Energy Fuels 2011, 25, 632–639 Published on Web 01/18/2011
: DOI:10.1021/ef101238d
Modeling the Autoignition of Fuel Blends with a Multistep Model Elisa Toulson,† Casey M. Allen,† Dennis J. Miller,‡ Joanna McFarlane,§ Harold J. Schock,† and Tonghun Lee*,† ‡
† Department of Mechanical Engineering, Michigan State University, East Lansing, Michigan 48824, United States, Department of Chemical Engineering and Material Science, Michigan State University, East Lansing, Michigan 48824, United States, and §Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
Received September 13, 2010. Revised Manuscript Received December 25, 2010
There is growing interest in using biodiesel in place of or in blends with petrodiesel in diesel engines; however, biodiesel oxidation chemistry is complicated to directly model and existing surrogate kinetic models are very large, making them computationally expensive. The present study describes a method for predicting the ignition behavior of blends of n-heptane and methyl butanoate, fuels whose blends have been used in the past as a surrogate for biodiesel. The autoignition is predicted using a multistep (8-step) model in order to reduce computational time and make this a viable tool for implementation into engine simulation codes. A detailed reaction mechanism for n-heptane-methyl butanoate blends was used as a basis for validating the multistep model results. The ignition delay trends predicted by the multistep model for the n-heptane-methyl butanoate blends matched well with that of the detailed CHEMKIN model for the majority of conditions tested.
oil with an alcohol are generally regarded as first generation biofuels.17 The most successful biofuels generated from these processes are ethanol and biodiesel, which can be used neat or in blends with their petroleum based counterparts, gasoline and diesel, with only minor modifications to current engines.18,19 Currently, a collective effort is underway to seek a new generation of advanced biofuels which are produced by advanced thermochemical processes to optimize yields and promote sustainable growth.17,18 These next generation biofuels are formulated by blending a variety of renewable, organic components that are derived from carbohydrates and from oils and fats to actively optimize physical properties and combustion characteristics.3,18 Since next generation biofuels are blended from many different components, the availability of detailed kinetic mechanisms is limited. For this reason, the work described here focuses on using a multistep modeling approach to simulate the ignition of both biofuels and their blends in a rapid compression machine (RCM). This work is a continuation of previous work20,21 that described modifications to the multistep model of Halstead et al.22,23 so that it could be used to predict the autoignition of oxygenated fuels as well as an optimization procedure that enables the determination of the 26 multistep kinetic parameters for new fuels.
Introduction Alternative fuels such as biofuels are presently receiving attention as potential substitutes for fossil fuels, as they can be renewable, carbon neutral and provide energy security.1,2 Several different liquid and gaseous fuels derived from biomass are being researched for use in the transportation sector.3 These fuels include biodiesel,3-6 bioethanol,3,7,8 biomethanol,9,10 biohydrogen,2,11,12 and biosyngas-derived Fischer-Tropsch Synthesis fuels.13-16 Alcohols created from fermentation processes and methylesters produced by the transesterification of raw vegetable *To whom correspondence should be addressed. Telephone: (517)432-3187. E-mail:
[email protected]. (1) Westbrook, C. K.; Pitz, W. J.; Westmoreland, P. R.; Dryer, F. L.; Chaos, M.; Osswald, P.; Kohse-H€ oinghaus, K.; Cool, T. A.; Wang, J.; Yang, B.; Hansen, N.; Kasper, T. Proc. Combust. Inst. 2009, 32 (1), 221–228. (2) Demirbas, A. Energy Convers. Manage. 2008, 49 (8), 2106–2116. (3) Demirbas, A. Prog. Energy Combust. Sci. 2007, 33 (1), xxxx. (4) Lapuerta, M.; Armas, O.; Rodrı´ guez-Fernandez, J. Prog. Energy Combust. Sci. 2008, 34 (2), 198–223. (5) Shahid, E. M.; Jamal, Y. Renewable Sustainable Energy Rev. 2008, 12 (9), 2484–2494. (6) Demirbas, A. Energy Convers. Manage. 2009, 50 (1), 14–34. (7) Balat, M.; Balat, H. Appl. Energy 2009, 86 (11), 2273–2282. (8) Gnansounou, E.; Dauriat, A.; Villegas, J.; Panichelli, L. Bioresour. Technol. 2009, 100 (21), 4919–4930. (9) Hasegawa, F.; Yokoyama, S.; Imou, K. Bioresour. Technol., In Press, Corrected Proof. (10) Lim, K. O.; Sims, R. E. H. Liquid and Gaseous Biomass Fuels Bioenergy Options for a Cleaner Environment; Elsevier: Oxford, 2004; pp 103-140. (11) Meher Kotay, S.; Das, D. Int. J. Hydrogen Energy IWHE 2006 2008, 33 (1), 258–263. (12) Liu, X.; Ren, N.; Song, F.; Yang, C.; Wang, A. Prog. Nat. Sci. 2008, 18 (3), 253–258. (13) Tijmensen, M. J. A.; Faaij, A. P. C.; Hamelinck, C. N.; van Hardeveld, M. R. M. Biomass Bioenergy 2002, 23 (2), 129–152. (14) Jun, K.-W.; Roh, H.-S.; Kim, K.-S.; Ryu, J.-S.; Lee, K.-W. Appl. Catal., A 2004, 259 (2), 221–226. (15) Takeshita, T.; Yamaji, K. Energy Policy 2008, 36 (8), 2773–2784. (16) Prins, M. J.; Ptasinski, K. J.; Janssen, F. J. J. G. Fuel Process. Technol. 2005, 86 (4), 375–389. r 2011 American Chemical Society
(17) Fatih Demirbas, M. Appl. Energy Bio-fuels in Asia 2009, 86 (Supplement 1), S151–S161. (18) Demirbas, A. Energy Policy 2007, 35 (9), 4661–4670. (19) Demirbas, A. Applied Energy Bio-fuels Asia 2009, 86 (Supplement 1), S108–S117. (20) Toulson, E.; Allen, C. M.; Miller, D. J.; Lee, T. Energy Fuels 2010, 24 (2), 888–896. (21) Toulson, E.; Allen, C. M.; Miller, D. J.; Schock, H. J.; Lee, T. Energy Fuels 2010, 24 (6), 3510–3516. (22) Halstead, M. P.; Kirsch, L. J.; Prothero, A.; Quinn, C. P. Proc. R. Soc. London, Ser. A 1975, 346, 515–538. (23) Halstead, M. P.; Kirsch, L. J.; Quinn, C. P. Combust. Flame 1977, 30, 45–60.
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Background Biodiesels are generally composed of a mixture of multiple monoalkyl esters of long-chain fatty acids (∼12-18 carbon atoms) made most commonly from soy or rapeseed oil by transesterification with an alcohol.1,24 The oxidation chemistry of biodiesels is much less well understood than that of traditional fossil fuels, as their chemical structure is considerably different due to the oxygen atoms present in the alkyl chain.25 Furthermore, the combination of chemical functional groups in an oxygenated biofuel molecule may cause reaction sequences not found in hydrocarbon chemistry, leading to the unavailability of information necessary for predicting combustion properties and pollution formation.26 Development of detailed chemical kinetic models of biodiesel is still in the early stages due to the very large size of the branched or unsaturated carbon chains that make up biodiesel together with the chemical variability of biodiesel.26 However, several recent studies describe kinetic mechanisms for methyl decanoate (8580 reactions and 3043 species)24 and the unsaturated esters methyl-5-decenoate and methyl-9-decenoate,27 both of which contain a double bond. Due to the complex nature of biodiesel, research often focuses on surrogates, which are simpler molecules that can produce the primary characteristics of biodiesel combustion.28 To date, small alkyl esters such as methyl butanoate1,24,25,29-35 have been used as biodiesel surrogates because they contain much of the same chemical structure of their larger counterparts (Figure 1) but with a chemical mechanism of a more manageable size.36 However, the methyl butanoate mechanism does not include low temperature chemistry to describe, for example, the isomerization of alkylperoxy radicals to hydroperoxyl radicals, as no negative temperature coefficient behavior was observed for methyl butanoate in experiments.25 Although, in general the longer chain methyl-esters components of biodiesel do show negative temperature coefficient behavior.25 In addition, biodiesel is often used in blends with petrodiesel, which further complicates the chemical kinetic modeling. It has been shown that the chemical interaction that occurs in fuel blends is significant as both the availability and the relative importance of the decomposition and oxidation reaction pathways can change due the availability of different
Figure 1. Chemical structures of methyl butanoate, n-heptane, and biodiesel.36
radical species that do not occur when the individual neat fuels are combusted and can lead to the production of different pollutant emissions.26 To overcome some of the issues of modeling diesel-biodiesel blends, Szybist et al.37 generated a combined mechanism consisting of a blend of a detailed n-heptane and methyl butanoate mechanism which contained 670 species and over 3000 reactions. In this research the authors compared simulated and experimental combustion of biodiesel blends in a diesel HCCI engine. Blends up to 50% biodiesel were examined and a zerodimensional model was used to simulate the HCCI combustion of the biodiesel-diesel blends. For the model, the n-heptanemethyl butanoate blends were matched to have the same equivalence ratio and oxygen content as the actual blends of diesel and biodiesel, as it has been shown that it is important for the surrogate fuel to contain approximately the same amount of oxygen as the actual biodiesel since this has a significant effect on combustion phasing.38 Szybist et al.’s study37 determined that the model did a good job of predicting the effects of intake temperature on the phasing of the low temperature heat release and the main combustion event together with the effect on the magnitude of the low temperature heat release. However, more discrepancy was found in the effect of the biodiesel concentration on the duration and phasing of the low temperature heat release and the main combustion event. Continuing this approach, but with the intention of applying it to computational fluid dynamic (CFD) engine simulations, Brakora et al.39 generated a reduced mechanism (53 species, 156 reactions) for biodiesel engine simulations using n-heptane and methyl butanoate. In order to retain the approximate 11% oxygen by mass property of biodiesel, a blend consisting of one mole of methyl butanoate and two moles of n-heptane was used. Furthermore, this combination also maintained a similar molecular weight to biodiesel. Following this study, Um and Park38 used Brakora et al.’s39 reduced mechanism to examine the effect of the biodiesel-diesel mixing ratio on combustion and emission characteristics, as biodiesel is often used in blends with petrodiesel rather than neat. In this study,38 the authors examine conventional diesel together with 20% biodiesel and 40% biodiesel blends. Golovitchev and Yang40 also developed a model for rapeseed biodiesel (RME) by modifying the model of Brakora et al.39 to include phenyl methyl ether (C7H8O) to represent
(24) Herbinet, O.; Pitz, W. J.; Westbrook, C. K. Combust. Flame 2008, 154 (3), 507–528. (25) Dooley, S.; Curran, H. J.; Simmie, J. M. Combust. Flame 2008, 153 (1-2), 2–32. (26) Kohse-H€ oinghaus, K.; Oβwald, P.; Cool, T.; Kasper, T.; Hansen, N.; Qi, F.; Westbrook, C.; Westmoreland, P. Angew. Chem., Int. Ed. 2010, 49 (21), 3572–3597. (27) Herbinet, O.; Pitz, W. J.; Westbrook, C. K. Combust. Flame 2010, 157 (5), 893–908. (28) Lai, J. Y. W.; Lin, K. C.; Violi, A. Prog. Energy Combust. Sci., In Press, Corrected Proof. (29) Hayes, C. J.; Burgess, D. R., Jr. Proc. Combust. Inst. 2009, 32 (1), 263–270. (30) Gaı¨ l, S.; Sarathy, S. M.; Thomson, M. J.; Dievart, P.; Dagaut, P. Combust. Flame 2008, 155 (4), 635–650. (31) HadjAli, K.; Crochet, M.; Vanhove, G.; Ribaucour, M.; Minetti, R. Proc. Combust. Inst. 2009, 32 (1), 239–246. (32) Fisher, E. M.; Pitz, W. J.; Curran, H. J.; Westbrook, C. K. Proc. Combust. Inst. 2000, 28, 1579–1586. (33) Metcalfe, W. K.; Dooley, S.; Curran, H. J.; Simmie, J. M.; El-Nahas, A. M.; Navarro, M. V. J. Phys. Chem. A 2007, 111, 4001–4014. (34) Farooq, A.; Davidson, D. F.; Hanson, R. K.; Huynh, L. K.; Violi, A. Proc. Combust. Inst. 2009, 32 (1), 247–253. (35) Gaı¨ l, S.; Thomson, M. J.; Sarathy, S. M.; Syed, S. A.; Dagaut, P.; Dievart, P.; Marchese, A. J.; Dryer, F. L. Proc. Combust. Inst. 2007, 31 (1), 305–311. (36) Westbrook, C. K.; Pitz, W. J.; Curran, H. J. J. Phys. Chem. A 2006, 110 (21), 6912–6922.
(37) Szybist, J. P.; McFarlane, J.; Bunting, B. G. SAE 2007-01-4010, 2007. (38) Um, S.; Park, S. W. Fuel 2010, 89 (7), 1415–1421. (39) Brakora, J. L.; Ra, Y.; Reitz, R. D.; McFarlane, J.; Daw, C. S. SAE 2008-01-1378, 2008. (40) Golovitchev, V. I.; Yang, J. Biotechnol. Adv. 2009, 27 (5), 641– 655.
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cyclic compounds, in addition to methyl butanoate and n-heptane. In this model a 1:1:1 volume ratio mixture of n-heptane, methyl butanoate, and phenyl methyl ether was used to model biodiesel in a Volvo D12C engine. Golovitchev and Yang’s40 reduced mechanism (88 species and 363 reactions) was constructed based on first cracking the long chain methyl esters into smaller esters by global reactions and then employing the reduced mechanism to calculate the further decomposition and emission formation. At present, there is a high computational cost when incorporating a detailed kinetic mechanism into a CFD model. Although, reduced mechanisms significantly decrease computational time, with biodiesel even reduced mechanisms contain a significant amount of reactions due to the biodiesel molecule’s large size. In order to reduce computational time, especially for situations where the calculation of emission formation is not required, a multistep ignition model such as that introduced by Halstead et al.23 can be employed in place of the detailed chemical kinetics. With a multistep model, the reaction steps are empirical and consequently only describe the overall behavior of the detailed kinetics.41 Because of this, the kinetic parameters may require modification if the model is used with different fuels, fuel blends, or even isomers of the same fuel. The objective of the current research was to determine a method by which the multistep model constants of individual fuels could be used to determine ignition characteristics of fuel blends. In addition to biodiesel modeling, a potential application for this type of multistep blend modeling is in homogeneous charge compression ignition (HCCI) combustion. HCCI engines often have very high pressure rise rates, and one strategy that has been proposed to mitigate this problem has been to blend two fuels that have different autoignition times thereby staggering and spreading out the combustion over time, consequently reducing the rate of pressure rise.28 This strategy requires knowledge of fuel chemistry and shows how chemical kinetics could facilitate combustion development of new technologies. Furthermore, the method described in this paper would enable the extension of this type of blended fuel study to CFD simulation of fuel blends. Over sixty sets of RCM detailed modeling data for the autoignition of blended n-heptane-methyl butanoate mixtures were used together with an optimization procedure to determine the multistep model’s 26 kinetic parameters for different fuel blends and to establish an algorithm valid for fuel blending. The optimization was performed for equivalence ratios of 0.5 and 1 and for conditions where the pressure and temperature at the end of the RCM compression stroke (or the compressed pressure and compressed temperature) were 24 bar and 610910 K, respectively.
step 1
reaction
rate coefficient kq
initiation RH þ O2 f 2R
2
propagation
kp R f R þ P þ Heat
3
propagation
f1kp R f R þ B
4
propagation
f4kp R f R þ Q
5
propagation
f2kp R þ Q f R þ B
6
branching
kb B f 2R
7
termination
f3kp R f termination
8
termination
kt 2R f termination
The multistep kinetics ignition model is based on the Shell Model of Halstead et al.,22,23 which was originally designed to predict hydrocarbon autoignition (knock) in gasoline engines. More recently, the model has also been shown applicable to
diesel and biodiesel ignition in compression ignition engines.42-46 Halstead et al.’s23 original model is shown in Table 1 and consists of seven species (five generic, O2 and N2) and eight reactions that are based on the degenerate chain branching characteristic of hydrocarbon autoignition. In addition, the model contains 26 constants that are unique to a particular fuel. The species involved in the multistep model adapted to accommodate oxygenated hydrocarbons are as follows: (1) RH, the hydrocarbon fuel of composition CnH2mOk; (2) O2, oxygen; (3) R*, the radical formed from the fuel; (4) B, the branching agent; (5) Q, the intermediate species; (6) P, the products; and (7) N2, nitrogen. The intermediate species (Q), formed in reaction 4, represents oxygenated compounds such as aldehydes (RCHO) during the first induction period and alkylperoxy radicals (RO2) and their isomerization products during the second induction period.43 These intermediate species are capable of enhancing the rate of formation of the degenerate branching intermediate (B) in reaction 5.47 The branching intermediate is related to hydroperoxide (RO2H) at low temperature and hydrogen peroxide (H2O2) at high temperature.48 A detailed description of the modifications made to Halstead et al.’s original model23 to adapt it to oxygenated fuels as well as improvements made by incorporating suggestions from Schapertons and Lee49 and Hamosfakidis and Reitz41 to maintain mass conservation have been previously reported by the authors.20,21 With the modifications to the model, it is
(41) Hamosfakidis, V.; Reitz, R. D. Combust. Flame 2003, 132 (3), 433–450. (42) Yuan, W.; Hansen, A. C.; Zhang, Q. Computational Study of Biodiesel Ignition in a Direct Injection Engine. In ASAE Annual International Meeting. 2003. Las Vegas, Nevada, USA. (43) Kong, S.-C.; Han, Z.; Reitz, R. D. SAE Paper 950278, 1995. (44) Kong, S.-C.; Reitz, R. D. J. Eng. Gas Turbines Power 1993, 115, 781–789.
(45) Yuan, W.; Hansen, A. C.; Tat, M. E.; Van Gerpen, J. H.; Tan, Z. Trans. ASAE 2005, 48 (3), 933–939. (46) Sazhina, E. M.; Sazhin, S. S.; Heikal, M. R.; Marooney, C. J. Fuel 1999, 78 (4), 389–401. (47) Griffiths Prog. Energy Combust. Sci. 1995, 21, 25–107. (48) Benson, S. W. Prog. Energy Combust. Sci. 1981, 7, 125. (49) Schapertons, H.; Lee, W. SAE Paper 850502, 1985.
Multistep Ignition Model
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possible to simulate cool flames, two-stage ignition and the variation of ignition delay with temperature. However, unlike a reduced or combined models the multistep model cannot be used to predict emission formation or provide information regarding specific chemical species. The application of the multistep model to new fuels can be accomplished by modifying the 26 model constants, essentially fitting the model to predict the results of the detailed kinetics or experiments. Consequently, the multistep model ignition delay predictions are only as good as it is fit to the experimental or detailed modeling data. Therefore, the greater the number of data points used to determine the optimized multistep model constants the more accurate the fit. Consequently, the use of the multistep model is only valid over the range of conditions that were employed to fit the multistep model constants. To date, the multistep model has been applied to diesel fuel by using the model constants suggested by Halstead et al.23 for PRF 90 but with the adjustment of parameter Af4.43,46,50 Hamosfakidis and Reitz also developed a genetic algorithm optimization methodology to determine the parameters for n-heptane (C7H16) and tetradecane (C14H30).41 Recently, suggestions for the constants for the oxygenated fuels, methyl butanoate and dimethyl ether, have been published.20,21
Figure 2. Pressure traces of the CHEMKIN modeling for different n-heptane-methyl butanoate mixtures using the combined mechanism and also the methyl butanoate mechanism of Dooley et al.25 and the LLNL n-heptane mechanism51 for initial RCM conditions of 1 atm, 338 K, and φ = 0.5.
cyclic transition states.52 It is important to note that even though the combustion kinetics of the smaller esters may not be telling of the complete combustion behavior of larger biodiesel molecules their kinetics make up an important subset of the larger more complicated models of larger molecules. In addition it should be pointed out that although the n-heptane pressure traces from the n-heptane mechanism and the blended mechanism match exactly, the methyl butanoate blended trace shows autoignition approximately 10% faster due to the duplicate reactions being removed from the original methyl butanoate mechanism.
Chemkin Model The detailed chemical kinetic calculations were completed using the CHEMKIN code with a 0-D reactor model. Following other researchers37-39 a combination of n-heptane and methyl butanoate was used as a surrogate for biodiesel fuel as this combination has similar chemical formula, lower heating value, and percent oxygen (by mass) to biodiesel. In order to determine the autoignition delay of the fuel blends, a detailed n-heptane and methyl butanoate mechanism generated by Szybist et al.37 and validated with HCCI experimental results was used. Where necessary the reaction parameters and thermodynamic data were updated in the reaction sets to correspond with the most up-todate parameters from the kinetics modelers at Lawrence Livermore National Laboratory51 (LLNL) and the Combustion Chemistry Centre at the National University of Ireland.25 A sensitivity study was performed on the reaction set, and it was found that the rate data for the key species were the same in both data sets. Subsequently, the combined mechanism was tested to ensure that it produced results similar to those of the original methyl butanoate and n-heptane mechanisms when used with each of the neat fuels. Figure 2 shows pressure traces for different n-heptane-methyl butanoate mixtures using the blended mechanism and also for the methyl-butanoate mechanism of Dooley et al.25 and the LLNL n-heptane mechanism51 for initial RCM conditions of 1 atm, 338 K, and an equivalence ratio of 0.5. It should be noted that the time scale is logarithmic in order to make the varying ignition delays for the blends more clear. The lower reactivity of the mixtures with higher concentrations of methyl butanoate is expected due to the lower reactivity of this smaller biodiesel surrogate molecule, which is not realistic for actual biodiesel compounds.26 However, many molecules in biodiesel are unsaturated esters, making them less reactive to low temperature oxidation than their saturated counterparts because of the difficulty in forming
Multistep Model Constants The objective of the current research was to determine a method by which the multistep model constants of individual fuels could be used to determine ignition characteristics of fuel blends. The mixture compositions, temperature, and pressure conditions used to validate the multistep model constants are shown in Table 2. The multistep model constants for neat methyl butanoate and n-heptane were used to determine those of the fuel blends. The methyl butanoate model constants have previously been published,20 and the n-heptane model constants were determined using the optimization procedure outlined by the authors in ref 21. Several n-heptane pressure traces calculated with both the multistep model using the optimized n-heptane constants and with the CHEMKIN detailed model are shown in Figure 3. Because some of the multistep constants are very large in magnitude and others small, the weighted geometric mean was used to calculate the constants for the n-heptane-methyl butanoate blends as the arithmetic mean is biased toward the larger constant. The weighted geometric mean is calculated as 0
1 w ln x i i B C B C C x ¼ expBi ¼ 1 n @ P A wi n P
ð1Þ
i¼1
(50) Theobald, M. A. MIT, 1986. (51) Mehl, M.; Pitz, W. J.; Sjoberg, M.; Dec, J. E. SAE 2009-011806, 2009.
(52) Zhang, Y.; Yang, Y.; Boehman, A. L. Combust. Flame 2009, 156 (6), 1202–1213.
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where xi is the multistep constant, and wi is the corresponding weight of the constant in terms of mole fraction of that component in the mixture. It should be pointed out that the geometric mean cannot be used for multistep model constants with a value of zero; therefore, in this situation the arithmetic mean was used. Using this approach, the multistep constants for methyl butanoate, n-heptane and several blends were
mix
φ
methyl butanoate: n-heptane (mole ratio)
Tc (K)
Pc (atm)
1 2 3 4 5
0.5, 1 0.5, 1 0.5, 1 0.5, 1 0.5, 1
0:1 1:2 1:1 2:1 1:0
610-850 650-900 680-910 740-910 735-950
12, 24 12, 24, 36, 48 24 24 12, 24
calculated and are shown in Table 3. To further justify this approach, it was also tested with the LLNL Primary Reference Fuel (PRF) mechanism53 (Version 2) for neat n-heptane (nh) and iso-octane (io) as well as 1:2, 1:1, and 2:1 blends of the two fuels. Figure 4 shows the ignition delay at a pressure of 20 atm for n-heptane, iso-octane, and the three n-heptane:isooctane blends. The filled symbols show the CHEMKIN modeling results with the LLNL PRF mechanism,53 and the hollow symbols show the results achieved with the multistep model. For the multistep model, the n-heptane and iso-octane results were achieved by optimizing the 26 multistep model for each of these fuels based on the results from the detailed model.53 Once the n-heptane and iso-octane multistep model constants were determined, the n-heptane:iso-octane blend constants were calculated using the weighted geometric mean (eq 1) of the neat constants.
Figure 3. Comparison of n-heptane multistep model and detailed pressure traces for RCM compressed temperatures of 646 K, 687, and 726 K, a compressed pressure of 12 atm, and φ = 0.5.
Figure 4. Autoignition delay times for n-heptane (nh), iso-octane (io), and their mixtures using CHEMKIN with the LLNL PRF53 detailed mechanism (solid triangles) and the multistep model (hollow triangles) at 20 atm, φ = 1, and varying temperature.
Table 2. Mixture Composition, Temperature, and Pressure of CHEMKIN and Multistep Simulations
Table 3. Multistep Model Constants for Methyl Butanoate,20 n-Heptane (Optimized Using the Technique Described in Ref 21), and Several of Their Blendsa parameter
methyl butanoate (MB)
n-heptane
2-n-heptane:1-MB
1-n-heptane:1-MB
1-n-heptane:2-MB
Ap1 Ep1 Ap2 Ep2 Ap3 Ep3 Aq Eq Ab Eb At Et Af1 Ef1 Af2 Ef2 Af3 Ef3 Af4 Ef4 x1 y1 x3 y3 x4 y4
1.0 1012 0 1.0 1011 1.5 104 1.0 1013 8.5 102 1.5 1010 5.0 104 6.51 1015 6.0 104 3.0 105 0 9.3 -1.5 104 1.8 102 -7.0 103 1.205 1.5 104 1.88 104 4.0 104 1.5 0 0 0 -0.3 0.35
1.0 1012 0 1.0 1011 1.5 104 1.0 1013 8.5 102 3.52 1013 3.74 104 2.0 1019 5.7 104 3.2 1012 0 1.6 10-5 -1.5 104 1.8 102 -7.0 103 2.89 1.0 104 8.0 105 3.0 104 1.0 -0.5 0 0 -1.3 1.0
1.0 1012 0 1.0 1011 1.5 104 1.0 1013 8.5 102 2.65 1012 4.12 104 1.38 1018 5.80 104 1.45 1010 0 1.3 10-3 -1.5 104 1.8 102 -7.0 103 2.16 1.14 104 2.29 105 3.30 104 1.14 -0.33 0 0 -0.80 0.70
1.0 1012 0 1.0 1011 1.5 104 1.0 1013 8.5 102 7.27 1011 4.32 104 3.61 1017 5.85 104 9.8 108 0 1.2 10-2 -1.5 104 1.8 102 -7.0 103 1.87 1.22 104 1.23 105 3.46 104 1.22 -0.25 0 0 -0.62 0.59
1.0 1012 0 1.0 1011 1.5 104 1.0 1013 8.5 102 1.99 1011 4.54 104 9.47 1016 5.90 104 6.6 107 0 1.1 10-1 -1.5 104 1.8 102 -7.0 103 1.61 1.31 104 6.56 104 3.63 104 1.31 -0.17 0 0 -0.49 0.50
a
Ai (cm,mol,s units), Ei (cal/mol), R = 1.9872 cal/mol K.
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Figure 7. Autoignition delay times for a 2 mol n-heptane - 1 mol methyl butanoate mixture with the CHEMKIN detailed model (solid) and the multistep model (hollow) at φ = 0.5 and varying compressed pressure and compressed temperature.
Figure 5. n-Heptane - methyl butanoate mixture autoignition delay times with the CHEMKIN detailed model (solid) and the multistep model (hollow) at a compressed pressure of 24 atm, φ = 1, and varying compressed temperature.
Figure 6. n-Heptane - methyl butanoate mixture autoignition delay times with the CHEMKIN detailed model (solid) and the multistep model (hollow) at a compressed pressure of 24 atm, φ = 0.5, and varying compressed temperature.
Figure 8. Contours of the ratio (multistep/detailed) of the ignition delays between the multistep model and the CHEMKIN results of Figure 5 at a compressed pressure of 24 atm, φ =1, and for varying compressed temperature and mole fraction of methyl butanoate in the fuel (1 = 100% methyl butanoate, 0 = 100% n-heptane).
Results and Discussion Figures 5-7 show a comparison of the ignition delay results attained with the multistep model (hollow symbols) and the detailed CHEMKIN model (solid symbols). The results shown in Figures 5 and 6 are for five different mixture compositions at a compressed pressure of approximately 24 atm, varying compressed temperature, and equivalence ratios of 1 and 0.5, respectively. Figure 7 shows a comparison of autoignition delay times for a 2 mol n-heptane - 1 mol methyl butanoate mixture at an equivalence ratio of 0.5 and with both varying compressed pressure and temperature. The ignition delays predicted by both the detailed CHEMKIN model and multistep model follow similar trends, with the computational time reduced by more than 3 orders of magnitude with the multistep model. As an example, for the same set of conditions on an Intel Core 2 Quad Q9550 processor clocked at 2.83 GHz, the computational time for the
multistep model is 1.73 s and for the detailed model is 2120 s (∼35 min), more than 1200 times longer. It can be clearly seen with both models that the ignition delay decreases with increasing concentrations of n-heptane in the mixture and with increasing compressed temperature and/ or compressed pressure. When comparing Figures 5 and 6 it can be seen that especially for higher compressed temperatures the ignition delay is generally longer for leaner mixtures. Furthermore, it should be pointed out that higher compressed temperatures are shown for the 0.5 equivalence ratio case. This is due to the fact that the same initial temperature and pressure conditions were tested for both equivalence ratios, and for the equivalent initial temperature the φ = 1 case has a 30-40 K lower compressed temperature due to the difference in the heat capacities of the mixtures. In Figure 7 it can be seen that for the 2 mol n-heptane - 1 mol methyl butanoate mixtures, at lower compressed pressures there is a negative temperature
(53) Curran, H. J.; Gaffuri, P.; Pitz, W. J.; Westbrook, C. K. Combust. Flame 2002, 129 (3), 253–280.
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Figure 9. Contours of the ratio (multistep/detailed) of the ignition delays between the multistep model and the CHEMKIN results of Figure 6 at a compressed pressure of 24 atm, φ =1, and for varying compressed temperature and mole fraction of methyl butanoate in the fuel (1 = 100% methyl butanoate, 0 = 100% n-heptane).
Figure 10. Contours of the ratio (multistep/detailed) of the ignition delays between the multistep model and the CHEMKIN results of Figure 7 for a 2 mol n-heptane - 1 mol methyl butanoate mixture at φ = 0.5 and for varying compressed temperature and pressure.
coefficient (NTC) region where the reaction rate decreases with increasing temperature, resulting in a longer ignition delay at these conditions. In general, relative to the detailed model, the multistep model blending technique overpredicts the ignition delay for blends at lower temperatures, while underpredicting it at higher temperatures. This effect is also visible in the contour plots shown in Figures 8-10. In these plots, contours of the ratio (multistep/ detailed) of the ignition delays between the multistep model and the CHEMKIN results shown in Figures 5-7 are displayed. In Figures 8-10 an error greater than 1 indicates that the multistep model predicted a longer ignition delay than the CHEMKIN model, and an error less than 1 indicates the opposite. Figures 8 and 9 indicate that for both equivalence ratios the multistep model predicts a longer ignition delay for higher compressed temperatures and for mixtures with higher n-heptane mole fractions. However, especially for the 0.5 equivalence ratio mixtures the multistep model predicts a shorter ignition delay than the detailed model for mixtures containing higher amounts of methyl butanoate, particularly at lower compressed temperatures. It should also be pointed out that the error between the detailed and multistep modeling results are greatest for the 1:1 n-heptane:methyl butanoate mixtures at both equivalence ratios. In Figure 10 it can be seen that the multistep model predicts a longer ignition delay than the detailed model at lower compressed temperature conditions and also in the NTC region that occurs at high compressed temperatures and low compressed pressures. The variation between the multistep model and the detailed kinetics is most likely a result of the fact that the optimizer used for determining the multistep model constants of the neat fuels has a goal of minimizing the sum of the errors for all the test points, and therefore there is a variation in the magnitude of the error between different test points. Furthermore, it can be seen that there is a larger error in the ignition delay for blends than for the neat fuels. This is likely due to the fact that the multistep constants were fitted and optimized for the neat methyl butanoate and n-heptane, while the multistep model
Figure 11. Autoignition delay times for n-heptane (nh) and isooctane (io) using the LLNL PRF53 detailed mechanism (solid triangles), the LLNL iso-octane and n-heptane mechanisms55 (solid squares and dashed line) and the multistep model (hollowtriangles) at 20 atm, φ = 1, and varying temperature.
constants of the blends were determined based on those of the neat fuels. The overall average absolute percentage error between the multistep and CHEMKIN modeling results was ∼33%. The agreement between the simulations, however, is satisfactory considering, as Floweday54 demonstrated, the autoignition discrepancies between the detailed n-heptane chemical models of Curran53 and Mehl55 for a randomly selected autoignition curve showed an average absolute percentage error of ∼38%. Using these same two mechanisms together with the iso-octane mechanism developed by Mehl et al.55 the authors also found similar levels of error between the different detailed mechanisms. An example of this can be seen in Figure 11 which shows the neat iso-octane and n-heptane ignition delay results generated with the LLNL PRF mechanism53 and the multistep model (also shown in Figure 4) together with results (54) Floweday, G. SAE 2010-01-2169, 2010. (55) Mehl, M.; Curran, H. J.; Pitz, W. J.; Westbrook, C. K. Proceedings of the European Combustion Meeting, 2009.
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from the more recent (2009) LLNL iso-octane and n-heptane mechanisms.55 For these conditions, the absolute relative error between the detailed mechanisms of Curran53 and Mehl,55 for n-heptane and iso-octane were 41.8% and 36.8%, respectively, a similar error to that found by Floweday.54 In contrast, the average relative error for the multistep model compared to the PRF detailed mechanism53 results is 9.3% and 5.9% for the iso-octane and n-heptane and overall for all the multistep results, including the blends shown in Figure 4 is 6.2%.
It is expected that the multistep model fuel blending technique described in this work could also be applied to determine the multistep model constants of other fuel blends based on the known model constants of the neat fuels. The main benefit of this type of modeling is the ability to capture the ignition behavior of novel blends of oxygenated compounds, for which no detailed kinetics data are available. The availability of multistep model constants for a range of fuels and blends will be a valuable tool in dramatically reducing the computational time of autoignition modeling, making possible computationally efficient, 2-stage autoignition modeling in CFD applications, particularly engine simulations. However, it is recognized that the multistep model is unable to compete with more complex models with respect to emissions prediction. Future plans include experimental RCM testing of a variety of oxygenate fuels and their blends in order to determine multistep model constants for different fuels. Additionally, the authors would like to examine the potential of applying a more complex biodiesel surrogate mechanism such as the methyl decanoate þ methyl9-decenoate þ n-heptane blend mechanism27 in order to improve the accuracy of the multistep model for binary and potentially tertiary blends.
Conclusions A multistep model adapted for use with oxygenated fuels has been shown to be capable of modeling the ignition delay of fuel blends. The results presented in this work indicate the feasibility of using this type of modeling to predict the ignition delay of blends of different fuels when the multistep constants for the neat fuels that make up the blends are known. The modeling was completed for five different fuel compositions consisting of a 1:0, 2:1, 1:1, 1:2, and 0:1 methyl butanoate to n-heptane fuel mole ratio, for equivalence ratios of 0.5 and 1, a compressed pressure of 24 bar, and compressed temperatures over the range of 610-910 K. Furthermore, for the 2:1 n-heptane: methyl butanoate mixture, which is commonly used to represent biodiesel, the modeling was also completed over a range of compressed pressures varying from 12 to 48 atm. Over this set of conditions, the overall trends of the detailed kinetics were correctly reproduced with the multistep model.
Acknowledgment. This work was preformed under the auspices of the US Department of Energy by Michigan State University under contract DE-FC26-07NT43278.
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