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1.
The effect of thermal stratification on the ignition of a lean homogeneous n-heptane/air mixture at constant volume and high pressure is investigated by direct numerical simulations (DNS) with a new 58-species reduced kinetic mechanism developed for very lean mixtures from the detailed LLNL mechanism (H.J. Curran et al., Combust. Flame 129 (2002) 253–280). Two-dimensional DNS are performed in a fixed volume with a two-dimensional isotropic velocity spectrum and temperature fluctuations superimposed on the initial scalar fields. The influence of variations in the initial temperature field, imposed by changing the mean and variance of temperature, and the ratio of turbulence to ignition delay timescale on multi-stage ignition of a lean n-heptane/air mixture is studied. In general, the mean heat release rate increases more slowly with increasing thermal stratification regardless of the mean initial temperature. Ignition delay decreases with increasing thermal stratification for high mean initial temperature relative to the negative temperature coefficient (NTC) regime. It is, however, increased with increasing thermal fluctuations for relatively low mean initial temperature resulting from a longer overall ignition delay of the mixture. Displacement speed and Damköhler number analyses reveal that the high degree of thermal stratification induces deflagration rather than spontaneous ignition at the reaction fronts, and hence, the mean heat release rate is smoother subsequent to thermal runaway occurring at the highest temperature regions in the domain. Chemical explosive mode analysis (CEMA) also verifies that mixing counterbalances chemical explosion at the reaction fronts for cases with large temperature fluctuation. It is also found that if the ratio of turbulence to ignition delay timescale is short, resultant diminished scalar fluctuations cause the overall ignition to occur by spontaneous ignition. However, the overall effect of turbulence is small compared to the effect of thermal stratification. These results suggest that the critical degree of thermal stratification for smooth operation of homogeneous charge compression-ignition (HCCI) engines depends on both the mean and fluctuations in initial temperature which should be considered in controlling ignition timing and preventing an overly rapid increase in pressure in HCCI combustion.  相似文献   

2.
The effects of fuel composition, thermal stratification, and turbulence on the ignition of lean homogeneous primary reference fuel (PRF)/air mixtures under the conditions of constant volume and elevated pressure are investigated by direct numerical simulations (DNSs) with a new 116-species reduced kinetic mechanism. Two-dimensional DNSs were performed in a fixed volume with a two-dimensional isotropic velocity spectrum and temperature fluctuations superimposed on the initial scalar fields with different fuel compositions to elucidate the influence of variations in the initial temperature fluctuation and turbulence intensity on the ignition of three different lean PRF/air mixtures. In general, it was found that the mean heat release rate increases slowly and the overall combustion occurs fast with increasing thermal stratification regardless of the fuel composition under elevated pressure and temperature conditions. In addition, the effect of the fuel composition on the ignition characteristics of PRF/air mixtures was found to vanish with increasing thermal stratification. Chemical explosive mode (CEM), displacement speed, and Damköhler number analyses revealed that the high degree of thermal stratification induces deflagration rather than spontaneous ignition at the reaction fronts, rendering the mean heat release rate more distributed over time subsequent to thermal runaway occurring at the highest temperature regions in the domain. These analyses also revealed that the vanishing of the fuel effect under the high degree of thermal stratification is caused by the nearly identical propagation characteristics of deflagrations of different PRF/air mixtures. It was also found that high intensity and short-timescale turbulence can effectively homogenize mixtures such that the overall ignition is apt to occur by spontaneous ignition. These results suggest that large thermal stratification leads to smooth operation of homogeneous charge compression-ignition (HCCI) engines regardless of the PRF composition.  相似文献   

3.
Three-dimensional direct numerical simulation with detailed chemical kinetics of lean premixed CH4/air and H2/air flames at high Karlovitz numbers (Ka ∼ 1800) is carried out. It is found that the high intensity turbulence along with differential diffusion result in a much more rapid transport of H radicals from the reaction zone to the low temperature unburned mixtures (∼500 K) than that in laminar flamelets. The enhanced concentration of H radicals in the low temperature zone drastically increases the reaction rates of exothermic chain terminating reactions (e.g., H + O2+M = HO2 + M in lean H2/air flames), which results in a significantly enhanced heat release rate at low temperatures. This effect is observed in both CH4/air and H2/air flames and locally, the heat release rate in the low temperature zone can exceed the peak heat release rate of a laminar flamelet. The effects of chemical kinetics and transport properties on the H2/air flame are investigated, from which it is concluded that the enhanced heat release rate in the low temperature zone is a convection–diffusion-reaction phenomenon, and to obtain it, detailed chemistry is essential and detailed transport is important.  相似文献   

4.
In this research, the effect of ignition, initial pressure (50–250 kPa) and temperature (20–100 °C) on the lower flammability limit (LFL) of hydrogen/air mixture are investigated experimentally and numerically. The results show that with the ignition energy increases, the LFL of hydrogen decreases. When high voltage direct current power supply (HVDC) is used, the time for the flame to propagate to the edge of the window is much shorter than that of 15 kV high voltage transformer (15 kV HVT) ignition. As the initial pressure increases, the LFL of hydrogen increases. When HVDC is used, the time to reach the peak deflagration overpressure increases with the increase of initial pressure. However, when 15 kV HVT is used, the time to reach the peak deflagration overpressure is almost the same. As the initial temperature increases, the LFL of hydrogen decreases. The change of the LFL of hydrogen with 15 kV HVT ignition is greater than that of HVDC. Through the analysis of chemical kinetic factors, the effect of OH radical generation when the LFL of hydrogen increases with the increase of initial pressure is revealed.  相似文献   

5.
Direct numerical simulations (DNSs), for a stratified flow in HCCI engine-like conditions, are performed to investigate the effects of exhaust gas recirculation (EGR) by NOx and temperature/mixture stratification on autoignition of dimethyl ether (DME) in the negative temperature coefficient (NTC) region. Detailed chemistry for a DME/air mixture with NOx addition is employed and solved by a hybrid multi-time scale (HMTS) algorithm. Three ignition stages are observed. The results show that adding (1000 ppm) NO enhances both low and intermediate temperature ignition delay times by the rapid OH radical pool formation (one to two orders of magnitude higher OH radicals concentrations are observed). In addition, NO from EGR was found to change the heat release rates differently at each ignition stage, where it mainly increases the low temperature ignition heat release rate with minimal effect on the ignition heat release rates at the second and third ignition stages. Sensitivity analysis is performed and the important reactions pathways for low temperature chemistry and ignition enhancement by NO addition are specified. The DNSs for stratified turbulent ignition show that the scales introduced by the mixture and thermal stratifications have a stronger effect on the second and third stage ignitions. Compared to homogenous ignition, stratified ignition shows a similar first autoignition delay time, but about 19% reduction in the second and third ignition delay times. Stratification, however, results in a lower averaged LTC ignition heat release rate and a higher averaged hot ignition heat release rate compared to homogenous ignition. The results also show that molecular transport plays an important role in stratified low temperature ignition, and that the scalar mixing time scale is strongly affected by local ignition. Two ignition-kernel propagation modes are observed: a wave-like, low-speed, deflagrative mode (the D-mode) and a spontaneous, high-speed, kinetically driven ignition mode (the S-mode). Three criteria are introduced to distinguish the two modes by different characteristic time scales and Damkhöler (Da) number using a progress variable conditioned by a proper ignition kernel indicator (IKI). The results show that the spontaneous ignition S-mode is characterized by low scalar dissipation rate, high displacement speed flame front, and high mixing Damkhöler number, while the D-mode is characterized by high scalar dissipation rate, low displacement speeds in the order of the laminar flame speed and a lower than unity Da number. The proposed criteria are applied at the different ignition stages.  相似文献   

6.
Rapid compression machine and shock-tube ignition experiments were performed for real fuel/air isobutane mixtures at equivalence ratios of 0.3, 0.5, 1, and 2. The wide range of experimental conditions included temperatures from 590 to 1567 K at pressures of approximately 1, 10, 20, and 30 atm. These data represent the most comprehensive set of experiments currently available for isobutane oxidation and further accentuate the complementary attributes of the two techniques toward high-pressure oxidation experiments over a wide range of temperatures. The experimental results were used to validate a detailed chemical kinetic model composed of 1328 reactions involving 230 species. This mechanism has been successfully used to simulate previously published ignition delay times as well. A thorough sensitivity analysis was performed to gain further insight to the chemical processes occurring at various conditions. Additionally, useful ignition delay time correlations were developed for temperatures greater than 1025 K. Comparisons are also made with available isobutane data from the literature, as well as with 100% n-butane and 50-50% n-butane-isobutane mixtures in air that were presented by the authors in recent studies. In general, the kinetic model shows excellent agreement with the data over the wide range of conditions of the present study.  相似文献   

7.
In this work, the outcomes of interactions of counter-rotating vortex pairs with developing ignition kernels are studied. The conditions are selected to represent those in a lean-burn natural-gas engine with hot-jet ignition. The evolution of flame surface area during kernel–vortex interaction is quantitatively and qualitatively examined. It is observed that flame development is accelerated and the net flame surface area growth rate, i.e. heat release rate, increased with increasing vortex velocity. In general, increasing the vortex length scale increases the surface growth rate, i.e. increases heat release rates, but for small length scales, i.e. when the ratio of vortex length scale to kernel diameter is small, high flame curvature induced during the interaction leads to flame weakening and slower growth rates. When the vortex velocity is high relative to the flame speed and the length scale is comparable to the kernel diameter, the vortex breaks through the ignition kernel carrying with it hot products of combustion. This accelerates growth of the flame surface area and heat release rates compared to a kernel with no vortex interaction. On decreasing the vortex velocity and increasing the length scale, the wrinkling of the kernel becomes important. This also results in increased surface growth rates and higher heat release rates.  相似文献   

8.
In this study, the effects of ignition advance on dual sequential ignition engine characteristics and exhaust gas emissions for hydrogen enriched butane usage and lean mixture were investigated numerically and experimentally. The main purpose of this study is to reveal the effects of h-butane application in a commercial spark ignition gasoline engine. One cylinder of the commercially dual sequential spark ignition engine was modeled in the Star-CD software, taking into account all the components of the combustion chamber (intake-exhaust manifold connections, intake-exhaust valves, cylinder, cylinder head, piston, spark plugs). Angelberger wall approximation, k-ε RNG turbulence model and G-equation combustion model were used for analysis. In the dual sequential spark ignition, the difference between the spark plugs was defined as 5° CAD. At the numerical analysis; 10.8:1 compression ratio, 1.3 air-fuel ratio, 2800 rpm engine speed, 0.0010 m the flame radius and 0.0001 m the flame thickness were kept constant. The hydrogen-butane mixture was defined as 4%–96% by mass. In the analysis, the optimal ignition advance was determined by the working conditions. In addition, the effects of changes in ignition advance were examined in detail at lean mixture. For engine operating conditions under investigation, it has been determined that the 50° CAD ignition advance from the top dead center is the optimal ignition advance in terms of engine performance and emission balance. It has also been found that the NOx formation rises up as the ignition advance increases. The BTE values were approximately 12.01% higher than butane experimental results. The experimental BTE values for h-butane were overall 3.01% lower than h-butane numerical results.  相似文献   

9.
In this paper, ignition characteristics of syngas (H2/CO) under homogeneous charge compression ignition environment have been studied using direct numerical simulation (DNS) and detailed reaction mechanism with temperature stratification. 2D DNS are performed by varying several parameters such as fuel composition, temperature fluctuation (T) and with different temperature and composition correlations. Results show that high H2 content syngas mixture exhibits increase in peak mean heat release rate (HRR) and decrease in spreading of mean HRR. Also, for large T, deflagration mode of ignition becomes dominant source of HRR and reduces the effects of fuel composition on peak mean HRR. On the contrary, spontaneous mode of ignition becomes dominant source of HRR and occurs more homogenously for small T, and this phenomenon becomes significant for low H2 content syngas mixture. The effect of different correlations between temperature and composition on ignition in syngas illustrate that HRR occurs from mixed mode of deflagration and spontaneous ignition for uncorrelated cases, whereas spontaneous mode of ignition occurring homogeneously is the major source of HRR for negatively correlated cases.  相似文献   

10.
Two and three dimensional direct numerical simulations (DNS) of an autoignitive premixture of air and ethanol in Homogeneous Charge Compression Ignition (HCCI) mode have been conducted. A special feature of these simulations is the use of compression heating through mass source/sink terms to emulate the compression and expansion due to piston motion. Furthermore, combustion phasing is adjusted such that peak heat release occurs after Top Dead Center (TDC) during the expansion stroke, as in a real engine. Zero dimensional simulations were first conducted to identify important parameters for the higher dimensional simulations. They showed that for ethanol, temperature and dilution are the parameters the problem is most sensitive to. One set of two dimensional simulations were conducted with a uniform mixture composition and different levels of temperature stratification, both with and without compression heating. Another set of simulations varied the mixture stratification with constant temperature stratification. Both sets showed considerable differences in ignition delay, heat release and peak temperature and peak pressure. Compression heating was also found to have a significant effect on the heat release profile. A three dimensional simulation was conducted for Spark-Assisted HCCI (SACI). It was initiated with a small spark kernel, which evolved into a premixed flame. The entire mixture eventually underwent autoignition. Distance function based analysis showed a strongly attenuating flame. Analysis of scalar mixing frequencies shows that differential diffusion and reaction induced mixing play an important role in predicting the mixing of reactive scalars. This has significant implications for mixing models for reactive flows. Chemical explosive mode analysis (CEMA) was applied to the 3D simulation and showed promise in identifying the transition from flame propagation to autoignition.  相似文献   

11.
The oxidation of methane/propane mixtures in “air” has been studied for blends containing 90% CH4/10% C3H8 and 70% CH4/30% C3H8 in the temperature range 740-1550 K, at compressed gas pressures of 10, 20 and 30 atm, and at varying equivalence ratios of 0.3, 0.5, 1.0, 2.0 and 3.0 in a high-pressure shock tube and in a rapid compression machine. These data are consistent with other experiments presented in the literature for other alkane fuels in that, when ignition delay times are plotted as a function of temperature, a characteristic negative coefficient behavior is observed, particularly for mixtures containing 30% propane. In addition, the results were simulated using a detailed chemical kinetic model. It was found that qualitatively, the model reproduces correctly the effect of change in equivalence ratio and pressure, predicting that fuel-rich, high-pressure mixtures ignite fastest while fuel-lean, low-pressure mixtures ignite slowest. Moreover, the reactivity as a function of temperature is well captured with the model predicting negative temperature coefficient behavior similar to the experiments. Quantitatively the model is faster than experiment for all mixtures at the lowest temperatures (740-950 K) and is also faster than experiment throughout the entire temperature range for fuel rich mixtures.  相似文献   

12.
The oxidation of methane/ethane/propane mixtures, for blends containing 90/6.6/3.3, 70/15/15 and 70/20/10 percent by volume of each fuel respectively in ‘air,’ has been studied over the temperature range 770-1580 K, at compressed gas pressures of approximately 1, 10, 20, 30, 40 and 50 atm, and at equivalence ratios of 0.5, 1.0 and 2.0 using both a high-pressure shock tube and a rapid compression machine. The present work represents the most comprehensive set of methane/ethane/propane ignition delay time measurements available in a single study which extends the composition envelope over an industrially relevant pressure range. It is also the first such study to present ignition delay times at significantly overlapping conditions from both a rapid compression machine and a shock tube. The data were simulated using a detailed chemical kinetic model comprised of 289 species and 1580 reactions. It was found that qualitatively, the model reproduces correctly the effect of change in equivalence ratio and pressure, predicting that fuel-rich, high-pressure mixtures ignite fastest while fuel-lean, low-pressure mixtures ignite slowest. Moreover, the reactivity as a function of temperature is well captured with the model predicting negative temperature coefficient behavior similar to the experiments. Quantitatively the model is in general excellent agreement with the experimental results but is faster than experiment for the fuel-rich (?=2.0) mixture containing the highest quantity of propane (70/15/15 mixture) at the lowest temperatures (770-900 K).  相似文献   

13.
The objective of this study is to characterize effects of turbulence and flow-field inhomogeneities on the mixing and ignition-dynamics in flow reactors. Specific focus is on investigating the ignition characteristics of hydrogen-containing fuels at gas-turbine-relevant operating conditions. Two different model formulations are developed to describe the mixing, induction, and subsequent ignition and combustion. Utilizing these models, parametric studies are performed in a generic flow reactor configuration that is representative of commonly employed facilities. Diagnostics is developed to quantify the ignition dynamics. Results show that in the case of an initially homogeneous mixture, the ignition process is fairly insensitive to the underlying flow-field. However, by considering inhomogeneities in temperature and mixture composition it is shown that the ignition process exhibits a more pronounced sensitivity to temperature perturbations, and the ignition delay is only weakly sensitive to initial equivalence ratio perturbations. Simulation results show that temperature fluctuations of less than 10% of the mean temperature are sufficient to significantly affect the ignition-onset. Results from this parametric study identify the need for quantitative measurements of temperature and composition to better characterize flow reactor facilities. A time-scale analysis is performed to characterize competing physical processes that are associated with turbulent mixing, autoignition, and flame propagation. Qualitative comparisons with experimental data suggest the possibility for deflagrative ignition modes that can occur at low temperature operating conditions.  相似文献   

14.
The laminar flame speeds of ammonia mixed with syngas at a high pressure, temperature, and different syngas ratios were measured. The data obtained were fitted at different pressures, temperatures, syngas ratios, and equivalence ratios. Four kinetic models (the Glarborg model, Shrestha model, Mei model, and Han model) were compared and validated with experimental data. Pathway, sensitivity and radical pool analysis are conducted to find out the deep kinetic insight on ammonia oxidation and NO formation. The pathway analysis shows that H abstraction reactions and NHi combination reactions play important roles in ammonia oxidation. NO formation is closely related to H, OH, the O radical produced, and formation reactions. NO is mainly formed from reaction, HNO+ H= NO+ H2. Furthermore, both ammonia oxidation and NO formation are sensitive to small radical reactions and ammonia related reactions.  相似文献   

15.
The shock-tube technique is used to measure the ignition delay time of a lean (?=0.5) mixture of n-pentane and air in a wide range of temperatures from 867 to 1534 K and pressures from 11 to 530 atm. The previously developed detailed kinetic model of ignition of hydrocarbons [Kinet. Catal. (2005), in press] is used to interpret the experimental data. The kinetic model includes mechanisms of ignition at high and low temperatures and a mechanism of ignition in the range of intermediate (1000-1200 K) temperatures. Each of these mechanisms is analyzed. The effect of the mixture pressure on the ignition at a temperature of 1000-1100 K is demonstrated.  相似文献   

16.
A direct numerical simulation (DNS) study is conducted on the various aspects of phase interactions in a planar turbulent gas-jet laden with non-evaporative and evaporative liquid droplets. A compressible computational model utilizing a finite difference scheme for the carrier gas and a Lagrangian solver for the droplet phase is used to conduct the numerical experiments. The effects of droplet time constant, mass-loading and mass/momentum/energy coupling between phases on droplet and gas-jet fields are investigated. Significant changes in velocity, temperature, density and turbulence production on account of the coupling between the liquid and gas phases are observed in non-isothermal jets with evaporating droplets. Most of these changes are attributed to the density stratification in the carrier gas that is caused by droplet momentum and heat transfer.  相似文献   

17.
Ammonia (NH3) is a carbon-free fuel that shows great research prospects due to its ideal production and storage systems. The experimental data of the laminar burning velocity of NH3/H2/air flame at different hydrogen ratios (XH2 = 0.1–0.5), equivalent ratios (φ = 0.8–1.3), initial pressures (P = 0.1–0.7 MPa), and initial temperatures (T = 298–493 K) were measured. The laminar burning velocity of the NH3/H2/air flame increased upon increasing the hydrogen ratios and temperature, but it decreased upon increasing the pressure. The equivalent ratio of the maximum laminar burning velocity was only affected by the proportion of reactants. The equivalence ratio value of the maximum laminar burning velocity was between 1.1 and 1.2 when XH2 = 0.3. The chemical reaction kinetics of NH3/H2/air flame under four different initial conditions was analyzed. The less NO maximum mole fraction was produced during rich combustion (φ > 1). The results provide a new reference for ammonia as an alternative fuel for internal combustion engines.  相似文献   

18.
Electric assisted combustion for hydrogen enriched hydrocarbons may even extend the lean burn limit and provide the further improvement on combustion stability. This study investigates the effect of hydrogen enrichment and DC electric field on lean CH4/air flame propagation. Electric field inside the chamber was generated by mesh and needle electrodes. Effect of hydrogen enrichment on the ion mole fraction in the flame was discussed based on reaction mechanism included neutral and ion reactions. The flame propagation images, flame displacement speed were used to evaluate the combined influences of hydrogen enrichment and electric field on propagating flame. Results showed that the hydrogen addition would increase positive ions mole fraction and the peak value is mainly determined by H3O+. This would be due to that CH increases with hydrogen fraction, which is the main species in the initial reaction for the ion reactions. Electric field effect about flame propagation was suppressed with hydrogen addition due to the competition between the increment in ion mole fraction and the decrement in flame time. Electric assisted combustion is more evident at leaner conditions and elevated pressure. The ratio of ionic wind velocity to flow velocity may be the determined factor to predict the electric field effect about propagating flame. The tendency based on this ratio is in accordance with the experimental results for various hydrogen fraction and equivalence ratio at elevated pressure.  相似文献   

19.
High-pressure hydrogen-rich gas producing experiments from various alcohol/water/metal-powder mixtures at low processing temperatures from 473 to 723 K are carried out in a prototype airtight apparatus possessing a withstand pressure of 15 MPa in the aim of technologizing an incidentally emerged high-pressure hydrogen-rich gas production from a methanol/water/aluminum-powder mixture at 723 K. Methanol/water due to a proven track record and ethanol/water in order to make an allowance for replacing the reagent to commercially-available potable alcohols are selected as main hydrogen sources. As tested metal-powders, aluminum, cobalt, iron, magnesium and nickel are chosen, taking their ready-availabilities and costs into consideration.Among tested metal-powders, aluminum and cobalt are found optimal adding metals for the high-pressure hydrogen-rich gas productions from 60.0 wt% methanol/water and ethanol/water solutions, respectively. From 60.0 wt% methanol/water and Al-powder mixture at 723 K, pure-hydrogen with 10.0 MPa is produced at a great hydrogen producing rate of 24.9 LN/(dm2min). All carbons discharged from methanol are fixed as a wide variety of solid higher hydrocarbons and organic liquid residues of benzyl alcohol and toluene. Almost all oxygens from methanol/water solution are fixed as aluminum-compounds of aluminum oxide hydroxide and aluminum hydroxide. From 60.0 wt% ethanol/water and Co-powder mixture, pure-hydrogen with pretty high pressure over 15 MPa can be produced at 723 K with simultaneous fixations of all the carbons and oxygens from the main hydrogen source as solid/liquid residues of wide variety of solid higher hydrocarbons, benzyl alcohol, toluene, cobalt oxide, cobalt hydroxide, tricobalt tetroxide and cobalt carbonate. Responding to the outcome from 60.0 wt% ethanol/water and Co-powder mixture, a certain rice-wine having an alcohol degree 60 with Co-powder at 723 K is experimented, and provides high-pressure hydrogen-rich gas with hydrogen concentration of 80 % and hydrogen partial pressure of around 8 MPa.All the produced hydrogen-rich gases are confirmed to keep a full declared potential in polymer electrolyte fuel cell for over 24 h without any exceptions. These findings speak by themselves that this developing high-pressure hydrogen-rich gas (pure-hydrogen) direct producing method is surely approaching a self-operating dispersed hydrogen producing appliance (i.e. a part of a dispersion type power source) anywhere whole the world. And, this method still leaves unlimited room for far higher pure-hydrogen pressures and hydrogen producing rates by slight changing the operating conditions, and its applicable fields are broadening for eternity. Finally, some recommended future strategies to improve this method so as to supply complete solutions to any global-scale issues are also proposed in every part through this paper.  相似文献   

20.
In the operation of natural gas engines using diesel pilot ignition (DPI), the ignition delay is longer than that in the operation of a comparable diesel engine. The cause of such effect is more complicated than reducing the concentration of oxidizer. In this research, the chemical kinetics of the ignition process is studied using a homogeneous model containing n-heptane, methane and air. The base fluid is the mixture of methane and air. The equivalence ratio of methane is varied to study the sensitivity of the ratio on the concentration of methane. The dependency on temperature is studied by varying the base fluid temperature. The base fluid is then mixed with the diesel surrogate fuel, n-heptane. The mole fraction of n-heptane, ZC7, covers a wide range to represent the local mixture in different locations of engine combustion chamber. To obtain a complete understanding of the ignition process, different ignition delay times are defined based on temperature increment, n-heptane conversion, and methane conversion. The effects of methane on the ignition reaction paths are analyzed for selected cases. The fundamental causes of the methane's effects are explained based on the reaction path analysis and sensitivity analysis.  相似文献   

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