Kinetics flame system

The flow velocities in flame systems are such that transport processes (diffusion and thermal conduction) make appreciable contributions to the overall flows, and must be considered in the analysis of the measured profiles. Indeed, these processes are responsible for the propagation of the flame into the fresh gas supporting it, and the exponential growth zone of the shock tube experiments is replaced by an initial stage of the reaction where active centres are supplied by diffusion from more reacted mixture sightly further downstream. The measured profiles are related to the kinetic reaction rates by means of the continuity equations governing the one-dimensional flowing system. Let Wi represent the concentration (g. cm" ) of any quantity i at distance y and time t, and let F,- represent the overall flux of the quantity (g. cm". sec ). Then continuity considerations require that the sum of the first distance derivative of the flux term and the first time derivative of the concentration term be equal to the mass chemical rate of formation q,- of the quantity, i.e. 

In contrast to the previously discussed reduction schemes, in which chemical species only are selected if they are in steady state throughout the process, the adaptive method allows species to be selected at each operating point or domain separately, generating adaptive chemical kinetics. This is a dynamic reduction procedure that can be employed to ignition systems that are changing over time and to flame systems that change over the flame coordinate. As discussed for the LOl, in some cases the maximum accumulated value over the computational... 

The majority of experimental studies are made in closed systems (without gain or loss of matter), isothermal (exchanging heat with the exterior), and homogeneous. However, in industrial practice, and in the study of rapid reactions and of strongly exothermic processes, one encounters kinetically open systems , which imply the existence of concentration gradients (continuous flow processes) or of thermally adiabatic processes (flames, explosions, etc.). The following definitions apply to closed systems, and their application to open systems will not be detailed until Chapter 3. 

In this section we apply the adaptive boundary value solution procedure and the pseudo-arclength continuation method to a set of strained premixed hydrogen-air flames. Our goal is to predict accurately and efficiently the extinction behavior of these flames as a function of the strain rate and the equivalence ratio. Detailed transport and complex chemical kinetics are included in all of the calculations. The reaction mechanism for the hydrogen-air system is listed in Table... 

The slow, thermal decomposition of hydrazoic acid in a static system has been studied by Meyer and Schumacher58. It turned out to be completely governed by heterogeneous catalysis. There are no studies on the kinetics of the homogeneous decomposition of this substance save for the investigation of its decomposition flame59. From the variation of flame properties with pressure it can be deduced that second-order reactions control the over-all rate. The unimolecular reaction... 

Nitric oxide has a very low ionization potential and could ionize at flame temperatures. For a normal composite solid propellant containing C—H—O—N—Cl—Al, many more products would have to be considered. In fact if one lists all the possible number of products for this system, the solution to the problem becomes more difficult, requiring the use of advanced computers and codes for exact results. However, knowledge of thermodynamic equilibrium constants and kinetics allows one to eliminate many possible product species. Although the computer codes listed in Appendix I essentially make it unnecessary to eliminate any product species, the following discussion gives one the opportunity to estimate which products can be important without running any computer code. 

In the previous chapters, the fundamental areas of thermodynamics and chemical kinetics were reviewed. These areas provide the background for the study of very fast reacting systems, termed explosions. In order for flames (deflagrations) or detonations to propagate, the reaction kinetics must be fast—that is, the mixture must be explosive. 

Equation (4.20) permits one to establish various trends of the flame speed as various physical parameters change. Consider, for example, how the flame speed should change with a variation of pressure. If the rate term j follows second-order kinetics, as one might expect from a hydrocarbon-air system, then the concentration terms in Co would be proportional to P2. However, the density term in n(=XJpcp) and the other density term in Eq. (4.20) also give a P2 dependence. Thus for a second-order reaction system the flame speed appears independent of pressure. A more general statement of the pressure... 

As the important effect of temperature on NO formation is discussed in the following sections, it is useful to remember that flame structure can play a most significant role in determining the overall NOx emitted. For premixed systems like those obtained on Bunsen and flat flame burners and almost obtained in carbureted spark-ignition engines, the temperature, and hence the mixture ratio, is the prime parameter in determining the quantities of NOx formed. Ideally, as in equilibrium systems, the NO formation should peak at the stoichiometric value and decline on both the fuel-rich and fuel-lean sides, just as the temperature does. Actually, because of kinetic (nonequilibrium) effects, the peak is found somewhat on the lean (oxygen-rich) side of stoichiometric. 

Although Bowman and Seery s results would, at first, seem to refute the suggestion by Fenimore that prompt NO forms by reactions other than the Zeldovich mechanism, one must remember that flames and shock tube-initiated reacting systems are distinctively different processes. In a flame there is a temperature profile that begins at the ambient temperature and proceeds to the flame temperature. Thus, although flame temperatures may be simulated in shock tubes, the reactions in flames are initiated at much lower temperatures than those in shock tubes. As stressed many times before, the temperature history frequently determines the kinetic route and the products. Therefore shock tube results do not prove that the Zeldovich mechanism alone determines prompt NO formation. The prompt NO could arise from other reactions in flames, as suggested by Fenimore. 

Using these methods, the elementary reaction steps that define a fuel s overall combustion can be compiled, generating an overall combustion mechanism. Combustion simulation software, like CHEMKIN, takes as input a fuel s combustion mechanism and other system parameters, along with a reactor model, and simulates a complex combustion environment (Fig. 4). For instance, one of CHEMKIN s applications can simulate the behavior of a flame in a given fuel, providing a wealth of information about flame speed, key intermediates, and dominant reactions. Computational fluid dynamics can be combined with detailed chemical kinetic models to also be able to simulate turbulent flames and macroscopic combustion environments. 

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. 

---