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1.
A two-step process was adopted to model turbulent ignition that takes advantage of the possibility of decoupling the mechanical flow from chemical reaction due to the small amount of heat release before ignition. In the first step, a Reynolds stress model is employed to calculate a chemically frozen, turbulent counterflow. The second step models the ignition event by solving a joint scalar PDF equation using a Monte Carlo technique. The frozen velocity field is used to initialize the PDF model and to govern its evolution. As observed in previous DNS calculations, ignition occurs at a “most reactive” mixture fraction. The present calculations indicated that turbulence intensity had little effect on ignition temperatures, which were about 30 K higher than, but parallel to, laminar ignition temperatures. Similar results were found for both the IEM and modified Curl's mixing model. Turbulent ignition temperatures were similar to laminar ones when the mixing model was modified to account for preferential diffusion. These results are different from turbulent ignition experiments since the experiments did indicate a turbulent intensity effect on ignition of up to 35 K. These discrepancies were attributed to shortcomings in the molecular mixing models in the flows of interest where the turbulent Reynolds numbers are low. A potential source of this problem was identified as the representation of the scalar mixing frequency as a constant ratio of the scalar to flow time.  相似文献   

2.
Remaining uncertainties in the kinetic mechanism of hydrogen combustion   总被引:2,自引:0,他引:2  
An analysis of the performance of an updated hydrogen combustion mechanism is presented. Particular attention was paid to different channels of reaction between H atoms and HO2 radicals, to pressure dependence of the recombination of HO2 radicals, and to the anomalous rate constant of reaction between OH and HO2 radicals. The contemporary choice of the reaction rate constants is presented with the emphasis on their uncertainties. Then the predictions of ignition, oxidation, flame burning velocities, and flame structure of hydrogen-oxygen-inert mixtures are shown. The modeling range covers ignition experiments from 950 to 2700 K and from subatmospheric pressures up to 87 atm; hydrogen oxidation in a flow reactor at temperatures around 900 K from 0.3 up to 15.7 atm; flame burning velocities in hydrogen-oxygen-inert mixtures from 0.35 up to 4 atm; and hydrogen flame structure at 1 and 10 atm. Comparison of the modeling and experiments is discussed in terms of the range of applicability of the present detailed mechanism. The necessity for analysis of the mechanism to have an exhaustive list of reactions is emphasized.  相似文献   

3.
The aim of this study is to find a reduced mechanism that accurately represents chemical kinetics for lean hydrogen combustion at elevated pressures, as present in a typical gas turbine combustor. Calculations of autoignition, extinction, and laminar premixed flames are used to identify the most relevant species and reactions and to compare the results of several reduced mechanisms with those of a detailed reaction mechanism. The investigations show that the species OH and H are generally the radicals with the highest concentrations, followed by the O radical. However, the accumulation of the radical pool in autoignition is dominated by HO2 for temperatures above, and by H2O2 below the crossover temperature. The influence of H2O2 reactions is negligible for laminar flames and extinction, but becomes significant for autoignition. At least 11 elementary reactions are necessary for a satisfactory prediction of the processes of ignition, extinction, and laminar flame propagation under gas turbine conditions. A 4-step reduced mechanism using steady-state approximations for HO2 and H2O2 yields good results for laminar flame speed and extinction limits, but fails to predict ignition delay at low temperatures. A further reduction to three steps using a steady-state approximation for O leads to significant errors in the prediction of the laminar flame speed and extinction limit.  相似文献   

4.
The autoignition of hydrogen/carbon monoxide in a turbulent jet with preheated co-flow air is studied using the one-dimensional turbulence (ODT) model. The simulations are performed at atmospheric pressure based on varying the jet Reynolds number and the oxidizer preheat temperature for two compositions corresponding to varying the ratios of H2 and CO in the fuel stream. Moreover, simulations for homogeneous autoignition are implemented for similar mixture conditions for comparison with the turbulent jet results. The results identify the key effects of differential diffusion and turbulence on the onset and eventual progress of autoignition in the turbulent jets. The differential diffusion of hydrogen fuels results in a reduction of the ignition delay relative to similar conditions of homogeneous autoignition. Turbulence may play an important role in delaying ignition at high-turbulence conditions, a process countered by the differential diffusion of hydrogen relative to carbon monoxide; however, when ignition is established, turbulence enhances the overall rates of combustion of the non-premixed flame downstream of the ignition point.  相似文献   

5.
Three theories of the liftoff of a turbulent jet flame were assessed using cinema-particle imaging velocimetry movies recorded at 8000 images/s. The images visualize the time histories of the eddies, the flame motion, the turbulence intensity, and streamline divergence. The first theory assumes that the flame base has a propagation speed that is controlled by the turbulence intensity. Results conflict with this idea; measured propagation speeds remains close to the laminar burning velocity and are not correlated with the turbulence levels. Even when the turbulence intensity increases by a factor of 3, there is no increase in the propagation speed. The second theory assumes that large eddies stabilize the flame; results also conflict with this idea since there is no significant correlation between propagation speed and the passage of large eddies. The data do support the “edge flame” concept. Even though the turbulence level and the mean velocity in the undisturbed jet are large (at jet Reynolds numbers of 4300 and 8500), the edge flame creates its own local low-velocity, low-turbulence-level region due to streamline divergence caused by heat release. The edge flame has two propagation velocities. The actual velocity of the flame base with respect to the disturbed local flow is found to be nearly equal to the laminar burning velocity; however, the effective propagation velocity of the entire edge flame with respect to the upstream (undisturbed) flow exceeds the laminar burning velocity. A simple model is proposed which simulates the divergence of the streamlines by considering the potential flow over a source. It predicts the well-established empirical formula for liftoff height, and it agrees with experiment in that the controlling factor is streamline divergence, and not turbulence intensity or large eddy passage. The results apply only to jet flames for Re<8500; for other geometries the role of turbulence could be larger.  相似文献   

6.
Recent discoveries and developments on the dynamic process of premixed turbulent spark ignition are reviewed. The focus here is on the variation of turbulent minimum ignition energies (MIET) against laminar MIE (MIEL) over a wide range of r.m.s. turbulence fluctuation velocity (uʹ) alongside effects of the spark gap between electrodes, Lewis number, and some other parameters on MIE. Two distinguishable spark ignition transitions are discussed. (1) A monotonic MIE transition, where MIEL sets the lower bound, marks a critical uʹc between linear and exponential increase in MIET with uʹ increased. (2) A non-monotonic MIE transition, where the lower bound is to be set by a MIET at some uʹc, stems from a great influence of Lewis number and spark gap despite turbulence. At sufficiently large Lewis number >> 1 and small spark gap (typically less than 1 mm), turbulence facilitated ignition (TFI), where MIET < MIEL, occurs; then MIET increases rapidly at larger uʹ > uʹc because turbulence re-asserts its dominating role. Both phenomena are explained by the coupling effects of differential diffusion, heat losses to electrodes, and turbulence on the spark kernel. In particular, the ratio of small-scale turbulence diffusivity to reaction zone thermal diffusivity, a reaction zone Péclet number, captures the similarity of monotonic MIE transition, regardless of different ignition sources (conventional electrodes versus laser), turbulent flows, pressure, and fuel types. Furthermore, TFI does and/or does not occur when conventional spark is replaced by nanosecond-repetitively-pulsed-discharge and/or laser spark. The latter is attributed to the third lobe formation of laser kernel with some negative curvature segments that enhance reaction rate through differential diffusion, where MIEL < MIET (no TFI). Finally, the implications of MIE transitions relevant to lean-burn spark ignition engines are briefly mentioned, and future studies are suggested.  相似文献   

7.
The spatial uniformity of combustion in a gas mixture initiated by a high-voltage nanosecond volume discharge has been investigated at gas pressures of 0.3-2.4 atm and temperatures of 1100-2250 K. The experiments were carried out behind a reflected shock wave propagating in a mixture of methane and air diluted with argon. The autoignition time and the time of discharge-induced ignition were determined. It was found that, at relatively low pressures (∼0.5 atm), the discharge significantly decreased the ignition temperature (by 600 K). At higher pressures (1.5-2 atm), the ignition temperature fell by only 100 K. The emission from the discharge and combustion were registered with a nanosecond ICCD camera under various experimental conditions. Comprehensive measurements of the deposited energy and the waveforms of the discharge voltage and current with a nanosecond time resolution made it possible to determine the efficiency of this type of discharge for igniting combustible mixtures.  相似文献   

8.
Flame propagation across a single perforated plate was experimentally studied in a square cross-section channel. Experiments were performed in premixed hydrogen-air mixture with different equivalence ratios and initial pressures, aiming at identifying the parametric influence. High-speed schlieren photography and pressure records were used to capture the flame front and obtain the pressure build-up. Four stages for the flame front crossing the perforated plate were obtained, namely, laminar flame, jet flame, turbulent flame and secondary flame front. Following ignition, a laminar flame was obtained, which was nearly not affected by the confinement. This laminar flame was squeezed to pass through the perforated plate, producing the jet flame with a step change on velocity. Turbulent flame was generated by merging the jets, which facilitated the acceleration of the flame front. Secondary flame front induced by Rayleigh-Taylor instability was clearly observed in the process of the turbulent front moving forward. Both velocity and pressure are enhanced in this stage. Parametric studies suggested that the secondary flame front is more obvious in the stoichiometric mixture with higher initial pressure, and characterized by a faster propagation velocity and a bigger pressure rise.  相似文献   

9.
Nonpremixed ignition in counterflowing CO/H2 vs. heated air jets is experimentally and computationally investigated. The experiments confirm the numerical modeling observation of the existence of three ignition regimes as a function of the hydrogen concentration. In all three regimes, we first detect experimentally the onset of chemiluminescent glow due to excited CO2 followed by flame ignition, as the temperature of the air jet is raised gradually. The temperature extent of the glow regime, however, is progressively reduced with increasing hydrogen addition; no glow is detected for H2 concentrations in excess of 73%. The temperatures for glow onset and flame ignition are represented by the boundary air temperatures for each threshold. The variation of these temperatures with system pressure and flow strain rate is explored, for pressures between 0.16 and 5 atm, and strain rates of 100 to 600 s−1. The pressure variation is found to result in three p-T ignition limits, similar to the ignition limits observed in the H2/O2 system. This similarity is also observed on the effects of aerodynamic transport on ignition: within the second limit the ignition temperatures are found to be essentially insensitive to flow strain rate, whereas the other two limits are significantly affected by strain. The transport insensitivity is maintained even in the limit of very low H2 concentrations, where an analogous H2/N2 mixture would fail to ignite. This behavior is explained computationally by the replacement of the shift reaction OH + H2 → H2O + H with the reaction CO + OH → CO2 + H, thereby minimizing the effect of diminishing H2 concentration. The experimental data are found to agree well with the calculated results, although discrepancies are noted in modeling the onset of chemiluminescence and its response to pressure variations.  相似文献   

10.
11.
In this paper, the combustion characteristics of premixed CH4-air and H2-air mixtures with different excess air coefficients ignited by hot jet or jet flame are investigated experimentally in a constant volume combustion chamber (CVCC). The small volume pre-chambers with different orifices (2 or 3 mm in diameter) in the passive or active pre-chamber were selected. Both the high-speed Schlieren and OH1 chemiluminescence imaging are applied to visualize the turbulent jet ignition (TJI) process in the main chamber. Results show that the variation of orifice has diverse influences on the turbulent jet ignitions of methane and hydrogen. Smaller orifices will reduce the temperature of the jet due to the stronger stretch and throttling effect, including change of lean flammability limit, ignition delay, and re-ignition location. Furthermore, shock waves and pressure oscillations were captured in the experiments with hydrogen jets. The former is related to the jet velocity, while the latter is mainly affected by the mixture thermodynamic states in the main chamber. Furthermore, the re-ignition location is discussed. If the mixture reactivity and the jet energy are sufficiently high, the reaction will be initiated at the tip of the jet in a short time. On the contrary, a relatively long time is required to prepare the mixture during the entrainment when the reactivity is not high enough, and the corresponding re-ignition location will move towards the orifice exit owing to the temperature decline at the tip. Finally, the ignition mode transition of hydrogen jet in lean cases with a 2 mm orifice is explained.  相似文献   

12.
In addition to the traditional spark ignition (SI), premixed, gasoline-like and compression ignition (CI), diffusion, Diesel-like operation of internal combustion engines, premixed, homogeneous charge, compression ignition (HCCI) operation has also been proposed to improve the fuel conversion efficiency and reduce the pollutant formation. To be attractive, the operation in HCCI mode has to be coupled with the other traditional operations, being HCCI in general difficult to be controlled and limited to values of the air-to-fuel equivalence ratio λ within a narrow windows set by the lean burn limits with large λ and the peak pressure limits with small λ. Furthermore, the specific kinetics of hydrogen makes this fuel more difficult than other hydrocarbons to work in an engine operating HCCI without assistance. In a recent paper, the design of a 12.8 L in-line six cylinder turbo charged directly injected heavy duty truck Diesel engine fuelled with hydrogen has been discussed. Conversion of a latest Diesel engine with a novel power turbine has been studied replacing the in-cylinder Diesel injector and glow plug with a hydrogen injector and a jet ignition pre-chamber. The pre-chamber is a small volume accommodating another hydrogen injector and a glow plug being connected to the in-cylinder through calibrated orifices. This design permits to operate the engine in four different modes:
-
diffusion with jet ignition M1 - an injection occurs in the jet ignition pre-chamber before the main chamber fuel is injected and the engine operates therefore Diesel-like;
-
mixed diffusion/premixed Diesel/gasoline like M2 - an injection occurs in the jet ignition pre-chamber after only part of the main chamber fuel is injected and mixed with air;
-
premixed with jet ignition M3 - an injection occurs in the jet ignition pre-chamber after the main chamber fuel is injected and mixed with air and the engine operates gasoline-like;
-
premixed without jet ignition M4 - no injection occurs in the jet ignition pre-chamber and the engine operates HCCI-like.
While only the Diesel-like operation was previously considered full load, all the modes including the operation HCCI-like are considered here over the full range of loads where the power turbine is either connected to the crankshaft or disconnected and the exhaust gases pass through this turbine or bypass the turbine.This paper deals with computational rather than experimental work. Computations are made with the latest predictive HCCI model using detailed kinetics of GT-POWER and the well established correlative Wiebe models for Diesel and gasoline combustion. HCCI-like operation is considered over a range of air-to-fuel equivalence ratio λ much wider than usually considered with other fuels being perhaps even more suitable than hydrogen to this operation thanks to the jet ignition assistance.  相似文献   

13.
The ignition limits of hydrogen/air mixtures in turbulent jets are necessary to establish safety distances based on ignitable hydrogen location for safety codes and standards development. Studies in turbulent natural gas jets have shown that the mean fuel concentration is insufficient to determine the flammable boundaries of the jet. Instead, integration of probability density functions of local fuel concentration within the quiescent flammability limits, termed the flammability factor, was shown to provide a better representation of ignition probability. Recent studies in turbulent hydrogen jets showed that the envelope of ignitable gas composition (based on the mean hydrogen concentration), did not correspond to the known flammability limits for quiescent hydrogen/air mixtures. The objective of this investigation is to validate the flammability factor approach to the prediction of ignition in hydrogen leak scenarios. The ignition probability within a turbulent hydrogen jet was determined using a pulsed Nd:YAG laser as the ignition source. Laser Rayleigh scattering was used to characterize the fuel concentration throughout the jet. Measurements in methane and hydrogen jets exhibit similar trends in the ignition contour, which broadens radially until an axial location is reached after which the contour moves inward to the centerline. Measurements of the mean and fluctuating hydrogen concentration are used to characterize the local composition statistics conditional on whether the laser spark results in a local ignition event or complete light-up of a stable jet flame. The flammability factor is obtained through direct integration of local probability density functions. A model was developed to predict the flammability factor using a presumed probability density function with parameters obtained from experimental data and computer simulations. Intermittency effects that are important in the shear layer are incorporated in a composite probability density function. By comparing the computed flammability factor with the measured ignition probability we have validated the flammability factor approach for application to ignition of hydrogen jets.  相似文献   

14.
This study presents the flame structure influenced by the differential diffusion effects and evaluates the structural modifications induced by the turbulence, thus to understand the coupling effects of the diffusively unstable flame fronts and the turbulence distortion. Lean premixed CH4/H2/air flames were conducted using a piloted Bunsen burner. Three hydrogen fractions of 0, 30% and 60% were adopted and the laminar flame speed was kept constant. The turbulence was generated with a single-layer perforated plate, which was combined with different bulk velocities to obtain varied turbulence intensities. Quasi-laminar flames without the plate were also performed. Explicit flame morphology was obtained using the OH-PLIF. The curvature, flame surface density and turbulent burning velocity were measured. Results show that the preferential transport of hydrogen produces negatively curved cusps flanked with positively curved bulges, which are featured by skewed curvature pdfs and consistent with the typical structure caused by the Darrieus-Landau instability. Prevalent bulge-cusp like wrinkles remain with relatively weak turbulence. However, stronger turbulence can break the bulges to be finer, and induce random positively curved cusps, therefore to destroy the bulge-cusp structures. Evident positive curvatures are generated in this process modifying the skewed curvature pdfs to be more symmetric, while the negative curvatures are not affected seriously. From low to high turbulence intensities, the hydrogen addition always strengthens the flame wrinkling. The augmentation of flame surface density and turbulent burning velocity with hydrogen is even more obvious at higher turbulence intensity. It is suggested that the differential diffusion can persist and even be strengthened with strong turbulence.  相似文献   

15.
The mechanism for the enhancement of stagnation-point heat transfer was explored analyzing the large-scale turbulent structures of an impinging round jet by a statistical technique with conditional sampling. It has been found that large-scale eddies impinging on the heat transfer surfaces produce a turbulent surface-renewal effect dominant for the enhancement of the jet impingement heat transfer. The effect of heat transfer enhancement can be described in terms of the turbulent Reynolds and Strouhal numbers based on the characteristic turbulence intensity and frequency of the large-scale eddies impinging on the stagnation-point boundary layer.  相似文献   

16.
Ignition properties of simulated syngas mixtures were systematically investigated at high-pressure low-temperature conditions relevant to gas turbine combustor operation using the University of Michigan Rapid Compression Facility. Pressure time history measurements and high-speed imaging of the ignition process in this facility were used to determine auto-ignition delay times and observe and characterize ignition behaviors. The simulated syngas mixtures were composed of H2 and CO with a molar ratio of 0.7, for equivalence ratios (φ) of 0.1 and 0.5, near air dilution (i.e. molar O2 to inert gas ratio of 1:3.76), with N2 as the primary diluent gas. The pressures and temperatures after compression ranged from 3–15 atm and 870–1150 K respectively. The comprehensive results of the present work combined with those from previous shocktube studies in the literature clearly illustrate the existence of both homogeneous and inhomogeneous auto-ignition behaviors at these conditions. Analysis of patterns in the ignition behaviors revealed a dependence on temperature, pressure, and equivalence ratio with distinct thermodynamic regions in which the ignition behavior is consistent and repeatable. Predicted locations of the strong ignition limit made using a criterion which compares laminar flame speed to a thermal gradient driven front propagation speed have excellent agreement with the experimental findings for each φ and an assumed gradient of 5 K/mm. Experimental validation of this unique and powerful criterion means that it can be used for a priori prediction of the strong ignition limit using basic computational simulations. The validity of this criterion is fundamentally important, quantitatively describing the roles of chemical kinetics, thermo-physical properties, and device dependent thermal characteristics in determining auto-ignition behavior. Additionally, a comparison of the measured auto-ignition delay times to predictions made using zero-dimensional homogeneous reactor modeling revealed that agreement was dependent on φ, with excellent agreement for φ = 0.1 and large discrepancies for φ = 0.5. These results indicate that while inhomogeneous ignition phenomena are not entirely avoidable by reducing equivalence ratio, the subsequent effects on the accuracy of typical auto-ignition delay time predictions may be reduced or eliminated.  相似文献   

17.
Z.S. Li  B. Li  X.S. Bai 《Combustion and Flame》2010,157(6):1087-3929
High resolution planar laser-induced fluorescence (PLIF) was applied to investigate the local flame front structures of turbulent premixed methane/air jet flames in order to reveal details about turbulence and flame interaction. The targeted turbulent flames were generated on a specially designed coaxial jet burner, in which low speed stoichiometric gas mixture was fed through the outer large tube to provide a laminar pilot flame for stabilization of the high speed jet flame issued through the small inner tube. By varying the inner tube flow speed and keeping the mixture composition as that of the outer tube, different flames were obtained covering both the laminar and turbulent flame regimes with different turbulent intensities. Simultaneous CH/CH2O, and also OH PLIF images were recorded to characterize the influence of turbulence eddies on the reaction zone structure, with a spatial resolution of about 40 μm and temporal resolution of around 10 ns. Under all experimental conditions, the CH radicals were found to exist only in a thin layer; the CH2O were found in the inner flame whereas the OH radicals were seen in the outer flame with the thin CH layer separating the OH and CH2O layers. The outer OH layer is thick and it corresponds to the oxidation zone and post-flame zone; the CH2O layer is thin in laminar flows; it becomes broad at high speed turbulent flow conditions. This phenomenon was analyzed using chemical kinetic calculations and eddy/flame interaction theory. It appears that under high turbulence intensity conditions, the small eddies in the preheat zone can transport species such as CH2O from the reaction zones to the preheat zone. The CH2O species are not consumed in the preheat zone due to the absence of H, O, and OH radicals by which CH2O is to be oxidized. The CH radicals cannot exist in the preheat zone due to the rapid reactions of this species with O2 and CO2 in the inner-layer of the reaction zones. The local PLIF intensities were evaluated using an area integrated PLIF signal. Substantial increase of the CH2O signal and decrease of CH signal was observed as the jet velocity increases. These observations raise new challenges to the current flamelet type models.  相似文献   

18.
The current study is a series of experiments designed to examine the role of turbulent instabilities on the ignition process of pressurized hydrogen jets which are released into oxidizer environments. The experiments were conducted in a shock tube where hydrogen gas is shock-accelerated into a partly confined oxygen environment across a perforated plate. Although the considered scenario differs from most practical applications where high pressure hydrogen is released into air, the results may be applicable toward cases where hydrogen leaks are shock assisted through holes in fuel cell membranes. Schlieren visualization permitted the reconstruction of the gas dynamic evolution of the release while time resolved self-luminosity records permitted us to record whether ignition was achieved. Despite the presence of confinement in the experiments, the ignition limits determined experimentally were found to be relatively agreeable with trends predicted by a previously developed 1-D numerical model (Maxwell and Radulescu, 2011), which assumes a release into an unconfined environments. However, the role of confinement in the experiments not only influence ignition at lower limits compared to the 1-D ignition model, but was also found to promote turbulent mixing through shock reflections and flow instabilities. Turbulent mixing thus influences how the ignition spots interact to ignite the entire jet.  相似文献   

19.
This study investigates effects of initial temperatures and pressures on dilution limits of CO/H2/air mixtures by numerical simulation of one-dimensional laminar premixed flames of CO/H2/air mixtures (50%CO–50%H2). Maximum flame temperatures, laminar flame speeds, mass burning rates and flame thickness near the dilution limits are analyzed. Results reveal that the dilution limits are extended at the elevated initial temperatures. The laminar flame speeds and mass burning rates at the dilution limits increase with the elevation of initial temperature, however, the flame thickness at the dilution limits decreases with increasing pressures and increases slightly with elevated initial temperature. The decreased flame thickness renders the flamelet modeling more favorable for turbulent combustion at elevated pressure conditions. The ratio of the flame thickness to the reaction thickness and the Zeldovich number increase first and then decrease with increasing pressure, but the non-monotonic trend of ratio of flame thickness to reaction thickness with the increasing pressures is unnoticeable. Sensitivity analysis suggested that the non-monotonic trend of the Zeldovich number could be caused by the combined effects of following elementary reactions: H + O2 + M → HO2 + M, 2HO2 → H2O2 + O2 and H2O2 + M → 2OH + M.  相似文献   

20.
Turbulent hot-jet ignition (THJI) is an advanced ignition enhancement technology which can potentially overcome the problem associated with lean burn combustion. The present study makes an effort on the comprehensive understanding of a hydrogen fueled THJI chamber with various pre-chamber spark locations. Computational fluid dynamics (CFD) simulations are performed using an in-house code based on the KIVA-3V release 2 program coupled with an in-house chemical solver. A detailed chemical kinetics mechanism with 10 species and 19 reversible reactions is used for the H2/air mixture in both the pre-chamber and the main chamber. The results show that moving the spark ignition location farther from the orifice significantly reduces the 0?10% mass fraction burn period. By analyzing the local Mach number, turbulence kinetic energy and turbulence length scale, the compressibility and turbulence level of the jet flow are evaluated. Further analysis of the OH mass fraction distribution identifies three regions in the hot jet, i.e. extinction region, just-igniting region and combustion region. A critical Damköhler number of 0.3 is determined to separate the extinction region from the other regions. Meanwhile, transition Damköhler numbers ranging from 0.3 to 0.6 are determined in the just-igniting region.  相似文献   

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