Global Reduced Model for Conventional and Alternative Jet and

Mar 27, 2014 - Global Reduced Model for Conventional and Alternative Jet and Diesel Fuel Autoignition. Sandeep Gowdagiri* and Matthew A. Oehlschlaeger...
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Global Reduced Model for Conventional and Alternative Jet and Diesel Fuel Autoignition Sandeep Gowdagiri* and Matthew A. Oehlschlaeger Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, United States ABSTRACT: A global reduced model for the autoignition of conventional petroleum-derived and alternative, hydroprocessed and Fischer−Tropsch, jet and diesel fuels is presented. The model is based on a seven-step model from the literature (Zheng, J.; Miller, D. L.; Cernansky, N. P. A Global Reaction Model for the HCCI Combustion Process, SAE Paper 2004-01-2950, 2004) and includes steps to predict oxidation and autoignition in the three temperature regimes of interest to engine applications, the high-, low-, and negative-temperature-coefficient (NTC) regimes. Here we have included dependence of reaction rate parameters on the derived cetane number (DCN) to predict the influence of fuel variability on autoignition and optimized the reduced model to best fit target shock tube ignition delay time data for jet and diesel fuels. The standard deviation between model predictions for ignition delay and the target shock tube data set is ±21% and the model captures all experimental trends for ignition delay variation with DCN, temperature, pressure, and fuel−air equivalence ratio in all temperature regimes. Comparisons to experimental ignition delay time data not contained in the target data set show model−experiment deviation similar to the comparisons with the target data, with global standard deviation of ±20−30% and differences of at most a factor of 2. The model comparisons with shock tube data suggest that the model is suitable for autoignition prediction for fuels containing large quantities of aliphatic compounds with DCN = 30−80 for 650−1300 K, 8−80 atm, and fuel−air equivalence ratios of 0.25−1.5.

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INTRODUCTION While increasing computational power is allowing for the inclusion of a growing number of chemical reactions in combustion computational fluid dynamics (CFD) simulations,1 the high computational cost of detailed chemical kinetic models for the combustion of large pure component fuels2 or multicomponent surrogate mixtures3 restricts or prevents their use in CFD. Hence, there is need for reduced models4 that greatly simplify combustion chemistry while retaining reasonable predictability for use in CFD simulations of complex turbulent and sometimes multiphase combustion phenomena. Of interest is the use of reduced reaction schemes for the prediction of autoignition in diesel and spark ignition engines; advanced compression ignition engine concepts, including homogeneous charge compression ignition (HCCI), premixed charge compression ignition (PCCI), and reactivity controlled compression ignition (RCCI) engines, and gas turbine premixers. Additionally, the performance of engines that rely on autoignition for the initiation of combustion is influenced by compositionally based variability in fuel reactivity. Models that capture the influence of fuel variability on combustion chemistry and autoignition are needed to predict fuel influence on engine operation and performance via CFD calculations. An important reduced kinetic model is the empirical Shell model, named for the Shell Oil Co., and introduced by Halstead et al.5,6 The Shell model describes low- to intermediate-temperature oxidation chemistry using eight reactions and five species. Following its original presentation it has been further modified by Schaperton and Lee7 to provide mass conservation and implemented with different parameters for different fuels and for simulations of different applications, for example, internal combustion engines and rapid compression machines, by a number of researchers.7−11 The Shell model has been also extended by several authors through the © 2014 American Chemical Society

addition of reaction steps to better capture low- to intermediate-temperature chemistry.12−14 In contrast to the low- to intermediate-temperature Shell model and derivatives, there have also been efforts to develop reduced models for high-temperature oxidation chemistry.15−17 Reduced modeling efforts attempting to include steps to describe both low- and high-temperature oxidation chemistry are fewer in number in the literature. Muller et al.18 introduced a four-step model for n-heptane oxidation for high to low temperatures (650−1500 K). Because the Muller et al. model relies on thermal feedback to provide autoignition, it does not predict negative-temperature-coefficient (NTC) behavior observed in the autoignition of many transportation-range hydrocarbon fuels. Schreiber et al.19 introduced a five-step model for primary reference fuels that includes steps for both low- and high-temperature chemistry and predicts both twostage ignition and NTC behavior. Zheng et al.20 later modified the Schreiber et al.19 model by adding two additional reaction steps to compete with low-temperature degenerate branching to better represent NTC regime autoignition. Here we use the Zheng et al. model,20 with modified parameters, to develop a global reduced model for jet and diesel fuel oxidation and autoignition.

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MODEL DESCRIPTION A seven-step global reduced reaction model is presented based on modification of the model of Zheng et al.20 The model is optimized to best predict shock tube ignition delay measurements carried out over a large range of conditions for jet and Received: February 7, 2014 Revised: March 24, 2014 Published: March 27, 2014 2795

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Table 1. Reduced Global Reaction Model from Zheng et al. (See Reference 20)a CmHn + (0.5m + 0.25n)O2 → (0.5n)H 2O + mCO

(1)

A1,f = 2.55 × 1011

= 34740

k1,f[CmHn]0.25[O2]1.5

A2,f = 1 × 10

= 40000

k2,f[CO][H2O]0.5[O2]0.25 − k2,r[CO2]

A4,fd = 1.2 × 106

E2,fc E2,rc E3,fc E3,rc E4,fc

A5,fd = 1 × 1018DCN0.25

E5,fc = 32670

k5,f[CmHn][Y]

A6,f = 4.23 × 10

E6,fc

k6,f[I1]

c

14

A2,r = 1.2 × 10 c

CmHn + 2O2 ↔ I1

7

A3,fd = 9.48 × 1019P−2.2DCN2

(3)

A3,rd = 1.38 × 1035P−3.5 I1 → 2Y

(4)

Y + 0.5CmHn + (0.5m + 0.25n − 1)O2 → (0.5n)H 2O + mCO I1 → I 2

I 2 → 2Y

(5)

d

(6) (7)

reaction rate (mol cm−3 s−1)

E1,fd

d

(2)

CO + 0.5O2 ↔ CO2

E (cal mol−1)

Ab

reaction

10

A7,fd = 1 × 1024

= 40000 = 37620

k3,f[CmHn][O2][M] − k3,r[I1]

= 88110 = 3960

= 13860

E7,fc = 53460

k4,f[I1]

k7,f[I2][M]

a c

Parameters have been optimized in the present study. Reaction rate coefficients given by k = A exp(−E/RT) [units: cal, K, mol, cm3, s]. bP, atm. From Zheng et al.20 dOptimized in present study.

Table 2. Enthalpy Assignments for Species in Global Reaction Model species

enthalpy

source Goos et al.23

O2

ΔfHfuel(298K): determined from heat of combustion for each fuel (Table 3) Hfuel(T): temperature dependence assigned as H(T) for jet A from Goos et al.23 in NASA polynomial format ΔfHO2(298K) = 0 kcal/mol

H2O

ΔfHH2O(298K) = −57.80 kcal/mol

fuel (CmHn)

Goos et al.23

HO2(T): NASA polynomial format Goos et al.23

HH2O(T): NASA polynomial format CO CO2

ΔfHCO(298 K) = −26.42 kcal/mol HCO(T): NASA polynomial format ΔfHCO2(298K) = −94.05 kcal/mol

Goos et al.23 Goos et al.23

HCO2(T): NASA polynomial format I1 − oxygenated branching agent (e.g., OOQOOH)

HI1(T) = −12.89 + Hfuel(T) kcal/mol

Zheng et al.20

I2 − oxygenated branching agent (e.g., H2O2)

HI2(T) = −20.0 + Hfuel kcal/mol

Zheng et al.20

Y − radical (e.g., OH)

HY(T) = 0.5(−14.35 + HI1) kcal/mol

Zheng et al.20

high-temperature ignition delay within the target data set. While the rate parameters for reaction 2 were taken from Zheng et al.20 At low and intermediate temperatures, oxidation and autoignition is embodied within the reduced model in reactions 3−7. Low-temperature radical branching is initiated by the addition of molecular oxygen to a parent fuel radical, R + O2 ↔ RO2. In the case of alkane fuels, this is the addition of O2 to an alkyl radical. R + O2 ↔ RO2 can be followed by isomerization, RO2 ↔ QOOH, and the addition of another O2, QOOH + O2 ↔ OOQOOH. This reaction sequence is represented in the reduced model by reaction 3, CmHn + 2O2 ↔ I1, allowing for two oxygen additions to the fuel to produce an oxygenated radical intemediate, I1. Reaction 3 is allowed to proceed in reverse to represent inhibitive (radical propagation) steps that reduce the reaction flux through the low-temperature radical branching sequence, including HO2 elimination from RO2 and QOOH, cyclic ether formation from QOOH, β-scission of QOOH, and RO2 dissociation back to R + O2. Under the reduced model, autoignition in the NTC and low-temperature regions is highly sensitive to the rate parameters for reaction 3; hence, the forward and reverse A-factors for reaction 3 were adjusted to best fit experimental target data. The oxygenated radical produced in reaction 3, I1, can react to produce chain-propagating radicals, Y, in reaction 4. Y can then react with fuel and O2 in reaction 5 to produce H2O and CO, resulting in heat release. Hence, low- to intermediate-

diesel fuels with a large range of reactivity, represented through the derived cetane number (DCN). The Zheng et al. model is a reduced model that uses composite chemical kinetic steps or quasi-global reactions to represent the reaction progress from fuel and oxidizer to major products. The composite reaction steps represent classes and/or sequences of reactions that carry reaction flux under high-temperature or low-temperature oxidation conditions. The seven-step model was developed by modifying the five-step reduced model of Schreiber et al.19 to include additional reaction steps and species to better represent oxidation behavior in the NTC regime. The Schreiber et al. model has its roots in previous reduced modeling efforts going back to the original work of Halstead et al.5,6 The reduced model is given in Table 1 for a generic CmHn hydrocarbon fuel. It is composed of seven generic reaction steps that provide atom conservation and allow for radical branching and its inhibition, which governs the rate of oxidation and autoignition, in different temperature regimes. The model embodies high-temperature (>1100 K) oxidation and ignition using two reaction steps, reactions 1 and 2. Reaction 1 describes fuel oxidation to H2O and CO, the global rate of which is governed by H + O2 → OH + O at high temperatures, the rate limiting chain branching reaction for high-temperature hydrocarbon oxidation and ignition. Reaction 2 then describes the oxidation of CO to CO2. For the purposes of the present study, the preexponential A-factor and activation energy of reaction 1 were adjusted to best fit the shock tube 2796

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Table 3. Target Ignition Delay Data Sets Used for Model Optimizationa fuel

ϕ

P (atm)

T (K)

DCN

CmHn (av)

heat of combustion (MJ/kg)

source

jet A: commercial petroleum jet fuel Sasol IPK: coal-to-liquid Fischer−Tropsch jet fuel S-8: gas-to-liquid Fischer−Tropsch jet fuel Shell GTL: gas-to-liquid Fischer−Tropsch jet fuel JP-5: U.S. Navy petroleum jet fuel HRD-5: hydroprocessed Camelina jet fuel F-76: military petroleum diesel HRD-76: hydroprocessed algal oil diesel

0.25, 0.5, 1, 1.5 1 1 1 1 1 0.5, 1 0.5, 1

8, 11, 20 20 20 20 20 20 10, 20 10, 20

674−1381 681−1323 673−1260 651−1290 667−1250 648−1246 705−1266 671−1224

47.1 31 58.7 61 42.3 59.3 48.8 78.5

C10.2H19.9 C10.9H23.6 C11.5H24.9 C10.4H22.9 C12.5H23.5 C13.8H29.6 C14.0H25.1 C15.4H32.7

43.4 44.0 43.9 44.2 43.0 43.9 42.6 44.1

25 25 25 25 26 26 27 27

a

All mixtures are fuel/air.

Figure 1. Model speciation and temperature calculations for the autoignition jet A/air at ϕ = 1 and 20 atm for 700 (top) and 1100 K (bottom) under a constant volume constraint. Initial concentrations of I1, I2, and Y are zero; they reach a maximum in concentration at extremely early times in the 1100 K case due to reactions 3−7.

temperature first-stage ignition is controlled by reactions 4 and 5 and their competition with reverse reaction 3. The intermediate oxygenated radical, I1, can also react via reaction 6 to form another branching agent, I2, which can react in reaction 7 to produce radicals, Y. This reaction sequence is representative of the buildup of H2O2, embodied in I2, and its dissociation to produce OH radicals, embodied in Y. These steps reduce degenerate radical branching through their competition with reaction 4, govern second-stage ignition, and control the turnover from the NTC regime to hightemperature ignition behavior. The major contribution of the work of Zheng et al.20 was the addition of reactions 6 and 7 to the Schreiber et al.19 model allowing for a better representation of NTC behavior.

Reaction rate expressions for the seven-step model are given in Table 1 and are unmodified from Zheng et al.,20 who adopted reaction rates for reactions 1−5 from Schreiber et al.19 Thermodynamic data for each species was defined using NASA polynomials21 per the standard method used in CHEMKIN.22 The enthalpy assignments for each species are detailed in Table 2. Data for O2, H2O, CO, and CO2 were taken from the Goos et al.23 database. For each target jet and diesel fuel, the enthalpy of formation was determined from the known heat of combustion and average molecular formula of the fuel and the temperature dependence of enthalpy was assigned to be that for jet A from the Goos et al. database. Species I1, I2, and Y were assigned enthalpies per the Zheng et al.20 model, where 2797

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Figure 2. Comparison of model with shock tube ignition delay measurements for jet A at variable equivalence ratio and pressure.25

Figure 3. Comparison of model with conventional petroleum-derived and alternative jet fuels at ϕ = 1 and 20 atm:25,26 left, U.S. Navy jet fuels; right, U.S. Air Force jet fuels. In the graph on the right the model predictions for S-8 (DCN = 58.7) and Shell GTL (DCN = 61) are effectively coincident.

DCN dependence in the A-factor allows for a best fit of modelpredicted NTC and low-temperature autoignition to the target data shown to be correlated with DCN.25 Reaction 5, which provides second-stage ignition, has influence on NTC ignition and high-temperature transition. Inclusion of DCN dependence in the reaction 5 A-factor was found to improve model predictability in this region. To best fit the target data DCN dependence of Af,3 ∝ DCN2 and Af,5 ∝ DCN0.25 was chosen. Note, the fuel average molecular formula, CmHn, also influences ignition through the coefficients in reactions 1 and 5. Hightemperature ignition for aliphatic or primarily aliphatic fuels has been shown to be relatively insensitive to fuel structure or composition and DCN;25 hence, no DCN dependence was included in the high-temperature reaction sequence, reactions 1 and 2. Starting with the original Zheng et al. model parameters, parameters were adjusted to best fit the target ignition delay data set. Reaction 1 was first adjusted manually to best fit hightemperature data (>1100 K). Next the DCN dependence of reaction 3 in the forward direction and reaction 5 were assigned through an iterative manual fit of the DCN dependence of measured ignition delay for T < 900 K. Finally, A-factors for reactions 3−7 were manually optimized to minimize the global

they were chosen to provide appropriate enthalpies of reaction for reactions 4, 6, and 7. Rate parameters within the reduced seven-step model were adjusted to best fit a target shock tube ignition delay data set described in Table 3. The target data set was composed of shock tube ignition delay data from experiments carried out in our laboratory for jet and diesel fuels, chosen because the experimental methods were consistent, the uncertainties known (±25% uncertainty in ignition delay, 2σ confidence interval), and because the data set represents a range of real fuel reactivity, equivalence ratio, pressure, and temperatures. The model was best fit to this data set and then subsequently compared with data from other laboratories to ascertain the consistency of the model with other data sets and indirectly the consistencies of experiments from different laboratories. To describe the influence of fuel reactivity variability on autoignition, the DCN, measured in the ignition quality tester24 using ASTM D613 and characterized for all fuels in the target data set, was chosen as a single parameter to represent fuel reactivity. The A-factors for reaction 3 in the forward direction and reaction 5 were modified to include DCN dependence. Reaction 3 in the forward direction is the pivotal step in the low-temperature chain branching sequence and inclusion of 2798

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Figure 4. Comparison of model with shock tube ignition delay measurements for conventional military grade diesel (F-76) and alternative diesel (HRD-76, hydroprocessed from algal oil).27

deviation between model and experimental data. The activation energies for reactions 2−7, the pressure dependence of the Afactors for reaction 3, and the A-factors for reaction 2 were left unchanged from the values assigned by Zheng et al.20 Two example model calculations are presented in Figure 1. The calculations are for constant volume oxidation and ignition of a stoichiometric jet A/air mixture at 20 atm and 700 and 1100 K. In the 1100 K case, high-temperature ignition controlled by reaction 1 occurs, as indicated by the singlestage ignition and the very small concentrations of I1, I2, and Y present. At 700 K, two-stage ignition occurs, where during the early time there is a buildup in I1, I2, and Y until heat release from reaction 5 drives the temperature up turning on the hightemperature chemistry, causing a second-stage hot ignition.

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MODEL−EXPERIMENT COMPARISONS Comparisons of the model to the target shock tube ignition delay (fuels, conditions, and sources are provided in Table 3) are shown in Figures 2−4. The two inputs to the model in all predictions are fuel molecular formula (CmHn) and DCN. The comparison is globally very good with the model generally predicting ignition delay within the ±25% uncertainty (2σ confidence interval) in measured ignition delay and capturing the ignition delay dependence on DCN, temperature, pressure, and equivalence ratio. The largest model−experiment deviation occurs at the extremely lean ϕ = 0.25 jet A/air case. Figure 5 illustrates the experimental and model-predicted ignition delay dependence on DCN. Again, because the model was adjusted to best fit the experiments, the model predicts measured ignition delay within the experimental uncertainties. The shaded regions in Figure 5 represent the range of modelpredicted ignition delay for variation in fuel hydrogen-to-carbon ratio (H/C) and average molecular weight, MWav. These fuel properties influence model-predicted ignition delay through the fuel average molecular formula, CmHn, where the coefficients m and n appear in reactions 1 and 5. A correlation between model-predicted and shock tube measured ignition delay are shown in Figure 6. The standard deviation between measured and modeled ignition delay is ±21% (1σ) close to the ±25% (2σ) experimental uncertainties, indicating that globally the model is close to but not fully predictive of the experiment, likely due to the simplified representation of low-temperature chemistry and its depend-

Figure 5. Comparison of model predictions (open points) with measured shock tube ignition delay (filled points) at 20 atm, 830 K, and ϕ = 0.5 and 1. Shaded regions represent model predictions for ignition delay variation with DCN for a range of fuel properties: H/C = 1.8−2.2 and MWav = 145−220 kg/kmol.

ence on fuel composition/structure, here highly simplified through the use of a single parameter, DCN. However, in comparison to other reduced and detailed kinetic modeling approaches, where factors of two deviations between model and experiment are common and in some cases considered predictive, the model-experiment deviation is encouraging. Of course the reasonably good agreement exists because the model was optimized to fit the data. Further interrogation of the predictive capabilities of the reduced model are shown in Figures 7−9 where model predictions are compared to shock tube ignition delay data for n-heptane (DCN = 54), n-decane (DCN = 67), and ndodecane (DCN = 78) from the Aachen,28,29 Stanford,30,31 Duisburg,32 and Moscow33 groups and n-decane rapid compression machine data from Case Western Reserve.34 These comparisons provide independent assessment of the model since the data were not part of the target set and the experiments were carried out by other groups. These 2799

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Figure 6. Model versus measured ignition delay for the target data set (left) and experiment to model correlation (right).

Figure 9. Comparison of model predictions for n-dodecane (DCN = 78) with shock tube ignition delay data of Vasu et al.31 (Stanford).

Figure 7. Comparison of model predictions for n-heptane (DCN = 54) with shock tube ignition delay data of Ciezki and Adomeit28 (Aachen), Gauthier et al.30 (Stanford), and Herzler et al.32 (Duisburg).

independent comparisons have model−experiment deviation similar to the target data comparisons shown in Figures 2−4, with deviations of at most a factor of 2 and globally at the ±20−30% (1σ) level. Additionally, the model performs very well at high pressures outside of the experimental target range, predicting the ignition delay times of n-heptane at 41, 50, and 55 atm and n-decane at 50 and 80 atm from four different laboratories to within tens of percent. Model comparisons to ignition delay data from our laboratory for n-alkanes35 show similar agreement. The comparisons shown in Figures 2−4 and 7−9 suggest that the model is suitable for autoignition prediction for fuel/air mixtures with ϕ = 0.25−1.5, at temperatures from 650 to 1300 K, at pressures from 8 to 80 atm, and for primarily aliphatic fuels with DCN = 30−80. This is a large range of conditions of importance to diesel and advanced compression ignition engines and gas turbines. The simplicity of the model allows for implementation into computational fluid dynamic simulations with limited computational cost relative to larger reduced, skeletal, or detailed reaction mechanisms and will be especially useful for cases where autoignition prediction is desired and the influence of fuel variability on autoignition is in question. It would be desirable to extend the model validation to richer conditions found in diesel engines; however, there is a

Figure 8. Comparison of model predictions for n-decane (DCN = 67) with shock tube ignition delay data from Pfahl et al.29 (Aachen) and Zhukov et al.33 (Moscow) and rapid compression machine data of Kumar et al.34 (Case Western Reserve).

2800

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(11) Toulson, E.; Allen, C. M.; Miller, D. J.; McFarlane, J.; Schock, H. J.; Lee, T. Energy Fuels 2011, 25, 632−639. (12) Cox, R. A.; Cole, J. A. Combust. Flame 1985, 60, 109−123. (13) Hu, H.; Keck, J. Autoignition of Adiabatically Compressed Combustible Gas Mixtures, SAE technical paper 872110; SAE International: Warrendale, PA, USA, 1987. (14) Cowart, J. S.; Keck, J. C.; Heywood, J. B.; Westbrook, C. K.; Pitz, W. J. Proc. Combust. Inst. 1991, 23, 1055−1062. (15) Westbrook, C. K.; Dryer, F. L. Combust. Sci. Technol. 1981, 27, 31−43. (16) Coffee, T. P.; Kotlar, A. J.; Miller, M. S. Combust. Flame 1983, 54, 155−169. (17) Jones, W. P.; Lindstedt, R. P. Combust. Flame 1988, 73, 233− 249. (18) Muller, C. U.; Peters, N.; Linan, A. Proc. Combust. Inst. 1992, 24, 777−784. (19) Schreiber, M.; Sakak, S. A.; Lingens, A.; Griffiths, F. J. Proc. Combust. Inst. 1994, 25, 933−940. (20) Zheng, J.; Miller, D. L.; Cernansky, N. P. A Global Reaction Model for the HCCI Combustion Process, SAE technical paper 2004-012950; SAE International: Warrendale, PA, USA, 2004. (21) McBride, B. J.; Gordon, S.; Reno, M. A. Coefficients for calculating thermodynamic and transport properties of individual species, NASA Report TM-4513; Glenn Research Center, NASA: Cleveland, OH, USA, 1993. (22) Kee, R. J.; Rupley, F. M.; Miller, J. A. The Chemkin thermodynamic data base, Sandia National Laboratories Report SAND87-8215B; Sandia National Laboratories: Livermore, CA, USA, 1990. (23) Goos, E.; Burcat, A.; Ruscic, B. Ideal Gas Thermochemical Database with Updates from Active Thermochemical Tables. Available at ftp://ftp.technion.ac.il/pub/supported/aetdd/thermodynamics and mirrored at http://garfield.chem.elte.hu/Burcat/burcat.html, 2013. (24) Allard, L. N.; Webster, G. D.; Hole, N. J.; Ryan, T. W., III; Ott, D.; Fairbridge, C. W. Diesel fuel ignition quality as determined in the Ignition Quality Tester (IQT), SAE technical paper 961182; SAE International: Warrendale, PA, USA, 1996. (25) Wang, H.; Oehlschlaeger, M. A. Fuel 2012, 98, 249−258. (26) Valco, D.; Gentz, G.; Allen, C.; Colket, M.; Edwards, T.; Gowdagiri, S.; Oehlschlaeger, M. A.; Toulson, E.; Lee, T. Autoignition behavior of synthetic alternative jet fuels: An examination of chemical composition effects on ignition delays at low to intermediate temperatures. Proc. Combust. Inst. 2014, submitted for publication. (27) Gowdagiri, S.; Wang, W.; Oehlschlaeger, M. A. A Shock Tube Ignition Delay Study of Conventional Diesel Fuel and Hydroprocessed Renewable Diesel Fuel from Algal Oil. Fuel 2014, 128, 21−29. (28) Ciezki, H. K.; Adomeit, G. Combust. Flame 1993, 93, 421−433. (29) Pfahl, U.; Fieweger, K.; Adometi, G. Proc. Combust. Inst. 1996, 26, 781−789. (30) Gauthier, B. M.; Davidson, D. F.; Hanson, R. K. Combust. Flame 2004, 139, 300−311. (31) Vasu, S. S.; Davidson, D. F.; Hong, Z.; Vasudevan, V.; Hanson, R. K. Proc. Combust. Inst. 2009, 32, 173−180. (32) Herzler, J.; Jerig, L.; Roth, P. Proc. Combust. Inst. 2005, 30, 1147−1153. (33) Zhukov, V. P.; Sechenov, V. A.; Starikovskii, A. Y. Combust. Flame 2008, 153, 130−136. (34) Kumar, K.; Mittal, G.; Sung, C. J. Combust. Flame 2009, 156, 1278−1288. (35) Shen, H. P. S.; Steinberg, J.; Vanderover, J.; Oehlschlaeger, M. A. Energy Fuels 2009, 23, 2482−2489.

lack of data available at rich, high-pressure, low-temperature conditions needed to optimize/validate the model at these conditions.

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SUMMARY A global reduced model for the autoignition of jet and diesel fuels is presented. The model is based on the seven-step model of Zheng et al.,20 which was a modification to the five-step model of Schreiber et al.19 and has its roots in the original Shell model of Halstead et al.5,6 In the present work, the seven-step model was written to predict fuel reactivity variability by including dependence of reaction rate parameters on the derived cetane number (DCN), effectively a transfer number for global fuel reactivity. The model was optimized, through adjustment of reaction A-factors, to best fit a target set of jet and diesel fuel shock tube ignition delay data from our laboratory.25−27 The model was then compared to shock tube ignition delay data for large n-alkanes outside the target data set and reported by other groups. In all cases the model captures the variation in ignition delay with DCN, temperature, pressure, and equivalence ratio and the model−experiment deviation is relatively small. For example, the model−target data comparisons show standard deviation ±21%, significantly smaller than most a priori comparisons of pure component or surrogate detailed kinetic modeling efforts found in the literature to measured ignition delay times from shock tubes or rapid compression machines. Comparisons with experiments suggest that the model is suitable for autoignition prediction for fuels containing primarily aliphatic compounds with DCN = 30−80 and for 650−1300 K, 8−80 atm, and fuel/air mixtures with equivalence ratios of 0.25−1.5.

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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 was supported by the Air Force Office of Scientific Research under Grant No. FA9550-11-1-0261 with Dr. Chiping Li as technical monitor.

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REFERENCES

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