Skeletal Mechanism of Ethyl Propionate Oxidation for CFD Modeling

Article Cite This: Energy Fuels XXXX, XXX, XXX−XXX

pubs.acs.org/EF

Skeletal Mechanism of Ethyl Propionate Oxidation for CFD Modeling to Predict Experimental Profiles of Unsaturated Products in a Nonpremixed Flame Kuang C. Lin* and Tzu-Wei Lee Department of Mechanical and Electromechanical Engineering, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan S Supporting Information *

ABSTRACT: This study proposes a skeletal kinetic mechanism to investigate the formation of C3−C4 hydrocarbons, carbonyls, and aromatic hydrocarbons from the nonpremixed combustion of ethyl propionate (EP), a biodiesel surrogate. The computational procedure started with the shrinking of an existing detailed EP mechanism to generate a minimized but functionally equivalent mechanism that was then used to combine with previously published submodels that describe polycyclic aromatic hydrocarbons (PAHs) and related compounds. The newly derived EP−PAH mechanism consisting of 79 species and 469 reactions was refined and systematically validated against results of the detailed EP mechanism as well as experimental data. Incorporated into a 2-D axisymmetric laminar finite-rate model, the EP−PAH mechanism without empirical adjustment of the kinetic parameters reproduces concentration profiles in accordance with mass-spectrometrically measured centerline mole fractions of four nonfuel hydrocarbons, three carbonyls, and six aromatic hydrocarbons in the diffusion flame of methane doped with EP. The computational results can be used to interpret experimental PAH data using representative species that are unavailable in the previously published mechanism of EP oxidation. Furthermore, the concentration contour diagrams and reaction pathway analysis reveal the correlation between the decomposition of EP and the formation of the investigated products.

1. INTRODUCTION Growing demand for fossil fuels, limited crude oil reserves, and the necessity to mitigate emissions from fossil-fuel combustion have brought attention to alternative energy sources. Among feasible solutions to these issues, biodiesel, which has been widely used in many countries,1 is one of the most promising alternatives to meet the aforementioned concerns.2 Transesterification,3−5 because of its favorable cost effectiveness, has been the method commonly used to produce biodiesel from vegetable or algal oil with alcohol. In making biodiesel using transesterification, triglycerides that are derived from vegetable oil or animal fats generally can react with methanol to produce fatty acid methyl esters (FAMEs) or with ethanol to yield fatty acid ethyl esters (FAEEs). Ethyl esters typically include aliphatic chains of 14−22 carbon atoms in length.6−11 Although methanol has been widely utilized in transesterification because of its short reaction time and low cost, ethanol is less toxic and more renewable. Furthermore, advantages of FAEEs over FAMEs as fuels include low emissions (CO, NOx, hydrocarbons, and smoke),12 better cold-flow properties,13 higher viscosity,14 higher cetane number,15 and higher flash point.14 Unregulated pollutants such as carbonyl compounds and polycyclic aromatic hydrocarbons (PAHs) have gained increasing interest over the past few years because of their mutagenic and carcinogenic properties.16,17 In the review article of Xue et al.,18 the majority of studies published before 2010 showed that the use of biodiesel as a replacement for or additive to diesel fuels leads to a reduction of the emissions of aromatic hydrocarbons and polycyclic aromatic hydrocarbons (PAHs) but increases in the emissions of carbonyl compounds. The findings, however, are contrary to those reported by relatively recent studies discussed in the same review study,18 © XXXX American Chemical Society

which indicated that engine types and operating conditions (load and cycle mode) appear to significantly alter the effects of biodiesel oxidation on unregulated emissions. Regarding the effects of the ester moiety on combustion emissions in diesel engines, Ballesteros et al.19 reported that the emissions of total PAHs are slightly lower upon the use of FAEEs rather than FAMEs. Aside from experimental investigations of unregulated pollutants, a fundamental understanding can be obtained from chemical the kinetic approach that is beneficial for aiding the development of technologies to reduce unregulated emissions from biodiesel combustion. For more than a decade, the computational description of the oxidation characteristics of real biodiesel fuels has been best approached by utilizing shorter-chain surrogate molecules to reduce the complexity of the chemical reactions without sacrificing the quality of the results.13,20 As FAMEs are major components of commercial biodiesel, there have been numerous chemical kinetic mechanisms developed for the combustion of C1−10 methyl esters. In contrast to methyl esters, FAEEs have received less attention in terms of research into chemical kinetics, where only small esters (i.e., Cn≤6) have been studied.21−32 Among the surrogates of ethyl esters, ethyl propionate [EP, CH3CH2C( O)OCH2CH3], which contains four carbons in its alkyl chain, is the most studied molecule. The pioneering study of EP was conducted by Metcalfe et al.,22 who proposed a kinetic mechanism by analogy with the kinetic parameters in the reaction scheme of methyl butanoate Received: September 18, 2017 Revised: November 17, 2017 Published: December 5, 2017 A

DOI: 10.1021/acs.energyfuels.7b02809 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels Table 1. Detailed Target Parameters Employed in the Path Flux Analysis for the Mechanism Reduction parameter target species primary species in EP oxidation major species measured in previous studies24,29,61 species shared between the EP and PAH submodels pressure (p) temperature (T) equivalence ratio (ϕ) threshold value (ε)

targets O2, N2, Ar, He, CH4, EP H2, H2O, CO, CO2, CH2, CH3, C2H2, C2H4, C2H6, C3H3, C3H4-a, C3H4-p, C3H5-a, C3H6, CH2O, CH2CO, CH3CHO, CH3CHCO, CH3COCH3, C2H3COOH, C2H5COOH HCO, HO2, H2O2, CH2, C2H, C2H3, C2H5, C3H2, CH2CHO 1 and 10 atm 900, 1200, and 1500 K 0.5, 1.0, 2.0 1.0, 1.1, 1.2

(MB, C5H10O2).22 This EP mechanism, with 139 species and 786 reactions, was validated against experimental results from shock-tube ignition delay times at temperatures over the range of 1333−1538 K, equivalence ratios of 0.5−1.5, and pressures of 1 and 4 atm. It was found that EP can be ignited faster than MB because of the presence of a unimolecular six-centered dissociation reaction forming propanoic acid (C2H5COOH) and ethylene (C2H4). Later, Metcalfe et al.24 updated several rate constants for key reactions of EP and validated the mechanism with jet-stirred reactor (JSR) data at 10 atm and a residence time of 0.7 s over temperatures in the range of 750− 1100 K and equivalence ratios of 0.3−2.0. Following the study of Metcalfe et al.,22 Walton et al.23 also updated the rate constants for abstraction reactions of EP and validated the mechanism with data on low-temperature ignition delay times in a rapid compression facility (RCF) over temperatures of 935−1117 K and pressures of 4.7−19.6 atm at equivalence ratios of 0.3 and 0.4. Furthermore, the EP mechanism of Metcalfe et al.24 was validated with concentration profiles of intermediate species in low-pressure flat premixed flames at 30 Torr29 and time-history measurements of EP pyrolysis in a shock tube at 1248−1634 K and 1.5 atm.32 Dayma et al.30 developed a new EP submodel in a C4−C7 ethyl ester mechanism that was derived from the reaction scheme in their published mechanism of ethyl pentanoate (C7H14O2).31 This EP submodel30 was validated with measurements of laminar burning velocities at 1−10 bar, initial temperatures of 323−473 K, and equivalence ratios of 0.7−1.5. From this brief review of EP kinetic mechanisms, it is apparent that these kinetic mechanisms have not been verified with experimental data on nonpremixed flames because of limited studies in this area. In general, the numbers of species and reactions in detailed mechanisms of fuel combustion can be reduced to make the mechanisms usable in computational fluid dynamics (CFD) studies for modeling laboratory- and industrial-scale combustion equipment such as internal combustion engines, gas turbines, burners, and furnace boilers. With the help of reduced mechanisms, chemistry-controlled phenomena such as ignition delay times, emission profiles, and soot formation can be determined in reactive flows. As ester fuels have more complex molecular structures than alkane fuels, mechanism reduction techniques33 are particularly well-suited for allowing oxygenated fuel mechanisms to be coupled with CFD modeling. Accordingly, numerous reduced or skeletal mechanisms of FAME combustion have been proposed and applied in CFD simulations of in-cylinder engine combustion,34−46 spray combustion,37,47 and laminar coflow nonpremixed flames.48−50 Recently, Cheng et al.51 reviewed the outcomes achieved through CFD modeling of in-cylinder biodiesel combustion

coupled with reduced surrogate mechanisms. So far, reduced kinetic mechanisms of methyl ester fuels consisting of 61−117 species39,41,52−54 have been successfully incorporated into three-dimensional (3-D) simulations of in-cylinder engine combustion, which are among the most complex and challenging subjects in CFD. Given the literature review above, mechanism reduction for detailed mechanisms of FAEEs seems to be unavailable at present. In this study, the proposed skeletal mechanism of EP oxidation is shown to be not only sufficiently small for use in CFD modeling but also reasonably accurate and comprehensive for the description of lightweight aromatic hydrocarbons that are unavailable in the existing detailed EP mechanisms. For the first time, the previous mass-spectrometric analysis of hydrocarbons, carbonyl compounds, and low-molecular-weight PAHs (containing up to four aromatic rings) in a nonpremixed flame of CH4/EP/air is verified by computational results from the present chemical kinetic mechanism incorporated into a twodimensional (2-D) CFD model. The novelty of this study bridges the gap between combustion physics and chemistry relating to CFD simulations of ethyl ester oxidation. Practically, this study contributes significant insight toward an understanding of the chemical kinetic mechanisms for the combustion of ethyl ester biodiesel fuels.

2. METHODOLOGY 2.1. Mechanism Reduction and Combination. The CHEM-RC code55,56 based on the path flux analysis (PFA) method is used in the present study to shrink an EP mechanism24 that contains 139 species and 790 reversible reactions. In our previous studies,49,50,57 the PFA method was used to effectively reduce the complexity of the kinetic mechanisms of methyl butanoate49,50 and propane57 in terms of the numbers of species and reactions. The PFA method, as an extension of direct-relation-graph- (DRG-) related methods,58−60 individually analyzes production and consumption fluxes over a two-generation flux analysis. In the analysis procedure, reaction fluxes in the autoignition of homogeneous mixtures and extinction of a perfectly stirred reactor are used to evaluate the importance of other species (B) with respect to target species (A) through an interaction coefficient (rAB) defined in eq S1 in the Supporting Information (SI). If rAB is less than a given threshold value (ε), species B is removed from the detailed mechanism. As we aim to develop a skeletal mechanism that is applicable for the general prediction of chemical reactions in both premixed and nonpremixed combustion, target parameters (see Table 1) used for the mechanism reduction process are chosen across a wide range of experimental conditions.22,24,29,61 In B


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Table 2. Changes Made to Rate Coefficientsa,b in the Skeletal EP−PAH Mechanism, Relative to the PAH Submodel of Wang et al.53 reaction 2C3H3 ↔ A1 C4H5 + C4H2↔ A1C2H + H A1C2H + H ↔ A1− + C2H2 A1− + C2H4 ↔ A1C2H3 + Hc

2C5H5 ↔ A2 + 2Hc

2C5H5 ↔ A2 + H2 A2− + H ↔ A2 C4H2 + A2R5 ↔ A4 A1C2H + A1− ↔ A3 + H A1C2H− + A1 ↔ A3 + H A3− + H ↔ A3

A

n

E

ref

1.00 × 1036 1.00 × 1036 3.16 × 1011 3.16 × 1011 3.30 × 1033 2.00 × 1014 2.51 × 1012 7.23 × 10 2.51 × 1012 4.30 × 1013 3.00 × 1016 4.53 × 105 4.30 × 1013 4.30 × 1036 4.30 × 1036 6.65 × 1015 7.80 × 1013 2.41 × 102 2.41 × 102 1.10 × 1023 1.10 × 1023 1.10 × 1023 1.10 × 1023 8.60 × 1019 1.00 × 1014

−7.18 −7.18 0 0 −5.70 0 0 3.50 0 0.00 0.00 1.83 0 −6.3 −6.3 −0.1 0 2.23 2.23 −2.92 −2.92 −2.92 −2.92 −1.55 0

4234 8413 900 1788 25.5 9701 3095 8345 6150 4888.3 23625 18041 9713 22835 45370 560 0 −569 −1131 8010 15920 8010 15920 1700 0

64 53 64 53 65 53 64 66 53 64 67 67 53 64 53 68 53 64 53 64 53 64 53 69 53

a Rate coefficients listed in modified Arrhenius form k = ATn exp(−E/RT). Units are moles, centimeters, seconds, calories, and kelvin. bPresent values shown in bold face. cDuplicate rate expression employed.

reactions sensitive to these PAH concentrations. Table 2 presents the replacement of these kinetic parameters in the PAH submodel of Wang et al.53 with the previously proposed values64−69 that better describe the experimental measurements of the formation of species A1−A4. The improved predictions of aromatic hydrocarbon formation in the nonpremixed flame are presented in section 3.2. 2.2. Two-Dimensional Nonpremixed Flame. A laminar coflow diffusion flame of CH4/air doped with EP61 is numerically simulated with ANSYS FLUENT v16.1.71 The computational model, based on the experimental setup of Schwartz et al.,61 is a 2-D axisymmetric CFD model with 90 × 40 cells. The bounding geometry, mesh, and boundary conditions used in the simulations are essentially the same as those used earlier,49,50 except that the dopant source is EP in the present study. Table 3 lists the gas flow boundary conditions used in the current investigation. The transient equations of mass, momentum, energy, and species for the reacting flow are documented in eqs S2−S7 in the Supporting

examining the production of skeletal mechanisms, the selection of a threshold value (ε) between 1.0 and 1.2 permits the removal of approximately 60% of the species from the detailed EP mechanism while achieving a kinetic mechanism trade-off between model complexity and predictive ability. Using the normal reflected shock tube reactor module in the Chemkin 4.1 package,62,63 we evaluate the accuracy of high-temperature autoignition predictions for three skeletal mechanisms produced at different values of ε. The simulation errors introduced by removing species and eliminating reaction pathways in the EP mechanism are shown in Figure S1 in the SI for the shock-tube conditions of Metcalfe et al.22 It can be seen that the 57-species skeletal mechanism produced at ε = 1.0 is the best choice, givinng an average error of 6% and a maximum error of 31%. To enhance the applicability of the skeletal EP mechanism for predicting unsaturated hydrocarbon products, the 57species skeletal mechanism with 311 reactions is further integrated with the reduced PAH submodel (17 species and 127 reactions) of Wang et al.53 and the C6H2 submodel (4 species and 14 reactions) in the methylcyclohexane mechanism of Weber et al.70 The singlet state of methylene CH2(s), removed in the reduction process, is added back to the skeletal ethyl propionate−polycyclic aromatic hydrocarbon (EP−PAH) mechanism to minimize the prediction error of the burning velocity introduced by the mechanism reduction. Accordingly, this skeletal EP−PAH mechanism is made up of 79 species and 469 reactions. The rate constants of reactions together with the thermodynamic and transport data in Chemkin format are available in the SI. Here, we improve the accuracy of the A1−A4 predictions by updating the rate constants for several

Table 3. Boundary Conditions Used in CFD modeling for CH4/EP/Air Coflow Nonpremixed Flames

inlet velocity (m/s) inlet gas temperature (K) gas composition (mole fraction, X)

fuel inlet

air inlet

0.0973 450 XEP = 0.005

0.505 300 XO2 = 0.22

XCH4 = 0.495

XN2 = 0.78

XN2 = 0.25 XAr = 0.25 C


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Energy & Fuels Information. Equations S2−S6, which govern this atmospheric reactive flow, are discretized with a second-order upwind scheme and solved by means of an implicit finite-volume based SIMPLE (semi-implicit method for pressure linked equations) algorithm. The mixture density is determined by the ideal gas law. In the energy equation (eq S5), the specific heat at constant pressure is calculated by the mixing law. Both the viscosity in the flow equations (eqs S3 and S4) and the thermal conductivity in the energy equation (eq S5) are estimated by the ideal gas mixing law. Based on the kinetic theory, the mass diffusivity in each species transport equation (eq S6) is obtained. The thermodynamic and transport properties of each gas are temperature-dependent. The Maxwell−Stefan equation (eq S7), which describes a full multicomponent diffusion model along with thermal diffusion, is used to close species transport equations using the diffusive mass flux vector Ji̅ in eq S6. Although the previous study72 on the laminar diffusion flame of CH4 indicated that the radiating species H2O, CO, CO2, and soot lead to a temperature drop of up to 122 K, our primary test on the radiative losses shows a limited change with the temperature, possibly because of the exclusion of soot formation. Thus, the radiation dominated by the molecular species is not taken into consideration in the present study. The chemical source term in eq S6 is modeled by a laminar finiterate model using the Arrhenius expression. When the finite-rate chemistry in the present model is solved by a stiff chemistry solver with the in situ adaptive tabulation (ISAT) method, the CFD modeling fails to converge to a physically correct solution. Instead, the finite-rate chemistry in the present study is solved by the CHEMKIN-CFD solver,73 which allows for wellconverged solutions with high under-relaxation factor values. Eventually, the normalized residuals of the continuity, momentum, and species equations are less than 10−4, and the solution of the energy equation is converged with a normalized residual of 10−6.

Figure 1. Ignition delay times and computational errors are introduced in the use of the skeletal EP−PAH mechanism. The reactive flow parameters are based on the shock-tube experiments by Metcalfe et al.22 and the rapid compression facility experiments by Walton et al.23

mechanism leads to increased ignition delay times in the temperature range of 1200−1600 K. Although the relative errors between the detailed EP and skeletal EP−PAH mechanisms range from 20% to 30% in the temperature range of 1200−1600 K, the ignition delay times computed with the skeletal EP−PAH mechanism lie within the experimental scatter. In the low-temperature range from approximately 830 to 1150 K, the simulation errors introduced by the use of the skeletal EP−PAH mechanism are quite small. Moreover, the skeletal EP−PAH mechanism well preserves the accuracy of the predicted autoignition delay times at an initial pressure of 40 atm and initial temperatures from 900 to 1800 K for equivalence ratios of 0.3−3. The comparison in Figure S2 in the SI shows that there are small errors (5−9%) between the ignition delay times obtained for the detailed and skeletal EP− PAH mechanisms. Figure 2 presents the calculated species profiles in a 0-D JSR compared with the experimental data.24 It can be seen that the mole fraction profiles are nearly uninfluenced by the mechanism reduction and addition of the PAH and C6H2 submodels. In accordance with the previous study,24 the JSR modeling underpredicts the formation of ethylene (C2H4) and propionic acid (C2H5COOH) at temperatures higher than 900 K under fuel-rich conditions. Figure S3 in the SI shows the relative errors between the detailed and reduced mechanisms for predictions of the JSR species profiles. The skeletal EP− PAH mechanism, which yields an average error of 7% and a maximum error of 35%, gives a close estimate of the calculated values obtained from the detailed mechanism with 139 species. The steady and isobaric 1-D equations for flow, energy, and species are numerically solved by a finite-difference scheme to calculate the laminar burning velocity and species profiles of low-pressure flat premixed flames. The adaptive grid control parameters for gradient and curvature are set to 0.05 to achieve grid-independent results. Figure 3 shows that the use of the skeletal EP−PAH mechanism introduces approximately 2.0% and 2.5% average errors in predicting the burning velocities at reaction pressures of 1 and 3 bar, respectively. Furthermore, the

3. RESULTS AND DISCUSSION 3.1. Validation of the Mechanism in Zero- and OneDimensional Premixed Flames. Table 4 summarizes the Table 4. Operating Conditions of Premixed Combustion Experiments Used for Validating the Skeletal EP−PAH Mechanism

autoignition22,23 JSR species profiles24 laminar burning velocity30 species spatial profiles29

pressure (atm)

temperature (K)

equivalence ratio (ϕ)

1−10 10 1−10

975−1538 775−1012 325−475

0.3−1 0.3−2 0.7−1.5

0.04

300

1.56

operating parameters with which the predictive ability of the skeletal EP−PAH mechanism is validated herein. The detailed EP mechanism and skeletal EP−PAH mechanism are incorporated into various zero-dimensional (0-D) and onedimensional (1-D) premixed codes, respectively, in the CHEMKIN 4.1 package62,63 for modeling different aspects of combustion performance. Figure 1 shows 0-D ignition delay time calculations compared with the experimental data from shock-tube22 and rapid compression facility23 experiments. It can be observed that adding the PAH and C6H2 submodels to the skeletal EP D


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and gas pressure on the burning velocity. The data (see Figure S4 in the SI) computed for the 79-species EP−PAH mechanism show good agreement with the experiments, as well as with the data predicted by the 139-species EP mechanism. Regarding the predictions of concentration profiles in the low-pressure premixed flame (see Figure 4), the skeletal

Figure 4. Comparisons of experimentally measured spatial mole fraction profiles29 with results predicted using the 139-species EP mechanism24 and the 79-species EP−PAH mechanism for the lowpressure flat premixed flame: (a.1−a.5) major species, (a.6−a.10) C1− C2 hydrocarbons, (b.1−b.4) C3 hydrocarbons, and (b.5−b.8) oxygenated intermediates.

Figure 2. Comparisons between experimental24 and computational mole fraction profiles of a jet-stirred reactor at 10 atm and 0.7-s residence time. The reactive flow parameters are based on the experiments by Metcalfe et al.24

EP−PAH mechanism preserves the accuracy of the original detailed mechanism except for propyne (C3H4-p), for which the removal of reactions lowers its formation rate. In general, the measured mole fractions of C1−C3 hydrocarbons and carbonyls are reasonably captured by the detailed EP mechanism with the exception of propyne (C3H4-p) and acetone (CH3COCH3), for which the computed mole fractions are 1−2 orders of magnitude lower than the experimental data. 3.2. Comparison between CFD and Experimental Results for a Nonpremixed Flame. Using the present skeletal EP−PAH mechanism coupled with the 2-D CFD model, the mass-spectrometically measured intermediate products in the nonpremixed flame of CH4/EP/air61 are verified for the first time by computational methods. The experimentally deduced isomers with molecular weights of 40− 202 amu comprise hydrocarbons, oxygenated byproducts, and aromatic hydrocarbons. Their chemical formulas/compounds in the present skeletal mechanism are listed in Table 5. Note that the original EP mechanism24 includes only six species to describe the experimentally observed products: C3H4, C3H6/ C2H2O, C3H4O/C4H8, and C3H6O2. In the present skeletal EP−PAH mechanism, we observe that several rate constants for the reactions forming lightweight aromatic hydrocarbons cause significant underpredicted mole fractions of A1−A4.

Figure 3. Laminar burning velocities and computational errors introduced by the use of skeletal mechanisms. The reactive flow parameters are based on the experimental conditions of spherically expanding flames studied by Dayma et al.30

prediction capability of the skeletal EP−PAH mechanism is examined in terms of the effects of unburned gas temperature E


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Table 5. Species Employed in the Present Skeletal Mechanism to Predict Mass-Spectrometrically Determined Products in the Nonpremixed Flame of CH4/EP/Air

nonpremixed flames,49,50,57 the existence of the overpredicted CO2 and temperature at flame heights of z/HT > 0.75 in Figure 5 is likely due to the ignorance of the soot radiation model. Table 6 shows that the CFD-computed temperature values on the flame centerline are in better agreement with the experimental value than is the analytical estimation.

The presently computed data and the mass-spectrometric data of Schwartz et al.61 at the centerline of the flame are compared in Figures 5−7. The heights of peak flame

Table 6. Comparisons between CFD-Computed and Previously Reported Tg1%a Values

experiments of Schwartz et al.61 analytical estimation61 EP mechanismb (57 species, 311 rxns) EP−PAH mechanismb (79 species, 469 rxns)

Tg1% (K)

error relative to experiment (%)

1238 1147 1178 1197

0 7.4 4.8 3.3

a

Temperature point captured at an EP concentration of 1% of the initial amount (50 ppm mol). bPresent CFD simulations with the skeletal mechanism.

The major C3−C6 products in the undoped and EP-doped flames are computed with the skeletal EP−PAH mechanism and compared with the experimental data of Schwartz et al.61 in Figure 6. In general, the predictions of these unsaturated C3− C6 products are in qualitative agreement with the trends of the experimental data. As indicated by both the experimental and computational results, the oxidation of EP gives rise to propadiene (C3H4-a, Figure 6a), propyne (C3H4-p, Figure 6a), propene (C3H6, Figure 6b), and propionic acid (C3H6O2, Figure 6d), as well as methyl ketene (CH3CHCO, Figure 6e). According to the rate-of-production (ROP) analysis at the mole fraction peaks, the yields of propadiene (C3H4-a), propyne (C3H4-p), and ethenone (CH2CO) are correlated with the decomposition of propene (C3H6). Moreover, the ROP analysis at the mole fraction peaks also shows that both propionic acid (C3H6O2, Figure 6d) and methyl ketene

Figure 5. Comparisons between measured61 and present computed centerline profiles of temperature and main species in the coflowing nonpremixed flame of CH4/EP/air at 1 atm.

temperatures, namely, HT = 3.86 cm for the CH4/EP/air flame and HT = 3.71 cm for the CH4/air flame, are used to normalize the axial coordinate z. The CFD-modeled profiles of temperature, CH4, O2, and CO2 shown in Figure 5 are not greatly affected by the addition of the PAH chemistry. Moreover, Figure 5 indicates the satisfactory agreement between the simulations and the experimental data. As also reported in our previous studies on the modeling of F


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benzene to PAHs,74 C6H2 (Figure 6d) is formed by the addition reaction of diacetylene (C4H2) and the ethynyl radical (C2H), where C4H2 is a byproduct yielded in the PAH submodel. The underpredicted C4H4 (Figure 6c) is primarily formed by the recombination of vinyl radicals (C2H3) and further undergoes cyclization reactions with other hydrocarbon radicals to form PAHs. Figure 7 presents comparisons between the previous measurements of Schwartz et al.61 and the presently computed

Figure 6. Centerline concentrations of C3−C6 intermediate products: comparisons between the experimental measurements of Schwartz et al.61 and the present CFD simulations using the skeletal EP−PAH mechanism (79 species).

(CH3CHCO, Figure 6e) are fragments of EP and that their fuel-bound oxygen comes from the ethyl ester moiety. As shown in both the experimental and computational data in Figure 6d,e, the increased mole fractions of the EP-derived carbonyls at flame heights of z/HT = 0.2−0.4 are in accordance with the location where EP is consumed (Figure 5). The computational results, however, are not able to describe well the experimentally observed destruction of CH3CHCO at flame heights z/HT near 0.5. In Figure 6b,d, the computed mole fractions for each isobaric species are separately depicted to better identify which species lead to the discrepancy between the experimental data and the predictions. We observe that the predicted peaks for carbonyl formation (Figure 6b,d,e) in the EP-doped flame are 1−2 orders of magnitude higher than the experimental data. The overpredicted formation of propionic acid (C3H6O2) is contradictory to the outcome where C3H6O2 is underpredicted in rich premixed jet-stirred flames (see Figure 2). Nevertheless, these oxygenated hydrocarbons in the CH4 flame are relatively well predicted, except for the overpredicted formation of ethenone (CH2CO) in Figure 6b. The present results suggest the need to improve the kinetic parameters or reaction schemes describing the oxidation of ethenone (CH2CO) in methane combustion. Furthermore, vinylacetylene (C4H4, Figure 6c) and 1,3,5-hexatriyne (C6H2, Figure 6d) are recognized to be the products of CH4 oxidation because their concentration profiles are not considerably changed by doping CH4 with EP. Playing a role in converting acetylene and

Figure 7. (a) Maxima and (b) profiles of the centerline concentrations of lightweight aromatic hydrocarbons. Symbols represent the experiments of Schwartz et al.61 (solid, CH4/EP/air; open, CH4/air). Lines represent CFD results with the EP−PAH mechanism (solid, CH4/EP/ air; dashed, unrefined reaction rate constants of CH4/EP/air; dashdotted, CH4/air).

concentrations of lightweight PAHs along the centerlines of the EP-doped flames. In general, the computed peaks of PAH mole fractions in Figure 7a capture well the order of magnitude measured experimentally for the EP-doped methane flame. In addition, the computed mole fraction profiles of PAHs in Figure 7b give qualitative support to the experimental results obtained for methane with and without EP as a dopant. It can G


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Energy & Fuels be seen in Figure 7b that the underprediction of the centerline profiles can be significantly improved by the refinement of the rate constants presented in Table 2. However, the refined mechanism of EP−PAH still consistently underpredicts PAHs in Figure 7b, suggesting a need for future research to refine the reaction pathways, kinetic parameters, and thermal data used in the PAH submodel. The causes of the underpredictions, especially for A1C2H (phenyl acetylene), A1C2H3 (styrene), and A2 (naphthalene), are explored in the reaction pathway analysis in section 3.4. Moreover, the computed centerline profiles in Figure 7b show that doping CH4 with EP increases the mole fractions for all of the PAHs investigated. This qualitative prediction is consistent with the experimental findings except for A3 (phenanthrene) and A4 (pyrene), for which the measured mole fractions are not raised by the EP decomposition. Furthermore, both the experimental and computational results indicate that most of the PAHs peak at the level of z/HT = 0.5−0.8 (Figure 7b), where no EP is present and methane drops from 0.1 to nearly 0 mol % (Figure 5). A1, A1C2H, and A1C2H3 are formed by a series of reactions initiated by the presence of the vinyl radical (C2H3) derived from ethylene (C2H4). These single-ring species further lead to the formation of multirings of aromatics through cyclization reactions. In examining the computational demands of performing CFD simulations using the skeletal mechanisms (see Table 7),

Figure 8. Flames of CH4/air (left) and CH4/EP/air (right): mole fraction contours computed for (a) temperature, (b) fuel, (c) O2, and (d) OH radical.

Table 7. Performance Comparisons for the Skeletal Mechanisms Used in the Present CFD Modeling of Nonpremixed CH4/EP/Air Flames after 3200 Time Steps in a Mesh of 3600 Cells skeletal mechanism

no. of species

no. of reactions

CPU timea (h)

EP EP−PAH

57 79

311 469

43.53 77.68

a

Computations performed on a Windows workstation running a 2.1 GHz processor (Intel Xeon E5-2620 V4) with 22 cores in parallel.

it is found that a 37% increase in the number of species for the PAH submodel leads to a 28% increase in the total simulation time. The converged solutions attainable at acceptable computational runtimes imply that the present mechanism reduction enables CFD practitioners to economically model complex chemistry in multidimensional combustion simulations. 3.3. Contour Analysis. The predicted 2-D maps of the temperature, fuel, O2, and OH radical are shown in Figure 8 for undoped and EP-doped flames. Similarly to the experimentally measured centerline profiles, the computational simulations reflect that the addition of EP to the CH4 flame does not alter the fields of temperature and oxygen gradients. It can be seen that O2 is fully oxidized around the surface of the hightemperature zone. The hydroxyl radical, OH, which is the principal oxidant, forms mainly in the wing region, and its concentration remains essentially unchanged with the added dopant. Moreover, in the fuel-port area (from r = −0.6 cm to r = 0.6 cm), where fuels are primarily pyrolyzed, EP is consumed faster than CH4. Figure 9 shows the mole fraction contours of the undoped and EP-doped flames corresponding to the species profiles presented in Figures 6 and 7b. For the CH4 flame doped with EP, the pronounced mole fraction of ethylene (C2H4) at the inner flame tip near z/HT = 0.3−0.4 is attributed to the

Figure 9. Flames of CH4/air (left) and CH4/EP/air (right): mole fraction contours computed for C2−C3 carbonyls, C2−C4 unsaturated hydrocarbons, C6H2, and lightweight PAHs.

decomposition of the fatty-acid-derived hydrocarbon chain. EPformed C2H4, in turn, can be converted to propene (C3H6), which can be seen to be concentrated at the slightly upper position (z/HT = 0.4−0.5). Propadiene (C3H4-a) and propyne (C3H4-p), which are derivatives of propene, appear to be slightly increased in the flame doped with EP. Furthermore, EPformed C2H4 can alternatively lead to the formation of vinylacetylene (C4H4), which attains a higher concentration level in the EP-doped flames than in the CH4 flame. C6H2, formed mainly by acetylene (C2H2), peaks at the inner flame tip, and its maximum concentration spatially corresponds to the fields where A1C2H3 and A3 are indirectly formed by C6H2. CH2CO, produced by the reaction of the propargyl radical (C3H3) with O2, correlates with the isopleth of propene (C3H6). As a product of six-centered EP elimination, the carbonyl C2H5COOH is considerably seen at z/HT = 0.3−0.4, H


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Energy & Fuels

Figure 10. Major reaction pathways from EP to C3−C4 unsaturated hydrocarbons, carbonyls and aromatic hydrocarbons in the CH4/EP/air nonpremixed flame. The rate-of-production (ROP) analysis was performed at r = 0 and z/HT = 0.246, where 35% of EP is consumed at 947 K. The notation “A/B” indicates that A% of reactant(s) produces B% of product(s) in the ROP analysis. Bold arrows represent the main reactions forming the products.

determinations obtained with the detailed EP mechanism (see Table S1 in the SI). However, some primary reactions consuming or forming target species A are removed from the original mechanism due to the fact that a nontarget species B in eq S1 does not play a significant role in reacting with a third species M. Figure 10 depicts the rate-of-production analysis performed in the nonpremixed flame of CH4/EP/air at a normalized flame height of z/HT = 0.246 along the flame centerline. It can be seen that 35% of EP is primarily consumed by the six-centered unimolecular decomposition reaction (R245), followed by the H-atom abstraction from EP (R253). C2H4 and C2H5COOH are directly formed by the initiation reactions of EP, reflecting their abundant concentrations among the products investigated in Figure 9. The formation of the secondary rich carbonyl, CH3CHCO, originates in the H-atom abstractions of EP (R253) and C2H5COOH (R290), followed by the β-scission reactions of the ensuing radicals. Triggered by the vinyl radical (C2H3), propene (C3H6) decomposes to form the allyl radical (C3H5-a), which can attract H atoms from various intermediates to be the main reactions forming propene. The allyl radical (C3H5-a) further undergoes subsequent H-atom abstractions to form propadiene (C3H4-a) and the propargyl radical (C3H3), respectively. It can be seen that various

where EP is primarily consumed. The other carbonyl, CH3CHCO, peaks at the relatively high position of z/HT = 0.4−0.5 because it is formed by a series of reactions that break down EP. With regard to the aromatic hydrocarbon isopleths, the high-concentration areas are substantially increased by the addition of EP to CH4. Their regions of maximum mole fraction are seen at the inner flame tip near z/HT = 0.6, except for A4, which is noticeably thicker along the centerline and spread upward (z/HT = 0.6−0.8) to the maximum-temperature region. The high-concentration area of A4 that grows upward in the flame is ascribed to the relatively greater number of reaction steps involved in the conversion of small hydrocarbons into aromatic hydrocarbons. 3.4. Reaction Pathway Analysis. As the rate-ofproduction (ROP) analysis uses the database of the skeletal mechanism, concern is raised over whether the reaction pathways for assessing species formation are accurate representations of the detailed chemistry. Accordingly, a preliminary assessment is performed using the reaction rate data obtained from the calculations of species profiles of Figure 4 for the low-pressure flat premixed flame. In examining the normalized rates of reaction for major species at 35% of the fuel consumption, the dominant reactions estimated for the skeletal EP−PAH mechanism are qualitatively consistent with the I


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Energy & Fuels

Figure 11. Major reaction pathways from C2H4 to C3−C4 unsaturated hydrocarbons and aromatic hydrocarbons in the CH4/EP/air nonpremixed flame. The rate-of-production (ROP) analysis was performed at r = 0 and z/HT = 0.5, where the reactive temperature is 1543 K. The notation “A/B” indicates that A% of reactant(s) produces B% of product(s) in the ROP analysis. Bold arrows represent the main reactions forming the products.

forming aromatic hydrocarbons are initiated by ring-opening reactions (R418 and R414) of A2 forming A1C2H.

bimolecular reactions consuming C3H3 lead to the formation, in order, of CH2CO > A1 > C5H5 > propadiene (C3H4-a). It is worth noting that the competing channels between R229 and R339 suggest a direction for further improving their rate constants, which cause the overpredicted CH2CO profile in Figure 6b and the underpredicted A2 profile in Figure 7. Further, A2 and A3 are formed, respectively, by the dimerization of C5H5 and the cyclization of benzene with the radical A1C2H−. Formed by the reaction of C2H3 and C2H2, C4H5 yields vinylacetylene (C4H4) by H-atom abstraction (R354) while producing A1C2H (R393) and A1C2H3 (R382) through cyclization reactions. A very small portion of A1C2H can be seen to lead the reaction pathways forming A2R5 (R422), A3 (R433), and A4 (R424) through consecutive cyclization reactions. Figure 11 shows the ROP analysis at a normalized flame height of z/HT = 0.5 along the centerline, where EP is fully consumed and the concentrations of intermediate hydrocarbon products are relatively high. As CH4 is highly decomposed at this location, the addition of the methyl radical CH3 to the double bond of C2H4 becomes the main reaction forming C3H6. Propyne (C3H4-p), near its maximum yield, has a negligible production rate and mainly decomposes to form the propargyl radical (C3H3). As propene is at its maximum concentration, the dimerization of propagyal radicals (R361) forming A1 is enhanced. At relatively high temperature, the reaction pathways from C2H3 to aromatic hydrocarbons become less significant, whereas the main reaction pathways

4. CONCLUSIONS In this study, a skeletal mechanism of EP−PAH is developed in response to the need for predicting the complex chemical kinetics associated with the nonpremixed combustion of fatty acid ethyl ester fuels. Using path flux analysis, a 57-species skeletal mechanism, selected as a trade-off between model complexity and prediction accuracy, is derived from the detailed 139-species mechanism. Integrated with PAH and carbonyl submodels, the skeletal EP−PAH mechanism made up of 79 species and 469 reactions offers a predictive capability suitable for 3-D CFD simulations of in-cylinder engine combustion. In general, the skeletal EP−PAH mechanism preserves the prediction accuracy exhibited by the original EP mechanism for estimating autoignition, burning velocity, and species formation. The operating conditions employed in this skeletal EP−PAH mechanism include a wide range of equivalence ratios (0.3−3), initial temperatures (900−1800 K), and initial pressures (0.04−40 atm). For the first time, previous experiments that mass-spectrometrically detected isobaric species in a nonpremixed methane/ air flame doped with ethyl propionate are computationally reproduced to yield detailed information on product mole fractions with spatial resolution, thereby providing valuable insights into the reaction−diffusion dynamics and reaction pathways. In addition to the predicted temperature and profiles J


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Energy & Fuels of CH4, EP, O2, and CO2 along the flame centerline, the intermediate products, which are identified in the CFD analysis for comparison with experiments, include propyne/propadiene (C3H4), propene (C3H6), vinylacetylene (C4H4), propionic acid (C2H5COOH), methyl ketene (CH3CHCO), ethenone (CH2CO), and 1,3,5-hexatriyne (C6H2), as well as benzene (C6H6), phenyl acetylene (C8H6), styrene (C8H8), naphthalene (C10H8), phenanthrene (C14H10), and pyrene (C16H10). Without empirically adjusted rate constants for elementary reactions, the CFD model coupled with the skeletal EP−PAH mechanism is able to adequately predict the previous measurements of species profiles. In particular, the results computationally verify the concentration increases of C2H5COOH and CH3CHCO as well as aromatic hydrocarbons upon the doping of CH4 with a small amount of EP. Quantitatively, the oxygenated products are overpredicted by 1 or 2 orders of magnitude, whereas C4H4, A1C2H, A1C2H3, A2, and A4 are underpredicted within 1 or 2 orders of magnitude. The reaction pathway indicates that the carbonyls C2H5COOH and CH3CHCO are the derivatives of the ethyl ester group, whereas ethylene, formed by the unimolecular sixcentered dissociation reaction of EP, is mainly responsible for the successive production of unsaturated C3−C4 hydrocarbons and aromatic hydrocarbons. In terms of computational cost, the CPU time needed in this study for simulating the nonpremixed combustion of EP with realistic chemistry is quite modest, suggesting an essential role for this skeletal mechanism as a base model for developing kinetic mechanisms of large ethyl ester fuels.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.energyfuels.7b02809. Supplementary data and kinetic mechanism in CHEMKIN format (PDF) Kinetic mechanism (TXT) Thermal data (TXT) Transport data (TXT)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Kuang C. Lin: 0000-0003-4177-8540 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Mr. Chuang-Te Chiu for his invaluable technical assistance in mechanism editing and coflow flame simulations. This study was financially supported by Ministry of Science & Technology (MOST) of Taiwan under Contract MOST 104-2628-E-110-004-MY3. The authors express their gratitude to Dr. Bill Schwartz of Yale University for kindly providing experimental data on esters in the nonpremixed flame study.

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Skeletal Mechanism of Ethyl Propionate Oxidation for CFD Modeling

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