Critical Conditions For Thermal Explosion Research Articles

Kinetic effects in thermal explosion with oscillating ambient conditions

Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is a new problem which was introduced in the preceding publication by the present author. It is directly applicable to a range of practical fire autoignition scenarios (e.g. in the storages of organic matter, explosives, propellants, etc.). Effects of kinetic mechanisms, however, need be further investigated as they are expected to alter critical conditions of thermal explosion. We consider several global kinetic mechanisms: first order reaction, second order reaction, and first order autocatalysis. It is demonstrated that kinetic effects related to reactants consumption do indeed shift respective critical boundaries. Effect of kinetics on oscillatory development of thermal explosion is of particular interest. In line with conclusions of the preceding publication, it is confirmed that temperature oscillations may develop during induction phase of thermal explosion when the effect of reactants consumption is properly taken into account. Moreover, development of thermal explosion instability through the prior oscillations is an inevitable and natural scenario. This fact is confirmed by a number of examples. Besides, effects of the other relevant parameter, Zeldovich number on critical conditions are also investigated.

The critical conditions for thermal explosion in a system heated at a constant rate

We have analyzed the condition needed for thermal explosion to occur in a solid sample when the temperature of the vessel walls is raised at a constant rate. We have developed a dimensionless model that allows its direct comparison with an isoperibolic system (constant vessel wall temperature). We have obtained an analytical expression for the critical condition as a function of the system parameters. Our solution takes into account reactant consumption and covers different geometries: thin film, finite and infinite cylinder. The critical condition has been validated with numerical simulations and experiments. We show that, compared to the isoperibolic system, thermal explosion is a little bit more difficult to achieve under constant heating conditions. Besides, we show that thermal explosion on submicrometric films is nearly impossible.

Critical conditions for thermal explosion in a plate with a nonlinear heat source

The exact analytical solution of the nonstationary heat conduction problem with a nonlinear internal heat source at the nonsymmetric third-type boundary conditions was obtained by the method of variable separation. The relations between the boundary condition parameters and a heat source separating the stationary processes from processes of an unlimited temperature increase (thermal explosion) were found. For known physical properties of medium, the maximum allowable value of the specific power of a heat source has been found. If nonsymmetric boundary conditions are exceeded on wall surfaces, it can lead to thermal destruction.

Thermal explosion in a binary homogeneous mixture

Self-heating processes in binary homogeneous mixtures are studied based on the analysis of phase trajectories on the heating rate–temperature plane. The proposed approach allows determining the characteristic regions of exothermic reactions in the parametric diagram of the Todes criterion versus the Semenov criterion. Generalized strict criteria for the degeneration of thermal explosion are determined for reactions with low activation energy and reactions with a low thermal effect for any reaction orders. An approximating formula describing the dependence of the Todes criterion on the Semenov criterion is derived for calculating the critical conditions of thermal explosion up to its complete degeneration for reaction orders higher (or equal to) one. A criterion for the applicability of the classical thermal explosion theory as a special case of the proposed model is found. A diagram of the critical parameters in the introduced new variables is considered to predict and control the self-heating kinetics of mixtures.

Effect of the geometrical parameters of a solid with a constant surface temperature on the critical conditions of thermal explosion

The problem of the effect of the geometry of a sample on the critical conditions for thermal explosion in an arbitrarily shaped solid with a constant surface temperature has been studied. The geometrical factors affecting the location of the hot spot and the critical conditions have been analyzed. It has been shown that the location of the hot spot is related to the dimension of the problem and can be quite accurately determined for a body with any shape. The concept of an equivalent ellipse or ellipsoid, which provides a higher accuracy than the concept of an equivalent sphere used in engineering calculations, has been introduced. Expressions for the critical conditions of a thermal explosion of two- and three-dimensional solids of an ellipsoidal shape and some other configurations have been derived to illustrate the application of the proposed approach.

Thermal modes of bimolecular exothermic reactions: Concentration limits of ignition

In the present work, the analytical investigation of the phase trajectories structures on the plane: heating rate-temperature for bimolecular exothermic reactions was carried out. This gave a possibility to divide the parametric plane Todes parameter–Semenov parameter into five characteristic regions with various modes of self-heating. It was established that all regions converge at a single point which determines the thermal explosion degeneration conditions. The correlation between Todes parameter, Semenov parameter and concentration ratio of initial reactants at the limit of the thermal explosion degeneration was found. The critical conditions for thermal explosion at any ratio of concentrations of initial reactants were determined. The approach proposed is a general one and allows analyzing both first and second order reactions.

A conjugate problem of thermal explosion of a hollow cylinder

A conjugated problem of heat conduction for two hollow cylinders that are in close contact, with one consisting of a reagent, has been solved analytically. The problem has been solved by the backward method under boundary conditions of the first kind. The critical conditions of thermal explosion were investigated as functions of the parameters of a reagent and of an inert body. An engineering method for determining the critical conditions of a thermal explosion is suggested.

Effect of the initial temperature of a reactive medium on the critical conditions for thermal explosion

A nonstationary formulation of critical conditions for thermal explosion in the Thomas problem (asymmetric self-ignition) and the classical Frank-Kamenetskii problem (symmetric self-ignition) are numerically studied. By the example of the Thomas problem, it is shown that the thermal explosion limit depends on the form of the initial spatial temperature distribution of the medium. For the Frank-Kamenetskii problem, the effect of the initial spatial temperature distribution and the initial overheating of the reactant on the critical value of the Frank-Kamenetskii number is studied. The particular initial spatial temperature distribution is determined; the investigation of its evolution allows one to make a conservative estimate of the thermal explosion limit. The limitation of the classical criterion for thermal explosion is shown, and the limits of applicability of the stationary theory are numerically determined from the initial overheating. For engineering calculations, an analytical formula for conservatively estimating the critical conditions for thermal explosion as a function of the initial reactant overheating is obtained.

Evaluating Thermal Explosion Hazard by Using Kinetics-Based Simulation Approach

Analysis of possible development of runaway at production, storage and use of a chemical product, and subsequent choice of measures that can prevent an accident or mitigate its consequences are the important tasks of reaction hazards assessment. A kinetic model evaluated from calorimetric data gives a reliable basis for implementing the analysis by means of numerical simulation. The purpose of this paper is to discuss some features of the approach as applied to such typical problems as determination of critical conditions of thermal explosion and the self accelerating decomposition temperature (SADT) for solid and liquid reactive chemicals. First a brief survey of some popular simplified theories is discussed to reveal their main limitations. Second the mathematical models of thermal explosion in solid and liquid reacting systems are presented followed by a basic sketch of the numerical methods chosen to solve the problems. Finally the practical usefulness of the kinetics-based simulation approach for analysing the influence of various factors on explosion development is illustrated with several examples. The discussed models and methods were included in the ThermEx and ConvEx program packages developed by CISP. All the presented results were obtained by means of this software.

Thermal explosion of autocatalytic reaction

Analytical and numerical solutions are used to determine the critical conditions for thermal explosion of autocatalytic reaction. The solutions covers both the reaction governed by the Arrhenius kinetics equation and the Frank-Kamenetskii approximation for that equation. The definition of criticality as the point at which d 2 θ / dβ 2 =0, d 3 θ / dβ 3 =0 and dθ / dβ 〉0 is used here. The study is dealt with low and high exothermicity ( B ) of the reaction and their effects on the critical parameters. The numerical solutions cover the whole reaction from start at β = 0 up to the end at β = 1.0. All trajectories from subcritical, critical to supercritical are offered. The effects of different parameters such as B , ψ and θ a (ambient temperature) on the critical conditions are presented. The results showed that the lower the autocatalytic factor ( β 0 ) is, the pronounced autocatalytic reaction explosion. The analytical solution offered analytical expressions for the critical condition and the different limits of the solutions are clarified. It was found that the numerical results confirm the analytical solution.

Conjugate problem of thermal explosion

The problem of thermal explosion of a reagent in the form a plane layer placed between two plane-parallel inert walls is solved analytically under boundary conditions of the third kind. Critical conditions for thermal explosion for the general case and particular cases are investigated. Results of calculations are compared with previously published data. An engineering method for evaluation of the critical conditions for thermal explosion is proposed.

The self-accelerating decomposition temperature (SADT) of solids of the quasi-autocatalytic decomposition type

Self-heating or thermally explosible chemicals are divided into two large groups, the thermal decomposition or TD type and the autocatalytic decomposition or AC type. The TD type is further divided into liquids, for each of which the critical temperature for thermal explosion or T c is calculated by applying the Semenov equation, and, solids, for each of which the T c is calculated by applying the Frank–Kamenetskii or F–K equation. On the other hand, the AC type is further divided into solids of the quasi-AC type, in each of which the exothermic decomposition reaction occurs almost simultaneously with the endothermic melting, and, liquid or solid high explosives of the true AC type, in each of which the self-accelerating exothermic decomposition reaction begins after an autocatalyst has appeared and accumulated. Neither of the two critical conditions for thermal explosion, i.e., the Semenov equation or the F–K equation, is applicable to the self-heating behaviour of each individual chemical of the AC type for the calculation of the T c. Instead, the respective self-heating behaviour of them is in accord with the concept of the self-accelerating decomposition temperature (SADT) in principle. The SADT of each individual solid of the quasi-AC type discussed in this paper as well as the critical temperature for self-heating or T cs of each individual high explosive of the true AC type is determined by the isothermal storage test. In this study, the respective SADTs of five solids of the quasi-AC type were determined using a simple and safe isothermal storage testing device. The SADT thus determined ranged from 28.4°C for 95% 2,2′-azobis(4-methoxy-2,4-dimethylvaleronitrile) to 86.5°C for 98% 1,1′-azobis(cyclohexanecarbonitrile). These temperature values are in fair agreement with a few corresponding values of the SADT measured by other researchers for them of large quantities.

Critical Conditions for Thermal Explosion with Reactant Consumption

Abstract The critical value of the dimensionless heat loss parameter is determined for a thermal explosion with reactant consumption. The critical phase trajectory of the system contains an unstable integral manifold as its own portion. Initial conditions corresponding to this trajectory conform to the explosion limit. The technique of asymptotic expansions is used to derive a critical explosion parameter

The influence of initial temperature-excess on critical conditions for thermal explosion

In the conductive theory of thermal explosion, an exothermic system is considered to be an ignition hazard only if the numerical value of the dimensionless group δ = Qσa 0 2A exp (− E/RT a κ(RT a 2/E) exceeds a critical value. [Here Q is the exothermicity, σ the density, a 0 the half-width, A exp(− E RT a ) the rate constant at ambient temperature, and κ the thermal conductivity.] This classical approach implicitly assumes that the material is initially assembled at or near to ambient temperature. Such initial conditions represent only a subclass of the whole problem. In some situations of technical importance the reactant may be initially considerably above T a . The present paper considers the temperature evolution in bodies subject to Frank-Kamenetskii boundary conditions but which are assembled with a positive, uniform temperature-excess. It is shown that in the usual exponential approximation, any system with δ ⩽ δ cr has a critical initial temperature, above which thermal runaway occurs. Exact numerical results for the critical conditions are presented for the three class A geometries (infinite slab, infinite cylinder, and sphere). Very accurate analytical approximations are also provided. For an Arrhenius rate-law, ignition cannot occur in this way for very low δ < δ ex, where δ ex ∼ O[ exp(−ϵ − 1 2 )] and ϵ = RT a E . A comparison is made between the predictions of this model and the critical conditions observed in an actual, practical example; the spontaneous ignition of piles of bagasse (extracted sugar cane) for which δ ≈ 0.02 ⪡ δ cr.

Direct evaluation of critical conditions for thermal explosion and catalytic reaction

A novel method of evaluating the critical conditions of a solid explosive is suggested. The procedure can be also used for calculation of ignition and extinction points of an exothermic catalytic reaction. The method is straightforward and can be used for any arbitrary geometry. The transport equations are replaced by a high-order difference scheme and the critical conditions are calculated numerically from an analytic condition for branching. The accuracy of the results is improved by an extrapolation procedure. Richardson's method and the ϵ-algorithm have been used for extrapolation. The method is very simple, inexpensive, and can be used also for multidimensional problems.

Ignition of a vapor-gas bubble in a liquid

Existing theories of hearth thermal ignition do not consider hydrodynamic expansion of the heating hearth, and are therefore limited in evaluating the possibility of ignition of a heated bubble in a liquid. This paper offers the results of a theroretical investigation of thermal explosion of a spherical bubble located within an infinite liquid and filled with a reactive mixture of gas and vapor. The equations describing the bubble boundary motion in the liquid, and the state of the gas within the bubble are derived. The following characteristics are distinguished: the adiabatic thermal explosion induction period, the expansion time, and the bubble thermal relaxation time. Numerical calculation is used to find the critical conditions for thermal explosion of an expanding gas bubble in a liquid explosive. The effect of gas parameters and liquid viscosity on gas ignition in the bubble is also considered.

Critical conditions for thermal explosion in reactive viscous flows

Thermal stability of some simple steady viscous flows of a reactive fluid with heated boundaries is investigated; only flows which are known exact solutions of the Navier-Stokes equations are considered. Two approaches are used: (i) a perturbation series about the inviscid solution; and, briefly, (ii) a step-function approximation to the reaction rate term. Results for the critical value of the Frank-Kameneskii parameter and the critical maximum temperature are presented and compared.

Thermal explosions and the disappearance of criticality at small activation energies: exact results for the slab

For exothermic reactions obeying the Arrhenius equation in circumstances in which heat flow is purely conductive, critical conditions for thermal explosion are satisfied when a dimensionless group = QE »/ kR T attains a critical value £Cr = ca. 0.88, 2 or ca. 3.32 for the infinite slab, infinite cylinder or sphere. This result (Frank-Kamenetskii 1938) of stationary state treatm ent is appropriate so long as activation energies are not too low or ambient temperatures are not too high: E &gt; RTa (or e = R Ta/E 1). Criticality persists for E decreasing or T increasing so long as e is smaller than a transitional value etr. At this transitional value etr, only continuous behaviour is possible: ignition phenomena disappear. Accurate transitional values for the reduced ambient temperature e, for the critical value of 8, and for the reduced central temperature excess 0m, have been calculated by quadrature for the infinite slab. The following results are obtained under Frank-Kamenetskii boundary conditions (α -&gt;∞) for two common temperature dependences.

Critical parameters of thermal explosion

An analysis of the critical conditions of thermal explosion based on bifurcation theory for nonlinear elliptic equations is presented. It has been proved that the value of the Frank-Kamenetsky parameter δ equals the principal eigenvalue of the equation of heat conduction linearized about the point of bifurcation of the solution u(δ), which correspond to self-ignition and extinction points. From this two computational procedures for determining critical conditions of self-ignition or extinction have been worked out. Both procedures are illustrated with examples of numerical calculations.

Critical conditions for thermal explosion in the presence of a supplementary heat source

Critical conditions for thermal explosion in the presence of a supplementary heat source