Prediction Accuracy and Efficiency of the n-Heptane Mechanism at

Article pubs.acs.org/EF

Prediction Accuracy and Efficiency of the n‑Heptane Mechanism at Different Reduction Levels Guorui Jia, Mingfa Yao, Hu Wang, Yang Wang, and Lixia Wei* State Key Laboratory of Engines, Tianjin University, Tianjin 30072, People’s Republic of China S Supporting Information *

ABSTRACT: The detailed combustion mechanism can be coupled with the computational fluid dynamics (CFD) software to simulate the combustion process in a practical engine. However, the computing time may be unfeasibly long. To improve the efficiency of the simulations, a reduced mechanism is preferable. However, the combustion characteristics and prediction accuracy will be influenced by the reduction of the combustion mechanism. In this work, the effects of the reduction of the detailed n-heptane mechanism on the prediction accuracy and efficiency were investigated theoretically. The reduction was based on the directed relation graph method without revising the original kinetic parameters. The results indicated that the reduced combustion mechanism at 1/2 size (1/2 mechanism) of the detailed mechanism performed well and the 1/4 mechanism showed some deviation from the experimental data as a result of the removal of some low-temperature reactions. The 1/8 mechanism performed even worse. An ideal combustion mechanism for coupling with CFD simulations should be of the size between that of the 1/2 mechanism and 1/4 mechanism.

1. INTRODUCTION Combustion is a complex process involving combustion chemistry and fluid dynamics.1 The coupling of these two factors complicates the understanding of combustion, especially in the engine cylinders. With the development of computer science and related technologies, simulation has become one of the most powerful methods to study the details of the combustion in engine cylinders, including the ignition, flame propagation, combustion stability, pollutant formation, etc.2−5 Computational fluid dynamics (CFD) is a preferable simulation method, with its few constrictions on the size of the combustion mechanism. Typically, over 90% of the computing resource is allocated to the combustion chemistry in such simulations. Coupling a detailed combustion mechanism is too time-consuming in CFD simulations. Therefore, the reduced combustion mechanism will be an alternative to improve the simulation efficiency.6,7 However, the adoption of the reduced combustion mechanism will sacrifice the accuracy as a trade-off. The reduction level of the combustion mechanism influences the accuracy and efficiency of the CFD simulation. Several reduction methods for the detailed combustion mechanisms have been reported, including the tabulation method involving in situ adaptive tabulation (ISAT),8 the dynamic adaptive chemistry (DAC),9 the directed relation graph (DRG) method,10 the directed relation graph with error propagation (DRGEP) method,11 the sensitivity and principal component analysis,12 the lumping method,13 the computational singular perturbation (CSP) method,14 etc. The accuracies and applications of these methods are also different. The DRG method consists of the generation of the skeletal mechanism from the detailed mechanism with specified accuracy requirement and the subsequent generation of the reduced mechanism from the skeletal mechanism. The whole reduction process is faster and automatic, has moderate central processing unit (CPU) and memory requirements, thus has a © 2016 American Chemical Society

higher efficiency and accuracy, and is adopted in reducing the combustion mechanism in this work. As for the combustion mechanism, that of n-heptane attracted extensive studies,15 because it is recognized as the most important surrogate components of gasoline and diesel. Pitz et al.16,17 reported that the combustion characteristics of the blend of n-heptane, iso-octane, methyl cyclohexane, and toluene were similar to those of diesel and the property of gasoline could be reproduced by the toluene reference fuel (TRF, including n-heptane, iso-octane, and toluene). A detailed TRF mechanism, proposed by Andrae et al.,18 only contained n-heptane and toluene. On the basis of this mechanism, Ra et al.19 constructed a reduced TRF mechanism, which contained the skeleton mechanism of n-heptane and toluene. The reduced mechanism showed very good applicability in coupling with the open-source three-dimensional (3D) CFD software of KIVA. The detailed n-heptane mechanism was further reduced to include only 88 species and 387 reactions by Yoo et al.20 This reduced mechanism was used to study the turbulence flow in the combustion of n-heptane and air in the homogeneous charge compression ignition (HCCI) combustion. A TRF chemistry with 109 species and 543 reactions was proposed for combustion and soot formation predictions in the directinjection compression ignition (CI) engine simulations by Hu et al. The submechanism of n-heptane showed good agreement in polycyclic aromatic hydrocarbon (PAH) species profiles and predictions of the ignition delays.21 In this work, the effects of the reduction of the detailed nheptane mechanism by the DRG method on the accuracies of the predictions and efficiencies of the CFD simulations were investigated theoretically. In coupling with CFD, the accuracy Received: May 5, 2016 Revised: July 13, 2016 Published: July 13, 2016 6822

DOI: 10.1021/acs.energyfuels.6b01071 Energy Fuels 2016, 30, 6822−6827

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Energy & Fuels of the prediction for some key species, such as the C2 and the C3 species, will influence the ability to predict the PAHs. Therefore, the predicted mole fraction profiles of these species were also analyzed and compared between the reduced mechanisms and detailed mechanism.

2. MECHANISM REDUCTION The detailed n-heptane mechanism was from Mehl et al.,15 containing 654 species and 2827 reactions. This mechanism was validated against the experimental results of shock tube and rapid compression machine over a wide range of conditions (p = 3−50 atm, T = 650−1200 K, and ϕ = 0.3−1.0). In the reduction with the DRG method, the closed homogeneous batch reactor model of SENKIN in CHEMKIN-II22 was selected as the aim reactor. The DRG method identifies the unimportant species in a reaction mechanism by resolving species couplings without any a priori knowledge of the system. It requires the local information, such as the temperature, pressure, species composition, etc., to calculate the production rate of a species. By this way, it constructs a DRG with all of the species in the mechanism and uses a user-specified error tolerance to remove the unimportant species from the mechanism. It requires no information concerning which reactions are to be assumed in equilibrium or which species are in quasi-steady state and does not require the inclusion of the sensitivity analysis results.10 This work is based on three assumptions. First, the detailed nheptane mechanism of Mehl et al.15 performs well under the condition of reduction and validation. Second, the effect of the number of species in the mechanism on the prediction ability and calculation efficiency is stronger than the number of reactions. Lastly, the DRG method may remove the “real” unimportant species from the mechanism with a user-specified error tolerance. The ignition delay time at the typical operating range of the diesel engines of p = 40 bar and ϕ = 0.5 was selected as the aim parameter. The temperature range was 600−1600 K, and the OH radical was chosen as the target species. During the reduction, no additional reactions from other mechanisms were incorporated, no new overall reactions were conceived, and no parameters were revised. Certain error tolerance limits were selected to obtain the expected size of the reduced mechanism. Mech1, Mech2, and Mech3 are about 1/2, 1/4, and 1/8 the size of that of the detailed mechanism (Mech0), respectively. The number of species and reactions in these mechanisms and error tolerance limits are shown in Table 1.

Figure 1. Comparisons of the ignition delay times in the homogeneous batch reactor simulated by the combustion mechanisms together with the experimental results24 (p = 42 bar and ϕ = 0.4).

much longer predicted ignition delay times than the experimental data. Because the ignition delay times were calculated by the time difference corresponding to a temperature increase of 400 K, the heat-releasing reactions determines this value. In the lowtemperature region, these reactions are related to the formation of H2O via the H abstractions by OH. Thus, the rates of production for OH were compared between Mech0 and Mech3, as shown in Figure 2. It can be seen that the predicted

Figure 2. Comparison of the production rates of OH between (a) Mech0 and (b) Mech3 at 900 K in the homogeneous batch reactor (p = 42 bar, Tini = 750 K, and ϕ = 0.4).

Table 1. Error Tolerance and Number of Species and Reactions in the n-Heptane Mechanisms mechanism

species

reactions

error (%)

Mech0 Mech1 Mech2 Mech3

654 327 160 83

2827 1570 760 361

0.0 0.5 9.8 50.1

production rates of OH by Mech0 are much higher than those by Mech3. A higher production rate of OH leads to a higher formation rate of H2O and, hence, a shorter ignition delay time. Because a practical diesel engine operates at a very wide pressure range, a reduced mechanism must be applicable for a wide pressure range. Figure 3 shows the comparisons of the simulated ignition delay times by the mechanisms and the experimental data at ϕ = 1.0 and p = 3, 10, 20, and 41 atm in a shock tube.15 It can be seen that the predicted ignition delay times by Mech0 and Mech1 are in reasonable agreements with the experimental data. Mech2 predicts higher ignition delay times than the Mech0 and Mech1 values uniformly in all cases. However, Mech3 predicts shorter simulated ignition delay times in the high-temperature region of T > 1050 K and longer simulated ignition delay times at T < 850 K in all four cases. The prediction accuracies of the reduced mechanisms at different reduction levels change slightly between each other under different pressures. The pressure has little effect on this trend. Fuel stratification is common in the cylinders of the diesel engines. This may lead to non-uniformed distribution of the fuel and, hence, the equivalence ratio distributions in the cylinders. The equivalence ratio may influence the ignition

3. RESULTS AND DISCUSSION 3.1. Ignition Delay Time. Ignition delay time is an important parameter in characterizing the combustion of a fuel.23 The reduced mechanisms were validated at different pressures and equivalence ratios against the experimental data. The simulations were performed using the closed homogeneous batch reactor in CHEMKIN-II.22 Figure 1 shows the simulated ignition delay times by the mechanisms with the experimental data for comparison.24 It can be seen that Mech1 shows good consistency with Mech0. The simulated ignition delay times agree with the experimental data at p = 42 bar and ϕ = 0.4. Mech2 predicts higher ignition delay times than the Mech0 and Mech1 values. Mech3 performs even worse, with 6823

DOI: 10.1021/acs.energyfuels.6b01071 Energy Fuels 2016, 30, 6822−6827

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Figure 3. Effects of pressure on the simulated ignition delay times by the mechanisms and the experimental data15 at ϕ = 1.0 and (a) p = 3 and 10 bar and (b) p = 20 and 41 bar.

delay times.25 Figure 4 shows the comparisons of the simulated ignition delay times by the mechanisms and experimental data26 in a shock tube at p = 13.5 bar and ϕ = 0.5, 1.0, and 2.0. It can be seen that all of the mechanisms underestimate the ignition delay times at ϕ = 2.0. The predicted ignition delay times by Mech0 and Mech1 show slight difference at ϕ = 2.0. In all of the cases, Mech2 predicts higher ignition delay times than the Mech0 and Mech1 values again. Mech3 predicts much higher ignition delay times at the low-temperature region and the low equivalence ratio (ϕ = 0.5). However, with the increase of the equivalence ratio, the predicted ignition delay times by all of the mechanisms tend to be consistent with each other at the lowtemperature region. At p = 13.5 bar, the predicted ignition delay times by the mechanisms tend to converge with the increase of the equivalence ratio, although all of them underestimate the ignition delay times at a higher equivalence ratio. 3.2. Laminar Burning Velocity. Flame propagation is very important in controlling the combustion process in engine cylinders, especially for low-temperature combustion modes, such as premixed charge CI, partially premixed combustion, and reactivity controlled CI.27 The laminar burning velocity is used to characterize the flame propagation in combustion. Figure 5 shows the simulated laminar burning velocities by the mechanism and experimental data.28−30 All of the simulations were performed using the premixed laminar flame speed calculation model from CHEMKIN-II22 with p = 1 bar and T = 298 K. Mech1 predicts slightly lower laminar burning velocities than Mech0 does. Mech2 and Mech3 show larger discrepancies in the predicted values from those of Mech0. Decreasing the mechanism size leads to lower predicted laminar burning velocities. However, the simulated results are in reasonable agreements with the experimental data (error < 10%). It can be seen that the simulated ignition delay times by Mech0 and Mech1 agree well from Figures 1 and 3 but the

Figure 4. Effects of the equivalence ratio on the simulated ignition delay times by the mechanisms and experimental data26 at p = 13.5 bar and (a) ϕ = 0.5, (b) ϕ = 1.0, and (c) ϕ = 2.0.

Figure 5. Comparisons of the simulated laminar burning velocities by the mechanisms and experimental data at p = 1 bar and T = 298 K.

simulated laminar burning velocities differ slightly in Figure 5. Because the ignition delay time is determined by the low6824

DOI: 10.1021/acs.energyfuels.6b01071 Energy Fuels 2016, 30, 6822−6827

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Energy & Fuels temperature reactions (LTRs), while the laminar burning velocity is determined by the high-temperature reactions (HTRs), the species in these mechanisms were analyzed, as shown in Figure 6. It can be seen that, from Mech0 to Mech1,

Figure 7. Comparisons of the mole fraction profiles of C2H2 and C2H4 in the laminar premixed flame of n-heptane (p = 0.1 MPa and ϕ = 1.9) between the simulated results and experimental data.32 Figure 6. Comparison of species distributions in terms of carbon numbers in n-heptane mechanisms.

the proportions of C4 and C6 species decrease dramatically and the proportion of C7 species increases correspondingly. In the high-temperature region, the fuel molecules were consumed mainly by H abstractions to form the corresponding C7 radicals and the following decompositions of these radicals to form the fragment species. In reduction of Mech0 to Mech2 or Mech3, the C4, C5, and C6 species were removed dramatically and the laminar burning velocities were further reduced. The reduction of the proportions of C4, C5, and C6 species coincide with the decrease of the laminar flame speed. The laminar burning velocity is determined by the HTRs (H + O2 = O + OH, CH3 + H = CH4, etc.). The removed C4, C5, and C6 species are those related to the LTRs, as seen in the Supporting Information. The simulated mole fraction profiles of the H atom can be seen in Figure S3 of the Supporting Information. The decreased mole fraction of the H atom should account for the decreased laminar burning velocities simulated by the reduced mechanisms. 3.3. Species Mole Fractions. In 3D CFD simulation, soot formation is always the most concerned emission. According to the H abstraction C2H2 addition (HACA) mechanism for soot formation,31 C2H2 and C2H4 are important species in predicting soot formation. In the HACA mechanism, C2H2 is the main factor to form the first aromatic ring and promote PAHs growth during combustion. Because C2H2 is mainly produced from C2H4, accurately predicting the formations of C2H2 and C2H4 should be important by the reduced mechanism. Figure 7 shows the simulated mole fraction profiles of C2H2 and C2H4 together with the experimental data32 in a premixed laminar flame at p = 0.1 MPa and ϕ = 1.9. The simulation was carried out with the premixed flame model of CHEMKIN-II.22 It can be seen that Mech0 and Mech1 can well reproduce the experimental results, while Mech2 slightly underestimates the values. Mech3 performs even worse, with a simulated mole fraction profile of C2H2 of an order lower. The formation of CH2O is another mostly concerned emission from engines. Figure 8 compares the simulated mole fraction profiles of CH2O by the mechanisms and experimental data33 in a jet-stirred reactor (JSR) at p = 10 atm and ϕ = 0.3, 0.5, 1.0, and 1.5. The simulation was conducted using the perfectly stirred reactor model in CHEMKIN-II.22 The model parameters can be found in ref 33. It can be seen

Figure 8. Comparisons of the mole fraction profiles of CH2O in a JSR at p = 10 atm, τ = 1 s, and (a) ϕ = 0.3, (b) ϕ = 0.5, (c) ϕ = 1.0, and (d) ϕ = 1.5 between the simulated results and experimental data.33

that the experimental data can be well reproduced by Mech0, Mech1, and Mech2. The bimodal distributions are well reproduced by the three mechanisms in the rich cases. Mech3 underestimates the experimental data at the lowtemperature region. The equivalence ratio has little effect on the performance of the reduced mechanisms. However, it should be pointed out that, as a result of the complexity and uncertainty of the detailed mechanism, the prediction abilities of the reduced mechanisms might be improved in some cases. In fact, Mech0 and Mech1 overpredict the experimental mole fraction profiles of C2H2 in a JSR at p = 10 atm and 600 < T < 800 K, while Mech2 and Mech3 perform better at this region, as shown in Figure S1 of the Supporting Information. This might originate from the cancellation of the uncertainties of the detailed mechanism and reduction. 3.4. Zero-Dimensional Numerical Simulation for a HCCI Engine. The performances of the mechanisms were also compared in a HCCI engine simulation using the closed internal combustion engine simulator model from CHEMKINII22 with the experimental results, as shown in Figure 9. The simulation parameters were adopted from ref 34. It shows that all of the mechanisms predict a longer ignition delay time than the experimental data. The peak pressure values predicted by Mech2 and Mech3 are lower than those predicted by Mech1 and Mech0 but are closer to the experimental data. The peak 6825

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Figure 10. Comparison of the computing time by 3D CFD simulations coupled with the mechanisms.

Figure 9. Comparisons of the simulated cylinder pressure and heat release rate profiles by the mechanisms with the experimental data in a HCCI engine fueled with n-heptane.

4. CONCLUSION The n-heptane combustion mechanism from the Laurence Livermore National Laboratory was reduced to 1/2, 1/4, and 1/8 size using the DRG method to study the effect of reduction on the accuracy and efficiency of the mechanism. The accuracies of the mechanisms were compared to the experimental data, including the ignition delay times, laminar burning velocities, and mole fraction profiles of some key species. The efficiencies of the mechanisms in coupling with 3D CFD were also compared. The conclusions are summarized as follows: (1) The detailed combustion mechanism and 1/2 mechanism agree well in simulating the ignition delay times, laminar burning velocities, and mole fraction profiles of some key species. The 1/4 mechanism and especially the 1/8 mechanism cannot reproduce these values well. (2) The computing time decreases dramatically with the decrease of the mechanism size in coupling with 3D CFD simulations. The 1/2 mechanism uses only 25% of the computing time of the detailed mechanism. (3) Considering the computing efficiency and simulation accuracy, the size of a reduced n-heptane mechanism suitable for coupling with the 3D CFD simulations should be between 1/2 and 1/4 size of the detailed combustion mechanism without revising the related parameters of the reactions. This point may apply for the mechanisms of n-alkanes.

heat releases are also overpredicted by Mech0 and Mech1, with the crank angle (CA) of 50% heat release (CA50) being retarded by 5° crank angle degree (CAD). In the experiments, the gas mixture in the cylinders might be heated by the residual exhaust gas or the cylinder wall and should be higher than the inlet gas temperature, which was used as the input for the simulations. The higher temperature in the experiment resulted in a shorter ignition delay time. From the point view of the simulations, the lower input temperature resulted in the longer ignition delay times. In the experiments, heat-transfer loss and gas leakage may decrease the peak experimental pressure. Both factors were not considered in the simulations; thus, Mech0 and Mech1 predicted higher peak pressures than the experimental value. Although the simulated peak pressure by Mech2 is close to the experimental value, this agreement should be the coincidence of the decreased experimental value as a result of the factors described above and the uncertainty of this reduced mechanism. As for Mech3, it shows a heat release only in the low-temperature region. This corresponds to a misfire. 3.5. Computing Time of 3D CFD Simulation. The performances of the mechanisms were also compared in a direct-injection CI diesel engine simulation using the Converge software coupling with these mechanisms. Details of the computational grid, related physical models, and engine parameters can be found in Figure S2 and Tables S1 and S2 of the Supporting Information, respectively. The efficiencies of the mechanisms were also compared in coupling with the 3D CFD Converge software, as shown in Figure 10. A 16 Intel core processor was used in all of the simulations. It can be seen that the 3D CFD computing times coupling with Mech0, Mech1, Mech2, and Mech3 are 175, 41, 15, and 6 h, respectively. The computing time decreases dramatically with the decrease of the mechanism size. Mech1 is about half of the size of Mech0, but its computing time is only a quarter of the latter. Thus, considering the period of research and development of an engine and accuracy of the related simulations, the size of a reduced mechanism suitable for coupling with the 3D CFD simulations should be between the size of Mech1 and Mech2, i.e., 1/2 and 1/4 size of the detailed combustion mechanism, without revising the related parameters of the reactions.

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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.6b01071 Reduced mechanisms are available upon request. Physical models used in 3D CFD simulations (Table S1), engine physical parameters in 3D CFD simulations (Table S2), comparisons of the mole fraction profiles of C2H2 in a JSR at p = 10 atm, τ = 1 s, and ϕ = 0.3, 0.5, 1.0, and 1.5 between the simulated results and experimental data33 (Figure S1), computational grids with a cell number of around 100 000 for the 3D CFD engine simulation, including an intake valve and exhaust valve (Figure S2), and simulated mole fraction profiles of the H atom and CH3 radical (Figure S3) (PDF) 6826

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Kinetics; Sandia National Laboratories: Albuquerque, NM, 1989; Report 89-8009B. (23) Zádor, J.; Taatjes, C. A.; Fernandes, R. X. Prog. Energy Combust. Sci. 2011, 37 (4), 371−421. (24) Herzler, J.; Jerig, L.; Roth, P. Proc. Combust. Inst. 2005, 30 (1), 1147−1153. (25) Reitz, R. D.; Duraisamy, G. Prog. Energy Combust. Sci. 2015, 46 (1), 12−71. (26) Ciezki, H. K.; Adomeit, G. Combust. Flame 1993, 93 (4), 421− 433. (27) Saxena, S.; Bedoya, I. D. Prog. Energy Combust. Sci. 2013, 39 (5), 457−488. (28) Kumar, K.; Freeh, J. E.; Sung, C. J.; Huang, Y. J. Propul. Power 2007, 23 (1), 428−436. (29) Huang, Y.; Sung, C. J.; Eng, J. A. Combust. Flame 2004, 139 (3), 239−251. (30) Davis, S. G.; Law, C. K. Combust. Sci. Technol. 1998, 140 (1−6), 427−449. (31) Wang, H.; Frenklach, M. Combust. Flame 1997, 110 (1−2), 173−221. (32) Marchal, C.; Delfau, J. L.; Vovelle, C.; Moréac, G.; MounaïmRousselle, C.; Mauss, F. Proc. Combust. Inst. 2009, 32 (1), 753−759. (33) Dagaut, P.; Reuillon, M.; Cathonnet, M. Combust. Flame 1995, 101 (1−2), 132−140. (34) Saisirirat, P.; Togbé, C.; Chanchaona, S.; Foucher, F.; MounaimRousselle, C.; Dagaut, P. Proc. Combust. Inst. 2011, 33 (2), 3007− 3014.

AUTHOR INFORMATION

Corresponding Author

*Telephone: +86-135-0219-5675. Fax: +86-22-2738-3362. Email: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Mingfa Yao received funding from the National Natural Science Foundation of China through Project 91541205. Lixia Wei received funding from the National Natural Science Foundation of China through Project 51176134.

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NOMENCLATURE 3D = three-dimensional CFD = computational fluid dynamics DRG = directed relation graph HCCI = homogeneous charge compression ignition HTR = high-temperature reaction LTR = low-temperature reaction CA = crank angle CI = compression ignition JSR = jet-stirred reactor PAH = polycyclic aromatic hydrocarbon

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DOI: 10.1021/acs.energyfuels.6b01071 Energy Fuels 2016, 30, 6822−6827