Thermal explosion theory

In the search for a better approach, investigators realized that the ignition of a combustible material requires the initiation of exothermic chemical reactions such that the rate of heat generation exceeds the rate of energy loss from the ignition reaction zone. Once this condition is achieved, the reaction rates will continue to accelerate because of the exponential dependence of reaction rate on temperature. The basic problem is then one of critical reaction rates which are determined by local reactant concentrations and local temperatures. This approach is essentially an outgrowth of the bulk thermal-explosion theory reported by Fra nk-Kamenetskii (F2). 

Adler, J. and Enig, J.W., 1964, The Critical Conditions in Thermal Explosion Theory with Reactant Consumption, Combustion and Flame 8, 97. 

The self-heating and ignition of baled or loose wool in bulk storage is discussed and analysed, and steady state thermal explosion theory is applied to the prediction of critical masses and induction periods for storage and transportation situations in relation to ambient temperature. Results obtained were consistent with current safety practices. 

In Section II of Macek s paper (Ref 13, pp 44-50) is discussed the "Thermal Explosion Theory . It will be discussed in our writeup separately. Section III contains "Transition from Deflagration to Detonation , which includes the "Precursor Shock in Solids (pp 50-2) discussed in our write-up separately, and other items. Section IV contains a brief description of Gap Test (pp 56-8) and of Impact Test (pp 58-60)... 

The aim of the thermal explosion theory is to obtain knowledge of the temperature of the system as a function of both. time and location. This can be calcd from the equation ... 

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... 

The reaction zone of NMe is too thin to be observed by the plate—velocity technique, but its presence can be inferred from other experiments. Its length was estimated to be ca 1000 A from an extrapolation of the unreacted equation of state discussed by Ilyukhin et al (Ref 64b) and the adiabatic thermal explosion theory dis cussed by Zinn Mader (Ref 64a). The pressure, p. . at the end of reaction zone which corres-ponds to the head of decay zone), was estimated to be I4lkbar, when free-surface velocity was determined using Dural plates and 135kbar when using Sierracin plate... 

From thermal explosion theory (eg see article on Hot Spots in this Vol)... 

A thermal explosion theory as developed by D.A. Frank-Kamenetskil (Ref 5) led to the equation AT = -[Pg.565]

The temperature rise, AT, may be made dimensionless by borrowing from thermal explosion theory. There the natural dimensionless temperature rise 6 is defined by... 

Now we must be specific about our choice of the concentration scale cref. For reasons partly based in the experiences of thermal explosion theory and partly by the desire to reduce the dimensionless equations to their simplest possible forms, we take... 

A new small-scale test has been developed which needs only a few g of thermally unstable material, which may be contained in an open cell version of the apparatus if aerobic processes are involved, otherwise in a closed cell apparatus, both with full temperature control and monitoring systems. Such materials may be divided into 2 types, depending on the behaviour of a sample after introduction into adiabatic storage at elevated temperature. The first type, which after attaining the adiabatic temperature shows a steady further increase in temperature in line with Frank-Kamenetski s thermal explosion theory, exhibit thermal combustion (TC) behaviour. In the second type, after adiabatic temperature has been reached, the sample shows a sudden rapid rate of rise, exhibiting autocatalytic (AC) behaviour as chain branching... 

J. Adler and J.W. Enig. The critical conditions in thermal explosion theory with reactant consumption. Combustion and Flame, 8 97-103, 1964. 

A careful study of self-heating during the spontaneous ignition of methyl nitrate vapour has given results in very satisfactory agreement with the predictions of thermal explosion theory [132(a), (b)]. 

In addition, the analysis presented there shows that the results from the model are both consistent with thermal explosion theory with chemically reasonable parameters, as well as with the behavior of real explosives. 

S. Vajda and H. Rabitz, Parametric Sensitivity and Self-Similarity in Thermal Explosion Theory. Chem. Eng. Sci. 47 (1992) 1063-1078. 

Inhomogeneities, however caused, can be amplified by pre-ignition reaction. The conditions under which they can give rise to autoignition centres and hot spots have been examined in terms of turbulent structure and simple thermal explosion theory. Bradley [180] assumed the size of an autoignition centre to have the spatial scale of temperature inhomogeneities, distributed about the integral thermal scale of the gas dynamic turbulence. These distributed sizes were compared with computed critical sizes for thermal explosion, for different values of chemical parameters in... 

Chapter 1 An approach to the thermal explosion theory 1.1 The basic concept of the thermal explosion theory... 

As stated in Preface, the basic concept of the thermal explosion theory is that whether the thermal explosion or the spontaneous ignition of a chemical of the TD type, including every gas-permeable oxidatively-heating substance, having an arbitrary shape and an arbitrary size, placed in the atmosphere under isothermal conditions, occurs or not is decided, based on the balance between the rate of heat generation in the chemical and the rate of heat transfer from the chemical to the atmosphere at the critical state for the thermal explosion which exists at the end of the early stages of the self-heating process. 

Incidentally, the effect of the concentration of a chemical of the TD type on the rate of the exothermic decomposition reaction, in the early stages of the selfheating process, of the chemical is assumed to be of the zeroth order in the thermal explosion theory [1], In other words, it is assumed in the thermal explosion theory that the concentration of the chemical remains virtually constant while the self-heating process is in the early stages, because the consumption of the chemical caused by the reaction can be neglected while the self-heating process is in the early stages. 

It thus follows that it is permitted to express the concentration term in the rate equation as [C ] , i.e., as unity virtually, in the thermal explosion theory. This approach is refemed to as the zeroth-order assumption. 

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