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A Skeletal and Reduced chemical kinetic mechanism for Methyl Butanoate Auto-ignition Chunhui Liu, Zhengxing Zuo, and Huihua Feng Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.6b02391 • Publication Date (Web): 28 Nov 2016 Downloaded from http://pubs.acs.org on December 7, 2016
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Energy & Fuels
A Skeletal and Reduced chemical kinetic mechanism for Methyl Butanoate Auto-ignition Chunhui Liu1,2, Zhengxing Zuo1, Huihua Feng1 *
1.School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081，China 2. School of Automobile and Transportation, Tianjin University of Technology and Education, Tianjin 300222, China
KEYWORDS：methyl butanoate; directed relation graph method; computational singular perturbation; skeletal mechanism; reduced mechanism
ABSTRACT ： The methyl butanoate (MB) auto-ignition detailed mechanism including 275 species and 1545 elementary reactions was reduced through the systematic mechanism reduction approach. First, a smallest skeletal mechanism containing 79 species and 399 elementary reactions was achieved from the detailed mechanism by comparing four different graph-based reduction methods. Then, 123 unimportant reactions were eliminated using the computational singular perturbation (CSP), generating the ultimate skeletal mechanism consisting of 79 species and 276 elementary reactions. Finally, 26 global quasisteady-state species were identified using a CSP-based time-scale analysis, resulting in a 53-species reduced mechanism. The 79-species skeletal and 53-species reduced mechanisms have been validated against the detailed mechanism, and the simulation results show good agreement with both ignition delay time and the distribution of species concentration over a wide range of simulation conditions.
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1 INTRUDCTION Biodiesel, a renewable fuel source, has become a promising alternative fuel for diesel engines because of its low cost compared with other alternative fuels. The application of biodiesel in diesel engines can reduce tailpipe emissions such as particulate matter, carbon dioxide (CO2), and unburned hydrocarbons effectively [1,2].The principal component of biodiesel is fatty acid methyl esters with long carbon chains, such as methyl palmitate (C17H34O2), methyl stearate (C19H36O2), methyl oleate (C19H34O2), methyl linoleate (C19H32O2), and methyl linolenate (C19H30O2). It's a great challenge for kinetic modeling of biodiesel because of very large fuel molecules [3]. Methyl butanoate (MB), a C4 methyl ester, reproduces kinetic features of the oxidation of the methyl ester in biodiesel, so it can be used as a surrogate for real biodiesel [4]. Fisher et al [4] earliest developed a MB detailed chemical kinetic mechanism consisting of 279 species and 1259 elementary reactions as a biodiesel mechanism in 2000. Since then MB has appeared more regularly in the literature: Gail et al. [5] proposed a detailed mechanism including 295 species and 1498 elementary reactions based on the experimental results obtained in a JSR. Dooley et al. [6] developed a detailed mechanism with 275 species and 1545 elementary reactions using the measurements in both shock tube and rapid compression machine. Hakka et al. [7] proposed a detailed mechanism consisting of 203 species and 1317 elementary reactions based on the JSR experimental results. Liu et al. [8] developed a detailed mechanism with 262 species and 1529 elementary reactions using the local sensitivity analyses. Ignition is the first step for normal operation of the engine. The ignition chemical kinetic mechanism helps us to understand the fuel nature and control emission. However, the large size and chemical stiffness of detailed chemical kinetic mechanism prevent it from computing
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complex combustion phenomena such as 3-D engine simulations [9]. Thus, it is necessary to obtain smaller size mechanisms through reducing the detailed mechanism. The mechanism reduction can be operated at two steps. The first step is to get skeletal mechanisms through eliminating redundant species and elementary reactions. In skeletal reduction methods, the directed relation graph (DRG) method proposed by Lu [10] is one of the most important reduction methods owing to its high efficiency and simplicity, and a lot of improvements and modifications have been made following the DRG method, such as DRG with error propagation (DRGEP) [11], path flux analysis (PFA) [12], revised DRG (DRGMAX) [3]. The DRG used a directed graph to map the direct coupling between species A and B and consequently seek out unimportant species based on setting target species and error threshold value. Besides direct coupling, the indirect coupling and the impact of the path linking species A and B were also considered by introducing the concept of error propagation in DRGEP. The revised DRG method with a different definition of the interaction coefficient in DRG was developed to handle the large isomer groups by Luo [3]. For improving the prediction of reaction fluxes, Sun [12] proposed the PFA method, which used consumption and production pathways to measure the coupling effect between species. Currently, the accuracy of the DRGEP-based approaches is mainly improved by researchers from the pairwise relation of a pair of species and the graph search algorithms [13, 14]. The second step is to get reduced mechanisms by the decomposition of motion in phase space into fast and slow modes using methods such as computational singular perturbation (CSP) [15-17], quasi steady state approximation (QSSA) [18], and intrinsic low dimensional manifold (ILDM) [19]. The primary goal of this study is to generate the skeletal and reduced chemical kinetics mechanisms for predicting biodiesel combustion characteristics in engine conditions. Fist, the
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smallest auto-ignition skeletal mechanism consisting of 79 species and 399 elementary reactions was obtained using the DRGEP method. Then, only the elementary reactions were eliminated using the computational singular perturbation (CSP) method. The finally generated skeletal mechanism consists of 79 species and 276 elementary reactions. Finally, applying CSP and the QSS assumption, the final skeletal mechanism can be further reduced to generate a reduced mechanism with 53 species. 2 Reduction methodologies 2.1 Graph-based approaches The four different reduction methods all need to quantify the influence of species A on species B. The interaction coefficients rAB can be defined as:
∑ v ωδ = ∑v ω A ,i
DRG rAB
i
i B
i =1, I
A ,i
(1)
i
i =1, I
∑v
ωiδ Bi
A,i
i =1, I
DRGEP rAB =
(2)
max（PA，C A ) max i (vA,iωiδ Bi )
DRGMAX rAB =
(3)
max i (vA,iωi )
PFA rAB = rAB1st − pro + rAB1st −con + rAB2 nd − pro + rAB2 nd −con
(4)
I
where PA = ∑ max(0,v A,iωi )
(5)
i =1
I
C A = ∑ max(0, − vA,iωi )
(6)
i =1
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rAB1st − pro =
∑ max( v
A ,i
i =1, I
max( ∑ max(v A,iωi， 0), ∑ max(−v A,iωi， 0)) i =1, I
rAB1st −con =
ωiδ Bi , 0) i =1, I
∑ max( - v
A ,i
ωiδ Bi , 0)
i =1, I
max( ∑ max(v A,iωi， 0), ∑ max(−vA,iωi， 0)) i =1, I
rAB2 nd − pro =
rAB2 nd −con =
(7)
(8)
i =1, I
∑
1st − pro 1st − pro rAM rM i B i
(9)
∑
1st − con 1st − con rAM rM i B i
(10)
M i ≠ A, B
Mi ≠ A, B
Choosing a small threshold value ε , if rAB ≥ ε , the dependence of A on B must be considered; otherwise, the dependence is negligible. The symbol I is the total number of elementary reactions. vA,i is the stoichiometric coefficient of species A in the ith elementary reaction. ωi is the net reaction rate of the ith elementary reaction. δ Bi =1, if the ith elementary reaction involves species B; otherwise, δ Bi =0.
The DRG method is one of the most important mechanism reduction methods, even though it
only considers the direct influence of species A on species B. The DRGEP method introduces the error propagation to consider the indirect coupling between species A and species B on the basis of DRG. Moreover, the DRGEP method also considers the impact of the path linking species A and B on the interaction coefficient rAB . For the DRGMAX method, the max operator replaces sum operator as the denominator in Eq.(1), which can more effectively handle large isomer groups in the combustion mechanism. The calculation of rAB for PFA method is most
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complicated in the four methods. Besides the direct coupling between two species A and species B (first generation), coupling between two species (second generation) via a third species (M) is also considered in PFA. Because of considering the indirect coupling between two species, PFA can get skeletal mechanisms with higher accuracy compared with DRG, while it is more timeconsuming. Each method has its advantages and disadvantages, so it is difficult to obtain a skeletal mechanism with smallest size only through a method. In practice, the smallest size of skeletal mechanism satisfying a fixed relative error level should be obtained by comparing various graphbased approaches.
2.2 CSP approach To remove the unimportant reactions after eliminating the unimportant species, Lu [20] defined an importance index I A,i to express the importance of the ith reaction to the production rate of species A. The importance index I A,i can be written as:
I A,i =
vA,iωi
∑v
A ,i
(11)
ωi
i =1, I
If IA,i
