Flame Time Scales

Fig. 23. Significant coarsening of the domain structure did not occur, at least for the time scale investigated. Thus, charge-induced reconstruction in sulfuric acid results in a much smaller domain size than that associated with a freshly flame-annealed crystal. The domain boundaries act as preferred nucleation sites for subsequent (hex) (1 X 1) transformation, which occurs much more rapidly than for a freshly flame-annealed sample. Studies of this nature have provided keen insight into aging effects that would be difficult to assess by other means.

The flame lift-off height, which is related to the ignition distance, was inversely affected by the excitation frequency. Since the flow time scale decreased with increasing frequency, the data were plotted as a function of the Damkohler number in Fig. 29.14, where the characteristic flow time scale was estimated by large-eddy turnover time as 1/17 and the characteristic chemical reaction time was computed using an ignition delay model [21] for ethylene jet. While the results did not show any evidence of critical Damkohler number, the range... 

Catalytic tests were performed in an isothermal flow quartz reactor apparatus under atmospheric pressure, provided with on-line gas chromatographic (GC) analysis of the reagent and products by two GC instrument equipped with flame ionization and thermoconducibility detectors. The activity data reported refers to the behavior after at least two hours of time on stream, but generally the catalytic behavior was found to be rather constant in a time scale of around 20 hours. 

For some reactions the rate constant kj can be very large, leading potentially to very rapid transients in the species concentrations (e.g., [A]). Of course, other species may be governed by reactions that have relatively slow rates. Chemical kinetics, especially for systems like combustion, is characterized by enormous disparities in the characteristic time scales for the response of different species. In a flame, for example, the characteristic time scales for free-radical species (e.g., H atoms) are extremely short, while the characteristic time scales for other species (e.g., NO) are quite long. It is this huge time-scale disparity that leads to a numerical (computational) property called stiffness. 

The results in Figure 1 imply that the abundance of chemiions initially present in the exhaust is 109/cm3. As noted by Yu and Turco [75], this number is consistent with the measurement of charge concentrations in flames, and with known ion-ion recombination coefficients, when the time scale of the exhaust emission into the atmosphere is taken into account. More recently, direct sampling of massive ion clusters (greater than 9500 amu) in fresh jet exhaust confirms that the chemiion concentration near the exit plane is of the order of 109/cm3 [90-92]. 

Figure 2. Space and time scales in the gedanken flame calculation. A naive direct solution of the problem could take 3000 years of computer time. The calculation should be possible in 100 sec.

Cool flames are difficult subjects for quantitative study since the time scale of events is generally too short to allow the use of conventional sampling. In addition, their non-isothermal character (which implies rate coefficients which change as reaction progresses) makes it difficult to develop theoretical models which satisfactorily describe the more important features (the periodicity and temperature rise). It is outside the scope of this review to discuss the more general theoretical aspects of cool-flame phenomena, and the reader is referred to VoL 2, Chap. 2 of this Series and also to the work of Yang and Gray [113], Halstead et al. [114, 115] and others [112,116,117]. 

In the past, combustion modeling was directed towards ffuid mechanics that included global heat release by chemical reaction. The latter was often described simply with the help of thermodynamics, assuming that the chemical reactions are much faster than the other processes like diffusion, heat conduction, and flow. However, in most cases chemistry occurs on time scales which are comparable with those of flow and molecular transport. As a consequence, detailed information about the individual elementary reactions is required if transient processes like ignition and flame quenching or pollutant formation shall be successfully modeled. The fundamental concept of using elementary reactions to describe a macroscopic... 

The slowest chemical time-scale which is decoupled must be faster than that of the physical processes. This is the only restriction which applies, however, there are no restrictions on the nature of the perturbation which may be caused by diffusion, convection, mixing processes etc. The technique has been successfully applied to laminar reacting flows and diffusion flames and could potentially be applied to autoignition systems, although it is unlikely that the degree of reduction will be as great as that found for diffusion flames [144]. 

The combustion process is initiated by an ignition source converting some number of methane molecules into free radicals. Free radicals are in turn converted to OH free radical. Possible oxygenated compounds include aldehyde, alcohol, carboxylic acid, and oxide. The hydroxyl free radical then reacts with methane and is regenerated. The successive (chain type) combustion reaction is impeded by destruction of the OH radicals. Solid surfaces often destroy the OH radicals before they can react with hydrocarbons. The same effect is exploited in a porous-bed flame arrestor. In general, the combustion rates are very fast and nearly measurable with a few exceptional situations where time scales can be expanded to microseconds (KT6 s). The... 

Interestingly, the high cycle of heat release or simply the hot spot in this case closely follows the vortex development. The main difference from the previous case was that the inlet velocity was much lower, while the equivalence ratio was higher. In other words, the convective time scale wtis less and the chemical time scale was higher. This suggests that one of the important parameters to consider in identifying the proper location of controlled fuel injection is the Damkohler number. Near the flame blow-off limit, however, one would expect the hot spot to lag the vortices slightly. 

Wang, C.-H., Clemens, N. T., Varghese, R L., and Barlow, R. S. "Turbulent time Scales in a Nonpremixed Turbulent Jet Flame by Using High-Repetition Rate Thermometry." Combustion and Flame 152 (2008) 317-35. 

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