Critical state for the thermal explosion

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. 

The critical state for the thermal explosion is a state corresponding to the point of tangency which is shown in Fig. 2 presented in Section 1.2, And, the self-heating process of a chemical of the TD type from a temperature, e.g., the which is also shown in Fig. 2, situated below Ti up to T is referred to as the early stages of the process. 

Now, the Semenov equation is certainly based on the nonstationary theory of the thermal explosion, because this equation holds on the assumption that the spatial distribution of temperature in a fluid fdled in the container and placed in the atmosphere maintained at a temperature situated below the critical state for the thermal explosion, is uniform (refer to Section 1.2). In this regard, it has been ascertained in a series of studies, which are described in Subsections 5.5.3 and 5.7.2, as well that the spatial distribution of temperature in an arbitrary volume of a liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions is perfectly uniform in the early stages of the self-heating process, except the thin upper surface layer, even if it is not stirred mechanically [18]. 

In this connection, the explosion limit, a term used in the F-K s scheme, corresponds to the critical state for the thermal explosion in the Semenov s scheme. 

Now, every liquid may also have the uniform distribution of internal temperature as a kind of fluid. In other words, as stated in Section 1.5, it will be permitted to say that a condition, UKK A, holds at all times, on account of its own fluidity, in an arbitrary volume of every liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions. The problem in considering the critical condition for the thermal explosion of a liquid is, thus, not the heat transfer by the convection in the mass of the liquid, but the heat transfer or the heat loss by the conduction from the liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions, through the whole liquid surface, across the container walls, to the atmosphere. 

Merzhanov Dubovitskii (Ref 4) formulated a general theory for the thermal explosion of condensed expls, which takes into consideration the removal of particles from the reaction volume. This theory makes it possible to calc all the basic characteristics of thermal explosion such as critical conditions, depth of preexplosion decompn induction period "Detonation is Condensed Explosives is the title of a book by J. Taylor (Ref 3) who discusses in detail the various aspects of the subject. See also studies reports listed as Refs 2, 5 6 Refs 1)L.D.Landau K.P.Stanyukovich, Dokl-AkadN 46, 396-98 (1945) 47, No 4, 273-76 (1945) CA 40, 4523 4217 (1946) 2)G.Morris H.Thomas, "On the Thermochemistry and Equation of State of the Explosion Products of Condensed Explosives , Research (London)... 

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. 

Fig. 5.4. Thermal diagram for Semenov model of thermal explosion the rate of chemical heat release varies with the dimensionless temperature excess 0 according to/(0) = e the rate of heat transfer is given by the straight line with a gradient of l/ifi. For small ifi the loss line is steep and makes two intersections corresponding to two steady-states for large tli the loss line has a low gradient and does not allow steady-state intersection points the critical case corresponds to tangency of the heat release and heat loss lines.

The critical condition of liquid flow in a tube corresponds to e = 2. For e > 2, there cannot be a steady-state rectilinear flow in the tube. In this case, the heat due to viscous friction cannot be completely released through the tube walls and results in a rapid increase in temperature (that is, a thermal explosion). 

Take for example a vessel containing butane at room temperature (20°C), in which liquid and vapor are at equilibrium at an absolute pressure of 2 atm (point M in Fig. 22.2). If, due to the thermal radiation from a fire, the temperature increases to 70°C, the pressure inside the vessel will be 8 atm (point N). If, at these conditions, the vessel bursts (due to the failure of the material or an impact, for example), there will be an instantaneous depressurization from 8 atm to the atmospheric pressure. At the atmospheric pressure, the temperature of the liquid-vapor mixture will be -0.5°C (point O in Fig. 22.2) and the depressurization process corresponds to the vertical line between N and O. As this line does not reach the tangent to the saturation curve at the critical point, the conventional theory states that there will be no BLEVE strictly speaking although there will be a strong instantaneous vaporization and even an explosion, nucleation in all the liquid mass will not occur. 

The specific characteristic of a thermal explosion is the existence of critical conditions for its development. The chemical nature of the fuel and the oxidizing substances differs, as does the mechanism of the combustion reactions. A pronounced relationship between the rate of heat liberation and the temperature is a major factor characterizing the reaction occurring in heat liberation. When the rate of heat input is equal to the rate of heat required to maintain the process plus losses to the surrounding atmosphere, then a steady - state combustion process has been established. 

A complete description of thermal explosion involves the consideration of both the system temperature and the reactant concentration. If one is concerned only with ignition, then it is reasonable to neglect reactant consumption. Moreover, for the analysis of critical conditions it is sufficient to consider only the steady-state solution to the temperature equation. 

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