Thermal Explosion Theory Research Articles

Philip Humphrey Thomas (16 June 1926 – 14 January 2014)

Philip Humphrey Thomas (16 June 1926 – 14 January 2014)

Features of Self-Heating for Homogeneous Exothermic Reactions

A new approach for consideration of the self-heating modes during monomolecular exothermic reaction has been proposed. The analysis of reactions in the phase plane heating rate and temperature enables detection of the variety of modes of the heating processes and allows consideration of two dimensional parametric model: Todes criterion and Semenov criterion. This gives the possibility of determining the characteristic regions in the corresponding parametric plane. The new thermokinetic parameters were introduced for the phase trajectories analysis. The characteristic values of parameters (and characteristic temperatures) can be determined at the intersection points of the phase trajectories and boundaries of regions. The analytical expression for the thermal explosion critical conditions, which includes Todes criterion, and the new thermokinetic parameters were obtained for the first-order reactions. The condition of applicability of the classical thermal explosion theory was proposed. It was shown that the classical theory of the thermal explosion is the partial case of the presented model.

Research of critical ambient temperature of cylindrical fireworks and crackers

To study the influence of temperature on cylindrical fireworks and crackers in production and storage, this article establishes a physical and mathematical model of thermal explosion critical ambient temperature of finite cylindrical fireworks with shell based on two-dimensional steady state thermal explosion theory. The numerical program is written by difference method and Newton-homotopy method. The partial differential equations of thermal explosion model are calculated in Matlab. Comparison of numerical solutions and classical solutions proves the accuracy of model. The influence of Biot number of each surface and length diameter ratio on critical ambient temperature is analyzed. It is founded that the scope of length diameter ratio is \( 0.08 < H < 4.3 \) when Biot number tends to infinite. The thermal safety temperature of the fireworks without inner barrel when it is stored individually is obtained. This provides theoretical support for the safety of fireworks and crackers in production, storage transportation, and setting off process.

Estimation of the critical rate of temperature rise for thermal explosion of nitrocellulose using non-isothermal DSC

The expressions to calculate the critical rate of temperature rise of thermal explosion \( ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} \) for energetic materials (EMs) were derived from the Semenov’s thermal explosion theory and autocatalytic reaction rate equation of nth order, CnB, Bna, first-order, apparent empiric-order, simple first-order, Au, apparent empiric-order of m = 0, n = 0, p = 1 and m = 0, n = 1, p = 1, using reasonable hypotheses. A method to determine the kinetic parameters in the autocatalytic-decomposing reaction rate equations and the \( ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} \) in EMs when autocatalytic decomposition converts into thermal explosion from data of DSC curves at different heating rate was presented. Results show that (1) under non-isothermal DSC conditions, the autocatalytic-decomposing reaction of NC (12.97 % N) can be described by the first-order autocatalytic reaction rate equation dα/dt = 1016.00exp(−174520/RT)(1 − α) + 1016.00exp(−163510/RT)α(1 − α); (2) the value of \( ({\text{d}}T / {\text{d}}t)_{{\text{T}_{\text{b}} }} \) for NC (12.97 % N) when autocatalytic decomposition converts into thermal explosion is 0.354 K s−1.

Biological self-heating in compost piles: A Semenov formulation

A uniformly distributed mathematical model (based on Semenov's theory of thermal explosions) is formulated to model the thermal behaviour of cellulosic materials in compost piles. The model consists of a mass balance equation for oxygen, a heat balance equation and incorporates the heat release due to biological activity within the pile. Singularity theory and degenerate Hopf bifurcation theory are used to investigate the generic properties of the model as well as to determine the loci of different singularities: the isola, cusp, double-limit points, boundary limit set, double-Hopf bifurcation, generalised Hopf (Bautin) bifurcation and Bogdanov–Takens bifurcation. These loci divide the secondary parameter plane into different regions of solution behaviours. Conditions under which biological activity can result in the initiation of an elevated-temperature branch within the compost pile which does not pose the risk of spontaneous ignition are identified. These are the ideal conditions for composting. The regions of parameter space when spontaneous ignition is likely are also determined.

Hot-spot contributions in shocked high explosives from mesoscale ignition models

High explosive performance and sensitivity is strongly related to the mesoscale defect densities. Bracketing the population of mesoscale hot spots that are active in the shocked ignition of explosives is important for the development of predictive reactive flow models. By coupling a multiphysics-capable hydrodynamics code (ale3d) with a chemical kinetics solver (cheetah), we can parametrically analyze different pore sizes undergoing collapse in high pressure shock conditions with evolving physical parameter fields. Implementing first-principles based decomposition kinetics, burning hot spots are monitored, and the regimes of pore sizes that contribute significantly to burnt mass faction and those that survive thermal conduction on the time scales of ignition are elucidated. Comparisons are drawn between the thermal explosion theory and the multiphysics models for the determination of nominal pore sizes that burn significantly during ignition for the explosive 1,3,5-triamino-2,4,6-trinitrobenzene.

Multiplicity and uniqueness of positive solutions for elliptic equations with nonlinear boundary conditions arising in a theory of thermal explosion

In this paper we study a model of thermal explosion which is described by positive solutions to the boundary value problem{−Δu=λf(u),x∈Ω,n⋅∇u+c(u)u=0,x∈∂Ω, where f,c:[0,∞)→(0,∞) are C1 and C1,γ non decreasing functions satisfying limu→∞f(u)u=0, Ω is a bounded domain in RN with smooth boundary ∂Ω and λ>0 is a parameter. Using the method of sub and super-solutions we show that the solution of this problem is unique for large and small values of parameter λ, whereas for intermediate values of λ solutions are multiple provided nonlinearity f satisfies some natural assumptions. An example of such nonlinearity which is most relevant to applications and satisfies all our hypotheses is f(u)=exp[αuα+u] for α≫1.

Explosion Characteristics of a Volatile Explosive

Thermal explosion of volatile energetic materials has been investigated based upon the thermal explosion theory of a gaseous mixture. The critical and transition condition expressions for the thermal explosion of these materials are obtained. The analytical solutions not only deal with the steady-state solution but also cover the unsteady state solution. The different cases and different parameters which affect the critical conditions are investigated in details. Also the numerical solution of the energy equation is offered to give the different families of temperature - time histories. The relation between the critical parameters as ignition timing, ignition temperature, Semenov number and others with different boundary conditions is offered. In this work, the critical and transition conditions of the explosion of the volatile energetic materials through the analytical solution to the problem was introduced. The numerical solution of the unsteady state equation to the problem was offered. The relation between the critical parameters was also presented. The effect of evaporation of the volatile materials as compared with the non-volatile materials on the critical conditions was shown.

Study of the spontaneous ignition of stoichiometric tetrafluoroethylene–air mixtures at elevated pressures

The Ignition Temperature (IT) of stoichiometric tetrafluoroethylene–air mixtures on hot walls was determined in a 3-dm³-reactor. Tests at elevated pressure conditions were performed, namely at 5, 15 and 25 bar(a), showing a decrease of the IT with the initial pressure. Furthermore, the measured ignition temperatures of stoichiometric tetrafluoroethylene–air mixtures were lower than the ignition temperatures required for the decomposition pure tetrafluoroethylene (Minimum Ignition Temperature of Decomposition, MITD) reported in previous works.Equations from the Semenov thermal explosion theory on spontaneous ignition were used to identify approximate combustion kinetics of tetrafluoroethylene from the experimental results. The determined kinetics was used for the prediction of the IT of stoichiometric tetrafluoroethylene-air by simplified calculation methods. A very good agreement with the experimental results was observed.

Thermal modes of monomolecular exothermic reactions: Two-dimensional model

A new method for theoretical analysis of the self-heating kinetics for monomolecular exothermic reactions has been proposed. It has been shown, that consideration of the phase trajectories of reaction in the phase plane: the heating rate – temperature enables detection of the qualitative changes of the phase portrait under the changes of the Todes or Semenov criteria. This gives a possibility to analyze the diversity of various reaction modes for any reaction order. From this point of view, the classical Semenov theory of thermal explosion developed for zero-order reactions is a particular case. As an illustration of this method, the detailed phase trajectories analysis has been performed for the case of first-order reactions. The regions of the thermal explosion degeneration, fastest reaction mode region and transition regions have been established. The necessary and sufficient conditions for the thermal explosion have been formulated.Examples of the application of the method for calculation of specific reactions are presented; the comparison with the classical theory is performed.

Thermal heating regimes during first-order homogeneous reactions

Qualitative features of self-heating regimes for first-order homogeneous reactions are considered by analyzing the structure of the phase trajectories. Consideration of the temperature dependence of the heating rate makes it possible to extend the main results of Semenov’s theory of thermal explosion and pass to a two-dimensional parameter diagram, which allows the determination of the critical ignition conditions taking into account kinetic inhibition. It is found that the diagram of the Todes criterion versus the reciprocal of the Semenov criterion has four characteristic regions with different kinetics, two of which are limiting and two transitional ones. The boundaries of the regions are calculated, and the classical theory of thermal explosion is shown to be a special case of the projections of these boundaries on the range of the Semenov criterion.

Analysis of the self-heating process of tetrafluoroethylene in a 100-dm3-reactor

There is a lack of data on the self-ignition behaviour of tetrafluoroethylene in industrial sized equipment. Therefore, a facility was designed and constructed for the determination of the Minimum Ignition Temperature of Decomposition of tetrafluoroethylene in a cylindrical reactor with a volume of 100 dm3. Tests with initial pressures of 5 and 10 bar(a) were performed. The Minimum Ignition Temperature of Decomposition of tetrafluoroethylene was observed to decrease with the initial pressure, in agreement with previous experiments with small scale cylindrical vessels. This paper describes the test set-up und gives an overview of the achieved experimental results. In particular the effect of the reactor orientation (vertical or horizontal) is discussed. Furthermore, simplified equations from the Semenov thermal explosion theory are used to attempt extrapolations of previous and current data on the Minimum Ignition Temperature of Decomposition of tetrafluoroethylene to other vessel volumes or initial pressures. Moreover, the experimental data are plotted together against the heated volume to heated surface ratio, which should provide a better extrapolation to other vessel dimensions by taking into account that the efficiency of the dispersion of the heat generated by the reaction is different for two reactors with the same volume but different diameter. Finally, simplified methods for predicting the Minimum Ignition Temperature of Decomposition of tetrafluoroethylene presented previously by the authors are validated for large scale reactors with the experimental data collected within the current work.

The method of phase trajectories in nonstationary thermal explosion theory

It is shown that consideration of the heating rate-temperature dependence, an analysis of self-heating for first-order exothermic reactions, and strict inclusion of kinetic deceleration puts forward fresh ideas about the diversity of reaction regimes on the Todes criterion-Semenov criterion parameter plane. From this point of view, classic Semenov theory is a particular case of the projection of two-dimensional regions onto the direction of Semenov criterion changes. An analysis of the mutual arrangement of reaction region boundaries with different kinetics and the shape of the representation point movement trajectory when the initial temperature of the system changed allowed us to determine the thermal explosion degeneration region, transition region, and regions of possible explosive reaction modes.

Thermal explosion model and calculation of sphere fireworks and crackers

In order to analyze thermal safety of fireworks and crackers, thermal explosion models of three kinds of sphere fireworks and crackers with different structures are achieved on the basis of thermal explosion theory, and thermal resistance of shell and effective Biot number are deduced as for boundary conditions. Two models are calculated with target-shooting method in Matlab program, and the rationality is proved through comparison of numerical solution and classical solution. Meanwhile, calculation steps are shown about a type of firework. The study has a great significance to thermal safety analysis of fireworks and crackers.

The spherical Liouville and associated differential equations

This paper is concerned with an ordinary non-linear differential equation that occurs in the theory of thermal explosion and, for the spherically symmetric case, in the theory of stellar structure. For plane and axial symmetry, closed form solutions are well known, but the spherically symmetric case can so far only be obtained numerically. By examining the problem in the phase plane, Enig (1967, Critical parameters in the Poisson-Boltzmann equation of steady-state thermal explosion theory. Combust. Flame, 10, 197–199enig1967 was able to obtain an equation from which the critical parameters of the equations can be determined. The equation is of Abel type and there is some difficulty in determining an integrating factor. We note that the partial differential equation for the integrating factor is more difficult to solve then the original equation. A general method is presented that allows the solution to be found in parametric form. Methods of solution for the spherically symmetric case have been presented by various authors. It is shown that these may all be reduced to the equation of Enig. The spherically symmetric case has been examined in some detail near its singular point. In a brilliant but largely ignored paper, it was Jules Enig who first discovered the existence of a vortex in the phase plane. It is hoped that my contribution has solved some of the mysteries of the vortex.

Numerical simulations applying to the analysis of thermal explosion of organic gel fuel in a hot gas

In this work we investigate theoretically and numerically the nature of the evolution of a hot gas mixture containing organic gel fuel droplets of different radii with oscillatory evaporation within the context of thermal explosion theory. The polydisperse spray is modeled using a probability density function (PDF). In this paper we take into account the time evolution of the size distribution due to the evaporation process by using the kinetic equation. This new model is in the form of singular perturbed system (SPS) of highly nonlinear of ordinary differential equations. This SPS form of the model and the non-dimensionalization of the equations enable us first to apply the methods of integral manifolds (MIM) and second to identify the parameters that play a major role in determining the dynamical regimes of the considered system. Our analytical and numerical simulations results that based on the MIM show that the dynamical behavior is different than that found with the conventional liquid droplets. An explicit expression of the critical condition for thermal explosion limit is derived analytically and represents a generalization of the critical parameter of the classical Semenov theory.

A new method based on the non-isothermal kinetic equation to estimate the critical temperature of thermal explosion for energetic materials using non-isothermal DSC

A method for estimating the critical temperature of thermal explosion for energetic materials using differential scanning calorimetry (DSC) measurement is derived from the Semenov’s thermal explosion theory and the non-isothermal kinetic equation based on Harcourt-Esson’s kinetic equation. The result obtained from this method coincides completely with that of the Hu-Yang-Liang-Wu method.

Investigation of the decomposition reaction and dust explosion characteristics of crystalline dicumyl peroxide

The dicumyl peroxide (DCP) is widely used as a polymerization initiator, catalyst and vulcanizing agent in the chemical industry. A number of accidents have been caused by its thermal instability in storage or manufacturing process. Thus, its hazard characteristics have to be clearly identified. First of all, the differential scanning calorimeter (DSC) is used to measure the heat of decomposition reaction, which can contribute to understanding the reaction characteristics of DCP. The accelerating rate calorimeter (ARC) is used to measure the rates of temperature and pressure rises of decomposition reaction, and then the kinetics parameters are estimated. Furthermore, the MIKE 3 apparatus and the 20-l-Apparatus are used to measure and analyze the dust explosion characteristics of DCP at room temperature and atmospheric pressure. Finally, Semenov's thermal explosion theory is applied to investigate the critical runaway condition and the stability criterion of decomposition reaction, and to build the relationship of critical temperature, convective heat transfer coefficient, heat transfer surface area and ambient temperature. These results contribute to improving the safety in the reaction, transportation and storage processes of DCP.

A Simple Method to Estimate the Critical Temperature of Thermal Explosion for Energetic Materials Using Nonisothermal DSC

A method for estimating critical temperature (T b) of thermal explosion for energetic materials was derived from Semenov's [9] thermal explosion theory and the nonisothermal kinetic equation based on Berthelot's expression using reasonable hypotheses. The final formula is , which is simple. We can easily obtain the onset temperature (T ei) from the nonisothermal DSC curves, the value of T e0 from the equation , the values of b from the equation , and then calculate the value of T b. The result obtained with this method coincides completely with the value of T b obtained by Zhang et al.'s [4] method.

Estimation of Critical Temperature of Thermal Explosion for Nitrosubstituted Azetidines Using Non‐isothermal DSC

AbstractBased on reasonable hypothesis, two general expressions and their six derived formulae for estimating the critical temperature (Tb) of thermal explosion for energetic materials (EM) were derived from the Semenov's thermal explosion theory and eight non‐isothermal kinetic equations. We can easily obtain the values of the initial temperature (T0i) at which DSC curve deviates from the baseline of the non‐isothermal DSC curve of EM, the onset temperature (Tei), the exothermic decomposition reaction kinetic parameters and the values of T00 and Te0 from the equation T0i or ei=T00 or e0+a1βi+a2βi2+···+aL−2βiL−2, i=1, 2, ;···, L and then calculate the values of Tb by the six derived formulae. The Tb values for seven nitrosubstituted azetidines, 3,3‐dinitroazetidinium nitrate (1), 3,3‐dinitroazetidinium picrate (2), 3,3‐dinitroazetidinium‐3‐nitro‐1,2,4‐triazol‐5‐onate (3), 1,3‐bis(3′,3′‐dinitroazetidine group)‐2,2‐dinitropropane (4), 1‐(2′,2′,2′‐trinitroethyl)‐3,3‐dinitroazetidine (5), 3,3‐dinitroazetidinium perchlorate (6) and 1‐(3′,3′‐dinitroazetidineyl)‐2,2‐dinitropropane (7), obtained with the six derived formulae are agreeable to each other, whose differences are within 1.5%. The results indicate that the heat‐resistance stability of the seven nitrosubstituted azetidines decreases in the order 6&gt;7&gt;5&gt;4&gt;3&gt;2&gt;1.