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Systematic analysis and reduction of combustion mechanisms for ignition of multi-component kerosene surrogate
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Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 187–195
Combustion Institute www.elsevier.com/locate/proci
Systematic analysis and reduction of combustion mechanisms for ignition of multi-component kerosene surrogate Quan-De Wang a, Ya-Mei Fang a, Fan Wang a,⇑, Xiang-Yuan Li b,⇑ a
b
College of Chemistry, Sichuan University, Chengdu 610064, PR China College of Chemical Engineering, Sichuan University, Chengdu 610065, PR China Available online 29 September 2012
Abstract Currently, most detailed chemical kinetic mechanisms for combustion are still not comprehensive enough and update of key reaction rate is still required to improve the combustion mechanisms. The development of systematic mechanism reduction methods have made significant progress, and have greatly facilitated analysis of the reaction mechanisms and identification of important species and key reactions. In the present work, time-integrated element flux analysis is employed to analyze a skeletal combustion mechanism of a tri-component kerosene surrogate mixture, consisting of n-decane, n-propylcyclohexane, and n-propylbenzene. The results of element flux analysis indicate that major reaction pathways for each component in the surrogate model are captured by the skeletal mechanism compared with the detailed mechanism. After that, sensitivity analysis (SA) and chemical explosive mode analysis (CEMA) are conducted to identify the dominant ignition chemistry. The SA and CEMA results demonstrate that the ignition of n-decane and n-propylcyclohexane is sensitive only to the oxidation chemistry of H2/CO and C1–C4 small hydrocarbons, while the ignition of n-propylbenzene is very sensitive to the initial reactions of n-propylbenzene and related aromatic intermediates. This demonstrates that the hierarchic structure should be maintained in the reduction of detailed mechanism of substituted aromatic fuels. The skeletal mechanism is further reduced by combining the computational singular perturbation (CSP) method and quasi steady state approximation (QSSA). A 34-species global reduced mechanism is obtained and validated over a wide range of parameters for ignition. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Element flux analysis; Sensitivity analysis; Mechanism reduction; Computational singular perturbation; Quasi-steady state approximation
1. Introduction Kerosene is a mixture of a large number of hydrocarbon compounds with different classes of
⇑ Corresponding authors. Fax: +86 28 85407797.
E-mail addresses: [email protected] (F. Wang), [email protected] (X.-Y. Li).
chemical structures, such as alkanes, aromatics, and cycloalkanes, and a wide range of molecular weights. Because of the limitation in available computational resources to deal with combustion processes of a large number of components in real kerosene, a surrogate mixture containing two to five pure compounds is usually adopted to mimic kerosene combustion behaviors [1–8]. In order to develop reliable chemical kinetic mechanisms for
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.06.011
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real fuels, comprehensive kinetic mechanisms have been developed for certain single-component compounds [9–24]. For linear and branched alkanes, it is generally recognized that detailed kinetic mechanisms are well-established [9–12]. However, for cycloalkanes and aromatic compounds, the ring structure in these fuels introduces additional kinetics pathways, and the development of comprehensive kinetic mechanisms for these hydrocarbon fuels is still in progress [13–24]. When detailed mechanisms for each component in the surrogate are established, they can be combined together to mimic combustion behaviors for real fuels. However, these detailed mechanisms of kerosene are highly complicated and numerical investigations are severely restricted to some zero- and onedimensional applications. In order to couple the combustion chemistry of kerosene with large-scale computational fluid dynamics (CFD) simulations, mechanism reduction is critical in combustion community [25]. Mechanism reduction has been extensively studied and various methodologies have been developed as reviewed in Ref. [25]. The first step in mechanism reduction is skeletal reduction [26], which removes unimportant species and reactions from the detailed mechanism. It should be noted that no matter what methods are adopted for skeletal mechanism generation, the realistic chemical kinetics and the major reaction pathways should be maintained in order to achieve reliable skeletal mechanism. When skeletal mechanism has been generated, model reduction methods, such as the quasi-steady state approximation (QSSA) [25–27] can be performed more effectively. Based on the above considerations, the first goal of the present work is to scrutinize how well the skeletal mechanism can reproduce the reaction pathways compared with the detailed mechanism. The detailed mechanism for the three-component kerosene surrogate mixture used in the present work is developed by Dagaut et al. [1,2], and includes 209 species and 1673 reversible reactions. The skeletal mechanism with 106 species and 382 reactions generated in our previous work [28] by using the DRG method combined with the iterative screening and structure analysis (ISSA) method is adopted. The three-component surrogate consists of n-decane (denoted as NC10H22, 74% molar fraction), n-propylbenzene (PHC3H7, 15%), and n-propylcyclohexane (CYC9H18, 11%), which are typical representative compounds of linear alkane, aromatics, and cycloalkanes in kerosene. The second objective is to clarify dominant ignition chemistry of the three different hydrocarbon fuels. This is achieved by using sensitivity analysis (SA) [29] and the chemical explosive mode analysis (CEMA) [30,31]. Furthermore, the skeletal mechanism is further reduced to facilitate CFD simulations. The paper is organized as following: Section 2 presents the methodologies
used in this work; analysis and comparison of results based on the detailed and skeletal mechanism are performed in Section 3; validation and discussion of the global mechanism are presented in Section 4, and main conclusions are summarized in Section 5. 2. Methodologies 2.1. Time-integrated element flux analysis The concept of element flux analysis, proposed by Revel et al. [32], provides a general methodology to identify reaction pathways under certain simulation condition with minimal computational effort. The method is briefly outlined as following. The instantaneous element flux for each element (such as C, H, O) from species k1 to k2 through reaction i, denoted as A_ i;k1!k2 ðtÞ, can be calculated using the following equation [32]: N A;k1 N A;k2 A_ i;k1!k2 ðtÞ ¼ qi ðtÞ N A;i
ð1Þ
where qi ðtÞ is the instantaneous reaction rate of reaction i at time t, N A;k1 , N A;k2 , and N A;i are the number of atom A in species k1, species k2, and reaction i, respectively. The total transformation for element A from species k1 to k2 in a mechanism consisting of I elementary reactions and K species at instantaneous time t can be calculated through the summation of contributions from all reactions: A_ k1!k2 ðtÞ ¼
I X A_ i;k1!k2 ðtÞ
ð2Þ
i¼1
To derive global information, a time-integrated flux indicator is proposed [33,34]: Z s ð3Þ A_ k1!k2 ¼ A_ k1!k2 ðtÞdt 0
Consequently, the time-integrated contribution of reaction i to the flux of element A from k1 to k2, and the normalized weight of element flux from k1 to k2 to the total out flux of species k1 can be easily identified with Eqs. (4) and (5), respectively: Rs _ _ ^ i;k1!k2 ¼ Ai;k1!k2 ¼ R0s Ai;k1!k2 ðtÞdt A ð4Þ A_ ðtÞdt A_ k1!k2 0 k1!k2 Rs A_ k1!k2 ðtÞdt A_ k1!k2 ^ ¼ PK0 R s Ak1!k2 ¼ PK _ _Ak1!k k 0 Ak1!k ðtÞdt k
ð5Þ
2.2. Brute force SA and CEMA Brute force SA is a useful method to identify important reactions which have the largest affects
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on the combustion behaviors. In this work, SA is conducted for ignition delay time based on adiabatic simulations with constant pressure. The percent sensitivity is defined by the following [29]: %Sensitivity ¼
sign ð2k i Þ sign ðk i Þ 100% sign ðk i Þ
ð6Þ
where k i is the rate constant of reaction i, sign ð2k i Þ is the ignition delay time when the rate constant of reaction i is doubled, and sign ðk i Þ is the original ignition delay time. Another method used to identify the dominant chemistry is the CEMA [30,31]. CEMA is based on the CSP method [35]. Both CSP and CEMA have been described in detail elsewhere [25,26,30,31,35] and the concept of the CEMA is only briefly discussed here. In implementing of the CEMA, the Jacobian matrix of the chemical source term is eigen-decomposed, and the eigenvalues indicate the reciprocal characteristic time scales of involved chemical modes. The eigenvector corresponding to a large positive eigenvalue indicates a chemical explosive mode. In order to quantitatively measure the contribution of a chemical species or reactions to a CEM, an explosion index (EI) and an explosion participation index (PI) are defined [30,31]. EI and PI provide important information to identify relevant species and elementary reactions at ignition. Thus, by using the PI in CEMA, we can readily identify the reactions and related species having the most direct and unambiguous influence on ignition. In this work, an in-house package is developed and coupled with CHEMKIN libraries [36,37] to post-process the results of kinetic simulations. Eigenvalue analysis is performed using the LAPACK library facilities [38]. 2.3. CSP and QSSA methods In the present work, QSSA is adopted to further reduce the mechanism. The criterion based on CSP analysis proposed by Lu and Law [39] is employed for QSS species identification. Densely sampled data from constant-pressure ignition processes over a wide range of simulation conditions is used for CSP analysis, and a 34-species global reduced mechanism is derived. The fixed-point algebraic iteration [40] is employed to calculate the concentration of QSS species. 3. Results and discussion 3.1. Results from time-integrated element flux analysis Time-integrated element flux analysis is performed by using the detailed and skeletal mechanism in simulation of the constant-pressure ignition processes. Figures 1–3 show the element flux analysis results for n-decane, n-propylcyclo-
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hexane, and n-propylbenzene, respectively. For ndecane, it can be seen that the skeletal mechanism captures the dominant reaction pathways compared with the detailed mechanism. The Habstraction reaction of n-decane by H, O, and OH radicals is the major reactions in the initial oxidation of n-decane, while the reaction of direct C– C bond-breaking to form ethyl and 1-octyl radicals becomes important as the temperature increases. The following step is the b-scission reaction, which proceeds very fast. For n-propylcyclohexane, once the ring structure is broken, the kinetics controlling subsequent reactions can be modeled with well-established normal and branched alkane mechanisms. Consequently, understanding the initial breakdown steps of n-propylcyclohexane molecule is a key issue to improve the combustion mechanism of these compounds and to validate the skeletal mechanisms. Figure 2 summarizes the major initial reaction pathways of n-propylcyclohexane. The reaction pathways are more complicated than that of n-decane. The H-abstraction reactions by H, OH, O and CH3 radicals at the sites of n-propyl radical and the sites of the ring structure are both important, especially at lowtemperatures. The reaction of C–C bond-breaking to form the n-propyl and the cyclohexyl radicals is the most important reaction in the direct C–C bond-breaking reactions. Another important reaction at high temperature is the lumped reaction of n-propylcyclohexane to form ethylene, propylene,
n-decane 13.18(13.10) 1-decyl 9.60(9.82) 5.41(6.70) 2-decyl 16.01(16.21) 9.14(9.36) 4.32(5.34) 21.54(21.38) 10.17(10.36) 4.65(5.77) 21.54(21.38) 10.17(10.36) 4.65(5.77) 21.54(21.38) 10.17(10.36) 4.65(5.77) 2.59(2.97) 22.32(25.24) 30.31(33.50) 0.64(0.71) 6.62(7.49) 10.45(11.56)
β-scission
1-octyl + C2H4 50.37(50.57) 12.59(12.64) 43.83(45.83) 10.96(11.46) 45.28(47.63) 11.32(11.91) isomerization 5-decyl
3-decyl
4-decyl
(1) β-scission reactions Similar to 1-decyl
5-decyl
(2) isomerization reactions
1-octyl
1-hexyl
Fig. 1. Time-integrated element flux analysis of ndecane during constant pressure auto-ignition processes. The percentages of the conversions (Figs. 1–3) calculated from the detailed mechanism (outside the parenthesis) and skeletal mechanism (inside the parenthesis) from top to bottom represent the analysis at initial temperatures of 1000 K, 1250 K, and 1500 K with equivalence ratio of 1.0 and pressure of 1.0 atm. The percentage of the conversions is defined as the percentage of the flux of element C from one species to another with respect to the total flux of C.
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AC9H17C BC9H17C CC9H17C DC9H17C EC9H17C FC9H17C GC9H17C AC9H17C n-propylcyclohexane 7.57(0) 5.23(7.30) β-scission 2.94(3.58) C3H6+CYC6H11 BC9H17C 10.22(12.88) 5.97(10.00) 3.24(4.07) C2H4+C5H913 CC9H17C 10.22(14.02) 5.97(10.11) Further reactions 3.24(4.07) DC9H17C + GC9H17C 11.44 11.44 4.79 4.79 2.28 2.28 isomerization BC9H17C EC9H17C + FC9H17C 22.85(33.22) 22.85(33.22) 9.57(19.01) 9.57(19.01) 4.57(7.29) 4.57(7.29) CYC6H11 + NC3H7 0.24(0.69) 0.35(1.03) 4.14(3.33) 6.22(4.99) 5.88(7.07) 8.82(10.53) C2H4 + C3H6 + AC5H10 0.00(0.00) 0.95(2.76) 0.39(1.15) 4.16(2.90) 16.58(13.30) 6.91(5.54) 5.88(7.00) 23.52(28.08) 9.80(11.70)
Fig. 2. Time-integrated element flux analysis of npropylcyclohexane during constant pressure auto-ignition processes.
+H, OH, O 17.98(27.11) 11.57(16.56) 4.54(6.72)
C2H4 + 22.24(22.22) 22.23(22.22) 22.22(22.22) C3H6 + 9.20(9.96) 18.59(18.56) 25.27(25.11)
+H, OH, O 10.68(6.31) 5.81(1.79) 1.80(0.50)
+H, OH, O 28.95(23.85) 9.12(3.14) 2.72(0.75)
77.76(77.78) 77.77(77.78) 77.78(77.78) 18.40(19.92) 37.15(37.11) 50.53(50.21) BPHPROPY 72.40(70.13) 44.26(44.33) 24.19(24.68)
CH3 + 10.61(11.11) 11.01(11.11) 11.07(11.11) C2H5 + 7.66(8.04) 13.67(15.26) 16.67(17.22) CH3 + 0.33(0.43) 0.94(1.08) 1.55(1.61)
89.33(88.89) 88.99(88.89) 88.92(88.89)
26.82(28.15) 47.86(53.41) 58.36(60.28)
2.61(3.45) 7.51(8.65) 12.44(12.90)
C2H4 + 25.0(25.0) 23.58(25.0) 23.85(25.0)
75.0(75.0) 70.75(75.0) 71.56(75.0)
Fig. 3. Time-integrated element flux analysis of npropylbenzene during constant pressure auto-ignition processes.
and 1-pentene. The initial H-abstraction of n-propylcyclohexane to form DC9H17C and GC9H17C is only important at low temperature (1000 K), and the two species are therefore removed in the skeletal mechanism. Following up reactions are isomerization and b-scission reaction, with major products to be the cyclohexyl radical as well as ethylene, propylene, and so on. Both the detailed and skeletal mechanism demonstrate that the cyclohexyl radical are nearly 100% transformed to 5hexenyl, a linear alkyl radical. From the above discussions, we can see that accurate reaction rate constants of H-abstraction reactions at different sites for such alkyl substituted cyclohexane compounds are highly important in order to gain deep understanding of the initial reaction pathways of cycloalkanes and to achieve reliable prediction
for the productions of smaller species (e.g., C1– C4 compounds), which play a key role in the oxidation of cycloalkanes. Figure 3 exhibits the reaction pathways of npropylbenzene. For these aromatic compounds, only a few studies have been carried out [18–24]. Previous works mainly focus on benzene and toluene. The reaction mechanisms of benzene and toluene can be considered as the base model for large aromatic compounds. From Fig. 3, the initial dominant reactions for n-propylbenzene combustion are the C–C bond-breaking to produce the ethyl and the benzyl radicals, and the most abundant intermediates during the oxidation of n-propylbenzene are benzyl (PHCH2) and styrene. Further reactions of styrene are mainly through the two reactions, STYREN = C6H6 + C2H2 and STYREN + H = C6H5 + C2H4. The oxidation reaction pathways of benzyl are controlled by the following reactions, toluene = PHCH2 + H, PHCH2 + O = C6H5 + CH2O, PHCH2 = C5H5 (cyclopentadienyl radical) + C2H2, and PHCH2 + O = PHHCO + H. The benzyl radical is the key intermediate in the combustion mechanism of toluene. Therefore, in the detailed and skeletal mechanisms, the mechanisms of benzene, toluene, and styrene are all subcomponent of that for n-propylbenzene. From element flux analysis, we find that further oxidation of C6H6 and C6H5 will form the C6H5O radical, which quickly undergoes a decomposition reaction to produce C5H5 and CO. This indicates that C5H5 is an important intermediate in the oxidation of n-propylbenzene. It will be shown later that this intermediate, C5H5, is also very important near the ignition point for n-propylbenzene with CEMA. Several possible products have been proposed for the decomposition of the benzyl radical. For example, in the reaction scheme of Narayanaswamy et al. [18], the products are proposed to be C5H5 and C2H2, which can be looked as a global reaction. It is thus assumed in their scheme that the fulvanallene species further undergoes a fast reaction with H to ultimately form C5H5 and C2H2. Our results also demonstrate that C5H5 is the dominant reaction intermediate in the oxidation of benzyl, but undergoes a series of important reactions. To sum up, based on the time-integrated element flux analysis, the skeletal mechanism retains the major reaction pathways of the three components in the surrogate mixture, and maintains the hierarchic structure of the detailed mechanism. The time-integrated element flux analysis clarifies the dominant reaction pathways and provides a better understanding for the combustion mechanism of the present multi-component kerosene surrogate. 3.2. Results from brute-force SA and CEMA To understand the dominant ignition chemistry, SA and CEMA are performed by using the
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been removed from the detailed mechanism. The SA results demonstrate that the reaction H + O2 = OH + O is the most sensitive reactions for the three fuels. The results further shows that the chemistry of C2H4 and C3H6 is fairly significant in the ignition process of n-decane and n-propylcyclohexane, while the initial reactions of npropylbenzene and toluene affect the ignition of n-propylbenzene considerably. Some other reactions involving CH3, AC3H5, C2H3, and HO2 also exhibit large influence, hence indicating the important role of C2H4 and C3H6 in the ignition of n-decane and n-propylcyclohexane. For n-propylbenzene, the ignition is affected by the initial reactions of n-propylbenzene notably, and the
detailed and skeletal mechanisms. Figure 4 summarize the elementary reactions with largest sensitivity coefficients and explosive participation index during the course of constant pressure ignition process for the three single hydrocarbon fuels. CEMA is conducted at the state near the ignition point, which is defined as the time point when the temperature is increased by 400 K compared with the initial temperature. It can be seen that the sensitivity coefficients of the dominant reactions are nearly the same in the detailed and skeletal mechanisms. On the other hand, the absolute values of the explosive participation index show slightly larger difference, which may be because that a large number of reactions have
(a) Brute-force sensitivity of n-decane
(b) Explosive participation index of n-decane
C2H3+O2=CH2HCO+O
Skeletal mechanism (1500K) Detailed mechanism (1500K) Skeletal mechanism (1250K) Detailed mechanism (1250K) Skeletal mechanism (1000K) Detailed mechanism (1000K)
C3H6+H=AC3H5+H2
AC3H5+H(+M)=C3H6(+M) 2CH3(+M)=C2H6(+M)
C3H6=C2H3+CH3
AC3H5+HO2=C3H5O+OH
CH2CO+H=CH3+CO
C3H6+H=AC3H5+H2 C3H6+OH=AC3H5+H2O
C2H4+O=CH3+HCO
C3H6=C2H3+CH3
CH3+O2=CH3O+O
C2H4+CH3=C2H3+CH4 C2H4+OH=C2H3+H2O
HCO+M=H+CO+M
CH3+HO2=CH3O+OH
H+O2=OH+O
H+O2=OH+O -50
-40
-30
-20
-10
0
10
20
0.00
0.02
Percent Sensitivity (%)
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Explosive Participation Index
(c) Brute-force sensitivity analysis of n-propylcyclohexane
(d) Explosive participation index of n-propylcyclohexane
C2H3+O2=CH2HCO+O
C3H6+H=AC3H5+H2
AC3H5+H(+M)=C3H6(+M)
CH2CO+H=CH3+CO
C3H6+H=AC3H5+H2 C3H6+OH=AC3H5+H2O
C2H4+O=CH2HCO+H
C3H6=C2H3+CH3
CH3+O2=CH3O+O
C2H4+OH=C2H3+H2O CH3+HO2=CH3O+OH
HCO+O2=CO+HO2
H+HO2=H2+O2
HCO+M=H+CO+M
HO2+OH=H2O+O2 H+O2=OH+O
H+O2=OH+O
-40
-30
-20
-10
0
10
20
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Percent Sensitivity (%)
Explosive Participation Index
(f) Explosive participation index of n-propylbenzene
(e) Brute-force sensitivity analysis of n-propylbenzene
TOLUEN+H=PHCH2+H2
PHC3H7=APHC2H4+CH3
TOLUEN=PHCH2+H
PHC3H7=PHCH2+C2H5 PHC3H7+H=APHC3H6+H2
C5H5+O=C5H4O+H
PHCH2+HO2=PHCH2O+OH
C5H5+OH=C4H6+CO
TOLUEN+H=PHCH2+H2
C2H2+OH=C2H+H2O
TOLUEN+OH=PHCH2+H2O
CH3+O2=CH3O+O
TOLUEN+O2=PHCH2+HO2
CH3+O=CH2O+H
TOLUEN=PHCH2+H
HCO+M=H+CO+M
C3H6=C2H3+CH3
CO+OH=CO2+H
C2H4+OH=C2H3+H2O
H+O2=OH+O
H+O2=OH+O
-60
-50
-40
-30
-20
-10
0
10
Percent Sensitivity (%)
20
30
40
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Explosive Participation Index
Fig. 4. Results of SA and CEMA for n-decane, n-propylcyclohexane, and n-propylbenzene, respectively. The SA and CEMA are performed during constant pressure auto-ignition simulations at pressure of 1 atm with equivalence ratio of 1.0. The PI in CEMA in this figure is conducted at the state near the ignition temperature.
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4. Global mechanism reduction and validation The validated 106-species skeletal mechanism in elementary reaction form is further reduced through QSSA by assuming the fast-depleting species to be QSS species. The CSP procedure outlined in Section 2 is employed to optimally select the QSS species. The results sampled from constant pressure ignition processes are used for CSP analysis. Based on the species time-scale analysis from CSP, we find that large radicals during the oxidation of n-decane, such as decyl, octyl, heptyl, and hexyl, are good candidates for QSS species. These radicals will undergo fast b-scission reactions to decompose to small species once formed. For n-propylcyclohexane and n-propylbenzene, the situation is a little different. The
initial radicals formed by H-abstraction reactions involving n-propylcyclohexane are not suitable for QSS species. On the other hand, the initial radicals formed by H-abstraction reactions of npropylbenzene, denoted as APHC3H6, BPHC3H6, and CPHC3H6, can be good candidates for QSS species, while other large intermediates including benzyl, styrene, toluene, and C5H5 are not suitable for QSS species. In order to make the global mechanism applicable in large-scale CFD
Ignition delay time (Sec)
0.1 0.01
=0.5 (a)Skeletal mechanism ϕ
34-species mechanism p = 1atm
1E-3
5 30
1E-4 1E-5 1E-6 0.6
0.7
0.8
0.9
1000/T(1/K) 0.1
Ignition delay time (Sec)
chemistry of ethylene, propene, and toluene also plays an important role in the ignition process. During the course of ignition, the CEMA results demonstrate that the dominant ignition chemistry for the three fuels with different chemical structures is the oxidation reactions of the small intermediates with H + O2 = OH + O, and HCO + M = H + CO + M being the two most important elementary reactions. The reactions involving C2H4 and C3H6 also demonstrate large explosive participation index in the ignition of ndecane and n-propylcyclohexane. However, CEMA demonstrates that the reactions of toluene and C5H5 have large participation index at the ignition point, which indicates that toluene and C5H5 are very important intermediates in the ignition process of n-propylbenzene. In summary, both SA and CEMA identify reactions of the H2/CO chemistry and those involving C2–C3 species play a critical role in the ignition process of ndecane and n-propylcyclohexane, while reactions of the H2/CO/C2H4 chemistry and those involving n-propylbenzene, toluene, and C5H5 species are very important in the ignition of n-propylbenzene. Results of some recent numerical simulations on flame propagation properties of certain fuels also demonstrate that for n-alkane and cycloalkanes fuels, the laminar flame speed is sensitive largely to the oxidation/combustion chemistry of H2/ CO and C1–C4 hydrocarbons [4,13]; while for alkylated benzene fuels, the flame propagation properties are highly sensitive to fuel-specific chemistry [22]. Therefore, the ignition and flame propagation properties of such hydrocarbon fuels share the same dominant chemistry. This indicates that ignition and laminar flame propagation properties may be independently as valuable criterions for high-temperature combustion mechanism validations. The present work mainly focuses on ignition properties of these hydrocarbon compounds; however, such analysis can be carried out directly on extinction and flame propagation properties.
(b) ϕ = 1.0
0.01 p = 1atm
1E-3
5 30
1E-4
1E-5
1E-6 0.6
0.7
0.8
0.9
1000/T (1/K) 0.1
Ignition delay time (Sec)
192
(c)
ϕ=2.0
0.01 p = 1atm 5
1E-3
30
1E-4
1E-5
1E-6 0.6
0.7
0.8
0.9
1000/T(1/K)
Fig. 5. Ignition delay time of the surrogate mixture, as a function of the initial temperature for constant pressure auto-ignition, with the skeletal mechanism (solid lines), and 34-species reduced mechanism (symbols), respectively.
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simulations, a 34-species reduced mechanism involving 30 linearly independent global reactions is obtained by using the QSSA reduction. The 34-species reduced mechanism is validated against a wide range of parameters for ignition simulation. Figure 5 shows the ignition delay time for constant pressure auto-ignition as a function of the initial temperature. The validation covers a wide range of parameters, i.e., pressure from 1 to 30 atm, initial temperature from 1100 to 1800 K, and equivalence ratio from 0.5 to 2.0. It is demonstrated that ignition delay times from the reduced mechanisms agree well compared with those from the skeletal mechanism, with slightly larger error for high-pressure and low-temperature conditions. This is because for homogeneous mixtures, the negative temperature coefficient (NTC) regime shifts to high temperatures at elevated pressure, and this phenomena is directly related to the oxidation of the alkyl radicals to form the alkylperoxy species. However, this type of reactions is not included in the detailed and skeletal mechanism.
(a)
2800 T0 = 1400K, p = 1atm
2600
Skeletal mechanism 34-species mechanism
Temperature (K)
2400 2200 2000 ϕ = 0.5
1800
ϕ = 2.0
1600
ϕ = 1.0
1400
193
The temperature and species profiles from constant pressure auto-ignition simulations is depicted in Fig. 6, and it can be seen that the 34-species mechanism shows good performance on the temperature and species histories as a function of time. In the present work, the 34-species reduced mechanism is not validated against experiments because large discrepancies exist between different experiment results for kerosene ignition properties [3]. However, the validation of the skeletal mechanism against PSR experiment is given in our previous work [28]. Overall, the global reduced mechanism reproduces the ignition delay time and the major species profiles well compared with the skeletal mechanism above 1000 K under a wide range of simulation parameters. Further, we have compared the CPU time used for constant-pressure auto-ignition simulations by using the detailed, skeletal, and the 34-species reduced mechanisms. The CPU time generally required for the skeletal mechanism is a few seconds, and is about one third of the detailed mechanism. The 34-species reduced mechanism takes a few minutes of CPU time on a 2.6-GHz 32-bit desktop PC, since so many species are assumed to be QSS species and a very large portion of the CPU time is required by the inner iteration loops for these QSS species. We expect new methods [25] for the solution of the QSS species in reduced mechanism involving larger amount of QSS species can be validated in order to further reduce the CPU time. However, the 34-species reduced mechanism derived in the present work provides a starting point toward to develop reliable reduced mechanisms for large scale CFD simulations.
1200 1E-6
1E-5
1E-4
1E-3
5. Conclusions
Time (sec)
(b)
0.1 0.01
C2H4
n-decane
Species Mole Fraction
CO
1E-3
CYC9H18
1E-4 PHC3H7
1E-5 1E-6 1E-7
T = 1500K p = 1atm ϕ = 1.0
Skeletal mechanism 34-species mechanism
1E-8 1E-7
1E-6
1E-5
1E-4
Time (sec)
Fig. 6. (a) Comparison of temperature profiles during constant pressure auto-ignition of the surrogate mixture for kerosene, as a function of equivalence ratio with initial temperature of 1400 K and pressure of 1 atm. (b) Major species profiles during auto-ignition of the surrogate mixture for kerosene at equivalence ratio of 1.0 with initial temperature of 1500 K and pressure of 1 atm.
Currently, most detailed mechanisms are still not comprehensive enough and frequent update of the reaction rate for key reactions is still required to improve predictability of the chemical kinetic mechanisms. Identifying key reactions are thus important for this purpose and it is much easier to be carried out based on skeletal mechanism than on detailed mechanism. The development of systematic and efficient reduction algorithms has made great progress during the past few decades. Based on the skeletal mechanism, we can easily perform SA, CEMA, and other analysis to identify key reaction pathways to facilitate the update of the combustion mechanism. However, one key issue that must be kept in mind in mechanism reduction is that the resulting skeletal mechanisms should preserve all the important species and reactions to avoid some spurious error cancellation. In the present work, we have employed the time-integrated element flux analysis to analyze a skeletal combustion mechanism of a tri-component surrogate mixture,
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consisting of n-decane, n-propylcyclohexane, and n-propylbenzene to scrutinize whether the skeletal mechanism can reproduce the reaction pathways compared with the detailed mechanism. In addition, the dominant ignition chemistry is identified by using SA and CEMA. Results from SA and CEMA demonstrate that the most sensitive reactions of the ignition process for the three different class compounds are different. For n-decane and n-propylcyclohexane, the ignition delay time is sensitive mainly to the oxidation chemistry of small H2/CO and C1–C4 species. However, for n-propylbenzene, the ignition delay time is very sensitive to the initial reactions of n-propylbenzene as well as the reactions of the important intermediate, toluene. This demonstrates that the hierarchic structure should be maintained in the reduction of detailed mechanism of substituted aromatic fuels. By comparing with previous numerical studies on flame propagation properties of certain fuels, we find that the ignition and flame propagation properties of such hydrocarbon fuels share the same dominant chemistry. According to our analysis, the reaction rates of the initial reactions for alkylated cyclohexane and alkylated benzene fuels should be improved in order to gain a better understanding of the initial reaction pathways of these fuels and to update the detailed mechanisms. The skeletal mechanism is further reduced by time-scale analysis. A systematic procedure based on CSP method is adopted to effectively identify the QSS species, and a 34-species global reduced mechanism is derived for ignition by using QSSA. The 34-species mechanism is validated over a wide range of parameters for ignition process, and can be readily used in largescale CFD simulations for jet-engine or related engine simulations. Acknowledgment This work is supported by the National Natural Science Foundation of China (No. 91016002). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.06.011. References [1] P. Dagaut, M. Cathonnet, Prog. Energy Combust. Sci. 32 (2006) 48–92. [2] P. Dagaut, Phys. Chem. Chem. Phys. 4 (2002) 2079– 2094. [3] S.S. Vasu, D.F. Davidson, R.K. Hanson, Combust. Flame 152 (2008) 125–143.
[4] X. You, F.N. Egolfopoulos, H. Wang, Proc. Combust. Inst. 32 (2009) 403–410. [5] S. Honnet, K. Seshadri, U. Niemann, N. Peters, Proc. Combust. Inst. 32 (2009) 485–492. [6] A. Violi, S. Yan, E.G. Eddings, et al., Combust. Sci. Technol. 174 (2002) 399–417. [7] S. Dooley, S.H. Won, M. Chaos, et al., Combust. Flame 157 (2010) 2333–2339. [8] C.V. Naik, K.V. Puduppakkam, A. Modak, et al., Combust. Flame 158 (2011) 434–445. [9] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 114 (1998) 149–177. [10] C.K. Westbrook, W.J. Pitz, O. Herbinet, H.J. Curran, E.J. Silke, Combust. Flame 156 (2009) 181–199. [11] H.J. Curran, P. Gaffuri, W.J. Pitz, C.K. Westbrook, Combust. Flame 129 (2002) 253–280. [12] S.M. Sarathy, C.K. Westbrook, M. Mehl, et al., Combust. Flame 158 (2011) 2338–2357. [13] C. Ji, E. Dames, B. Sirjean, H. Wang, F.N. Egolfopoulos, Proc. Combust. Inst. 33 (2011) 971– 978. [14] Z. Hong, K.Y. Lam, D.F. Davidson, R.K. Hanson, Combust. Flame 158 (2011) 1456–1468. [15] J.P. Orme, H.J. Curran, J.M. Simmie, J. Phys. Chem. A 110 (2006) 114–131. [16] E.J. Silke, W.J. Pitz, C.K. Westbrook, M. Ribaucour, J. Phys. Chem. A 111 (2007) 3761–3775. [17] R.H. Natelson, M.S. Kurman, N.P. Cernansky, D.L. Miller, Combust. Flame 158 (2011) 2325–2337. [18] K. Narayanaswamy, G. Blanquart, H. Pitsch, Combust. Flame 157 (2010) 1879–1898. [19] W.K. Metcalfe, S. Dooley, F.L. Dryer, Energy Fuels 25 (2011) 4915–4936. [20] S. Gudiyella, K. Brezinsky, Combust. Flame 159 (2012) 940–958. [21] P. Dagaut, A. Ristori, A.E. Bakali, M. Cathonnet, Fuel 81 (2002) 173–184. [22] C. Ji, E. Dames, H. Wang, F.N. Egolfopoulos, Combust. Flame 159 (2012) 1070–1081. [23] F. Battin-Leclerc, R. Bounaceur, N. Belmekki, P.A. Glaude, Int. J. Chem. Kinet. 38 (2006) 284–302. [24] S.H. Won, S. Dooley, F.L. Dryer, Y. Ju, Proc. Combust. Inst. 33 (2011) 1163–1170. [25] T.F. Lu, C.K. Law, Prog. Energy Combust. Sci. 35 (2009) 192–215. [26] M. Valorani, F. Creta, D.A. Goussis, J.C. Lee, H.N. Najm, Combust. Flame 146 (2006) 29–51. [27] J.Y. Chen, Combust. Sci. Technol. 57 (1988) 89–94. [28] Q.D. Wang, Y.M. Fang, F. Wang, X.Y. Li, Combust. Flame 159 (2012) 91–102. [29] B.W. Weber, K. Kumar, Y. Zhang, C.J. Sung, Combust. Flame 158 (2011) 809–819. [30] T.F. Lu, C.S. Yoo, J.H. Chen, C.K. Law, J. Fluid Mech. 652 (1) (2010) 45–64. [31] Z.Y. Luo, C.S. Yoo, E.S. Richardson, J.H. Chen, C.K. Law, T.F. Lu, Combust. Flame 159 (2012) 265–274. [32] J. Revel, J.C. Boettner, M. Cathonnet, J.S. Bachman, J. Chim. Phys. – Chim. Biol. 91 (1994) 365– 382. [33] I.P. Androulakis, J.M. Grenda, J.W. Bozzelli, AIChE J. 50 (2004) 2956–2970. [34] K. He, M.G. Ierapetritou, I.P. Androulakis, AIChE J., in press. doi:10.1002/aic.12608. [35] A. Kazakov, M. Chaos, Z. Zhao, F.L. Dryer, J. Phys. Chem. A 110 (2006) 7003–7009.
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Proceedings of the
Proceedings of the Combustion Institute 34 (2013) 187–195
Combustion Institute www.elsevier.com/locate/proci
Systematic analysis and reduction of combustion mechanisms for ignition of multi-component kerosene surrogate Quan-De Wang a, Ya-Mei Fang a, Fan Wang a,⇑, Xiang-Yuan Li b,⇑ a
b
College of Chemistry, Sichuan University, Chengdu 610064, PR China College of Chemical Engineering, Sichuan University, Chengdu 610065, PR China Available online 29 September 2012
Abstract Currently, most detailed chemical kinetic mechanisms for combustion are still not comprehensive enough and update of key reaction rate is still required to improve the combustion mechanisms. The development of systematic mechanism reduction methods have made significant progress, and have greatly facilitated analysis of the reaction mechanisms and identification of important species and key reactions. In the present work, time-integrated element flux analysis is employed to analyze a skeletal combustion mechanism of a tri-component kerosene surrogate mixture, consisting of n-decane, n-propylcyclohexane, and n-propylbenzene. The results of element flux analysis indicate that major reaction pathways for each component in the surrogate model are captured by the skeletal mechanism compared with the detailed mechanism. After that, sensitivity analysis (SA) and chemical explosive mode analysis (CEMA) are conducted to identify the dominant ignition chemistry. The SA and CEMA results demonstrate that the ignition of n-decane and n-propylcyclohexane is sensitive only to the oxidation chemistry of H2/CO and C1–C4 small hydrocarbons, while the ignition of n-propylbenzene is very sensitive to the initial reactions of n-propylbenzene and related aromatic intermediates. This demonstrates that the hierarchic structure should be maintained in the reduction of detailed mechanism of substituted aromatic fuels. The skeletal mechanism is further reduced by combining the computational singular perturbation (CSP) method and quasi steady state approximation (QSSA). A 34-species global reduced mechanism is obtained and validated over a wide range of parameters for ignition. Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Element flux analysis; Sensitivity analysis; Mechanism reduction; Computational singular perturbation; Quasi-steady state approximation
1. Introduction Kerosene is a mixture of a large number of hydrocarbon compounds with different classes of
⇑ Corresponding authors. Fax: +86 28 85407797.
E-mail addresses: [email protected] (F. Wang), [email protected] (X.-Y. Li).
chemical structures, such as alkanes, aromatics, and cycloalkanes, and a wide range of molecular weights. Because of the limitation in available computational resources to deal with combustion processes of a large number of components in real kerosene, a surrogate mixture containing two to five pure compounds is usually adopted to mimic kerosene combustion behaviors [1–8]. In order to develop reliable chemical kinetic mechanisms for
1540-7489/$ - see front matter Ó 2012 The Combustion Institute. Published by Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.proci.2012.06.011
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real fuels, comprehensive kinetic mechanisms have been developed for certain single-component compounds [9–24]. For linear and branched alkanes, it is generally recognized that detailed kinetic mechanisms are well-established [9–12]. However, for cycloalkanes and aromatic compounds, the ring structure in these fuels introduces additional kinetics pathways, and the development of comprehensive kinetic mechanisms for these hydrocarbon fuels is still in progress [13–24]. When detailed mechanisms for each component in the surrogate are established, they can be combined together to mimic combustion behaviors for real fuels. However, these detailed mechanisms of kerosene are highly complicated and numerical investigations are severely restricted to some zero- and onedimensional applications. In order to couple the combustion chemistry of kerosene with large-scale computational fluid dynamics (CFD) simulations, mechanism reduction is critical in combustion community [25]. Mechanism reduction has been extensively studied and various methodologies have been developed as reviewed in Ref. [25]. The first step in mechanism reduction is skeletal reduction [26], which removes unimportant species and reactions from the detailed mechanism. It should be noted that no matter what methods are adopted for skeletal mechanism generation, the realistic chemical kinetics and the major reaction pathways should be maintained in order to achieve reliable skeletal mechanism. When skeletal mechanism has been generated, model reduction methods, such as the quasi-steady state approximation (QSSA) [25–27] can be performed more effectively. Based on the above considerations, the first goal of the present work is to scrutinize how well the skeletal mechanism can reproduce the reaction pathways compared with the detailed mechanism. The detailed mechanism for the three-component kerosene surrogate mixture used in the present work is developed by Dagaut et al. [1,2], and includes 209 species and 1673 reversible reactions. The skeletal mechanism with 106 species and 382 reactions generated in our previous work [28] by using the DRG method combined with the iterative screening and structure analysis (ISSA) method is adopted. The three-component surrogate consists of n-decane (denoted as NC10H22, 74% molar fraction), n-propylbenzene (PHC3H7, 15%), and n-propylcyclohexane (CYC9H18, 11%), which are typical representative compounds of linear alkane, aromatics, and cycloalkanes in kerosene. The second objective is to clarify dominant ignition chemistry of the three different hydrocarbon fuels. This is achieved by using sensitivity analysis (SA) [29] and the chemical explosive mode analysis (CEMA) [30,31]. Furthermore, the skeletal mechanism is further reduced to facilitate CFD simulations. The paper is organized as following: Section 2 presents the methodologies
used in this work; analysis and comparison of results based on the detailed and skeletal mechanism are performed in Section 3; validation and discussion of the global mechanism are presented in Section 4, and main conclusions are summarized in Section 5. 2. Methodologies 2.1. Time-integrated element flux analysis The concept of element flux analysis, proposed by Revel et al. [32], provides a general methodology to identify reaction pathways under certain simulation condition with minimal computational effort. The method is briefly outlined as following. The instantaneous element flux for each element (such as C, H, O) from species k1 to k2 through reaction i, denoted as A_ i;k1!k2 ðtÞ, can be calculated using the following equation [32]: N A;k1 N A;k2 A_ i;k1!k2 ðtÞ ¼ qi ðtÞ N A;i
ð1Þ
where qi ðtÞ is the instantaneous reaction rate of reaction i at time t, N A;k1 , N A;k2 , and N A;i are the number of atom A in species k1, species k2, and reaction i, respectively. The total transformation for element A from species k1 to k2 in a mechanism consisting of I elementary reactions and K species at instantaneous time t can be calculated through the summation of contributions from all reactions: A_ k1!k2 ðtÞ ¼
I X A_ i;k1!k2 ðtÞ
ð2Þ
i¼1
To derive global information, a time-integrated flux indicator is proposed [33,34]: Z s ð3Þ A_ k1!k2 ¼ A_ k1!k2 ðtÞdt 0
Consequently, the time-integrated contribution of reaction i to the flux of element A from k1 to k2, and the normalized weight of element flux from k1 to k2 to the total out flux of species k1 can be easily identified with Eqs. (4) and (5), respectively: Rs _ _ ^ i;k1!k2 ¼ Ai;k1!k2 ¼ R0s Ai;k1!k2 ðtÞdt A ð4Þ A_ ðtÞdt A_ k1!k2 0 k1!k2 Rs A_ k1!k2 ðtÞdt A_ k1!k2 ^ ¼ PK0 R s Ak1!k2 ¼ PK _ _Ak1!k k 0 Ak1!k ðtÞdt k
ð5Þ
2.2. Brute force SA and CEMA Brute force SA is a useful method to identify important reactions which have the largest affects
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on the combustion behaviors. In this work, SA is conducted for ignition delay time based on adiabatic simulations with constant pressure. The percent sensitivity is defined by the following [29]: %Sensitivity ¼
sign ð2k i Þ sign ðk i Þ 100% sign ðk i Þ
ð6Þ
where k i is the rate constant of reaction i, sign ð2k i Þ is the ignition delay time when the rate constant of reaction i is doubled, and sign ðk i Þ is the original ignition delay time. Another method used to identify the dominant chemistry is the CEMA [30,31]. CEMA is based on the CSP method [35]. Both CSP and CEMA have been described in detail elsewhere [25,26,30,31,35] and the concept of the CEMA is only briefly discussed here. In implementing of the CEMA, the Jacobian matrix of the chemical source term is eigen-decomposed, and the eigenvalues indicate the reciprocal characteristic time scales of involved chemical modes. The eigenvector corresponding to a large positive eigenvalue indicates a chemical explosive mode. In order to quantitatively measure the contribution of a chemical species or reactions to a CEM, an explosion index (EI) and an explosion participation index (PI) are defined [30,31]. EI and PI provide important information to identify relevant species and elementary reactions at ignition. Thus, by using the PI in CEMA, we can readily identify the reactions and related species having the most direct and unambiguous influence on ignition. In this work, an in-house package is developed and coupled with CHEMKIN libraries [36,37] to post-process the results of kinetic simulations. Eigenvalue analysis is performed using the LAPACK library facilities [38]. 2.3. CSP and QSSA methods In the present work, QSSA is adopted to further reduce the mechanism. The criterion based on CSP analysis proposed by Lu and Law [39] is employed for QSS species identification. Densely sampled data from constant-pressure ignition processes over a wide range of simulation conditions is used for CSP analysis, and a 34-species global reduced mechanism is derived. The fixed-point algebraic iteration [40] is employed to calculate the concentration of QSS species. 3. Results and discussion 3.1. Results from time-integrated element flux analysis Time-integrated element flux analysis is performed by using the detailed and skeletal mechanism in simulation of the constant-pressure ignition processes. Figures 1–3 show the element flux analysis results for n-decane, n-propylcyclo-
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hexane, and n-propylbenzene, respectively. For ndecane, it can be seen that the skeletal mechanism captures the dominant reaction pathways compared with the detailed mechanism. The Habstraction reaction of n-decane by H, O, and OH radicals is the major reactions in the initial oxidation of n-decane, while the reaction of direct C– C bond-breaking to form ethyl and 1-octyl radicals becomes important as the temperature increases. The following step is the b-scission reaction, which proceeds very fast. For n-propylcyclohexane, once the ring structure is broken, the kinetics controlling subsequent reactions can be modeled with well-established normal and branched alkane mechanisms. Consequently, understanding the initial breakdown steps of n-propylcyclohexane molecule is a key issue to improve the combustion mechanism of these compounds and to validate the skeletal mechanisms. Figure 2 summarizes the major initial reaction pathways of n-propylcyclohexane. The reaction pathways are more complicated than that of n-decane. The H-abstraction reactions by H, OH, O and CH3 radicals at the sites of n-propyl radical and the sites of the ring structure are both important, especially at lowtemperatures. The reaction of C–C bond-breaking to form the n-propyl and the cyclohexyl radicals is the most important reaction in the direct C–C bond-breaking reactions. Another important reaction at high temperature is the lumped reaction of n-propylcyclohexane to form ethylene, propylene,
n-decane 13.18(13.10) 1-decyl 9.60(9.82) 5.41(6.70) 2-decyl 16.01(16.21) 9.14(9.36) 4.32(5.34) 21.54(21.38) 10.17(10.36) 4.65(5.77) 21.54(21.38) 10.17(10.36) 4.65(5.77) 21.54(21.38) 10.17(10.36) 4.65(5.77) 2.59(2.97) 22.32(25.24) 30.31(33.50) 0.64(0.71) 6.62(7.49) 10.45(11.56)
β-scission
1-octyl + C2H4 50.37(50.57) 12.59(12.64) 43.83(45.83) 10.96(11.46) 45.28(47.63) 11.32(11.91) isomerization 5-decyl
3-decyl
4-decyl
(1) β-scission reactions Similar to 1-decyl
5-decyl
(2) isomerization reactions
1-octyl
1-hexyl
Fig. 1. Time-integrated element flux analysis of ndecane during constant pressure auto-ignition processes. The percentages of the conversions (Figs. 1–3) calculated from the detailed mechanism (outside the parenthesis) and skeletal mechanism (inside the parenthesis) from top to bottom represent the analysis at initial temperatures of 1000 K, 1250 K, and 1500 K with equivalence ratio of 1.0 and pressure of 1.0 atm. The percentage of the conversions is defined as the percentage of the flux of element C from one species to another with respect to the total flux of C.
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AC9H17C BC9H17C CC9H17C DC9H17C EC9H17C FC9H17C GC9H17C AC9H17C n-propylcyclohexane 7.57(0) 5.23(7.30) β-scission 2.94(3.58) C3H6+CYC6H11 BC9H17C 10.22(12.88) 5.97(10.00) 3.24(4.07) C2H4+C5H913 CC9H17C 10.22(14.02) 5.97(10.11) Further reactions 3.24(4.07) DC9H17C + GC9H17C 11.44 11.44 4.79 4.79 2.28 2.28 isomerization BC9H17C EC9H17C + FC9H17C 22.85(33.22) 22.85(33.22) 9.57(19.01) 9.57(19.01) 4.57(7.29) 4.57(7.29) CYC6H11 + NC3H7 0.24(0.69) 0.35(1.03) 4.14(3.33) 6.22(4.99) 5.88(7.07) 8.82(10.53) C2H4 + C3H6 + AC5H10 0.00(0.00) 0.95(2.76) 0.39(1.15) 4.16(2.90) 16.58(13.30) 6.91(5.54) 5.88(7.00) 23.52(28.08) 9.80(11.70)
Fig. 2. Time-integrated element flux analysis of npropylcyclohexane during constant pressure auto-ignition processes.
+H, OH, O 17.98(27.11) 11.57(16.56) 4.54(6.72)
C2H4 + 22.24(22.22) 22.23(22.22) 22.22(22.22) C3H6 + 9.20(9.96) 18.59(18.56) 25.27(25.11)
+H, OH, O 10.68(6.31) 5.81(1.79) 1.80(0.50)
+H, OH, O 28.95(23.85) 9.12(3.14) 2.72(0.75)
77.76(77.78) 77.77(77.78) 77.78(77.78) 18.40(19.92) 37.15(37.11) 50.53(50.21) BPHPROPY 72.40(70.13) 44.26(44.33) 24.19(24.68)
CH3 + 10.61(11.11) 11.01(11.11) 11.07(11.11) C2H5 + 7.66(8.04) 13.67(15.26) 16.67(17.22) CH3 + 0.33(0.43) 0.94(1.08) 1.55(1.61)
89.33(88.89) 88.99(88.89) 88.92(88.89)
26.82(28.15) 47.86(53.41) 58.36(60.28)
2.61(3.45) 7.51(8.65) 12.44(12.90)
C2H4 + 25.0(25.0) 23.58(25.0) 23.85(25.0)
75.0(75.0) 70.75(75.0) 71.56(75.0)
Fig. 3. Time-integrated element flux analysis of npropylbenzene during constant pressure auto-ignition processes.
and 1-pentene. The initial H-abstraction of n-propylcyclohexane to form DC9H17C and GC9H17C is only important at low temperature (1000 K), and the two species are therefore removed in the skeletal mechanism. Following up reactions are isomerization and b-scission reaction, with major products to be the cyclohexyl radical as well as ethylene, propylene, and so on. Both the detailed and skeletal mechanism demonstrate that the cyclohexyl radical are nearly 100% transformed to 5hexenyl, a linear alkyl radical. From the above discussions, we can see that accurate reaction rate constants of H-abstraction reactions at different sites for such alkyl substituted cyclohexane compounds are highly important in order to gain deep understanding of the initial reaction pathways of cycloalkanes and to achieve reliable prediction
for the productions of smaller species (e.g., C1– C4 compounds), which play a key role in the oxidation of cycloalkanes. Figure 3 exhibits the reaction pathways of npropylbenzene. For these aromatic compounds, only a few studies have been carried out [18–24]. Previous works mainly focus on benzene and toluene. The reaction mechanisms of benzene and toluene can be considered as the base model for large aromatic compounds. From Fig. 3, the initial dominant reactions for n-propylbenzene combustion are the C–C bond-breaking to produce the ethyl and the benzyl radicals, and the most abundant intermediates during the oxidation of n-propylbenzene are benzyl (PHCH2) and styrene. Further reactions of styrene are mainly through the two reactions, STYREN = C6H6 + C2H2 and STYREN + H = C6H5 + C2H4. The oxidation reaction pathways of benzyl are controlled by the following reactions, toluene = PHCH2 + H, PHCH2 + O = C6H5 + CH2O, PHCH2 = C5H5 (cyclopentadienyl radical) + C2H2, and PHCH2 + O = PHHCO + H. The benzyl radical is the key intermediate in the combustion mechanism of toluene. Therefore, in the detailed and skeletal mechanisms, the mechanisms of benzene, toluene, and styrene are all subcomponent of that for n-propylbenzene. From element flux analysis, we find that further oxidation of C6H6 and C6H5 will form the C6H5O radical, which quickly undergoes a decomposition reaction to produce C5H5 and CO. This indicates that C5H5 is an important intermediate in the oxidation of n-propylbenzene. It will be shown later that this intermediate, C5H5, is also very important near the ignition point for n-propylbenzene with CEMA. Several possible products have been proposed for the decomposition of the benzyl radical. For example, in the reaction scheme of Narayanaswamy et al. [18], the products are proposed to be C5H5 and C2H2, which can be looked as a global reaction. It is thus assumed in their scheme that the fulvanallene species further undergoes a fast reaction with H to ultimately form C5H5 and C2H2. Our results also demonstrate that C5H5 is the dominant reaction intermediate in the oxidation of benzyl, but undergoes a series of important reactions. To sum up, based on the time-integrated element flux analysis, the skeletal mechanism retains the major reaction pathways of the three components in the surrogate mixture, and maintains the hierarchic structure of the detailed mechanism. The time-integrated element flux analysis clarifies the dominant reaction pathways and provides a better understanding for the combustion mechanism of the present multi-component kerosene surrogate. 3.2. Results from brute-force SA and CEMA To understand the dominant ignition chemistry, SA and CEMA are performed by using the
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been removed from the detailed mechanism. The SA results demonstrate that the reaction H + O2 = OH + O is the most sensitive reactions for the three fuels. The results further shows that the chemistry of C2H4 and C3H6 is fairly significant in the ignition process of n-decane and n-propylcyclohexane, while the initial reactions of npropylbenzene and toluene affect the ignition of n-propylbenzene considerably. Some other reactions involving CH3, AC3H5, C2H3, and HO2 also exhibit large influence, hence indicating the important role of C2H4 and C3H6 in the ignition of n-decane and n-propylcyclohexane. For n-propylbenzene, the ignition is affected by the initial reactions of n-propylbenzene notably, and the
detailed and skeletal mechanisms. Figure 4 summarize the elementary reactions with largest sensitivity coefficients and explosive participation index during the course of constant pressure ignition process for the three single hydrocarbon fuels. CEMA is conducted at the state near the ignition point, which is defined as the time point when the temperature is increased by 400 K compared with the initial temperature. It can be seen that the sensitivity coefficients of the dominant reactions are nearly the same in the detailed and skeletal mechanisms. On the other hand, the absolute values of the explosive participation index show slightly larger difference, which may be because that a large number of reactions have
(a) Brute-force sensitivity of n-decane
(b) Explosive participation index of n-decane
C2H3+O2=CH2HCO+O
Skeletal mechanism (1500K) Detailed mechanism (1500K) Skeletal mechanism (1250K) Detailed mechanism (1250K) Skeletal mechanism (1000K) Detailed mechanism (1000K)
C3H6+H=AC3H5+H2
AC3H5+H(+M)=C3H6(+M) 2CH3(+M)=C2H6(+M)
C3H6=C2H3+CH3
AC3H5+HO2=C3H5O+OH
CH2CO+H=CH3+CO
C3H6+H=AC3H5+H2 C3H6+OH=AC3H5+H2O
C2H4+O=CH3+HCO
C3H6=C2H3+CH3
CH3+O2=CH3O+O
C2H4+CH3=C2H3+CH4 C2H4+OH=C2H3+H2O
HCO+M=H+CO+M
CH3+HO2=CH3O+OH
H+O2=OH+O
H+O2=OH+O -50
-40
-30
-20
-10
0
10
20
0.00
0.02
Percent Sensitivity (%)
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
Explosive Participation Index
(c) Brute-force sensitivity analysis of n-propylcyclohexane
(d) Explosive participation index of n-propylcyclohexane
C2H3+O2=CH2HCO+O
C3H6+H=AC3H5+H2
AC3H5+H(+M)=C3H6(+M)
CH2CO+H=CH3+CO
C3H6+H=AC3H5+H2 C3H6+OH=AC3H5+H2O
C2H4+O=CH2HCO+H
C3H6=C2H3+CH3
CH3+O2=CH3O+O
C2H4+OH=C2H3+H2O CH3+HO2=CH3O+OH
HCO+O2=CO+HO2
H+HO2=H2+O2
HCO+M=H+CO+M
HO2+OH=H2O+O2 H+O2=OH+O
H+O2=OH+O
-40
-30
-20
-10
0
10
20
0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18
Percent Sensitivity (%)
Explosive Participation Index
(f) Explosive participation index of n-propylbenzene
(e) Brute-force sensitivity analysis of n-propylbenzene
TOLUEN+H=PHCH2+H2
PHC3H7=APHC2H4+CH3
TOLUEN=PHCH2+H
PHC3H7=PHCH2+C2H5 PHC3H7+H=APHC3H6+H2
C5H5+O=C5H4O+H
PHCH2+HO2=PHCH2O+OH
C5H5+OH=C4H6+CO
TOLUEN+H=PHCH2+H2
C2H2+OH=C2H+H2O
TOLUEN+OH=PHCH2+H2O
CH3+O2=CH3O+O
TOLUEN+O2=PHCH2+HO2
CH3+O=CH2O+H
TOLUEN=PHCH2+H
HCO+M=H+CO+M
C3H6=C2H3+CH3
CO+OH=CO2+H
C2H4+OH=C2H3+H2O
H+O2=OH+O
H+O2=OH+O
-60
-50
-40
-30
-20
-10
0
10
Percent Sensitivity (%)
20
30
40
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
Explosive Participation Index
Fig. 4. Results of SA and CEMA for n-decane, n-propylcyclohexane, and n-propylbenzene, respectively. The SA and CEMA are performed during constant pressure auto-ignition simulations at pressure of 1 atm with equivalence ratio of 1.0. The PI in CEMA in this figure is conducted at the state near the ignition temperature.
Q.-D. Wang et al. / Proceedings of the Combustion Institute 34 (2013) 187–195
4. Global mechanism reduction and validation The validated 106-species skeletal mechanism in elementary reaction form is further reduced through QSSA by assuming the fast-depleting species to be QSS species. The CSP procedure outlined in Section 2 is employed to optimally select the QSS species. The results sampled from constant pressure ignition processes are used for CSP analysis. Based on the species time-scale analysis from CSP, we find that large radicals during the oxidation of n-decane, such as decyl, octyl, heptyl, and hexyl, are good candidates for QSS species. These radicals will undergo fast b-scission reactions to decompose to small species once formed. For n-propylcyclohexane and n-propylbenzene, the situation is a little different. The
initial radicals formed by H-abstraction reactions involving n-propylcyclohexane are not suitable for QSS species. On the other hand, the initial radicals formed by H-abstraction reactions of npropylbenzene, denoted as APHC3H6, BPHC3H6, and CPHC3H6, can be good candidates for QSS species, while other large intermediates including benzyl, styrene, toluene, and C5H5 are not suitable for QSS species. In order to make the global mechanism applicable in large-scale CFD
Ignition delay time (Sec)
0.1 0.01
=0.5 (a)Skeletal mechanism ϕ
34-species mechanism p = 1atm
1E-3
5 30
1E-4 1E-5 1E-6 0.6
0.7
0.8
0.9
1000/T(1/K) 0.1
Ignition delay time (Sec)
chemistry of ethylene, propene, and toluene also plays an important role in the ignition process. During the course of ignition, the CEMA results demonstrate that the dominant ignition chemistry for the three fuels with different chemical structures is the oxidation reactions of the small intermediates with H + O2 = OH + O, and HCO + M = H + CO + M being the two most important elementary reactions. The reactions involving C2H4 and C3H6 also demonstrate large explosive participation index in the ignition of ndecane and n-propylcyclohexane. However, CEMA demonstrates that the reactions of toluene and C5H5 have large participation index at the ignition point, which indicates that toluene and C5H5 are very important intermediates in the ignition process of n-propylbenzene. In summary, both SA and CEMA identify reactions of the H2/CO chemistry and those involving C2–C3 species play a critical role in the ignition process of ndecane and n-propylcyclohexane, while reactions of the H2/CO/C2H4 chemistry and those involving n-propylbenzene, toluene, and C5H5 species are very important in the ignition of n-propylbenzene. Results of some recent numerical simulations on flame propagation properties of certain fuels also demonstrate that for n-alkane and cycloalkanes fuels, the laminar flame speed is sensitive largely to the oxidation/combustion chemistry of H2/ CO and C1–C4 hydrocarbons [4,13]; while for alkylated benzene fuels, the flame propagation properties are highly sensitive to fuel-specific chemistry [22]. Therefore, the ignition and flame propagation properties of such hydrocarbon fuels share the same dominant chemistry. This indicates that ignition and laminar flame propagation properties may be independently as valuable criterions for high-temperature combustion mechanism validations. The present work mainly focuses on ignition properties of these hydrocarbon compounds; however, such analysis can be carried out directly on extinction and flame propagation properties.
(b) ϕ = 1.0
0.01 p = 1atm
1E-3
5 30
1E-4
1E-5
1E-6 0.6
0.7
0.8
0.9
1000/T (1/K) 0.1
Ignition delay time (Sec)
192
(c)
ϕ=2.0
0.01 p = 1atm 5
1E-3
30
1E-4
1E-5
1E-6 0.6
0.7
0.8
0.9
1000/T(1/K)
Fig. 5. Ignition delay time of the surrogate mixture, as a function of the initial temperature for constant pressure auto-ignition, with the skeletal mechanism (solid lines), and 34-species reduced mechanism (symbols), respectively.
Q.-D. Wang et al. / Proceedings of the Combustion Institute 34 (2013) 187–195
simulations, a 34-species reduced mechanism involving 30 linearly independent global reactions is obtained by using the QSSA reduction. The 34-species reduced mechanism is validated against a wide range of parameters for ignition simulation. Figure 5 shows the ignition delay time for constant pressure auto-ignition as a function of the initial temperature. The validation covers a wide range of parameters, i.e., pressure from 1 to 30 atm, initial temperature from 1100 to 1800 K, and equivalence ratio from 0.5 to 2.0. It is demonstrated that ignition delay times from the reduced mechanisms agree well compared with those from the skeletal mechanism, with slightly larger error for high-pressure and low-temperature conditions. This is because for homogeneous mixtures, the negative temperature coefficient (NTC) regime shifts to high temperatures at elevated pressure, and this phenomena is directly related to the oxidation of the alkyl radicals to form the alkylperoxy species. However, this type of reactions is not included in the detailed and skeletal mechanism.
(a)
2800 T0 = 1400K, p = 1atm
2600
Skeletal mechanism 34-species mechanism
Temperature (K)
2400 2200 2000 ϕ = 0.5
1800
ϕ = 2.0
1600
ϕ = 1.0
1400
193
The temperature and species profiles from constant pressure auto-ignition simulations is depicted in Fig. 6, and it can be seen that the 34-species mechanism shows good performance on the temperature and species histories as a function of time. In the present work, the 34-species reduced mechanism is not validated against experiments because large discrepancies exist between different experiment results for kerosene ignition properties [3]. However, the validation of the skeletal mechanism against PSR experiment is given in our previous work [28]. Overall, the global reduced mechanism reproduces the ignition delay time and the major species profiles well compared with the skeletal mechanism above 1000 K under a wide range of simulation parameters. Further, we have compared the CPU time used for constant-pressure auto-ignition simulations by using the detailed, skeletal, and the 34-species reduced mechanisms. The CPU time generally required for the skeletal mechanism is a few seconds, and is about one third of the detailed mechanism. The 34-species reduced mechanism takes a few minutes of CPU time on a 2.6-GHz 32-bit desktop PC, since so many species are assumed to be QSS species and a very large portion of the CPU time is required by the inner iteration loops for these QSS species. We expect new methods [25] for the solution of the QSS species in reduced mechanism involving larger amount of QSS species can be validated in order to further reduce the CPU time. However, the 34-species reduced mechanism derived in the present work provides a starting point toward to develop reliable reduced mechanisms for large scale CFD simulations.
1200 1E-6
1E-5
1E-4
1E-3
5. Conclusions
Time (sec)
(b)
0.1 0.01
C2H4
n-decane
Species Mole Fraction
CO
1E-3
CYC9H18
1E-4 PHC3H7
1E-5 1E-6 1E-7
T = 1500K p = 1atm ϕ = 1.0
Skeletal mechanism 34-species mechanism
1E-8 1E-7
1E-6
1E-5
1E-4
Time (sec)
Fig. 6. (a) Comparison of temperature profiles during constant pressure auto-ignition of the surrogate mixture for kerosene, as a function of equivalence ratio with initial temperature of 1400 K and pressure of 1 atm. (b) Major species profiles during auto-ignition of the surrogate mixture for kerosene at equivalence ratio of 1.0 with initial temperature of 1500 K and pressure of 1 atm.
Currently, most detailed mechanisms are still not comprehensive enough and frequent update of the reaction rate for key reactions is still required to improve predictability of the chemical kinetic mechanisms. Identifying key reactions are thus important for this purpose and it is much easier to be carried out based on skeletal mechanism than on detailed mechanism. The development of systematic and efficient reduction algorithms has made great progress during the past few decades. Based on the skeletal mechanism, we can easily perform SA, CEMA, and other analysis to identify key reaction pathways to facilitate the update of the combustion mechanism. However, one key issue that must be kept in mind in mechanism reduction is that the resulting skeletal mechanisms should preserve all the important species and reactions to avoid some spurious error cancellation. In the present work, we have employed the time-integrated element flux analysis to analyze a skeletal combustion mechanism of a tri-component surrogate mixture,
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consisting of n-decane, n-propylcyclohexane, and n-propylbenzene to scrutinize whether the skeletal mechanism can reproduce the reaction pathways compared with the detailed mechanism. In addition, the dominant ignition chemistry is identified by using SA and CEMA. Results from SA and CEMA demonstrate that the most sensitive reactions of the ignition process for the three different class compounds are different. For n-decane and n-propylcyclohexane, the ignition delay time is sensitive mainly to the oxidation chemistry of small H2/CO and C1–C4 species. However, for n-propylbenzene, the ignition delay time is very sensitive to the initial reactions of n-propylbenzene as well as the reactions of the important intermediate, toluene. This demonstrates that the hierarchic structure should be maintained in the reduction of detailed mechanism of substituted aromatic fuels. By comparing with previous numerical studies on flame propagation properties of certain fuels, we find that the ignition and flame propagation properties of such hydrocarbon fuels share the same dominant chemistry. According to our analysis, the reaction rates of the initial reactions for alkylated cyclohexane and alkylated benzene fuels should be improved in order to gain a better understanding of the initial reaction pathways of these fuels and to update the detailed mechanisms. The skeletal mechanism is further reduced by time-scale analysis. A systematic procedure based on CSP method is adopted to effectively identify the QSS species, and a 34-species global reduced mechanism is derived for ignition by using QSSA. The 34-species mechanism is validated over a wide range of parameters for ignition process, and can be readily used in largescale CFD simulations for jet-engine or related engine simulations. Acknowledgment This work is supported by the National Natural Science Foundation of China (No. 91016002). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http:// dx.doi.org/10.1016/j.proci.2012.06.011. References [1] P. Dagaut, M. Cathonnet, Prog. Energy Combust. Sci. 32 (2006) 48–92. [2] P. Dagaut, Phys. Chem. Chem. Phys. 4 (2002) 2079– 2094. [3] S.S. Vasu, D.F. Davidson, R.K. Hanson, Combust. Flame 152 (2008) 125–143.
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