Enhancement on a Skeletal Kinetic Model for Primary Reference Fuel

Article pubs.acs.org/EF

Enhancement on a Skeletal Kinetic Model for Primary Reference Fuel Oxidation by Using a Semidecoupling Methodology Yao-Dong Liu, Ming Jia, Mao-Zhao Xie,* and Bin Pang School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, China ABSTRACT: A semidecoupling methodology for developing skeletal chemical kinetic models is presented and applied to construct an enhanced skeletal model for PRF (primary reference fuel) oxidation, which consists of 41 species and 124 reactions. The basic idea and the semidecoupling methodology are to consider the oxidation mechanism of alkane as two parts: a comprehensive part to describe detailed reaction processes of C0−C1 radicals and molecules as the ‘core’ and a skeletal part that couples the ‘core’ to control the ignition characteristics. Accounting for the major weakness in the existing skeletal models for PRF oxidation, the enhancement on the new skeletal model mainly focuses on the laminar flame speed and important species evolution while maintaining the precise ignition delay prediction of the previous models. The new PRF skeletal model is validated against various experimental data including shock tube, jet-stirred reactor, flow reactor, premixed laminar flame speed, and internal combustion engines over a wide range of temperatures, pressures, and equivalence ratios. The results show good agreement with the experimental data, indicating that the semidecoupling methodology and the new skeletal model are promising for various reactors and engine applications incorporated with a multidimensional computational fluid dynamics (CFD) model. mechanisms; Tsurushima5 developed a very simple, and thus, the most compact, PRF kinetic model for HCCI combustion. It should be noted that nearly all of the existing skeletal models mainly focus on the ignition characteristics in shock tube and HCCI engine for validation. However, there are more concerning issues in practical combustion systems, such as flame propagating in Spark Ignition (SI) engine and dilute atmosphere in EGR. These existing skeletal models are not comprehensive ones, so they may fail to capture some important information during the combustion process, as mentioned; on the other hand, reduced (or so-called “semi-detailed”) models developed by using reliable algorithms6,7 still contain a relatively large number of species (usually more than 100) and further reduction will reach the limit of the method.8 In this view, the basic objective of this paper is to propose a methodology of developing a skeletal model for PRF or other fuels that have negative temperature coefficient (NTC) behavior by employing a new practical approach, called as “semi-decoupling”, by keeping the number of species as few as possible while maintaining its good performance in various reactors and under wide operating conditions. In this way, the model could be used for engineering applications, coupled with multidimensional CFD codes. Based on this idea, in a previous study,9 a skeletal model for iso-octane oxidation has been developed and good performance was demonstrated. In this paper, the model is further expanded to PRF and extensively validated against various experimental data. It should be noted that although PRF surrogate fuel is not a realistic way to mimic combustion of real fuels in modern engine settings, it has been extensively used in the engine research both theoretically and experimentally. Moreover, the enhancement on the PRF skeletal model presented in this

1. INTRODUCTION In recent decades, various advanced combustion modes for internal combustion engines have been designed and extensively investigated, such like Homogeneous Charge Compression Ignition (HCCI), Premixed Charge Compression Ignition (PCCI), Reactivity Controlled Compression Ignition (RCCI), and Gasoline Direct Injection (GDI), which cover a wide range of operation condition. In this respect, as an indispensable prerequisite for studying autoignition, flame propagation, and combustion process in engines, investigation on chemical kinetics mechanisms of hydrocarbons and diverse surrogate fuels has become very active. However, it is still impossible to apply a detailed chemical kinetic mechanism directly to the engine combustion simulation using multidimensional computational fluid dynamics (CFD) codes because the requested computer resource and cost is too high to be acceptable presently. Therefore, it is very necessary to develop mechanisms with a suitable size that can properly describe combustion characteristics in these new concept engines as much as possible. It is well-known that primary reference fuel (PRF), which is obtained from mixture of n-heptane and iso-octane and has an octane numbers from 0 to 100, is widely used as a representative or model fuel of actual fuels. Efforts have been made to develop skeletal chemical kinetic models for the oxidation chemistry of PRF.1−5 For example, Tanaka et al.1 developed a skeletal kinetic model of PRF for HCCI combustion in a rapid compression machine. This model omits intermediate reactions such as olefins and aldehydes, which leads to higher heat release and causes earlier ignition in the shock tube. To solve this problem, Jia and Xie3 developed a practical skeletal model for iso-octane, which performs well in shock tube, rapid compression machine, jet-stirred reactor, and HCCI engine; Ra and Reitz4 used a combination of the chemical lumping, graphical reaction flow analysis, and elimination methods to generate a reduced PRF model from more comprehensive reaction © 2012 American Chemical Society

Received: July 25, 2012 Revised: September 25, 2012 Published: September 26, 2012 7069

dx.doi.org/10.1021/ef301242b | Energy Fuels 2012, 26, 7069−7083

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Figure 1. Comparison of experimental18−21 and modeling results for laminar flame speed. Ti = 298 K and P i = 0.1 MPa.

The target of this study is a skeletal model for engineering application. According to the suggestion by Farrell et al,15 there are two different types of targets for the development of kinetic mechanisms: development targets and application targets. Development target refers to kinetic and fluid dynamic processes that are important for validating mechanism and that are typically evaluated in devices with better controlled conditions than those in real engines. Thus, in this study, we take autoignition delay (in shock tube), relevant species concentrations (fuel, CO, and CO2 in jet-stirred reactor and flow reactor) and laminar flame speed as our development target. Application target refers to operating conditions relevant to the ignition and combustion in real engines. In this work, we chose a wide range of operating conditions (650−1250 K, 0.1−4 MPa, and equivalence ratio of 0.5−2) as the application target. With these considerations for skeletal model targets, before introducing our model developing methodology, simulation results of four skeletal models2−5 and a detailed mechanism16,17 of PRF are compared against available data from laminar flame speed experiment (Figure 1) and jet-stirred reactor (Figure 2). It can be seen from Figure 1 that all of the four skeletal models fail to predict laminar flame speed at the atmospheric pressure and an initial temperature of 298 K. According to refs 18, 21, and 23, most of the high sensitivity reactions involved in the laminar flame of PRF are related to small radicals and molecules. Hence, during the combustion process of PRF, the key characteristics of laminar flame speed should be mainly dominated by the small radical and molecule reactions rather than by those connected with low temperature oxidation and large molecule decomposition. Therefore, the main reason for the failure in predicting laminar flame speed should be that, for all the four skeletal models, the reduction process was carried out globally from small to large molecules and from low to high temperature reactions, which may destroy the highly coupled characteristics among these reactions. Figure 2 shows that the model of Patel2 and Ra4 fails to predict the evolution of CO and CO2, while Jia model3 exhibits a sudden decrease on isooctane concentration at the low temperature around 650 K mainly because of the decomposition pathways of ketohydroperoxide. Among the three skeletal models, the Tsurushima model5 performs better than the other two and shows a similar trend in the low and intermediate temperature range with the detailed mechanism by Curran et al.,16,17 which indicates that the skeletal reaction pathways of low temperature and large

paper is an exploration in the developing the semidecoupling methodology. In view of the good performance achieved, model development for gasoline surrogate fuel including isooctane, n-heptane, and toluene is being carried out and will be reported in the future. In the following, first, an analysis and comparison between several existing skeletal models will be presented to introduce the basic idea of the semidecoupling methodology. Then, the new skeletal model for PRF oxidation is presented, and detailed results from the validation of the model against experimental data including various reactors and internal combustion engines are reported. Finally, some important findings and observations of this work are summarized in the conclusion.

2. MODEL DEVELOPING METHODOLOGY 2.1. Analysis on Existing Skeletal Models. It is obvious that, to develop a predictive and reliable kinetic mechanism, we have to validate it with as much experimental data as possible. For the validation, we consider two combustion parameters as particularly relevant, which have not received sufficient attention in previous skeletal models, namely, laminar flame speed and concentrations of some critical species. As a function of its thermodynamic states of temperature, pressure, and composition, the laminar flame speed of a combustible mixture is a rigorously defined fundamental property of this mixture, embodying and thereby manifesting the net effects of its diffusivity, exothermicity, and reactivity. Consequently, it is also the elemental unit in the description of complex combustion phenomena such as the turbulent flame structure and speed.10 Hence, in most combustion processes, combustion behavior is closely linked to the laminar flame speed,11,12 especially for SI engines. Knowledge of this fundamental parameter can provide a better understanding of combustion characteristics. For SI engines, a thorough understanding of the transition from laminar to turbulent flame kernel and to turbulent flame propagation is essential for designing more efficient engines. Even for turbulent combustion, the laminar flame speed is often a critical parameter, as for determining the propagation of the flame front surface in the G-equation-based turbulent combustion model.13,14 To various reactors, the concentration evolutions of fuel, CO and CO2, which reveal the consumption rate of fuel, heat release rate, and amounts of final products, are of great importance for the study on combustion mechanisms. 7070


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Figure 2. Comparison of experimental22 and modeling results for species concentration in a jet-stirred reactor. φ = 1.0 and P i = 1 MPa, resident time is 1 s, 0.1% fuel.

range of ignition of these two fuels, in which small radical and molecules still play an important role, we treat the relationship between the kinetics of smaller molecular fragments and the low-temperature chemistry in a ‘semidecoupling’ manner. That is to say, the mechanism for flame propagation is seen as dominated by the small radicals and molecules and decoupled from the low-temperature chemistry, while the ignition characteristics depend on both the smaller molecular fragments and low-temperature chemistry in coupling. Another important issue is how to select the basic species for the “core” of the new mechanism. Ranzi et al.10 collected, consolidated, and reviewed a vast amount of experimental data on the laminar flame speeds of hydrocarbon and oxygenated fuels recently. They concluded that small radical and molecular species created from high temperature decomposition processes are active species in all cases, and hydrogen radical is the most effective flame speed enhancer because of its branching activation, while methyl radical significantly reduces the flame speed,

molecule decomposition in the Tsurushima model are relatively reliable. 2.2. Semidecoupling Methodology. As aforementioned, to enhance the performance of existing skeletal models, one of the key issues we care about is the laminar flame speed. Besides our analysis of Figure 1, You et al.24 also pointed out that the underlying heat release rate in a laminar premixed flame is sensitive neither to low-temperature chemistry nor to the fuel cracking rate. They revealed that, in laminar premixed flames and for induction period chemistry above 1100 K, the kinetics of fuel cracking to form smaller molecular fragments (H2, CH4, C2H4, and C3H6) is fast and may be decoupled from the oxidation kinetics of these fragments. Moreover, the same conclusion may be drawn by examining the results of sensitivity analysis over a broad range of equivalence ratio for n-dodecane and other straight-chain alkanes. In this paper, we try to extend this conclusion to n-heptane and iso-octane oxidation at temperatures below 1100 K. Considering the low temperature 7071


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especially by removing H atom from the system through the recombination reaction to form CH4. Based on the observations and suggestions of Ranzi et al., in this paper, differing from other skeletal models that take only H2/CO reactions as the base, we add C1 reactions supplementally into the ‘core’, because C1 molecules such as CH2O and CH4 are the basis and representative of hydrocarbon fuels. Therefore, according to this analysis, the semidecoupling methodology employed here considers the combustion process of alkane as two parts: one is ignition, which is largely dependent on the specific fuel, and the other is flame propagating after ignition, which is mainly controlled by reactions involving small radicals and molecules of C0−C1 and is less dependent on the specific fuel. Based on this idea, for developing a skeletal model, a complete fuel oxidation mechanism can be represented by two submechanisms, that is, a general, or somewhat “comprehensive” C0−C1 subset, which is the key part for describing laminar flame propagation, and a skeletal C2−C3, as well as some larger molecule subset, which, in coupling with the C0−C1 one, describes ignition and evolution of important species (such as fuel, CO and CO2 etc.). In other words, the former “comprehensive” part describes the detailed reaction process of small radicals and molecules and acts as a ‘core’, while the latter skeletal one couples the ‘core’ to control the ignition characteristics including low temperature oxidation, large molecule decomposition and C2−C3 transition reactions. Thus, differing from the global reduction method employed by most existing skeletal models, we only reduce large molecule mechanisms, while keep mechanisms involving small radicals and molecules retaining their original and general form, because these species are nearly indispensable. Therefore, this semidecoupling methodology can substantially reduce the number of species involved in the model while keep most essential information of the combustion process. Another advantage of this practical methodology is that, in developing a skeletal model for fuel blends, instead of a complicated rebuilding procedure, one only needs to integrate the large molecule subset of the corresponding fuel into the “comprehensive” C0−C1 core to control the ignition characteristics. 2.3. Model Description. The skeletal model to be developed starts from small radicals and molecules (C0−C1), then, larger molecules are added into it gradually. Klippenstein et al.25 improved the mechanism of Li et al.26 for the ignition of methanol at high pressure by using the ab initio transition state theory. This mechanism is a comprehensive one including CO, CH2O, and CH3OH oxidation, which has a suitable size and has already been validated against experimental data from various reactors under wide operating conditions. Therefore, we choose the C0−C1 subset from it as the ‘core’ for the new skeletal model, which includes 18 species as follows: O2, N2, CO2, H2O, CO, H2, OH, H2O2, HO2, H, O, CH4, CH3O, CH2O, HCO, CH3, CH3OH, and CH2OH. As a transition or bridge between the core and the large molecule subset, the C2−C3 submodel is chosen from the model of Patel et al.2 because of its reliability, practicability, and small size.3,4 Further, according to the above discussion on Figure 2, the reaction pathways of low temperature and decomposition mechanism are built up based on the Tananka model1 and Tsurushima’s recommendation.5 The well-known H-atom abstraction from alkane isomerization and secondary O2 addition to form ketohydroperoxide and alkyl oxidation are taken from the Tanaka model, as follows:

RH + O2 = R + HO2

(R1, R13)

RH + OH ⇒ R + H 2O

(R2, R14)

R + O2 = RO2

(R4, R16)

RO2 = QOOH

(R5, R17)

QOOH + O2 = O2 QOOH

(R6, R18)

O2 QOOH ⇒ CnKET + OH

(R7, R19)

R + O2 = olefin + HO2

(R8, R20)

where, R denotes alkyl radical or CnH2n+1 structure, Q denotes CnH2n structure, RO2 denotes alkylperoxy radical, QOOH denotes hydroperoxyalkyl radical, O2QOOH denotes peroxyalkylhydroperoxide and CnKET denotes ketohydroperoxide. R3 and R15 are added to maintain the balance of production and consumption of alkyl radical. RH + HO2 ⇒ R + H 2O2

(R3, R15)

The decomposition process of ketohydroperoxide, R9 and R21 are taken from the Tsurushima model: CnKET ⇒ R′CO + CH 2O + OH

(R9, R21)

where R′ denotes C5 or C6 alkyl radicals. Based on the observation of Zheng et al.27 that C2H3 and C3H5 are primary small hydrocarbons, the reaction ′C5H11CO + O2 ⇒ C3H6 + C2H4 + CO + HO2′ and ′C6H13CO + O2 ⇒ C3H6 + C3H6 + CO + HO2′ from the Tsurushima model is now changed into C5H11CO + O2 ⇒ C3H 7 + C2H3 + CO + HO2

(R10)

C6H13CO + O2 ⇒ C3H 7 + C3H5 + CO + HO2

(R22)

According to the graphical reaction flow analysis, species C5H11 and C6H13 (represented by R′) from the Tsurushima model are eliminated in order to keep a compact size of the skeletal model. Therefore, the following relevant reactions olefin + O2 ⇒ R′ + CH 2O + HCO

R ⇒ R′ + C2H4 R′ = C3H 7 + small olefins

are combined into C7H14 + O2 ⇒ C3H 7 + C2H4 + CH 2O + HCO

(R11′)

C7H15 ⇒ C3H 7 + C2H4 + C2H4

(R12′)

C8H16 + O2 ⇒ C3H 7 + C3H6 + CH 2O + HCO

(R23)

C8H17 ⇒ C3H 7 + C3H6 + C2H4

(R24)

To fit the evolutions of n-heptane, CO, and CO2 in a JSR reactor, the reaction pathways of R11′ and R12′ are changed into C7H14 + O2 ⇒ C3H6 + C2H5 + CH 2O + HCO

(R11)

C7H15 ⇒ C3H6 + C2H5 + C2H4

(R12)

After the basic frame and reaction pathways have been settled, a similar method suggested by Ra4 is used to modify the reaction rates. The reaction rates of the ‘core’ reactions are kept unchanged while the modification focuses on the preexponential factors in the reactions from R11 to R24, which 7072


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play, coupled with the ‘core’, an important role in controlling ignition characteristics, to fit the ignition delay time in shock tube and species evolution in jet-stirred reactor. Through this procedure, finally, a new skeletal model for PRF oxidation is obtained, which consists of 41 species and 124 reactions, and is presented in the Appendix.

3.2. Jet Stirred Reactor. PRF oxidation was investigated in a jet-stirred reactor by Dagaut et al.22,31 with very high dilution (0.1% fuel) in the temperature range of 650−1150 K and under a pressure of 1 MPa. Simulations are performed under the assumptions of isothermal, constant pressure, and perfect mixing conditions. Comparisons between modeling results and the experimental data of n-heptane, CO, and CO2 concentrations are shown in Figures 6−8 with equivalence ratios of 0.5, 1.0 and 1.5, respectively. It can be seen that the profiles of n-heptane, CO, and CO2 are well reproduced by the skeletal model for equivalence ratios of 0.5 and 1.0, although the predicted profiles have slight shifts toward high temperature for equivalence ratio of 0.5 (Figure 6). However, the simulated trend of CO profile does not well fit the experimental data at temperatures above 1000 K for equivalence ratio of 1.5 (Figure 8). It is observed that the CO concentration is underpredicted, while CO2 is overpredicted, indicating that a higher convertion rate of CO to CO2 is provided by the model. The comparison between experimental and modeling results for different PRF blends is shown in Figures 9−11. Again, lower CO concentration and higher CO2 concentration are offered by the model in the higher temperature range above 1000 K; otherwise, below 1000 K, the predicted concentrations of fuel, CO and CO2 show very good agreement with experimental data. The main reason is attributed to the omitted reaction paths of large molecule decomposition. Hence, factors effecting reaction paths need to be further studied. 3.3. Flow Reactor. Callanhan et al.32 studied PRF oxidation in a flow reactor with 1% carbon in the temperature range of 600−850 K, at pressure of 1.25 MPa and equivalence of 1.0. Simulations are performed under the assumptions of perfect mixing conditions. Comparisons between modeling results and experimental data of O2, CO, CO2, and H2O concentrations for PRF blends oxidation are shown in Figures 12 and 13. In general, these species concentrations are well reproduced by the new skeletal model. Figure 14 compares experimental and modeling results of temperature increases for various PRF blends. Although the predicted profiles have slight shifts toward high temperature, the evolution profiles show good agreement with experimental data except for PRF0 (n-heptane). 3.4. Laminar Flame Speed. To our knowledge, none of existing skeletal models for PRF oxidation with less than 50 species provide satisfactory predictions for laminar flame speed under various temperature and pressure conditions. In the following, validation of our new model under these conditions will be carried out. Kumar et al.21 measured laminar flame speed for premixed PRF/air mixture under conditions of the atmospheric pressure, equivalence ratios ranging from 0.7 to 1.4, and unburned mixture temperatures of 298, 360, 400, and 470 K using the counterflow flame technique. Figure 15 shows the comparison of experimental and modeling results for laminar flame speed using n-heptane as fuel. It can be seen that the skeletal model performs well against experimental data although the predicted speed is a little lower for lean mixtures. It should be noted that the discrepancies in the flame speed prediction under 0.1 MPa are not the key issue we care about, because it is not the enginerelevant condition. The validation under 0.1 MPa is to prove the concept of the semidecoupling methodology and make the model more reliable. Compared to the existing skeletal models, the predicted trends of laminar flame speed with equivalence ratio under 0.1 MPa are also clearly closer to the experimental data.

3. MODEL VALIDATION Most validations in the following, except HCCI engine, are carried out by a zero-dimensional gas-phase kinetics program from the software package CHEMKIN PRO.28 The thermal and transport properties are taken from references by Tsurushima5 and Klippenstein.25 Validations on iso-octane are not shown in this paper, which can be seen in ref 9. 3.1. Shock Tube. Modeling results for ignition delay time against the shock tube experimental data of n-heptane by Ciezki et al.29 are shown in Figures 3 and 4. The comparison between

Figure 3. Measured29 and calculated ignition delay of n-heptane/air at various equivalence ratios and initial pressure of 4 MPa.

Figure 4. Measured29 and calculated ignition delay of n-heptane/air at various pressures and equivalence ratio of 1.

modeling results and experimental data by Fieweger et al.30 for different PRF blends are shown in Figure 5. Simulations are performed for a completely homogeneous, constant volume and under adiabatic condition. It can be seen that both calculated main ignition time and first stage ignition show very good agreement with the measured data. The NTC behavior and the influences of the equivalence ratio and pressure on ignition delay are reproduced quite well. 7073


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Figure 5. Measured30 and calculated ignition delay for various PRF blends. Equivalence ratio is 1.0; initial pressure is 4 MPa.

Figure 6. Comparison of experimental22 and modeling results for some species concentration in a jet stirred reactor. φ = 0.5 and P i = 1 MPa; resident time is 1 s; 0.1% n-heptane.

Figure 8. Comparison of experimental22 and modeling results for some species concentration in a jet stirred reactor. φ = 1.5, and P i = 1 MPa; resident time is 1 s; 0.1% n-heptane.

Figure 7. Comparison of experimental22 and modeling results for some species concentration in a jet stirred reactor. φ = 1.0, and P i = 1 MPa; resident time is 1 s; 0.1% n-heptane.

Figure 9. Comparison of experimental31 and modeling results for some species concentration in a jet stirred reactor. PRF10, φ = 1.0, and P i = 1 MPa; resident time is 1 s; 0.1% fuel.

Figure 16 shows a sensitivity analysis of laminar flame speed with respect to the pre-exponential factor for n-heptane/air and iso-octane/air mixtures at initial pressure of 0.1 MPa and temperatures of 298 and 470 K. As expected, the reaction H + O2 = O + OH is the most sensitive reaction enhancing laminar flame speed. The sensitivity of H + O2 = O + OH and CH3 + H(+M) = CH4(+M) verify the conclusion of Ranzi et al.10 that

hydrogen radical is the most effective flame speed enhancer because of its branching activation, while the methyl radical significantly reduces the flame speed, especially in removing H from the system through the recombination reaction to form CH4. Furthermore, laminar flame speed is also highly sensitive to the CO oxidation reaction, which has a major contribution 7074


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Figure 13. Comparison of experimental32 and modeling results for some species concentration in a flow reactor. PRF92, φ = 1.0, and P i = 1.25 MPa; resident time is 1.8 s; 1% carbon.

Figure 10. Comparison of experimental31 and modeling results for some species concentration in a jet stirred reactor. PRF50, φ = 1.0 and P i = 1 MPa; resident time is 1 s; 0.1% fuel.

Figure 11. Comparison of experimental31 and modeling results for some species concentration in a jet stirred reactor. PRF90, φ = 1.0, and P i = 1 MPa; resident time is 1 s; 0.1% fuel.

Figure 14. Comparison of experimental32 and modeling results of temperature increases for various PRF blends in a flow reactor. φ = 1.0, and P i = 1.25 MPa; resident time is 1.8 s; 1% carbon.

Figure 12. Comparison of experimental32 and modeling results for some species concentration in a flow reactor. PRF87, φ = 1.0, and P i = 1.25 MPa; resident time is 1.8 s; 1% carbon.

Figure 15. Comparison of experimental21 and modeling laminar flame speed at various initial temperatures using n-heptane as fuel.

to the overall heat release. The three most sensitive reactions agree with the results of ref 21. Jerzembeck et al. 12 investigated spherical flames of n-heptane/air, iso-octane/air, and PRF/air mixtures by using a constant volume bomb. Data were obtained for an initial temperature of 373 K, equivalence ratios varying from 0.7 to 1.2, and initial pressures from 1 to 2.5 MPa. Figures 17 and 18

show comparisons of experimental and modeling results for n-heptane/air and PRF 87/air at various pressures, respectively. It seems that, overall, at relative high pressures, the new skeletal model shows almost the same performance as the reduced mechanism by Jerzembeck et al., which contains more than a 7075


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Figure 16. Sensitivity analysis of laminar flame speed with respect to pre-exponential factor, computed for n-heptane/air and iso-octane/air mixtures at φ = 1.0, Pi = 0.1 MPa, and Ti = 298/470 K.

Huang et al.20 measured laminar flame speed of PRF blends over a range of equivalence ratios at atmospheric pressure using a counterflow configuration. Figure 19 shows the comparison between

Figure 17. Comparison of experimental12 and modeling laminar flame speed of n-heptane/air at various initial pressures. Figure 19. Comparison of experimental20 and modeling laminar flame speed for various PRF/air.

the experimental and modeling laminar flame speeds for different PRF blends. It is seen again that the skeletal model performs well against experimental data for different PRF although the predicted profiles have slight shifts toward high equivalence ratio. 3.5. HCCI engine. Finally, the new skeletal model is used in coupling with a multidimensional engine CFD model to examine the interactions between chemical kinetics and engine in-cylinder flows. If SI engines were simulated, submodels for spark ignition would be indespensible, which would introduce more complicated and uncertain factors into the simulation; hence, only HCCI and PCCI combustion is considered in this paper. However, in view of good performance in the flame speed prediction, this skeletal model will be evaluated in SI engines at the next stage. The chemical kinetics code CHEMKIN is implemented into the CFD code KIVA-3 V.33 The original KIVA code has been improved by introducing several submodels including a RNG k−ε turbulence model,34 heat transfer model of Han and Reitz,35 KH-RT model for fuel injection and breakup,36 droplet collision model of Nordin37 and spray/wall interaction model of Han.38 Simulations start at the intake valve close crank angle and end at the time of the exhaust valve opening.

Figure 18. Comparison of experimental12 and modeling laminar flame speed of PRF87/air at various initial pressures.

hundred species and a thousand reactions. For lean mixture, both mechanisms provide satisfactory prediction of the flame speed, while for rich mixture the new model produces higher values which are closer to the measured data than the Jerzembeck model. 7076


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Table 1. Specifications of Simulated Engines fuel

engine type

bore × stroke

compression ratio

equivalence ratio

engine speed (r/min)

expt Ti (K)

simulated Ti (K)

ref

n-heptane PRF70 PRF73

PCCI HCCI HCCI

135 mm ×140 mm 86 mm ×86 mm 102 mm ×120 mm

16.5 14 14

0.422 0.2857 0.44

1000 1200 1200

367 523 333

380 524 362

39 40 41

Figure 20. Computational grids used in engine simulations. (a) Three-dimensional, 153978 cells for n-heptane PCCI combustion simulation. (b) Three-dimensional, 93174 cells for PRF70 HCCI combustion simulation. (c) Two-dimensional axisymmetric section, 9450 cells for PRF73 HCCI combustion simulation.

ignition timing agrees well with the measured data. Figure 22 shows comparison of experimental39 and modeling results for

Validations of cylinder pressure trace and emissions at various equivalence ratios of HCCI engine fueled with isooctane have already been conducted in our previous study.9 In the following, simulations on a PCCI engine using n-heptane as fuel, and HCCI engines using PRF73 and PRF70 as fuel are performed and validated. Specifications of the engines are listed in Table 1. Computational grids used for the three simulated engines are shown in Figure 20. In-cylinder gas sampling experiments were conducted by Tsurushima et al.39 in a PCCI engine, where n-heptane is injected into cylinder very early to form a homogeneous mixture. Simulation input of start timing, initial pressure, and species mole fraction are the same as in ref 5. Figure 21 shows

Figure 22. Comparison of experimental39 and modeling results for some intermediate species revolution in a PCCI engine.

some intermediate species evolution. It can be seen that the predicted CO2 concentration is lower and CO is higher than the corresponding experimental data after the main ignition around −10 °CA. The trace of O2 concentration is predicted quite well against measured data. The reason for the discrepancy might be that the initial value of CO2 mole fraction used in the simulation is higher than that in the experiment. This problem also causes the discrepancy of pressure and heat release rate profile. Kalghatgi and Head40 experimentally studied the autoignition quality of gasoline-like fuels in HCCI engines at high temperatures. Figure 23 shows comparison of their experimental40 and our modeling results for cylinder pressure and heat release rate history using PRF70 as fuel. It can be seen that both the predicted pressure and heat release rate have good agreement with measured data although their maximum value is higher. The main reason for the little discrepancy might lie in that the accurate size and geometry of the real combustion chamber and cylinder head are not available, the computational configuration does not exactly coincide with the original engine, so that some tiny error in the input parameters could be introduced. Another set of experimental data of an HCCI engine from Yang et al.41 is chosen for further validation. Figure 24 shows

Figure 21. Comparison of experimental39 and modeling results for cylinder pressure and heat release rate history in a PCCI engine.

comparison of experimental39 and modeling results for cylinder pressure and heat release rate history of this engine. It can be seen that the simulated pressure trace is in an excellent agreement with the experiment. As for the heat release rate (HRR), although there are some discrepancies between the computed and measured values, the HRR of the first stage is lower and little delayed, while the HRR of the main stage is higher than the experiment, the simulation captures the time instants of three peak values in the HRR and the predicted 7077


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satisfactorily using such a small size PRF skeletal model. In view of the successful exploration of improving a skeletal model on iso-octane and PRF, the semidecoupling methodology presented in this paper is reliable and maybe generally applicable for different alkane fuels. Major findings and observations of this work are summarized as follows: 1. For different operating conditions, certain paths may play (e.g., ketohydroperoxide decomposition) important roles for the reaction processes, thus careful identifying and modeling these paths become the key for extending the applicable range of the skeletal model. For a skeletal chemical model, because of the omission of some intermediate reaction processes, it may perform well in one reactor while performing poorly in another. In conclusion, it is of critical importance to identify and establish the key reaction path in the skeletal model development. 2. The new PRF skeletal model developed in this work shows very good agreement in the prediction of the first and main ignition delay times with experimental data for shock tube under wide temperature, pressure, and equivalence ratio ranges. Thus, the ignition delay can be accurately reproduced by the skeletal model. 3. The validations against jet stirred reactor and flow reactor results show that the new model can predict the mole fraction of n-heptane, iso-octane, CO, and CO2 for different PRF well in the temperature range below 1000 K, while the CO concentration is underpredicted and CO2 is overpredicted for temperatures above 1000 K, indicating that a higher convertion rate of CO to CO2 at high temperatures is provided by the model. The main reason is attributed to the omitted reaction path of large molecule decomposition. Factors effecting reaction paths need to be further studied. 4. In the prediction of laminar flame speed in enginerelevant condition, the new skeletal model shows good performance, and reaches almost the same accuracy as the reduced mechanism by Jerzembeck et al., whose scale is much greater than the new model. 5. The comparison with three HCCI engine experiments shows that the simulated pressure trace is in an excellent agreement with the experiment, while for the heat release rate there are some discrepancies between the computed and measured values. However, the model captures satisfactorily the major characteristics of HRR (the ignition timing and the phases of the peak values). In this view, the new skeletal model is promising for the simulation of engine combustion processes incorporated with a multidimensional CFD model. 6. Although the new skeletal model presents promising performance under wide operating range and various reactors, especially for the prediction of laminar flame speed, it should be noted that the new PRF model, in its current state, is still incomplete and further improvement and optimization are needed. The key reaction path should be investigated more deeply. Relevant constants in the reaction rates could be further tuned and optimized as the reaction path is confirmed.

Figure 23. Comparison of experimental40 and modeling results for cylinder pressure and heat release rate history in a HCCI engine using PRF70 as fuel.

Figure 24. Comparison of experimental41 and modeling results for cylinder pressure and heat release rate history in a HCCI engine using PRF73 as fuel.

comparison of the experimental41 and modeling results for cylinder pressure and heat release rate history using PRF73 as fuel. Again, good agreement between the predictions and the measurements is observed although a slight difference still exists in the magnitude and trace. The reason for the discrepancy could be attributed to the fact that at present only ignition delays were considered in the optimization of the reaction rate constants. It is desirable to eliminate these discrepancies in further improvement of the present skeletal PRF model.

4. CONCLUSIONS A semidecoupling methodology for developing a skeletal chemical kinetic model is presented based on the sensitivity analysis and skeletal model targets. This methodology separates the comprehensive subset of H2/CO and C1 chemistry from the skeletal subsets of C2−C3 and large molecule reactions in a “semi-decoupling” manner. The former part describes the flame propagation in detail and the latter part control the ignition characteristic coupled with the former part. By using this methodology, a skeletal model for PRF consisting of 41 species and 124 reactions is developed. The new skeletal model is validated against experimental data in various reactors under diverse operating conditions, with emphasis on premixed laminar flame speed and important species evolution. The predicted results show good agreement with experiments, especially for laminar flame speed, which is first predicted

■

APPENDIX. SKELETAL MODEL IN CHEMKIN FORMAT Table A1 shows the skeltal model in CHEMKIN format. 7078


Energy & Fuels

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Table A1. Skeletal Model in CHEMKIN Formata species O2 N2 OH H2O2 CH3O CH2O C2H3 C2H4 C3H7 C7H16 C7KET C5H11CO C8H16OOH O2C8H16OOH no. reactions (k = AT**b exp(−E/RT)) 1. reverse 2. 3. 4. reverse 5. reverse 6. reverse 7. 8. reverse 9. 10. 11. 12.

C7H16+O2=C7H15+HO2 Arrhenius coefficients: C7H16+OH⇒C7H15+H2O C7H16+HO2⇒C7H15+H2O2 C7H15+O2=C7H15O2 Arrhenius coefficients: C7H15O2=C7H14OOH Arrhenius coefficients: C7H14OOH+O2=O2C7H14OOH Arrhenius coefficients: O2C7H14OOH⇒C7KET+OH C7H15+O2=C7H14+HO2 Arrhenius coefficients: C7KET⇒C5H11CO+CH2O+OH C5H11CO+O2⇒C3H7+C2H3+CO+HO2 C7H14+O2⇒C3H6+C2H5+CH2O+HCO C7H15⇒C3H6+C2H5+C2H4

13. reverse 14. 15. 16. reverse 17. reverse 18. reverse 19. 20. reverse 21. 22. 23. 24.

C8H18+O2=C8H17+HO2 Arrhenius coefficients: C8H18+OH⇒C8H17+H2O C8H18+HO2⇒C8H17+H2O2 C8H17+O2=C8H17O2 Arrhenius coefficients: C8H17O2=C8H16OOH Arrhenius coefficients: C8H16OOH+O2=O2C8H16OOH Arrhenius coefficients: O2C8H16OOH⇒C8KET+OH C8H17+O2=C8H16+HO2 Arrhenius coefficients: C8KET⇒C6H13CO+CH2O+OH C6H13CO+O2⇒C3H7+C3H5+CO+HO2 C8H16+O2⇒C3H7+C3H6+CH2O+HCO C8H17⇒C3H7+C3H6+C2H4

25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

C3H7=C2H4+CH3 C3H7=C3H6+H C3H6=C2H3+CH3 C3H6+CH3=C3H5+CH4 C3H5+O2=C3H4+HO2 C3H4+OH=C2H3+CH2O C3H4+OH=C2H4+HCO C2H5+O2=C2H4+HO2 C2H4+OH=CH2O+CH3 C2H4+OH=C2H3+H2O C2H3+O2=CH2O+HCO C2H3+HCO=C2H4+CO

37. 38.

H+O2=O+OH O+H2=H+OH

CO2 HO2 HCO C2H5 C7H15 C7H14 C8KET

H2O H CH3 C3H4 C7H15O2 C8H18 C6H13CO

A

b

n-Heptane Oxidation Branch × 1016 0.0 × 1012 0.0 × 1013 0.0 × 1013 0.0 × 1012 0.0 × 1013 0.0 × 1011 0.0 × 1011 0.0 × 1010 0.0 × 1013 0.0 × 1010 0.0 × 1011 0.0 × 1011 0.0 × 1015 0.0 × 1013 0.0 × 1013 0.0 × 1012 0.0 Iso-octane Oxidation Branch 6.00 × 1015 0.0 1.00 × 1012 0.0 2.00 × 1013 0.0 1.00 × 1013 0.0 1.00 × 1012 0.0 2.51 × 1013 0.0 1.51 × 1011 0.0 1.00 × 1011 0.0 1.16 × 1011 0.0 2.51 × 1013 0.0 8.91 × 1010 0.0 3.16 × 1011 0.0 3.16 × 1011 0.0 3.98 × 1015 0.0 3.16 × 1013 0.0 3.16 × 1013 0.0 1.12 × 1017 −1.3 C2−C3 Reactions 9.60 × 1013 0.0 1.25 × 1014 0.0 3.15 × 1015 0.0 9.00 × 1012 0.0 6.00 × 1011 0.0 1.00 × 1012 0.0 1.00 × 1012 0.0 2.00 × 1010 0.0 6.00 × 1013 0.0 8.02 × 1013 0.0 4.00 × 1012 0.0 6.03 × 1013 0.0 C0−C1 Reactions 3.55 × 1015 −0.4 5.08 × 104 2.7 1.00 1.00 5.00 1.00 3.00 2.51 1.51 1.00 6.16 2.51 8.91 3.16 3.16 3.98 3.16 3.16 6.50

7079

CO O CH2OH C3H5 C7H14OOH C8H17 C8H16

H2 CH4 CH3OH C3H6 O2C7H14OOH C8H17O2

E

ref

46000.0 0.0 3000.0 16950.0 0.0 27400.0 19000.0 11000.0 0.0 27400.0 17000.0 6000.0 19500.0 43000.0 10000.0 10000.0 28810.0

1 1 modified ref 1 5 modified ref 1 1 1 1 modified ref 1 1 1 1 1 5 changed ref 5 combined, changed ref 5 combined, changed, modified ref 5

46000.0 0.0 3000.0 16950.0 0.0 27400.0 21800.0 11000.0 0.0 27400.0 17000.0 6000.0 19500.0 43000.0 10000.0 10000.0 29700.0

modified ref 1 1 modified ref 1 5 1 1 1 1 modified ref 1 1 1 1 1 5 changed ref 5 combined ref 5 combined, modified ref 5

30950.0 36900.0 85500.0 8480.0 10000.0 0.0 0.0 −2200.0 960.0 5955.0 −250.0 0.0

2

16599.0 6290.0

25


Energy & Fuels

Article

Table A1. continued no. 39. 40. 41.

42.

43.

44.

45.

46. 47. 48. 49. 50. 51. 52.

53. 54. 55. 56. 57. 58.

59.

reactions (k = AT**b exp(−E/RT)) H2+OH=H2O+H O+H2O=OH+OH H2+M=H+H+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 O+O+M=O2+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 O+H+M=OH+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 H+OH+M=H2O+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 H+O2(+M)=HO2(+M) low pressure limit: TROE centering: H2 enhanced by 2.000 H2O enhanced by 1.100 × 101 O2 enhanced by 7.800 × 10−1 CO enhanced by 1.900 CO2 enhanced by 3.800 HO2+H=H2+O2 HO2+H=OH+OH HO2+O=O2+OH HO2+OH=H2O+O2 HO2+HO2=H2O2+O2 declared duplicate reaction... HO2+HO2=H2O2+O2 declared duplicate reaction... H2O2(+M)=OH+OH(+M) low pressure limit: TROE centering: H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 H2O2+H=H2O+OH H2O2+H=HO2+H2 H2O2+O=OH+HO2 H2O2+OH=HO2+H2O declared duplicate reaction... H2O2+OH=HO2+H2O declared duplicate reaction... CO+O(+M)=CO2(+M) low pressure limit: H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 CO+O2=CO2+O

A

b

E

C0−C1 Reactions 1.5 2.16 × 108 2.97 × 106 2.0 4.58 × 1019 −1.4

3430.0 13400.0 104380.0

6.16 × 1015

−0.5

0.0

4.71 × 1018

−1.0

0.0

3.80 × 1022

−2.0

0.0

1.48 × 1012 0.63660 × 1021 0.80000

0.6 −0.17200 × 101 0.10000 × 10−29

0.0 0.52480 × 103 0.10000 × 1031

1013 1013 1013 1013 1014

0.0 0.0 0.0 0.0 0.0

823.0 295.0 0.0 −497.0 11982.0

1.30 × 1011

0.0

−1629.3

2.95 × 1014 0.12020 × 1018 0.50000

0.0 0.00000 0.10000 × 10−29

48430.0 0.45500 × 105 0.10000 × 1031

1013 1013 106 1012

0.0 0.0 2.0 0.0

3970.0 7950.0 3970.0 0.0

5.80 × 1014

0.0

9557.0

1.80 × 1010 0.15500 × 1025

0.0 −0.27900 × 101

2384.0 0.41910 × 104

2.53 × 1012

0.0

47700.0

1.66 7.08 3.25 2.89 4.20

2.41 4.82 9.55 1.00

× × × × ×

× × × ×

7080

ref


Energy & Fuels

Article

Table A1. continued no. 60. 61. 62.

63. 64. 65. 66. 67. 68. 69. 70. 71. 72.

73.

74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84.

85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99. 100. 101.

reactions (k = AT**b exp(−E/RT)) CO+HO2=CO2+OH CO+OH=CO2+H HCO+M=H+CO+M H2 enhanced by 2.500 H2O enhanced by 6.000 CO enhanced by 1.900 CO2 enhanced by 3.800 HCO+O2=CO+HO2 HCO+H=CO+H2 HCO+O=CO+OH HCO+OH=CO+H2O HCO+O=CO2+H HCO+HO2=CO2+OH+H HCO+CH3=CO+CH4 HCO+HCO=H2+CO+CO HCO+HCO=CH2O+CO CH2O+M=HCO+H+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 CH2O+M=CO+H2+M H2 enhanced by 2.500 H2O enhanced by 1.200 × 101 CO enhanced by 1.900 CO2 enhanced by 3.800 CH2O+H=HCO+H2 CH2O+O=HCO+OH CH2O+OH=HCO+H2O CH2O+O2=HCO+HO2 CH2O+HO2=HCO+H2O2 CH2O+CH3=HCO+CH4 CH3+O=CH2O+H CH3+O2=CH3O+O CH3+O2=CH2O+OH CH3+HO2=CH3O+OH CH3+H(+M)=CH4(+M) low pressure limit: TROE centering: H2 enhanced by 2.000 H2O enhanced by 6.000 CH4 enhanced by 2.000 CO enhanced by 1.500 CO2 enhanced by 2.000 CH4+H=CH3+H2 CH4+O=CH3+OH CH4+OH=CH3+H2O CH3+HO2=CH4+O2 CH4+HO2=CH3+H2O2 CH2OH+M=CH2O+H+M CH2OH+H=CH2O+H2 CH2OH+H=CH3+OH CH2OH+O=CH2O+OH CH2OH+OH=CH2O+H2O CH2OH+O2=CH2O+HO2 declared duplicate reaction... CH2OH+O2=CH2O+HO2 declared duplicate reaction... CH2OH+HO2=CH2O+H2O2 CH2OH+HCO=CH3OH+CO CH2OH+HCO=CH2O+CH2O 2CH2OH=CH3OH+CH2O CH2OH+CH3O=CH3OH+CH2O

A

b

C0−C1 Reactions 0.0 3.01 × 1013 1.9 2.23 × 105 0.7 4.75 × 1011

× × × × × × × × × ×

E 23000.0 −1158.7 14874.0

1012 1013 1013 1013 1013 1013 1014 1012 1013 1039

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 −6.3

410.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 99900.0

3.10 × 1045

−8.0

97510.0

5.74 × 107 1.81 × 1013 3.43 × 109 1.23 × 106 4.11 × 104 3.64 × 10−6 8.43 × 1013 1.99 × 1018 3.74 × 1011 2.41 × 1010 1.27 × 1016 0.24770 × 1034 0.78300

1.9 0.0 1.2 3.0 2.5 5.4 0.0 −1.6 0.0 0.8 −0.6 −0.47600 × 101 0.74000 × 102

2748.6 3080.0 −447.0 52000.0 10210.0 998.0 0.0 29230.0 14640.0 −2325.0 383.0 0.24400 × 104 0.29410 × 104

2.0 0.5 2.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

11210.0 10290.0 2639.0 0.0 18580.0 25100.0 0.0 0.0 0.0 0.0 5017.0

−1.0

0.0

0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

7.58 7.23 3.02 3.02 3.00 3.00 1.20 3.00 3.00 3.30

5.47 3.15 5.72 3.16 1.81 1.00 6.00 9.64 4.20 2.40 2.41

× × × × × × × × × × ×

107 1012 106 1012 1011 1014 1012 1013 1013 1013 1014

1.51 × 1015 1.20 1.00 1.50 3.00 2.40

× × × × ×

1013 1013 1013 1012 1013 7081

ref

0.69640 × 104


Energy & Fuels

Article

Table A1. continued no. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112.

113.

114.

115. 116. 117. 118. 119. 120. 121. 122. 123. 124. a

reactions (k = AT**b exp(−E/RT)) CH3O+M=CH2O+H+M CH3O+H=CH3+OH CH3O+O=CH2O+OH CH3O+OH=CH2O+H2O CH3O+O2=CH2O+HO2 declared duplicate reaction... CH3O+O2=CH2O+HO2 declared duplicate reaction... CH3O+HO2=CH2O+H2O2 CH3O+CO=CH3+CO2 CH3O+HCO=CH3OH+CO 2CH3O=CH3OH+CH2O OH+CH3(+M)≤>CH3OH(+M) low pressure limit: TROE centering: H2 enhanced by 2.000 H2O enhanced by 6.000 CH4 enhanced by 2.000 CO enhanced by 1.500 CO2 enhanced by 2.000 H+CH2OH(+M)≤>CH3OH(+M) low pressure limit: TROE centering: H2 enhanced by 2.000 H2O enhanced by 6.000 CH4 enhanced by 2.000 CO enhanced by 1.500 CO2 enhanced by 2.000 H+CH3O(+M)≤>CH3OH(+M) Low pressure limit: TROE centering: H2 enhanced by 2.000 H2O enhanced by 6.000 CH4 enhanced by 2.000 CO enhanced by 1.500 CO2 enhanced by 2.000 CH3OH+H=CH2OH+H2 CH3OH+H=CH3O+H2 CH3OH+O=CH2OH+OH CH3OH+OH=CH3O+H2O CH3OH+OH=CH2OH+H2O CH3OH+O2=CH2OH+HO2 CH3OH+HCO=CH2OH+CH2O CH3OH+HO2=CH2OH+H2O2 CH3OH+CH3=CH2OH+CH4 CH3O+CH3OH=CH3OH+CH2OH

A 8.30 3.20 6.00 1.80 9.03

b × × × × ×

15500.0 0.0 0.0 0.0 11980.0

0.0

1748.0

3.00 × 1011 1.60 × 1013 9.00 × 1013 6.00 × 1013 2.79 × 1018 0.40000 × 1037 0.41200

0.0 0.0 0.0 0.0 −1.4 −0.59200 × 101 0.19500 × 103

0.0 11800.0 0.0 0.0 1330.0 0.31400 × 104 0.59000 × 104

0.63940 × 104

1.06 × 1012 0.43600 × 1032 0.60000

0.5 −0.46500 × 101 0.10000 × 103

86.0 0.50800 × 104 0.90000 × 105

0.10000 × 105

2.43 × 1012 0.46600 × 1042 0.70000

0.5 −0.74400 × 101 0.10000 × 103

50.0 0.14080 × 105 0.90000 × 105

0.10000 × 105

0.0 0.0 2.5 2.1 1.8 0.0 2.9 0.0 3.2 0.0

6095.0 6095.0 3080.0 496.7 −596.0 44900.0 13110.0 19400.0 7172.0 4060.0

3.20 8.00 3.88 1.00 7.10 2.05 9.64 3.98 3.19 3.00

× × × × × × × × × ×

1013 1012 105 106 106 1013 103 1013 101 1011

■

AUTHOR INFORMATION

REFERENCES

(1) Tanaka, S.; Ayala, F. A.; Keck, J. C. Combust. Flame 2003, 133, 467−481. (2) Patel, A.; Kong, S. C.; Reitz, R. D. SAE Technical Paper 2004-010558, 2004, DOI: 10.4271/2004-01-0558. (3) Jia, M.; Xie, M. Z. Fuel 2006, 85 (17), 2593−2604. (4) Ra, Y.; Reitz, R. D. Combust. Flame 2008, 155 (4), 713−738. (5) Tsurushima, T. Proc. Combust. Inst. 2009, 32 (2), 2835−2841. (6) Yoo, C. S.; Lu, T. F.; Chen, J. H.; Law, C. K. Combust. Flame 2011, 158, 1727−1741. (7) Kelley, A. P.; Liu, W.; Xin, Y. X.; Smallbone, A. J.; Law, C. K. Proc. Combust. Inst. 2011, 33 (1), 501−508. (8) Sun, W. T.; Chen, Z.; Gou, X. L.; Ju, Y. G. Combust. Flame 2010, 157 (7), 1298−1307.

Corresponding Author

*Phone: +86-411 84706302. Fax: +86-411 84708460. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ref

2.20 × 1010

A units mole-cm-s-K, E units cal/mole.

■

E

C0−C1 Reactions −1.2 1017 0.0 1013 0.0 1012 0.0 1013 0.0 1013

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (Grant Nos. 51176020, 51176021) and General Motors Global Research and Development (Grant No. GM024705-NV584). 7082


Energy & Fuels

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7083


Enhancement on a Skeletal Kinetic Model for Primary Reference Fuel

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