pressures for φ = 0.5 and 1 are shown in Figures 2 and 3, respectively. It can be seen that the model predictions show good agreement with the measured data, except for slightly underestimating the experimental results of Shen et al.14 at temperatures below 1000 K for n-dodecane and overpredicting the n-tetradecane results at low pressures. The deviation could be further improved by optimizing the reaction rate constants in reactions R1, R2, and R3 if enough experimental data are available. An NTC region can be seen for the temperatures from about 700 to 950 K, and it occurs more easily toward higher pressures. The model calculations show the same trend with the experimental data. Meanwhile, the decrease in the ignition delay with the increased pressure is also well reproduced by the model within the investigated temperature range for all the nalkanes. 3.2. Validation of Species Concentration in a Shock Tube. A set of high-pressure shock tube experiments were performed by Malewicki and Brezinsky48 for the pyrolysis and oxidation of n-decane and n-dodecane. The concentrations of stable species were measured by gas chromatography and mass spectroscopy at a reaction time (τ) of 1.15−3.47 ms. The comparisons between the experimental and simulation results E


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Figure 7. Chemical species concentrations in JSR for n-alkane diluted in nitrogen at a pressure of 1 atm and a residence time of 70 ms for φ = 1.0: (a) 1000 ppm n-nonane and (b) 300 ppm hexadecane. (Symbols are experimental data;9,13 lines are simulation results of the present model.)

precursor for soot formation. In order to develop a reliable soot model, it is necessary for the fuel chemical kinetic model to provide accurate prediction on C2H2 concentration. As can be seen from Figures 4 and 5, both the experiment and simulation indicate that the C2H2 concentration rises rapidly with the increase of equivalence ratio. However, the peak concentration of C2H2 is slightly underestimated by the model. It is worth noting that Malewicki and Brezinsky48 also found that the deviations between the measurement and the prediction from detailed chemical models on the species concentrations are evident. 3.3. Validation of Species Concentration in Jet-Stirred Reactor (JSR). Dagaut and collaborators have studied the oxidation of large n-alkanes in a jet-stirred reactor (JSR) from low to high temperaturess at 1 and 10 atm.9,10,12,13 The concentrations of reactant, intermediate, and product species were measured, which provides a set of valuable data to validate the performance of large n-alkanes’ oxidation mechanism. 3.3.1. High-Temperature Oxidation of n-Alkane in JetStirred Reactor. Dagaut et al. investigated the oxidation of nnonane,9 n-decane,10 and n-hexadecane13 in a jet-stirred reactor at atmospheric pressure over the high temperature range of 900−1300 K and equivalence ratios from 0.5 to 2 with a constant residence time of 70 ms. They also attempted to develop a detailed mechanism to simulate the experimental data. The detailed mechanism satisfactorily reproduces the measured concentrations for most species except for the underestimation of the consumption of fuel at temperatures above 1000 K. The discrepancy is improved toward the fuelrich mixture.10,13 The comparisons between the simulated and experimental results for n-nonane and n-hexadecane at equivalence ratios of 0.5, 1.0, 1.5, and 2.0 are shown in Figure 6, 7, 8, and 9, respectively. It can be seen that the model accurately reproduces the oxygen consumption at all equivalence ratios. For the fuel consumption, the model well predicts the conversion of n-nonane at φ = 1, but a slight deviation can be observed for temperatures above 1050 K at φ = 0.5 in Figure 6a and temperatures above 1150 K at φ = 2.0 in Figure 9. Moreover, the reactivity of n-hexadecane is underestimated for temperatures above 1050 K in all cases. The model prediction also shows satisfactory agreement with experimental results for the formation of hydrogen (H2), CO, methane (CH4), and propylene (C3H6). However, since an extremely simplified C2−

Figure 8. Chemical species concentrations in JSR for n-alkane diluted in nitrogen at a pressure of 1 atm and a residence time of 70 ms for φ = 1.5 and 300 ppm hexadecane. (Symbols are experimental data;13 lines simulation results of the present model.)

Figure 9. Chemical species concentrations in JSR for n-alkane diluted in nitrogen at a pressure of 1 atm and a residence time of 70 ms for φ = 2.0 and 1000 ppm n-nonane. (Symbols are experimental data;9 lines are simulation results of the present model.)

C3 mechanism was employed in the model, the concentration of ethylene (C2H4) is underestimated at temperatures higher than 1100 K for all the tested equivalence ratios. Moreover, the F


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Figure 10. Chemical species concentrations in JSR for 0.1% n-alkane diluted in nitrogen at a pressure of 10 atm, φ = 0.5, and a residence time of 1.0 s: (a) n-nonane, (b) n-undecane, and (c) n-dodecane. (Symbols are experimental data;9,12 lines are simulation results of the present model.)

final production of water (H2O) is reasonable well reproduced by the model. For CO2, its concentration is accurately reproduced in fuel-rich mixtures in Figure 9 but is underestimated at φ = 0.5 and 1.0 in Figures 6 and 7, respectively. The discrepancies between the predictions and measurements on the concentrations of small hydrocarbons at high temperatures are primarily caused by the deficiency in the skeletal C2−C3 mechanism and the detailed H2/CO/C1 mechanism. Thus, further optimization of the present mechanism still needs to be conducted in the next work, especially for the H2/CO/C1−C3 submechanism, which plays a crucial role in the predictions on the evolution histories of small hydrocarbons. 3.3.2. Low- to High-Temperature Oxidation of n-Alkane in Jet-Stirred Reactor. The oxidation of n-nonane,9 n-decane,10 nundecane and n-dodecane12 in a high-pressure jet-stirred reactor were also investigated experimentally by Dagaut et al. The experiments were carried out for a wide range of temperatures covering the entire NTC regime and the beginning of the high temperature regime from 550 to 1150 K at a pressure of 10 atm; equivalence ratios of 0.5, 1.0, and 2.0; and a residence time of 1 s with an initial concentration of 0.01% n-alkane diluting in nitrogen. Figures 10−12 show the comparisons between the experimentally derived and numerically predicted profiles of reactants, intermediates and final products at φ = 0.5, 1.0 and 2.0, respectively. In general, the model could well reproduce the experimental data within the investigated conditions. The

consumption of O2 is accurately predicted by the model in all cases, except for overpredicting its consumption for n-undecane oxidation at φ = 2.0 in Figure 12b. Between 600 and 750 K, an NTC behavior is observed experimentally, and it occurs more evidently toward a fuel-rich mixture, which is accurately reproduced by the model. The profile of fuel concentration shows a lesser NTC behavior at a fuel-lean mixture than that at a fuel-rich mixture, which is also well simulated by the model. However, the temperature for the initial NTC regime is slightly underestimated by the skeletal mechanism, and the deviation is improved toward a fuel-rich mixture. The concentration of CO is well estimated at high temperatures at φ = 0.5 and 1.0 but is overpredicted at φ = 2.0. At low temperatures, the comparisons between the experimental data and calculated results of CO concentration for various n-alkanes show different trends. For n-nonane, the CO concentration is accurately reproduced at φ = 1.0 in Figure 11a. However, the model underestimates the CO concentration at φ = 0.5 in Figure 10a and overpredicts the experimental results at φ = 2.0 in Figure 12a. For n-undecane and ndodecane, the CO concentration at low temperatures is underestimated at φ = 0.5 and 1.0 and is well predicted at φ = 2.0. The final products, CO2 and H2O, are well reproduced by the model at high temperatures, whereas they are underestimated at low temperatures as a consequence of lower conversion levels of fuel predicted by the model. The underestimation of CO2 concentration in the low temperature regime was also reported by Westbrook et al.,17 Mzé-Ahmed et G


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al.,12 and Mehl et al.49 One of the possible reasons suggested by Mehl et al.49 is that the partially oxidized products are not fully described by their model, and the same condition holds for the present model. For C2H2, the model gives satisfactory predictions. The rapid increase in the amount of C2H2 with the increased equivalence ratio indicates the potential of soot formation under the fuel-rich mixture conditions. Recently, Biet et al.50 investigated the oxidation of n-decane and a n-decane/n-hexadecane blend in a jet-stirred reactor from low to intermediate temperatures (550−1100 K) including the NTC zone at atmospheric pressure for a stoichiometric mixture with a residence time of 1.5 s. The comparisons of the model predictions and experimental data in reactants, major intermediates, and final products for n-decane/n-hexadecane blend oxidation are shown in Figure 13. The fuel, O2, and CO profiles show a strong NTC behavior, while fewer NTC effects are observed for CO2 and CH4, which is satisfactorily reproduced by the model. The concentrations of O2, n-decane, and n-hexadecane are also well estimated by the model within the investigated temperature range in Figure 13. As a major paraffinic intermediate of n-decane oxidation in the hightemperature regime,51 CH4 is satisfactorily predicted by the model except for slight overestimation of CH4 concentration at temperatures from 900 to 1000 K. A very small amount of CH4 in the low-temperature regime, following a fast increase above 850 K and reaching the peak at 1000 K, is exhibited both by the experimental data and by the prediction. For CO, the NTC behavior is well reproduced, whereas the first peak concen-

tration is slightly overpredicted by the model. However, at high temperatures, the model presents earlier consumption of CO, which leads to more CO2 production. 3.4. Validation of Species Concentration in Flow Reactor. Dryer and Brezinsky52 studied the oxidation of n-octane in an adiabatic turbulent plug-flow reactor at atmospheric pressure with an initial temperature of 1080 K. Figure 14 presents the comparison between the experimental and simulation results of n-octane oxidation in the flow reactor. The simulations presented in this section were performed by using the PREMIX module in the CHEMKIN PRO package with the experimental temperature profile as the input data. It can be seen that the predictions on n-octane and C3H6 match the experimental results reasonably well. Meanwhile, the model accurately reproduces the concentration of CO at times before 100 ms but cannot predict the subsequent consumption of CO. For C2H2, the profile is well reproduced, whereas the peak is overpredicted by the model as shown in Figure 14. In order to investigate the autoignition and combustion behavior of the full boiling range hydrocarbon fuels, Agosta et al.4 studied the oxidation chemistry of neat distillate hydrocarbons and their mixtures in a Drexel pressurized flow reactor over a range of pressure up to 12 atm and temperatures in the interval of 600−900 K. In the experiment, CO was measured to obtain a reactivity map over 600−900 K. Figure 15 shows the comparison between the experimental data and simulation results of CO concentration at φ = 0.2, 0.25, and 0.3 for ndodecane oxidation. It can be seen that CO concentration H


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Figure 14. Chemical species concentration in a flow reactor for an noctane/O2/N2 66/1.2/0.095 mixture at 1 atm, φ = 1.0, and T = 1080 K. Model computations are shifted by −30.5 ms. (Symbols are experimental data;52 lines are simulation results of the present model.)

Figure 13. Chemical species concentrations in JSR for stoichiometric mixtures containing 0.148% n-decane and 0.052% n-hexadecane diluted in helium at a pressure of 1 atm and a residence time of 1.5 s. (Symbols are experimental data from Biet et al.;50 lines are simulation results of the present model.)

prediction of CO concentration can be seen at φ = 0.2. The overprediction behavior of the n-dodecane model is also exhibited by the mechanisms of Agosta et al.4 and Ranzi et al.18 3.5. Validation of Temperature and Species Concentration in Counterflow Flame. Sarathy et al.53 studied the noctane combustion in a counterflow flame. The flame was stabilized between two identical flat flame burners spaced 2 cm apart. The fuel mixture of 98.14% N2 and 1.86% fuel in mole

increases with the increase of temperature and reaches the peak at about 700 K. Then CO decreases as temperature continues to increase. The temperature range for the NTC regime can be well identified by the CO concentration. The model prediction shows the same behavior with the experiment. For φ = 0.25 and 0.3, the model accurately predicts the location and the maximum value of CO concentration. Only a slight overI


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diffusivity, exothermicity, and reactivity, and thereby is often used to validate the performance of chemical kinetic mechanisms. In this section, the model was validated with available experimental data on the laminar flame speed of nalkane/air blends. The predictions were obtained using the PREMIX module in the CHEMKIN PRO software package with an average mixture diffusion coefficient. Kumar and Sung26 measured the laminar flame speeds of ndecane/air and n-dodecane/air mixtures in a counterflow twinflame configuration at atmospheric pressure with the unburned temperature (Tu) ranging from 360 to 470 K and the equivalence ratio ranging from 0.7 to 1.4. The laminar flame speeds of premixed C5−C12 n-alkane were measured by Ji et al.15 in a counterflow configuration. The experiment of Ji et al.15 was carried out at the preheated fuel/air temperature of 353 K for C5−C8 and 403 K for C9−C12 under atmospheric pressure and equivalence ratios from 0.7 to 1.5. Kelley et al.54 further determined the laminar flame speeds of C5−C8 n-alkane/air mixtures at elevated pressures and in an extensive range of equivalence ratios by spark-ignited, expanding flame in a constant-pressure chamber. Recently, Hui and Sung55 measured the laminar flame speeds of the mixtures of air with n-decane and n-dodecane in a counterflow configuration at the pressures of 1−3 atm and an elevated unburned mixture temperature of 400 K in various equivalence ratios. Figure 17a−c presents the comparisons of the laminar flame speeds of n-octane/air, n-decane/air, and n-dodecane/air mixtures between the simulation results and experimental data at various pressures. The predicted and measured laminar flame speeds show the same trend for all the tested fuels. It can be seen from Figure 17 that the laminar flame speed increases with the increase of equivalence ratio and reaches the peak value at an equivalence ratio of 1.1. Then the flame speed decreases with the increase of equivalence ratio as the equivalence ratio is higher than 1.1. The behavior of flame speed with the variation of the equivalence ratio is accurately captured by the model. The increase of pressure resulting in the decrease of flame speed is also well reproduced by the model in Figure 17. However, small discrepancies between the prediction and measurement still remain for the stoichiometric and fuelrich mixture, and the discrepancies are improved toward higher pressures. The comparison between the predictions using the present model and the experimental results on the laminar flame speed of n-dodecane/air mixture at atmospheric pressure and various temperatures is shown in Figure 18. It can be seen that good agreement between the prediction and measurement on laminar flame speed is obtained under the tested equivalence ratio range. Moreover, the increase of laminar flame speed with the increased temperature is also well reproduced by the model as shown in Figure 18. 3.7. Validation of Extinction Strain Rate. Extinction strain rate characterizes the interaction between a characteristic flame/flow time and a chemical time26 and is often used to assess the performance of chemical mechanisms. This section focuses on the evaluation of the mechanism capability in predicting the extinction strain rate at various equivalence ratios. A set of simulations was carried out by using the Flame Extinction Simulator in the CHEMKIN PRO software package. For all the simulations, the Soret thermal diffusion effect and multicomponent transport were considered. Kumar and Sung26 measured the extinction strain rates of ndecane/air and n-dodecane/air mixtures in a counterflow twin-

Figure 15. CO concentrations in a flow reactor for the oxidation of ndodecane at a pressure of 8 atm and a residence time of 120 ms. (Symbols are experimental data from Agosta et al.;4 lines simulation results of the present model.)

fractions was injected from the bottom port with a mass flow rate of 0.015 g/cm2·s at 350 K, and the oxidizer mixture of 42.25% O2 and 57.75% N2 in mole fractions was injected from the top port with a mass flow rate of 0.014 g/cm2·s at 420 K. The simulation presented in this section was performed using the OPPDIF module in the CHEMKIN PRO package with consideration of the multicomponent transport coefficient formulations and the Soret effect. In the simulation, the experimental data were shifted by 0.5 mm away from the fuel port to account for a positioning uncertainty in the experiment.53 Figure 16 presents the comparisons between the

Figure 16. Experimental (symbols)53 and computed profiles (lines) obtained from the oxidation of n-octane in an atmospheric opposedflow flame with 1.86% n-octane and 42% O2.

predictions and experimental data for the n-octane flame. It can be seen that the model reproduces the profiles of temperature and species well with only slight discrepancies against the experimental data on the distribution of temperature and locations of species peak. The peaks of CO2 and C2H2 are well predicted, whereas the CO peak is underestimated by a factor of 1.3. The maximum temperature is also underestimated by about 50 K relative to the measured value. 3.6. Validation of Laminar Flame Speed. The laminar flame speed is a rigorously defined fundamental property of combustible mixtures, embodying the net effects of its J


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Figure 17. Laminar flame speeds of fuel/air mixture as a function of equivalence ratio at various pressures for (a) n-octane, Tu = 353 K; (b) n-decane, Tu = 400 K; and (c) n-dodecane Tu = 400 K. (Symbols are experimental data;15,54,55 and lines are simulation results of the present model.)

in counterflow against a fuel/air jet. The preheated fuel/air temperature was chosen to be 353 K for C5−C8 n-alkanes and 403 K for C9−C12 n-alkanes. The comparisons between the simulation results and experimental data on extinction strain rate for n-octane, nnonane and n-dodecane are shown in Figure 19. It can be seen that the peak of extinction strain rate locates at φ ≈ 1.2 for the experiment of Ji et al.15 and φ ≈ 1.3 for the experiment of Kumar and Sung,26 which shows a rich-shift trend realtive to the peak of laminar flame speed shown in Figures 17 and 18. The rich-shift trend is the consequence of the combined effects of positive stretch and a subunity Lewis number for the rich mixture,15,26 which is well captured by the model. For the experiment of Ji et al.,15 the model well predicts the extinction strain rate for stoichiometric and fuel-rich mixtures and slightly underestimates the experimental data for the fuel-lean mixture as shown in Figure 19. However, for the experiment of Kumar and Sung,26 the predictions show a different trend, in which the extinction strain rate at φ < 1.1 is well reproduced, while it is overpredicted at φ > 1.1. Overall, the model accurately captures the trend of the extinction strain rate for all the three n-alkanes as shown in Figure 19. However, some discrepancies still exist between the model prediction and experimental data. The deficiencies in the chemical model and the diffusion coefficients of species and the assumption of quasi-one-dimensional of the counterflow flame may be responsible for the discrepancies.15,26,56

Figure 18. Laminar flame speeds of an n-dodecane/air mixture as a function of equivalence ratio at 1 atm and various temperatures. (Symbols are experimental data;15,26 and lines are simulation results of the present model.)

flame configuration over a wide range of equivalence ratio at a preheated fuel/air temperature of 400 K and atmospheric pressure. In the experiment, the “air” is a mixture of oxygen and nitrogen in the molar ratio of 1:5.25. Moreover, the extinction strain rates of premixed C5−C12 n-alkane were experimentally measured by Ji et al.15 with a counterflow configuration at equivalence ratios from 0.7 to 1.5 under atmospheric pressure. In their experiment, a nitrogen jet at ambient temperature was K


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Figure 19. Extinction strain rate of fuel/air mixture as a function of equivalence ratio at various unburned mixture temperatures: (a) n-octane, (b) nnonane, and (c) n-dodecane. (Symbols are experimental data;15,26 and lines are simulation results of the present model.)

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4. CONCLUSION

ASSOCIATED CONTENT

S Supporting Information *

A series of skeletal mechanisms were developed to describe the oxidation of n-alkanes from n-octane to n-hexadecane based on the decoupling methodology in this study. In the decoupling methodology, an extremely simplified model for species with a carbon atom number larger than two was used to simulate the ignition characteristics of heavy hydrocarbon, while a detailed mechanism for H2/CO/C1 was considered in order to accurately predict the concentrations of small molecules, laminar flame speed, and extinction strain rate. The skeletal mechanism includes 36 species and 128 reactions for each nalkane and was validated against the experimental data in a shock tube, jet-stirred reactor, variable pressure flow reactor, and counterflow flame under wide ranges of pressure (up to 80 atm), equivalence ratio (0.5−2.0), and temperature (including low-temperature, NTC, and high-temperature regimes). The results indicate that both the ignition delay and the concentrations of major species were well predicted by the model. Moreover, the experimental data on the laminar flame speed and extinction strain rate in premixed laminar flame and counterflow flame were also used to validate the mechanism, and the model simulations show good agreement with the measurements. Thus, the potential of the decoupling methodology for the development of the skeletal oxidation mechanism for heavy n-alkanes is well demonstrated.

Model comparisons, sensitivity analysis and flow rate analysis, and the skeletal mechanism in CHEMKIN format (PDF). A ZIP file containing chem.inp, therm.dat, and tran.dat. This information is available free of charge via the Internet at http:// pubs.acs.org/.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grant No. 51176020, 51176021) and National Basic Research Project of China (Grant No. 2013CB228400).

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REFERENCES

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Application of a Decoupling Methodology for Development of Skeletal

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