Spatial dynamics of steady flames 1. Phase space structure and the dynamics of individual trajectories

The spatial dynamics of steady, one-dimensional premixed H 2/O 2 flames are studied. The emphasis in this Article is the geometry of the phase space of the dynamical system describing the steady flames. It is shown that steady flames are described by trajectories on the stable manifolds of saddle fixed points. The saddle fixed points correspond to equilibrium points of time-dependent chemical-kinetic systems that are adiabatic and isobaric and whose constant enthalpy matches the asymptotic enthalpy of the flames. The dimensions of the stable manifolds match the dimensions of the chemical-kinetic systems under most conditions, although the dynamics on them are different. It is further shown that the stable manifolds have low-dimensional attractive submanifolds near the saddlepoint. An algorithm for generating trajectories over the spatial domain of these flames is proposed, and it is used to study individual trajectories and trajectory ensembles, whose collective behavior suggests that there are low-dimensional submanifolds away from the saddlepoint.     

The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics

This work addresses the construction and use of low-dimensional invariant manifolds to simplify complex chemical kinetics. Typically, chemical kinetic systems have a wide range of time scales. As a consequence, reaction trajectories rapidly approach a hierarchy of attracting manifolds of decreasing dimension in the full composition space. In previous research, several different methods have been proposed to identify these low-dimensional attracting manifolds. Here we propose a new method based on an invariant constrained equilibrium edge (ICE) manifold. This manifold (of dimension nr) is generated by the reaction trajectories emanating from its (nr-1)-dimensional edge, on which the composition is in a constrained equilibrium state. A reasonable choice of the nr represented variables (e.g., nr "major" species) ensures that there exists a unique point on the ICE manifold corresponding to each realizable value of the represented variables. The process of identifying this point is referred to as species reconstruction. A second contribution of this work is a local method of species reconstruction, called ICE-PIC, which is based on the ICE manifold and uses preimage curves (PICs). The ICE-PIC method is local in the sense that species reconstruction can be performed without generating the whole of the manifold (or a significant portion thereof). The ICE-PIC method is the first approach that locally determines points on a low-dimensional invariant manifold, and its application to high-dimensional chemical systems is straightforward. The "inputs" to the method are the detailed kinetic mechanism and the chosen reduced representation (e.g., some major species). The ICE-PIC method is illustrated and demonstrated using an idealized H2O system with six chemical species. It is then tested and compared to three other dimension-reduction methods for the test case of a one-dimensional premixed laminar flame of stoichiometric hydrogen/air, which is described by a detailed mechanism containing nine species and 21 reactions. It is shown that the error incurred by the ICE-PIC method with four represented species is small across the whole flame, even in the low temperature region.     

Low-dimensional manifolds in reaction-diffusion equations. 2. Numerical analysis and method development

Calculations are undertaken to study the approach to equilibrium for systems of reaction-diffusion equations on bounded domains. It is demonstrated that a number of systems approach equilibrium along attractive low-dimensional manifolds over significant ranges of parameter space. Numerical methods for generating the manifolds are adapted from methods that were developed for systems of ordinary differential equations. The truncation of the infinite spectrum of the partial differential equations makes it necessary to devise a new version of one of these methods, the well-known algorithm of Maas and Pope.     

Low-dimensional manifolds in reaction-diffusion equations. 1. Fundamental aspects

The approach to equilibrium for systems of reaction-diffusion equations on bounded domains is studied geometrically. It is shown that equilibrium is approached via low-dimensional manifolds in the infinite-dimensional function space for these dissipative, parabolic systems. The fundamental aspects of this process are mapped out in some detail for single species cases and for two-species cases where there is an exact solution. It is shown how the manifolds reduce the dimensionality of the system from infinite dimensions to only a few dimensions.     

Modes of interaction of counterflow flames in diluted methane–oxygen mixtures in a closed reactor

The features of the interaction of counterflow flames in diluted methane–oxygen mixtures at a total pressure of up to 200 Torr in a closed reactor were established. It was found that in the mode of interaction of flames propagating in hot reaction products, two-dimensional flame vortices arise due to density stratification; flames, propagating through the initial mixture, interact with the formation of only three-dimensional structures.     

The functional equation truncation method for approximating slow invariant manifolds: a rapid method for computing intrinsic low-dimensional manifolds

A slow manifold is a low-dimensional invariant manifold to which trajectories nearby are rapidly attracted on the way to the equilibrium point. The exact computation of the slow manifold simplifies the model without sacrificing accuracy on the slow time scales of the system. The Maas-Pope intrinsic low-dimensional manifold (ILDM) [Combust. Flame 88, 239 (1992)] is frequently used as an approximation to the slow manifold. This approximation is based on a linearized analysis of the differential equations and thus neglects curvature. We present here an efficient way to calculate an approximation equivalent to the ILDM. Our method, called functional equation truncation (FET), first develops a hierarchy of functional equations involving higher derivatives which can then be truncated at second-derivative terms to explicitly neglect the curvature. We prove that the ILDM and FET-approximated (FETA) manifolds are identical for the one-dimensional slow manifold of any planar system. In higher-dimensional spaces, the ILDM and FETA manifolds agree to numerical accuracy almost everywhere. Solution of the FET equations is, however, expected to generally be faster than the ILDM method.     

Absorption profiles of flames used in atomic-absorption spectroscopy

A study has been made of the distributions of metallic atoms in their ground electronic state when an aqueous or an organic solvent containing the metal present in the solution in various combined forms is sprayed into various flames used in atomic-absorption spectroscopy. It has been found that with almost all elements studied, rich flames give greater peak absorbances than lean flames, and the flame stoichiometry determines the number of free atoms in a flame. It has also been observed that the spatial distribution of free atoms in a flame depends not only on the flame stoichiometry but also on the species which the desired metal forms in the solution and the flame, on the other anions, complexing agents, and cations present in the solution, on chemical and physical properties of the solvent, on the type of atomizer-burner and on the flame temperature.     

"Imaging" combustion chemistry via multiplexed synchrotron-photoionization mass spectrometry

The combination of multiplexed mass spectrometry with photoionization by tunable-synchrotron radiation has proved to be a powerful tool to investigate elementary reaction kinetics and the chemistry of low-pressure flames. In both of these applications, multiple-mass detection and the ease of tunability of synchrotron radiation make it possible to acquire full sets of data as a function of mass, photon energy, and of the physical dimension of the system, e.g. distance from the burner or time after reaction initiation. The data are in essence an indirect image of the chemistry. The data can be quantitatively correlated and integrated along any of several dimensions to compare to traditional measurements such as time or distance profiles of individual chemical species, but it can also be directly interpreted in image form. This perspective offers an overview of flame chemistry and chemical kinetics measurements that combine tunable photoionization with multiple-mass detection, emphasizing the overall insight that can be gained from multidimensional data on these systems. The low-pressure flame apparatus is capable of providing isomer-resolved mass spectra of stable and radical species as a function of position in the flame. The overall chemical structure of the flames can be readily seen from images of the evolving mass spectrum as distance from the burner increases, with isomer-specific information given in images of the photoionization efficiency. Several flames are compared in this manner, with a focus on identification of global differences in fuel-decomposition and soot-formation pathways. Differences in the chemistry of flames of isomeric fuels can be discerned. The application of multiplexed synchrotron photoionization to elementary reaction kinetics permits identification of time-resolved isomeric composition in reacting systems. The power of this technique is illustrated by the separation of direct and dissociative ionization signals in the reaction of C(2)H(5) with O(2); by the resolution of isomeric products in reactions of the ethynyl (C(2)H) radical; and by preliminary observation of branching to methyl + propargyl products in the self-reaction of vinyl radicals. Finally, prospects for future research using multiplexed photoionization mass spectrometry are explored.     

Reduction of PAH and soot precursors in benzene flames by addition of ethanol

A one-dimensional premixed flame model (PREMIX) and schemes resulting from the merging of validated kinetic schemes for the oxidation of the components of the present mixtures (benzene and ethanol) were used to investigate the effect of oxygenated additives on aromatic species, which are known to be soot precursors, in fuel-rich benzene combustion. The specific flames were low-pressure (45 mbar), laminar, premixed flames at an equivalence ratio of 2.0. The blended fuels were formed by incrementally adding 4% wt of oxygen (ethanol) to the neat benzene flame and by keeping the inert mole fraction (argon) and the equivalence ratio constants. Special emphasis was directed toward the causes for the concentration-dependent influence of the blends on the amount of polycyclic aromatic hydrocarbons (PAHs) formed. The effects of oxygenate addition to the benzene base flame were seen to result in interesting differences, especially regarding trends to form PAH. The modeling results indicated that the concentration of acetylene and propargyl radicals, the main PAH precursors, as well as the PAH amounts were lower in the flame of the ethanol-benzene fuel mixture than in the pure benzene flame and that all of the formed PAHs were issued from the phenyl radical. Finally, the modeling results provided evidence that the PAH reduction was a result of simply replacing "sooting" benzene with "nonsooting" ethanol without influencing the combustion chemistry of the benzene.     

Combustion chemistry of enols: possible ethenol precursors in flames

Before the recent discovery that enols are intermediates in many flames, they appeared in no combustion models. Furthermore, little is known about enols' flame chemistry. Enol formation in low-pressure flames takes place in the preheat zone, and its precursors are most likely fuel species or the early products of fuel decomposition. The OH + ethene reaction has been shown to dominate ethenol production in ethene flames although this reaction has appeared insufficient to describe ethenol formation in all hydrocarbon oxidation systems. In this work, the mole fraction profiles of ethenol in several representative low-pressure flames are correlated with those of possible precursor species as a means for judging likely formation pathways in flames. These correlations and modeling suggest that the reaction of OH with ethene is in fact the dominant source of ethenol in many hydrocarbon flames, and that addition-elimination reactions of OH with other alkenes are also likely to be responsible for enol formation in flames. On this basis, enols are predicted to be minor intermediates in most flames and should be most prevalent in olefinic flames where reactions of the fuel with OH can produce enols directly.     

Comparison of atomic fluorescence power efficiencies for the helium-oxygen-acetylene and air-acetylene flames

Power efficiencies for five elements have been measured for the helium-oxygen-acetylene and air-acetylene flames. The increased power efficiencies found in this study for the helium-diluted flame, coupled with its enhanced atom-formation capabilities, suggest that lower atomic fluorescence detection limits should exist. However, in a comparison study with an air-acetylene flame using identical experimental conditions, a decreased atomic fluorescence signal-to-noise ratio was found for most elements in the helium-diluted flame. This decrease is ascribed to greater background emission noise in the hotter helium-diluted flame and decreased nebulization efficiency caused by the low density of the helium-containing nebulizer gas. A comparison of flame emission detection limits for the two flames confirms the increased sensitivity of the hotter helium-oxygen-acetylene flame, despite its lower nebulization efficiency.     

NCO quantitative measurement in premixed low pressure flames by combining LIF and CRDS techniques

NCO is a short-lived species involved in NO(x) formation. It has never been quantitatively measured in flame conditions. In the present study, laser-induced fluorescence (LIF) and cavity ring-down spectroscopy (CRDS) were combined to measure NCO radical concentrations in premixed low-pressure flames (p = 5.3 kPa). NCO LIF excitation spectrum and absorption spectrum (using CRDS) measured in a stoichiometric CH(4)/O(2)/N(2)O/N(2) flame were found in good agreement with a simulated spectrum using PGOPHER program that was used to calculate the high-temperature absorption cross section of NCO in the A(2)Σ(+)-X(2)Π transition around 440.479 nm. The relative NCO-LIF profiles were measured in stoichiometric CH(4)/O(2)/N(2)O/N(2) flames where the ratio N(2)O/O(2) was progressively decreased from 0.50 to 0.01 and in rich CH(4)/O(2)/N(2) premixed flames. Then, the LIF profiles were converted into NCO mole fraction profiles from the absorption measurements using CRDS in a N(2)O-doped flame.     

Experimental estimation of fluorescence power efficiencies of several atoms in three turbulent flames used in atomic fluorescence flame spectrometry

An experimental system for the measurement of approximate atomic fluorescence power efficiencies of atoms in turbulent flames used in atomic fluorescence flame spectrometry is described. An expression is derived for the power efficiency as a function of instrumental parameters. Experimentally measured power efficiencies for eleven elements in fuel-rich oxyhydrogen, fuel-rich oxyacetylene, and fuel-rich hydrogen/argon/entrained air flames are given. The power efficiencies vary considerably from one spectral line to another, but as a result of the entrainment of ambient air into the turbulent flames, the values obtained in different flames are approximately equal. It is also shown that fluorescence radiation should rarely produce a significant error in atomic absorption spectrometry.     

Oil-water interfacial self-assembly: a novel strategy for nanofilm and nanodevice fabrication

How to integrate individual nanostructures into macroscopic thin films has become one of the most intriguing fields in nanoscience and nanotechnology due to the unique properties and important applications of these functional films. Since being discovered in 2004, oil-water interfacial self-assembly of nanostructures has become a novel strategy for fabrication of nanofilms. It is a powerful bottom-up approach for film fabrication due to the low cost and high efficiency, and is simple and universal for almost all low-dimensional nanostructures. In this article, we provide a critical review of the state-of-the-art research activities in this burgeoning self-assembly strategy. We first discuss the thermodynamic mechanism of the oil-water interfacial self-assembly, then the self-assembly of various low-dimensional nanostructures including nanoparticles, one-dimensional (1D) nanostructures, two-dimensional (2D) nanostructures at an oil-water interface developed so far to fabricate high-quality nanofilms. Finally, we present some progress on the construction of functional nanofilm-based nanodevices from this novel strategy based on our research. We conclude this review with critical comments on advantages and the experimental challenges, and further propose the future research and development of this self-assembly strategy for nanodevice construction (105 references).     

CH and C2 measurements imply a radical pool within a pool in acetylene flames

Measured CH and C2 profiles show a striking resemblance as a function of time in a series of seven well-characterized fuel-rich (phi=1.2-2.0) non-sooting acetylene flames. This implied commonality and interrelationship are unexpected as these radicals have dissimilar chemical kinetic natures. As a result, a rigorous examination was undertaken of the behavior of each of the hydrocarbon species known to be present, C, CH, CH2, CH3, CH4, CHO, CHOH, CH2O, CH2OH, CH3O, CH3OH, C2, C2H, C2H2, CHCO, CH2CO, and C2O. This emphasized the main region where CH and C2 are observed (50-600 micros) and reduced the kinetic reactions to only those that operate efficiently and are dominant. It was immediately apparent that this region of the flame reflects the nature of a hydrogen flame heavily doped with CO and CO2 and containing traces of hydrocarbons. The radical species, H, OH, O, along with H2, H2O, and O2, form an important controlling radical pool that is in partial equilibrium, and the concentrations of each of the hydrocarbon radicals are minor to this, playing secondary roles. As a result, the dominant fast reactions are those between the hydrocarbons and the basic hydrogen/oxygen radicals. Hydrocarbon-hydrocarbon reactions are unimportant here at these equivalence ratios. CH and C2 are formed and destroyed on a sub-microsecond time scale so that their flame profiles are the reflection of a complex kinetically dynamic system. This is found to be the case for all of the hydrocarbon species examined. As might be expected, these rapidly form steady-state distributions. However, with the exceptions of C, CHO, CHOH, and CH2O, which are irreversibly being oxidized, the others all form an interconnected hydrocarbon pool that is under the control of the larger hydrogen radical pool. The hydrocarbon pool can rapidly adjust, and the CH and C2 decay together as the pool is drained. This is either by continuing oxidation in less rich mixtures, or in richer flames where this is negligible by the onset of hydrocarbon-hydrocarbon reactions. The implications of such a hydrocarbon pool are significant. It introduces a buffering effect on their distribution and provides the indirect connection between CH and C2. Moreover, because they are members of this radical pool, flame studies alone cannot answer questions concerning their specific importance in combustion other than their contributing role to this pool. The presence of such a pool modifies the exactness that is needed for kinetic mechanisms, and knowledge of every species in the system no longer is necessary. Furthermore, as rate constants become refined, it will allow for the calculation of the relative concentrations of the hydrocarbon species and facilitate reduced kinetic mechanisms. It provides an explanation for previous isotopically labeled experiments and illustrates the difficulty of exactly identifying in flames the role of individual species. It resolves the fact that differing kinetic models can show similar levels of accuracy and has implications for sensitivity analyses. It finally unveils the mechanism of the flame ionization detector and has implications for the differing interpretations of diamond formation mechanisms.     

Emission spectra of nitrous oxide supported acetylene flames at atmospheric pressure

The emission spectra of a premixed flame of acetylene supported by nitrous oxide have been recorded under different fuel-gas mixture conditions. The emission spectra in these flames of a series of metals, for which it is difficult to obtain a significant population of ground state atoms for atomic absorption spectroscopy in more conventional flames, have also been studied. The red secondary zone which is present in the fuel-rich flames shows emission attributable to long-lived CN and NH species which form a strongly reducing atmosphere to inhibit refractory oxide formation from elements such as molybdenum, titanium and aluminium introduced into the flame. An attempt has also been made to explain some of the reactions which may occur between the flame species above the primary reaction zone.     

Synergy between theory and experiment in structure resolution of low-dimensional oxides

In this paper, I review recent progress in joint theoretical and experimental studies aiming at atomic structure determination of low-dimensional metal oxides. Low-dimensional systems can be generally defined as materials of unusual structure that extend to less than three dimensions. In recent years low-dimensional systems have attracted increasing attention of physicists and chemists, and the interest is expected to rise in the near future. Two- and one-dimensional structures in form of thin oxide films or elongated oxide chains have many potential applications including model supports for heterogeneous catalysts and insulating layers in semiconductor industry. The interest in zero-dimensional gas-phase oxide clusters ranges from astrophysics to studies of elementary steps in catalysis. The key prerequisite for understanding physical and chemical properties of low-dimensional systems is a detailed knowledge of their atomic structures. However, such systems frequently present complex structures to solve. Only in a few cases experimental data can provide some information about possible arrangement of atoms, but data interpretation relies to a large extent on intuition. Therefore, in the recent years quantum chemical calculations became an indispensable tool in structure identification of low-dimensional systems, yet the accuracy of theoretical tools is often limited. The results reviewed here demonstrate that often the only way of an unambiguous atomic structure determination of low-dimensional systems are experimental studies combined with theoretical calculations. Particularly the global optimization methods such as genetic algorithm in combination with the density functional theory prove very useful in automatic structure determination of the observed surface structures and gas-phase clusters.     

Laser absorption spectroscopy diagnostics of nitrogen-containing radicals in low-pressure hydrocarbon flames doped with nitrogen oxides

Absolute concentration profiles of NH2 and HNO have been measured in low-pressure methane/air flat flames doped with small amounts of NO and N2O. Addition of a small amount of nitrogen oxides does not alter significantly the flame speeds, temperature profiles and other parameters of the relatively well-understood methane/air flames. Intracavity laser absorption spectroscopy (ICLAS) and cavity ring-down spectroscopy (CRDS) are high-sensitivity techniques used to measure absolute concentrations of minor species in flames. In this work ICLAS is used to monitor NH2 and HNO, whereas CRDS is used for temperature measurements using OH spectra in the UV range. The (090)-(000) and (080)-(000) bands of the A2A1-X2B1 electronic transition of NH2 and (100)-(000) and (011)-(000) bands of the A1A"-X1A' transition of HNO are used. Methane flames of different equivalence ratios are used. NH2 and HNO are observed in the flame as well as in the zone surrounding the flame, closer to the walls of the low-pressure chamber where the burner is located. An absorption originating from the species in this zone can affect substantially the results of line-of-sight experiments. A slow flow of nitrogen through the optical window holders was added in order to separate the spectra of HNO originating from the central flame zone. Calculations based on the commonly used GRI-Mech chemical mechanism predict two maxima in the HNO concentration profile in the NO doped flames. The first is located in the vicinity of the burner, and the second is closer to the luminescence flame zone. We were able to observe the first maximum, and its measured location agrees well with prediction. On the other hand, GRI-Mech strongly underpredicts the observed absolute concentration of HNO in this maximum. The measured absolute concentrations of NH2 are in reasonable agreement with the GRI-Mech predictions.     

基于激光诱导荧光法的同轴射流火焰中羟基自由基、甲醛、发热率与一氧化氮的二维可视化测量

对现有单一组分羟基自由基(OH)平面激光诱导荧光系统(PLIF)装置进行功能扩展研发,在不增加激光器和探测器的情况下,拓展了甲醛(CH2 O)、发热率(heat release rate,HRR)和一氧化氮(NO)三个参量的PLIF成像测试模块.同时,利用所研制的同轴射流火焰装置开展了所建立的多参量PLIF测量技术的实...