Combustion wave microstructure

Fig. 24. Profiles of the experimental and calculated combustion wave microstructure.

While the microscopic processes occurring in the combustion wave need to be understood, the microstructure of the combustion wave itself is also a significant consideration. In other words, it is important not only to understand the local structural transformations occurring during CS, but to link them with variations in local conditions of the combustion wave. The two approaches for investigating the combustion wave microstructure examine the temperature-time profiles and heterogeneity of the combustion wave shape and propagation, at the local level. 

The microscopic high-speed video recording method has recently been developed further and used to investigate the combustion wave microstructure in the Ti-Si and Ti-N2 systems (Mukasyan et al., 1996 Hwang et al., 1997). The location of the combustion front was estimated using image analysis techniques, and its shape and propagation were characterized quantitatively. 

Further, we can normalize three measures of the combustion wave microstructure d, ffp, and a, with the appropriate length (jct) or velocity (I/macm) scales (see... 

Hwang, S., Mukasyan, A. S., Rogachev, A. S., and Varma, A., Combustion wave microstructure in gas-solid system Experiments and theory. Combust. Sci. Tech., 123,165 (1997). 

E. Microstructure of Combustion Wave E Concluding Remarks Nomenclature... 

While providing a simple method for analyzing the redistribution of energy in the combustion wave, the models discussed in the previous section do not account for the local structural features of the reaction medium. Microstructural models account for details such as reactant particle size and distribution, product layer thickness, etc., and correlate them with the characteristics of combustion (e.g., U,T,). 

The equations used to describe the combustion wave propagation for microstructural models are similar to those in Section IV,A [see Eq. (6)]. However, the kinetics of heat release, 4>h may be controlled by phenomena other than reaction kinetics, such as diffusion through a product layer or melting and spreading of reactants. Since these phenomena often have Arrhenius-type dependences [e.g., for diffusion, 2)=9)o exp(— d// T)], microstructural models have similar temperature dependences as those obtained in Section IV,A. Let us consider, for example, the dependence of velocity, U, on the reactant particle size, d, a parameter of medium heterogeneity ... 

The microstructural models described here represent theoretical milestones in gasless combustion. Using similar approaches, other models have also been developed. For example, Makino and Law (1994) used the solid-liquid model (Fig. 20c) to determine the combustion velocity as a function of stoichiometry, degree of dilution, and initial particle size. Calculations for a variety of systems compared favorably with experimental data. In addition, an analytical solution was developed for diffusion-controlled reactions, which accounted for changes in X, p, and Cp within the combustion wave, and led to the conclusion that U< Ud(Lak-shmikantha and Sekhar, 1993). 

With this model, the microstructure of the combustion wave was studied, and compared with experimental results (Hwang et al, 1997 Mukasyan et al, 1996). For example, sequences of combustion front propagation at the microscopic level, obtained experimentally and by calculation, are shown in Fig. 24. In addition, it was demonstrated that fluctuations in combustion wave shape and propagation correlate with the heterogeneity of the reactant mixture (e.g., porosity and particle size). 

The microstructure of the initial titanium-graphite mixture is shown in Figure 62a. When the temperature in the combustion wave reaches 1660°C, titanium melts. It was determined from quenching results that a thin film ( 0.1 / m) of the Ti melt spreads over the solid carbon surface with simultaneous formation of titanium carbide grains (Fig. 62b). Small rounded TiC particles were observed to appear within the liquid rather than in the form of a continuous product layer (Rogachev et al, 1987). To illustrate this fact further, the typical microstructure formed during combustion reaction of titanium melts with graphite whiskers (10 /.im in diameter) is shown in Fig. 62c. 

Fig. 72. Scheme of experimental technique for microstructure of combustion wave study (Adapted from Rogachev et al., 1994b). 

Table XXII shows some of the parameters used to characterize the microstructure of the combustion wave. In general, the parameters can be divided into two groups. The first group characterizes the shape of the combustion front, and includes the local [F(y,f)] and average [F(r)] front profiles, as well as the front dispersion, CTp, which is a measure of roughness of the combustion front. The second group describes the combustion front propagation at the microscopic level. For this, the instantaneous, U(y,t) and average, U, velocities of the combustion wave, as well as the dispersion of the instantaneous velocities, ar calculated.

To study the variety of structural transformation processes that occur simultaneously in the combustion wave, it is necessary to utilize a wide range of methods. The evolution and morphological features of the microstructure during com-... 

Rogachev, A. S., Varma, A., and Merzhanov, A. G., The mechanism of self-propagating high-temperature synthesis of nickel aluminides. Part I Formation of the product microstructure in a combustion wave. Int. J. SHS, 2,25 (1993). 

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