Kinetics combustion wave velocity

The theory discussed here applies mainly to kinetic-controlled reactions. However, combustion synthesis reactions involve many processes, including diffusion control, phase transitions, and multistage reactions, which result in a complex heat release function, Z4> (r/,7). An analysis of the system of combustion equations for various types of heat sources was compared with experimental data, which led to the conclusion that in general, the combustion wave velocity can be represented as follows (Merzhanov, 1990a) ... 

The second model (Fig. 20c) assumes that upon melting of reactant A, a layer of initial product forms on the solid reactant surface. The reaction proceeds by diffusion of reactant B through this layer, whose thickness is assumed to remain constant during the reaction (Aleksandrov et al., 1987 Aleksandrov and Korchagin, 1988). The final product crystallizes (C) in the volume of the melt after saturation. Based on this model, Kanury (1992) has developed a kinetic expression for the diffusion-controlled rate. Using this rate equation, an analytical expression for the combustion wave velocity has been reported (Cao and Varma, 1994)... 

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 ... 

Theoretical analysis of the problem (Aldushin et ai, 1974, 1975) shows that combustion wave propagation can occur for incomplete conversion of the solid reactants. Whether full conversion is achieved can be estimated by the dimensionless parameter, co = UJvf, the ratio of the kinetically controlled combustion velocity (I/k), and gas filtration (Vf) rates. The former can be calculated from Eq. (57), while the latter can be calculated as follows ... 

The Chapman-Jongnet (CJ) theory is a one-dimensional model that treats the detonation shock wave as a discontinnity with infinite reaction rate. The conservation equations for mass, momentum, and energy across the one-dimensional wave gives a unique solution for the detonation velocity (CJ velocity) and the state of combustion products immediately behind the detonation wave. Based on the CJ theory it is possible to calculate detonation velocity, detonation pressure, etc. if the gas mixtnre composition is known. The CJ theory does not require any information about the chemical reaction rate (i.e., chemical kinetics). 

In a gas the combustion rate falls with the combustion temperature—if the lower combustion temperature occurs for a given initial state as a result of incomplete combustion. The combustion rate, however, again increases when the combustion temperature does not exceed TB so that the reaction is limited to the liquid phase the reasons for the increase are indicated above. However, it is better here to speak not of the combustion rate, but of the propagation rate of the heating wave of the liquid due to reaction in the liquid phase. The maximum temperature achievable in a liquid is limited by the quantity TB, just as the combustion temperature, in the strict sense, is limited by the quantity Tc. Calculation of the velocity of the heating wave in a liquid is not difficult [see formulas (3.32), (3.34)] if the kinetics of the chemical reaction in the liquid phase are known. 

This chapter concerns the structures and propagation velocities of the deflagration waves defined in Chapter 2. Deflagrations, or laminar flames, constitute the central problem of combustion theory in at least two respects. First, the earliest combustion problem to require the simultaneous consideration of transport phenomena and of chemical kinetics was the deflagration problem. Second, knowledge of the concepts developed and results obtained in laminar-flame theory is essential for many other studies in combustion. Attention here is restricted to the steadily propagating, planar laminar flame. Time-dependent and multidimensional effects are considered in Chapter 9. 

Comparison of the values A calculated taking into account the detailed kinetic mechanisms with measured detonation cell sizes a was performed in [3]. Using that procedure, C-J parameters are found for a particular combustion mixture, then, using the detonation velocity value D, temperature, pressure and particle velocity behind the shock wave in the non-reacted gas are determined. These are the initial parameters for the induction time calculation taking into account detailed kinetic schemes. 

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