Thermal Theory of Ignition

One assumes that a reactive gas is kept in a container and an exothermic reaction occurs. The rate of heat generation of the reactive material qR (self-heating by the exothermic reaction) is represented, using Eq. (3.33), as 

Equations (3.35) and (3.36) are illustrated in Fig. 3-8 as a function of temperature. The temperature T) indicates the ignition temperature of the reactive gas. If the rate of heat generation of the reactant is given by the curve qR1, self-heating occurs at T0 

The ignition criteria of the thermal theory for ignition is then represented by 

It is seen from Eqs. (3.35) and (3.38) that the ignition temperature decreases as the density of reactant increases, i.e., as pressure increases. 

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Baum et al (Ref 13, pp 366ff) describe two theories of ignition of gases, the "thermal and the "chain ... 

Works published on this subject include Semenov s fundamental theory of thermal explosion [1], Todes analysis of the kinetics of thermal explosion [2], Frank-Kamenetskii s calculation of the absolute values of the limit of thermal explosion [3], the theory of ignition [4], and finally, most closely related to the first part of this paper, the theory of flame propagation by Frank-Kamenetskii and the author [5]. 

T. Boddington, P. Gray and D. I. Harvey, Thermal Theory of Spontaneous Ignition Criticality in Bodies of Arbitrary Shape, Phil. Trans. Roy. London, 270, 471 (1971). 

The problems of simultaneously treating spatial distributions of both temperature and concentration are currently the concern of the chemical engineer in his treatment of catalyst particles, catalyst beds, and tubular reactors. These treatments are still concerned with systems that are kineticaliy simple. The need for a unified theory of ignition has been highlighted by contemporary studies of gas-phase oxidations, many features being revealed that neither thermal theory, nor branched-chain theory for that matter, can resolve alone. A successful theoretical basis for such reactions necessarily involves the treatment of both the enorgy balance and mass balance equations. Such equations are invariably coupled and cannot be solved independently of each other. However, much information is offered by the phase-plane analj s of the syst (e.g. stability of equilibrium solutions, existence of oscillations) without the need for a formal solution of the balance equations. 

THERMAL THEORY OF SPONTANEOUS IGNITION IN CLOSED SYSTEMS... 

Peaking and Non-isothermal Polymerizations. Biesenberger a (3) have studied the theory of "thermal ignition" applied to chain addition polymerization and worked out computational and experimental cases for batch styrene polymerization with various catalysts. They define thermal ignition as the condition where the reaction temperature increases rapidly with time and the rate of increase in temperature also increases with time (concave upward curve). Their theory, computations, and experiments were for well stirred batch reactors with constant heat transfer coefficients. Their work is of interest for understanding the boundaries of stability for abnormal situations like catalyst mischarge or control malfunctions. In practice, however, the criterion for stability in low conversion... 

Let us return to our discussion of the prediction of ignition time by thermal conduction models. The problem reduces to the prediction of a heat conduction problem for which many have been analytically solved (e.g. see Reference [13]). Therefore, we will not dwell on these multitudinous solutions, especially since more can be generated by finite difference analysis using digital computers and available software. Instead, we will illustrate the basic theory to relatively simple problems to show the exact nature of their solution and its applicability to data. 

The theory of thermally thin ignition is straightforward and can apply to (a) a material of thickness d insulated on one side or (b) a material of thickness 2d heated symmetrically. The boundary conditions are given as... 

A. Ma ek, ChemRevs 62, 44-47 (1962) (Thermal decomposition of explosives including a thermal explosion theory) 14) A.M. Grishin O.M. Todes, DoklAkadN 151(2), 366-68 (1963) CA 59, 12585(1963) (Thermal explosion with heat transfer by convection and conduction) 15) P.G. Ashmore T.A.B. Wesley, "A Test of Thermal-Ignition Theory in Autocatalytic Reactions , lOthSympCombstn (1965), pp 217-226... 

Some of this material was presented in Sect 1 above. Other material will be described under Thermal Explosions in a future Vol. Below we list and abstract several references specifically directed to the theory and/or mechanism of ignition of explosives... 

However, most important and complicated are those processes in which the chemical combustion reaction occurs in space and time. Let us note a brief paper by Ya.B. on the theory of gas ignition by a heated surface (18). This work may be considered a generalization of D. A. Frank-Kamenetskii s theory of thermal explosion. However, when part of the surface has a high temperature, Ya.B. was able to formulate a general principle of ignition which is applicable under the broadest variety of geometric and gasdynamic conditions. 

The theoretical questions which are posed and solved in these papers by Ya.B. and by Ya.B. with Yu. A. Zysin (articles 17 and 17a) have developed into an extensive separate branch of science—the theory of chemical reactors. Combustion in a reactor with ideal mixing is an example of the simplest thermal and gasdynamic situation, when the analysis requires only algebraic relations. This allows explicit demonstration of the basic features of exothermic chemical reactions in a flow which are also present in more complicated form in other combustion regimes—a laminar flame, diffusive combustion, detonation wave and others. Critical conditions of ignition and extinction and the existence of several regimes whose occurrence depends on the initial conditions—these are the most remarkable effects of combustion which attract the attention even of laymen. The relative ease of recording them makes them a convenient tool for physico-chemical research. 

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