Thermal Explosion Theory Research Articles

The estimation of critical temperatures of thermal explosion for energetic materials using non-isothermal DSC

A method for estimating critical temperatures ( T b) of thermal explosion for energetic materials is derived from Semenov's thermal explosion theory and the non-isothermal kinetic equation dα/d t = Af(α)e − E/RT using reasonable hypotheses. The final formula is simple: E( T b − T i0) − RT 2 2 = 0. We can easily obtain the values of the thermal decomposition activation energy ( E) and the onset temperature ( T i) from the non-isothermal DSC curves of any kind of energetic materials, and then calculate the critical temperature ( T b) of thermal explosion. The results obtained with this method coincide very well with the measured values for the common explosives HMX, RDX, Tetryl, and NTO as well as its ethylenediammonium salt (ENTO), potassium salt (KNTO), lead salt (PbNTO) and copper salt (CuNTO).

Critical conditions in uniform temperature systems with variable heat transfer coefficient in thermal explosion theory

It is common in thermal explosion theory to neglect the temperature dependence of thermophysical properties except in the reaction rate. In practice, there are certain circumstances in which this is not suitable. This paper examines how the criterion for criticality for a system with uniform temperature (Semenov case) is affected when the heat transfer coefficient h is not constant, but depends on temperature. The lower boundary at which criticality disappears (transition) is determined.

Critical conditions in uniform temperature systems with variable heat transfer coefficients in thermal explosion theory

Abstract It is common in thermal explosion theory that the temperature dependence of thermophysical properties other than the reaction rate may be neglected. In practice, there are certain circumstances in which this is not suitable. This paper examines how criteria for criticality for a system with uniform temperature (Semenov case) are affected when the heat transfer coefficient, h , is not constant but depends on the temperature. The lower boundary at which criticality disappears (transition) is determined.

Laser ignition of pyrotechnic mixtures: Ignition mechanisms

A laser method for studying the ignition processes of a pyrotechnic mixture is presented. The experimental equipment consists mainly of a 250 W CO2 laser, an explosive chamber, a power meter, and a mechanical shutter. Using the laser ignition apparatus a parametrical study of the ignitability of a pyrotechnic mixture (Mg/NaNO3) was conducted. The influence of the following parameters on the ignition energy was studied: pulse width, beam radius, particle size, different sorts of Mg, and gas pressure. These measurements are complemented by some ignition measurements on a Mg/BaO2 mixture where the influence of catalysis is studied. Furthermore some high-speed photography of the ignition process is presented. The thermal explosion theory is then applied to these measurements for a calculation of some of the important parameters followed by a discussion of the ignition mechanisms. The activation energy (Ea=148 kJ/mol), frequency factor (K0=7.1×1017 s−1), and absorption coefficient (α=3.1104 m−1) were calculated from the measurements. Using the experimentally determined parameters a 2D finite-element computer modeling of the ignition was carried out, showing that the ignition energy can be calculated with a fair degree of accuracy but that the time to ignition cannot be modeled with a pure heat transfer model. The study is concluded with a discussion of ignition mechanisms for pyrotechnic mixtures, which especially points out that the ignition mechanism for Mg/NaNO3 is a melting of the oxidizer followed by a decomposition of the oxidizer, diffusion of the produced oxygen through the oxide layer on the magnesium particles with a consecutive reaction of oxygen and magnesium.

Ignition of flammable atmospheres by radiation-heated fibrous agglomerates

The conditions under which laser irradiation of loose agglomerates of fine fibres or particles leads to the ignition of a surrounding flammable gas mixture are studied in relation to the hazard associated with the use of optical sensing in explosive atmospheres. Results for stoichiometric mixtures in air of a range of hydrocarbons as well as of diethyl ether, carbon disulphide and hydrogen, are presented in the form of minimum igniting radiation flux as a function of the time to ignition. The minimum igniting fluxes at long induction times prove to be surprisingly low, down to 22 kW m–2for carbon disulphide/air mixtures. Traverses with small thermocouples, along with equilibrium temperature measurements during irradiation in air and cooling curves obtained following switch off, show that the system acts as a two-dimensional slab, though its heat transfer properties differ somewhat from bodies with well-defined boundaries. Irradiation with lasers of widely differing wavelengths and the use of different target surface coatings leads to widely varying equilibrium temperatures. While the minimum igniting flux cannot be correlated simply with any of the obvious ignition criteria, the corresponding equilibrium temperature reached in an inert atmosphere points to a critical ignition temperature for each particular flammable mixture. This is used to propose a tentative hazard assessment based on the concept of black body radiation interacting with a ‘black ’ particle which, although not the worst case for monochromatic radiation, proves to be more hazardous than the worst case yet encountered in practice. The variation of ignition lag with radiant power flux is such that the total energy flux varies linearly with time; effective activation energies for various fuels are deduced from the variation of induction time with temperature. A simplified theoretical model is proposed, based on classical thermal explosion theory and the large activation energy idealization. It is shown that the radiant power flux is the sole ignition criterion so long as the irradiated area is large by comparison with the quenching dimensions of the mixture. Measurements on smaller beam diameters carried out by refocusing the beam emerging from an optical fibre indicate that, below these dimensions, minimum igniting power fluxes rise, while hazardous laser powers fall to values of the order of 100 mW.

Studies on the critical temperature of thermal explosion for 3‐Nitro‐1,2,4‐triazol‐5‐one (NTO) and its salts

AbstractThe critical temperature of thermal explosion for 3‐nitro‐1,2,4‐triazol‐5‐one (NTO) and its ethylenediammonium salt (ENTO), potassium salt (KNTO), copper salt (CuNTO) and lead salt (PbNTO) were obtained using the stationary theory of thermal explosion, the calculation formula of estimating the critical temperature of thermal explosion under non‐isothermal DSC condition, and the determination method for the critical temperature of thermal explosion of small‐scale solid explosive and its data treatment method. The results of the four methods are agreeable to each other, whose differences are within 5%. The results indicate that the heat‐resistance ability of NTO and its salts and of the common explosives, cyclotetramethylenetetranitramine (HMX), cyclotrimethylenetrinitramine (RDX), pentaerythritoltetranitrate (PETN) and tetryl decreases in the order HMX > NTO > ENTO > KNTO > RDX > PETN > tetryl > PbNTO > CuNTO.

Parametric sensitivity and self-similarity in thermal explosion theory

Abstract We study the relations between thermal runaway (also called parametric sensitivity) and self-similarity, an interesting property of the sensitivity functions that has been numerically verified in many explosion and combustion systems. Both concepts are sensitivity related but independent of the particular parameter being perturbed. This independence is emphasized by proposing a new generalized condition for parametric sensitivity. Critically is defined as the point in the parameter space where the nominal trajectory exhibits maximum sensitivity to arbitrary, unstructured perturbations applied at the maximum temperature. The condition for critically reduces to the analysis of the eigenvalues of the Jacobian matrix. In addition to its conceptual generality, the new condition shows that in certain cases there exists no critical Semenov number. The sensitivity functions are shown to satisfy self-similarity relations if and only if the system exhibits critical or supercritical behavior. The onset of self-similarity is explained in terms of two properties of explosion systems, both related to parametric sensitivity. First, the temperature is a dominant variable, and any perturbation in the system affects the conversion mainly through the changes induced in the temperature. This strong coupling of the variables is shown by decomposing the sensitivity functions into direct and indirect terms. Second, the sensitivity equations are pseudo-homogeneous in a characteristic time window, in which the system becomes relatively insensitive to parameter perturbations applied within the same interval. The two properties are shown to imply self-similarity of the sensitivity functions. Relations to earlier parametric sensitivity and self-similarity conditions are discussed.

Short Communication on Self-Ignition of Potato Chips Waste

This paper describes an application of the theory of self-heating and thermal explosion of the spontaneous ignition of potato chip waste. Long term heating experiments were carried out in thermostats over the temperature range of 30-140°C in an air atmospher. Sample potato chips were set in spherical stainless stell cages of 6, 15, 20, 30, 40, 50, and 70cm diameter and their temperature changes were monitored. Physical parameters of apparent activation energy, and overall heat of reaction value were also estimated by TG-DSC analysis. Thermal conductivity of the bulk sample was measured independently. The correlations between ambient temperature and bulk size of the chips, which lead to the spontaneous-ignition, were estimated experimentally and by theoretical calculations. The estimations showed close coincidence with each other.

Dissociation–recombination relaxation behind a normal shock

Mathematical methods developed originally for thermal explosion theory are used to study the evolution of a dissociation–recombination process occurring in a compressible gas behind a normal shock. The dissociation–recombination reaction, AB+M■A+B+M, is assumed to have a relatively large dissociation temperature, so that high activation energy perturbation techniques can be used to derive general parameter dependent analytical solutions. Spatial variation of the dependent variables is described in three zones, each of distinct length scale and physical character. Initially, small changes in temperature, concentrations, density, and pressure occur in the relatively high temperature dissociation initiation zone. In the subsequent broader major dissociation region, most of the specie AB is converted to A and B and there are significant variations in all physical variables. In the last and thickest zone, recombination becomes important as the reactive flow evolves to a final equilibrium state. The results provide an analytical counterpart to numerical solutions obtained earlier by Freeman [J. Fluid Mech. 4, 407 (1958)] and Matthews [Phys. Fluids 2, 170 (1959)] for the now classical problem of idealized diatomic gas dissociation.

High-Speed Reaction Zone Structure for Variable Mole Chemistry

The structure of a high-speed deflagration downstream of a specific origin is investigated theoretically for the exothermic irreversible Arrhenius-type reaction $F + Ox \to \nu P$. Perturbation methods, and, in particular, a nonlinear transformation used in thermal explosion theory, are used to find fully analytical solutions for the spatial structure of the high-speed reaction zone when the activation energy is large. In the rapid reaction region beyond the induction zone, there is a strong interaction between large chemical heat release and flow compressibility. When the chemical reaction causes a mole reduction $( \nu < 2 )$ and there is sufficiently large heat release, the flow velocity reaches a maximum and then declines while the temperature increases monotonically throughout the process. Significantly, it is shown that the flow cannot evolve to the Chapman-Jouguet (C.J.) state where the final local Mach number is unity and the reactant concentration is zero. When the mole number of the evolving flo...

Thermal explosion theory with Arrhenius kinetics: homogeneous and inhomogeneous media

The classical thermal explosion problem for a reactive slab with Arrhenius kinetics and small activation energy parameter is considered. Perturbation series expansions are obtained that give an expression for the critical Frank-Kamenetskii parameter. We verify that the often used ‘Frank-Kamenetskii approximation’ is the first-order problem in such an expansion procedure. The analysis is extended to a reactive slab with a random distribution of reactant. The statistical properties are incorporated in an effective thermal diffusivity that may be expressed as a function of its mean and the variance about the mean. Some other expressions are also considered. It is shown that a random distribution decreases the thermal stability when compared with criticality with mean properties.

Analysis of chemical kinetic systems over the entire parameter space. III. A wet combustion system

A simple generalization of Semenov thermal explosion theory is studied here; one exothermic reaction taking place at the same time as a second one involving water as a reactant. Evaporation and condensation are also considered. The resulting two ordinary differential equations containing three parameters are treated by recently developed methods outlined in the first paper of this series. This model is a simple representation of the combustion of wet cellulosic materials such as bagasse, cotton and sawdust. The theory predicts an amazing variety of behaviour arising in association with the degenerate singularities that occur. These include degeneracies up to and including the quartic fold, H3 2 bifurcation and degenerate double zero eigenvalue points.

The critical jet flow regime

The critical jet flow regime is investigated on the basis of the equations for the Reynolds stresses, the boundary layer equations and the elements of the theory of thermal explosion. The results of calculating the transition Reynolds numbers for plane and axisymmetric jets and for wake flows are compared with the theoretical values obtained by other methods and with the data of experimental research.

Thermal explosions, criticality and the disappearance of criticality in systems with distributed temperatures IV. Rigorous bounds and their practical relevance

In thermal explosion theory it is usually impossible analytically, and sometimes a substantial task numerically, to locate the ambient temperature at which transition from discontinuous to continuous behaviour occurs. It is possible to establish analytically a lower bound that is remarkably close to the numerically computed value.

The effects of a linearly increasing ambient temperature on an exothermic reaction in a closed system

Thermal analysis in general, and differential scanning calorimetry in particular, offer rapid and automated techniques for studying exothermic decompositions. When reaction is not too complex, values for the exothermicities and Arrhenius parameters may be extracted. The basis of most mathematical treatments is not deep and quite commonly rests on analyses of ‘static’ situations, in which the responses to constant ambient temperatures are the starting point. In this paper we give an economical analysis of the dynamic process of heating a reactive sample continuously. The reduced variables of thermal explosion theory provide a compact representation of the standard case of a single reaction obeying a first-order rate law with an Arrhenius temperature dependence. An asymptotic treatment is used to refine the equations of mass and energy conservation to a practically important form. The natural variables that arise in this way lead to a model of the system in terms of the rate of the chemical reaction, rather than the more usual temperature of the sample. This new treatment leads to a clear and compact description of the behaviour of the reaction for all useful operating conditions. The well-known Kissinger relation normally derived from static treatments is seen to be relevant in this model, but care must be taken in choosing the precise physical quantities to which it relates.

Thermal analysis of energetic materials

Substances which undergo strongly exothermic chemical reactions may constitute hazards in various situations. The techniques of thermal analysis, in general, and differential scanning calorimetry (DSC) in particular, provide ways of examining such substances, in small quanitities under relatively safe conditions. A brief review of some developments in thermal explosion theory relevant to thermoanalytical studies is given. Extrapolation of the results obtained from thermoanalytical tests to more realistic situations has to be done with great care. The findings of some recent studies on energetic materials are reviewed.

Thermal explosion upon exponential change in the temperature of the surrounding medium

Many technological processes in industry occur at the temperature of the surrounding medium, which changes by some specified law. In connection with this, the theory of thermal explosion under dynamic conditions has achieved practical importance. In [1, 2] thermal self-ignition was studied for linear heating only, which narrows the applicability of the theory to actual industrial devices. The present study will analyze thermal explosion for the model of an infinite cylinder with exponential change in temperature at the external boundary. We will consider the problem of heating an inert infinite cylinder of radius r with thermal conductivity A and thermal diffus~vity a, located in a medium with temperature Tra, which changes with time as

A Unified Formulation for Diffusive and Nondiffusive Thermal Explosion Theory

Abstract A mathematical model is developed for the induction period of a parcel of slightly warm reactive gas mixture embedded in a cooler gaseous environment. High activation energy asymptotic methods are used to formulate the problem. The important parameters in the nondimensional equations are ratios of characteristic reaction, acoustic and conduction times in the thermally disturbed parcel of dimension l′. The results of the formulation imply that a specified physicochemical system, with a known characteristic chemical time, will experience a traditional diffusively dominated thermal explosion if the dimension l′ is sufficiently small. In larger systems transport effects are negligible and the induction period process is described by reactive gasdynamic equations. The study provides a unified formulation for the induction period of all thermal reaction problems and specifies the relationship between classical thermal explosion theory for rigid materials and compressible gases and more contemporary eff...

Total blow-up versus single point blow-up

Traditional thermal explosion theory is used to describe reaction initiation in condensed explosives and is limited formally to nondeformable materials. Kassoy and Poland [4] significantly extended this theory to develop an ignition model for a reactive gas in a bounded container in order to describe the induction period. During this induction period there is a spatially homogeneous pressure rise in the system which causes a com- pressive heating effect in the constant volume container. Mathematically this compressibility of the gas is expressed by means of an integral term in the induction model for the temperature perturbation 0(x, t). This model is given by e,-Ak&“+::-1.&j e,(x, t)dx Y x-2 0(x, 0) = d(x) 2 0,

An asymptotic analysis of the Sal’nikov thermokinetic oscillator

The Sal’nikov thermokinetic oscillator is studied in the limiting case where the dimensionless heat capacity tends to zero. This is equivalent to the ‘no fuel consumption’ approximation in classical thermal explosion theory and is equally revealing in that many exact results can be obtained by simple algebraic methods. Regions in parameter space are found where, although the system is asymptotically stable, a large single excursion occurs before the steady state is approached. These regions border the region of oscillations which in the limiting case are of the relaxation type. All the interesting behaviour requires RT / E &lt; 1/4, an obvious parallel with thermal explosion theory. The unstable limit cycles that occur in the Sal’nikov oscillator disappear in this limiting case. However, the requirements for an unstable limit cycle to exist in the ‘relaxation’ limit are discussed. The homoclinic bifurcation in the limiting case is also examined and it is shown that this bifurcation can (in theory) be calculated exactly. In addition, an extension to the Sal’nikov oscillator scheme in a closed system to include fuel consumption is studied both numerically and in a limiting case. It is shown that the full scheme exhibits finite trains of almost periodic behaviour before monotonically approaching equilibrium.