Problem Of Thermal Explosion Research Articles

Determining critical conditions in the thermal explosion problem using approximate variational formulations

Determining critical conditions in the thermal explosion problem using approximate variational formulations

Термическое разложение D-циклосерина и теризидона

Thermal decomposition of D-cycloserine and terizidone in the air and in the inert helium and nitrogen media was studied using differential thermal analysis. It is shown that upon reaching 145 °C and 135 °C respectively, the intense exothermic decomposition begins. In the inert environment the substances retain ability to intensively exothermic decomposition, which is a required condition for the possibility of explosive transformation occurrence. To confirm the possibility of explosive transformation, the flash points of substances were calculated according to the formula, which is a consequence of the problem of thermal explosion during convective heat exchange with the environment. The obtained result is close to the experimental one (temperatures 102 and 104 °C, respectively). The calculations used the kinetic parameters determined by the Kissinger method and corresponding to the values obtained by the Ozawa — Flynn — Wall method. Densities of the substances found using an automatic pycnometer, and the heat of explosive transformation obtained experimentally and with the use of the computer thermodynamic program Real are also considered. It is concluded that both substances are prone to intense exothermic decomposition, and, under certain conditions, the development of a thermal explosion is possible. Recommendations on ensuring industrial safety when working with D-cycloserine and terizidone are sent to FGUP «GNTs «NIOPIK». Particular attention should be paid to temperature control at all the stages of the production process. Based on the results obtained in the study, it should not exceed 110 °C for D-cycloserine, and 120 °C for terizidone considering the error of measuring instruments.

Способность нафтохинондиазидных фоторезистов к экзотермическому разложению

The article considers two intermediate products of positive photoresists (1,2-naphthoquinonediazide-(2)-5-sulfonic acid of monosodium salt — Dye M and 1,2-naphthoquinonediazide-(2)-5-sulfochloride — Dye N2) from the standpoint of the tendency to explosive transformation. The experimental values of flash points determined on the OTP setup were 130 °C for Dye M and 95 °C for Dye N2. These values are close to the temperatures of the beginning of intensive exothermic decomposition (132 and 111 °C, respectively) obtained by thermogravimetric analysis. In addition, this analysis showed the presence of exothermic peaks in the studied samples both in the air and in an inert atmosphere of helium, which is a necessary condition for the manifestation of a tendency to explosive transformation. To confirm the possibility of explosive transformation, the flash points of substances were also determined by the calculation method according to the formula, which is a consequence of the problem of thermal explosion during convective heat exchange with the environment, and gave a result close to the experimental one (the values were 138 and 105 °C, respectively). For this calculation the following was used: the kinetic parameters determined by the Kissinger method, the values of the density of substances determined on an automatic pycnometer, as well as the values of the heat of explosive transformation obtained with the help of the Real computer thermodynamic program. The research results confirming the tendency of the investigated compounds to explosive transformation, as well as the critical temperatures, exceeding which is unacceptable, were transferred to the production of FGUP GNTs NIOPIK to create a safe technological process, safe storage and transportation conditions. Considering the accuracy of the measuring devices, the process temperature should not exceed 125 °C for Dye M and 90 °C for Dye N2. The conducted studies and calculations show that the computational and experimental approaches have good convergence, give values in a close temperature range, and increase the reliability of the obtained results.

Singular perturbed vector field method applied to combustion in diesel engine: Continuous case with thermal runaway

• The singular perturbed vector filed is a new method (SPVF) for extracting and exposing the hierarchy of a given ODE system. • We apply the SPVF to the problem of thermal explosion of polydisperse fuel spray combustion . • We describe the droplets size using probability density function. • We take into account the thermal radiation effects on the droplets evaporation. In this study, we employ the well-known method of a singularly perturbed vector field (SPVF) and its application to the thermal runaway of diesel spray combustion. Given a system of governing equations, consisting of hidden multi-scale variables, the SPVF method transfers and decomposes such a system into fast and slow singularly perturbed subsystems. The resulting subsystem enables us to better understand the complex system and simplify the calculations. Powerful analytical, numerical, and asymptotic methods (e.g., the method of slow invariant manifolds and the homotopy analysis method) can subsequently be applied to each subsystem. In this paper, we compare the results obtained by the methods of slow invariant manifolds and SPVF, as applied to the spray (polydisperse) droplets combustion model.

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.

Mathematical Modelling of Spray Combustion-Numerical and Analytical Analysis with application to Engineering Science

In the present paper we applied two well- known analytical method to the problem of thermal explosion of monodisperse and polydisperse fuel spray. The methods are the method of integral manifold (MIM) and the homotopy analysis method (HAM). The MIM method used as a basic tools for the analysis of SPS system of ordinary differential equations which means that the physical/ mathematical model should contain a small parameter in the governing equations. The HAM is always valid no matter whether there exist small physical parameters or not in contrast to the classical perturbation methods which requires the existence of a small parameter in the system (in general this is not the case). According to the theory of HAM, the convergence and the rate of solution series are dependent on the convergent control parameter h. This means that this parameter gives one a convenient way to adjust and to control the convergent region of the solutions.

Thermal explosion in oscillating ambient conditions.

Thermal explosion problem for a medium with oscillating ambient temperature at its boundaries is considered. This is a new problem in thermal explosion theory, not previously considered in a distributed system formulation, but important for combustion and fire science. It describes autoignition of wide range of fires (such as but not limited to piles of biosolids and other organic matter; storages of munitions, explosives, propellants) subjected to temperature variations, such as seasonal or day/night variation. The problem is considered in formulation adopted in classical studies of thermal explosion. Critical conditions are determined by frequency and amplitude of ambient temperature oscillations, as well as by a number of other parameters. Effects of all the parameters on critical conditions are quantified. Results are presented for the case of planar symmetry. Development of thermal explosion in time is also considered, and a new type of unsteady thermal explosion development is discovered where thermal runaway occurs after several periods of temperature oscillations within the medium.

Simulation of Fuel Ignition Delay in Diesel Engines with Various Fuel Feeding Systems

A mathematical model for numerical simulation of the fuel combustion delay in a diesel engine as a problem of dynamic thermal explosion during the adiabatic compression has been established. Ignition of fuel and air mixture in the local volume is considered at simultaneous evaporation of drops and gas chemical reaction within overall kinetics. Satisfactory correlation of computation and experimental fuel combustion delays on speed ability and load ability of the diesel is obtained. Numerical modeling of ipact of general kinetics constants on the fuel combustion delay is carried out. The features of self-ignition in the diesel are considered at low values of chemical reaction activation energy.

Study on critical ambient temperature of cylindrical battery

In order to study the thermal safety of cylindrical battery and solve the three-dimensional cylindrical battery thermal explosion problem, a common thermal explosion physical model of cylindrical battery and three-dimensional thermal explosion mathematical model of cylindrical fireworks with non-uniform heat dissipation of the lateral surface were established for the first time. By applying the theory of heat transfer, the boundary conditions of cylindrical battery were simplified reasonably. The seven-point difference method was introduced to disperse the model. The three-dimensional numerical program was written by homotopy continuation method and Newton iteration method based on Matlab. Comparison of two-dimensional numerical solutions obtained by taking ϕ = 0 and classical solutions proved the accuracy of model. A common kind of fireworks was calculated in this paper. When this single cylinder firework stored individually, the criterion of thermal explosion is 1.796, and critical ambient temperature is 450.484 K. When stored in combination form (that is battery), the criterion of thermal explosion is 1.363 and critical ambient temperature is 447.964 K. The results show that the cylindrical fireworks stored in combination form is more dangerous than this single cylinder firework stored individually, so the cylindrical battery is the focus of safety prevention of fireworks.

Thermal explosion in semi-batch reactors

The problem of thermal explosion in a semi-batch reactor is solved. The critical conditions for the thermal explosion are studied. It is shown that the ignition resulting from the chemical reaction is possible both during the stage of feeding of the second reactant solution and after its completion. The dynamic behavior of the reactor depending on the temperature of the heat exchanger and the volumetric feed rate of the second reactant is analyzed. It is shown that ignition at the feeding stage occurs at high temperature of the heat exchanger and involves two macroscopic stages. In the first stage, the temperature increases with increasing rate (thermal explosion regime), and in the second stage, its further increase occurs in the regime of combustion of the second reactant. The critical ignition conditions are found to be independent on the feed rate of the second reactant in a particular range of its values.

Singularly perturbed homotopy analysis method

In this paper we combined the homotopy analysis method (HAM) and the method of integral manifold (MIM) to investigate the problem of thermal explosion in two-phases polydisperse combustible mixtures of gas with fuel droplets. The size distribution of the fuel droplets is assumed to be continuous in the form of an exponential distribution and is found from the solution of the kinetic equation for the probability density function. The system of the polydisperse fuel spray takes into account the effects of the thermal radiation and convection. By applying the HAM and the MIM, we derived an analytical solution of the system and we compared our results with the numerical solutions.

Gelfand-type problem for two-phase porous media

We consider a generalization of the Gelfand problem arising in Frank-Kamenetskii theory of thermal explosion. This generalization is a natural extension of the Gelfand problem to two-phase materials, where, in contrast to the classical Gelfand problem which uses a single temperature approach, the state of the system is described by two different temperatures. We show that similar to the classical Gelfand problem the thermal explosion occurs exclusively owing to the absence of stationary temperature distribution. We also show that the presence of interphase heat exchange delays a thermal explosion. Moreover, we prove that in the limit of infinite heat exchange between phases the problem of thermal explosion in two-phase porous media reduces to the classical Gelfand problem with renormalized constants.

Lattice Boltzmann Modeling of Thermal Explosion in Natural Convection Conditions

Lattice Boltzmann (LB) computational code developed by the authors is used to simulate the development of thermal explosion in reactive mixtures subjected to convection. The work demonstrates an LB modeling application to reactive flows by considering practically important combustion and fire research problem. The problem of convection-affected thermal explosion is of particular interest from both theoretical and practical points of view. Critical conditions for convection-affected thermal explosion are found in the range of Rayleigh numbers 103–108.

Comparison of the Homotopy Perturbation Method (HPM) and Method of Integral Manifolds (MIM) on a Thermal Explosion of Polydisperse Fuel Spray System

The aim of this work is to carry out a comparative analysis of a more recent homotopy perturbation method and the method of integral manifolds for solving the problem of thermal explosion in a combustible mixture containing vaporizing fuel droplets of different radii, i.e., polydisperse fuel spray. The model under consideration, known as parcel approximation, is a system of nonlinear ordinary differential equations. Our results include a comparative analysis between the following models: (1) the parcel model, which is solved numerically, by applying the method of integral manifolds for zero-order and third-order approximation and by applying the homotopy perturbation method, and (2) the continuous model, which is solved by Runge--Kutta methods. We compare these methods applied to experimental fuel spray data such as $n$-Butanol, $n$-Decane, and $n$-Heptane. Although these methods are in agreement with each other, application of the homotopy perturbation method to these systems of equations shows rapid con...

On criticality and disappearance of criticality for a branched-chain thermal reaction with distributed temperature

Criticality and disappearance of criticality in a branched-chain thermal explosion problem for a reactive slab with generalized Arrhenius kinetics and initiation reaction is considered. A numerical investigation is performed. The effects of the non-dimensional number a (initiation rate compared with the diffusion coefficient), n (order of the branching reaction), on the criticality as well as disappearance of criticality are compared with existing results; explained using graphs and then discussed. The results help to enhance understanding of the interplay between thermal and branched-chain thermal explosions.

Application of the Homotopy Perturbation Method (HPM) and the Homotopy Analysis Method (HAM) to the Problem of the Thermal Explosion in a Radiation Gas with Polydisperse Fuel Spray

The aim of this work is to apply the homotopy perturbation method and homotopy analysis method to the problem of thermal explosion in a flammable gas mixture with the addition of volatile fuel droplets. The system of equations that describes the effects of heating, evaporation, and combustion of fuel in a polydisperse spray is simplified. Both convective and radiative heating of droplets is taken into account in the model. The model for the radiative heating of droplets takes into account the semitransparency of the droplets. The results of the analysis have been applied to the modeling of the thermal explosion in diesel engines. We applied the Homotopy Perturbation Method and the Homotopy Analysis Method to the new model and we found the region of the convergence of the considered solutions of the relevant physical parameters. The results demonstrate that these methods are very effective for solving nonlinear problems in science and engineering.

Thermal explosion of an annular layer with boundary conditions of the third kind

An analytical solution of the problem of thermal explosion of an annular layer is obtained for two cases: 1) the inner cylinder is thermally insulated (heat exchange with the environment through the surface of the outer cylinder follows Newton’s law); 2) the outer cylinder is thermally insulated (heat exchange through the surface of the inner cylinder follows the same law). The dependence of the critical value of the Frank-Kamenetskii parameter on the ratio of the radius of the inner cylinder to the radius of the outer cylinder is constructed for various values of the Biot number. The limiting cases where this ratio tends to zero and unity are considered.

Thermal explosion characteristics in a reduced kinetics model

The problem of thermal explosion arising from a spatially homogeneous reduced five steps reaction kinetic model, which comprises of the chain initiation, chain propagation/branching and chain termination steps is considered. By assuming realistic approximations, the pertubation technique was used to obtain expressions for thermal ignition time for the adiabatic system. In the non-adiabatic system, expressions for the critical heat loss parameter and the ignition temperature in the line of Semenov theory have been obtained. Analysis of the system involving some parameters, and the contributions of the heat released due to the termination reactions on the behaviour of the ignition times and Semenov parameters have been carried out and expressed graphically. Apart from confirming known results in literature, the results shed more light on hitherto unknown behaviour.

Approximate analytic solution for critical parameters in a thermal explosion problem

In this paper, a new approximate analytical solution based on the homotopy perturbation method (HPM) is applied to predict critical conditions for a thermal explosion problem. Apart from the conceptual simplicity and flexibility, the method gives rise to an easy converging solution leading to the predictions of critical parameters for thermal explosion.

The time evolution of the size distribution of droplets effects on the thermal explosion of polydisperse fuel spray

In this paper we investigate the problem of thermal explosion in a two-phase polydisperse combustible mixture (oxygen and fuel concentrations are takes into account). The current work presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a probability density function (PDF). The evolution of the size distribution of droplets due to the evaporation process is described by the kinetic equation for the PDF. 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.