Reactions, Zeldovich

Zeldovich mechanism Zeldovich reactions Zelec DP Zenite Zenz plot... 

Equally important is the fact that Fig. 8.2 reveals large overshoots within the reaction zone. If these occur within the reaction zone, the O atom concentration could be orders of magnitude greater than its equilibrium value, in which case this condition could lead to the prompt NO found in flames. The mechanism analyzed to obtain the results depicted in Fig. 8.2 was essentially that given in Chapter 3 Section G2 with the Zeldovich reactions. Thus it was thought possible that the Zeldovich mechanism could account for the prompt NO. 

A detailed quasiclassical trajectory (QCT) study of the first Zeldovich reaction (reaction 5a, Table 1)... 

It was assumed that the first Zeldovich reaction occurs with the products and the reactants in their ground electronic states. 

Attempts to correlate total NO emissions on an absolute basis have met with varying degrees of success. However, all investigators found that correlation required a system more detailed than the two-step Zeldo-vich scheme—Reactions 1 and 2—and equilibrium hydrocarbon chemistry. Thompson et al. (15) obtained satisfactory agreement with experimental NO formation in an oscillating combustor by using the Zeldovich reactions in conjunction with a more advanced hydrocarbon scheme. He assumed an equilibrium of the following reactions and used them with measured H2 concentrations to calculate [O] for the NO formation ... 

The formation of NO in high-temperature N2/O2 systems, including the postflame regions of air-breathing combustors, occurs largely through the Zeldovich reactions ... 

Bas, A.I., Ya.B. Zeldovich and A.M. Perelomov, 1971, Scattering Reactions and Decays in the Non-relativistic Quantum Mechanics (Nauka, Moscow [in Russian)]. 

The work of Thiele (1939) and Zeldovich (1939) called attention to the fact that reaction rates can be influenced by diffusion in the pores of particulate catalysts. For industrial, high-performance catalysts, where reaction rates are high, the pore diffusion limitation can reduce both productivity and selectivity. The latter problem emerges because 80% of the processes for the production of basic intermediates are oxidations and hydrogenations. In these processes the reactive intermediates are the valuable products, but because of their reactivity are subject to secondary degradations. In addition both oxidations and hydrogenation are exothermic processes and inside temperature gradients further complicate secondary processes inside the pores. 

An improvement on the CJ model is the ZND (Zeldovich, von Neumann, and Doring) model, which takes the reaction rate into account (Nettleton 1987, Classman 1996, Lewis and von Elbe 1987). The ZND model describes the detonation wave as a shock wave, immediately fol-... 

A reaction mechanism is a series of simple molecular processes, such as the Zeldovich mechanism, that lead to the formation of the product. As with the empirical rate law, the reaction mechanism must be determined experimentally. The process of assembling individual molecular steps to describe complex reactions has probably enjoyed its greatest success for gas phase reactions in the atmosphere. In the condensed phase, molecules spend a substantial fraction of the time in association with other molecules and it has proved difficult to characterize these associations. Once the mecharrism is known, however, the rate law can be determined directly from the chemical equations for the individual molecular steps. Several examples are given below. 

The first and most prominent source is known as thermal NO or Zeldovich-NO. The label thermal refers to the high temperatures required to break the N2 triple bond in its reaction with O atom and its location of appearance in a flame. 

In the next section, the flame speed development of Zeldovich, Frank-Kamenetskii, and Semenov will be discussed. They essentially evaluate this term to eliminate the unknown ignition temperature 7] by following what is now the standard procedure of narrow reaction zone asymptotics, which assumes that the reaction rate decreases very rapidly with a decrease in temperature. Thus, in the course of the integration of the rate term lv in the reaction zone, they extend the limits over the entire flame temperature range T0 to T. This approach is, of course, especially valid for large activation energy chemical processes, which are usually the norm in flame studies. Anticipating this development, one sees that the temperature term essentially becomes... 

As implied in the previous section, the Russian investigators Zeldovich, Frank-Kamenetskii, and Semenov derived an expression for the laminar flame speed by an important extension of the very simplified Mallard-Le Chatelier approach. Their basic equation included diffusion of species as well as heat. Since their initial insight was that flame propagation was fundamentally a thermal mechanism, they were not concerned with the diffusion of radicals and its effect on the reaction rate. They were concerned with the energy transported by the diffusion of species. 

Reasonable models for the detonation wave structure have been presented by Zeldovich [9], von Neumann [10], and Doring [11], Essentially, they constructed the detonation wave to be a planar shock followed by a reaction zone initiated after an induction delay. This structure, which is generally referred to as the ZND model, will be discussed further in a later section. 

In this section, consideration is given to an analytical development of this chain explosion induction period that has its roots in the early work on chain reactions carried out by Semenov [3] and Hinshelwood [4] and reviewed by Zeldovich et al. [5],... 

Considering that the temperature difference 9 must be equivalent to (T - T9 in the Zeldovich-Frank-Kamenetskii-Semenov thermal flame theory, the reaction time corresponding to the reaction zone 6 in the flame can also be approximated by... 

In order to determine the errors that may be introduced by the Zeldovich model, Miller and Bowman [6] calculated the maximum (initial) NO formation rates from the model and compared them with the maximum NO formation rates calculated from a detailed kinetics model for a fuel-rich (isothermal system was assumed and the type of prompt NO reactions to be discussed next were omitted. Thus, the observed differences in NO formation rates are due entirely to the nonequilibrium radical concentrations that exist during the combustion process. Their results are shown in Fig. 8.1, which indicates... 

FIGURE 8.1 The effect of superequilibrium radical concentrations on NO formation rates in the isothermal reaction of 13% methane in air ( = 1.37). The upper curve is the ratio of the maximum NO formation rate calculated using the detailed reaction mechanism of Ref. [6] to the initial NO formation rate calculated using the Zeldovich model. The lower curve is the ratio of the NO concentration at the time of the maximum NO formation rate calculated using the detailed reaction mechanism to the equilibrium NO concentration (from Miller and Bowman [6]). 

Prompt NO mechanisms In dealing with the presentation of prompt NO mechanisms, much can be learned by considering the historical development of the concept of prompt NO. With the development of the Zeldovich mechanism, many investigators followed the concept that in premixed flame systems, NO would form only in the post-flame or burned gas zone. Thus, it was thought possible to experimentally determine thermal NO formation rates and, from these rates, to find the rate constant of Eq. (8.49) by measurement of the NO concentration profiles in the post-flame zone. Such measurements can be performed readily on flat flame burners. Of course, in order to make these determinations, it is necessary to know the O atom concentrations. Since hydrocarbon-air flames were always considered, the nitrogen concentration was always in large excess. As discussed in the preceding subsection, the O atom concentration was taken as the equilibrium concentration at the flame temperature and all other reactions were assumed very fast compared to the Zeldovich mechanism. 

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. 

The structural model of a detonation wave proposed by Zeldovich, von Neumann, and Doring (ZND model) involves the pressure at the shock front increasing along the Hugoniot curve without chemical reaction until it attains the value at the point of intersection of the Rayleigh line and the Hugoniot curve. 

Formation of Nitric Oxide at High Temperature Another important chain reaction is the mechanism identified by Zeldovich in 1946 [446] for formation of nitric... 

The explosion of gaseous methyl nitrate subjected to the influence of an electric spark at 25°C was investigated by Zeldovich and Shaoulov [4] who found that it differs from an explosion initiated by heat. According to these authors, the fo low-ing equations express the decomposition reaction caused by an electric spark ... 

Attention was first drawn to reaction (49) by Zeldovich,462 following a suggestion by Semenov, in order to explain the high-temperature oxidation of nitrogen in explosions. Indications of the very rapid rate of this reaction came from the almost simultaneous work of Glick, Klein, and Squire,167 Harteck and Dondes,181 and Kistiakowsky and Volpi.253... 

Following Zeldovich and Ovchinnikov [35], let us consider the role of reactant diffusion in establishing equilibrium in a reversible A B + B reaction. In terms of formal kinetics, it is described by the equations... 

Let us consider now the irreversible A + B —> C reaction in the case of equal reactant concentrations, tj-a = nB, following Ovchinnikov and Zeldovich [35], The reaction kinetics obeys the equations... 

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