The influence of the flow of the reacting gas on the conditions for a thermal explosion (original) (raw)
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Combustion and Flame, 2010
Whether or not a chemical reaction in a fluid leads to an explosion is shown to depend on four timescales: that for the chemical reaction to heat up the fluid containing the reactants and products, for heat conduction out of the reactor, for natural convection in the fluid, and finally for chemical reaction. This approach is developed for an irreversible, nth-order chemical reaction, A ? B occurring exothermically in a closed spherical vessel, whose wall is held at a fixed temperature. These four timescales are expressed in terms of the physical and chemical parameters of the system. A new three-dimensional regime diagram is proposed, in which the three effects inhibiting explosion, viz. the consumption of reactant, and heat removal both by thermal conduction and by natural convection, appear separately. Numerical simulations are performed for laminar natural convection occurring, so that the development of temperature, composition and velocity throughout a reacting gas is computed for increasing times. The results are compared with previous experimental measurements in the gas phase for the decomposition of azomethane. The criterion for an explosion is considered in some detail; it appears that these systems explode if and when the maximum dimensionless rise in temperature exceeds a value close to 5.
Whether or not a chemical reaction in a fluid leads to an explosion is shown to depend on four timescales, viz. those for: the chemical reaction to heat up the fluid containing the reactants and products, heat conduction out of the reactor, for natural convection in the fluid, and finally for chemical reaction. This approach is developed for an irreversible, n-th order chemical reaction, A → B occurring exothermically in a spherical vessel, whose walls are held at a fixed temperature. The four timescales are expressed in terms of the physical and chemical parameters of the system. A new three-dimensional regime diagram is proposed, in which the three effects inhibiting explosion, viz. the consumption of reactant, and heat removal both by thermal conduction and by natural convection, appear separately. Numerical simulations are performed for laminar natural convection occurring. The results are compared with previous experimental measurements in the gas phase for the decomposition of azomethane.
Mathematical modeling of thermal explosion with natural convection: a brief survey
Mathematical Modelling of Natural Phenomena
Thermal (or heat) explosion occurs in a reacting medium if the heat production due to an exothermic chemical reaction exceeds the heat loss through the boundary. In the mathematical approximation heat explosion is characterized by an unbounded temperature growth. If the reaction occurs in a liquid or gaseous medium, then a nonuniform temperature distribution can lead to natural convection. The interaction of heat explosion with natural convection can result in various regimes with a bounded temperature distribution (stationary, periodic, chaotic) and to a transition to heat explosion. The latter can be accompanied by a monotonic temperature growth or by temperature oscillations (oscillating heat explosion). This paper presents a review on mathematical modelling of heat explosion with natural convection in a homogeneous fluid and in a porous medium.
The Influence of Reactant Consumption on the Critical Conditions for Homogeneous Thermal Explosions
The Quarterly Journal of Mechanics and Applied Mathematics, 1978
The spatially homogeneous model of a high activation energy thermal explosion is studied when the heat loss parameter a is close to the classically-defined critical value a = e. Asymptotic solutions are developed which describe the time-history of the temperature and reactant depletion. It is shown that there is a critical time period, large with respect to the characteristic conduction time, in which the temperature variation is described by a Riccati equation. The solution properties of this nonlinear equation permit one to define a value of A = a-e which separates subsequent subcritical and supercritical behaviour.
Modeling of what may happen after a thermal explosion
SHOCK COMPRESSION OF CONDENSED MATTER - 2019: Proceedings of the Conference of the American Physical Society Topical Group on Shock Compression of Condensed Matter
Thermal explosion may happen when an explosive is in a temperature field, and when its boundary temperature is between the critical and ignition temperatures. Semenov and Frank-Kamenetzky solved the thermal explosion problem analytically in 1D and for a constant boundary temperature. Since the 1960s thermal explosion problems have been simulated numerically in 3D and for realistic boundary conditions. In thermal explosion tests it is easier to apply the boundary temperature gradually, and in this way they become cookoff tests. When thermal explosion happens in a small region of an explosive body, the events that follow, and their overall resultant violence, may be quite diverse, like: 1) slow decaying pressure wave; 2) fast non decaying wave; 3) strengthening pressure wave that builds up to shock initiation and detonation. The outcome of a thermal explosion depends on: 1) the sensitivity of the explosive; 2) the temperature field throughout the explosive body at the time of thermal explosion; 3) the geometry of the explosive body; and 4) the degree of confinement of the explosive body. To model what may happen after a thermal explosion event, we use our PDSR (= Pressure Dependent Shear Reaction) together with our TDRR (= Temperature Dependent Reaction Rate) reactive flow models. For each computational cell these two models work in sequence. Initially there is a shear reaction handled by PDSR. If as a result pressure and temperature there go beyond the threshold for reaction out of hot spots, TDRR takes over to compute shock initiation and detonation. We present computed examples of different outcomes of thermal explosion events.
Modelling the Behaviour of Homogeneous Explosion in a Closed Vessel with Three-Step Reaction Model
2019
This study presents numerical simulations of a spatially homogeneous explosion in a closed vessel having thermal and chain-branching reaction models. The simulations are performed using three-step models of chemical kinetics. A fourth-order Runge-Kutta method was used to carry out the simulations. The result of the study revealed that when values of crossover temperature, , is sufficiently less than unity, the homogeneous explosion is described by the purely three-step chain-branching reaction model. While for greater than unity, the homogeneous explosion exhibits a considerable thermal explosion structure. This indicates that the crossover temperature influence the nature of explosion and hence determines the exothermicity of the reaction (thermal explosion) or its chain character (branched-chain explosion). For more exploration, there may be need to extend to an asymptotic method. For further study, it was suggested that higher values of activation energy and the crossover tempe...
New definitions for the criticality conditions of the thermal explosion problem are founded on the mathematical behavior of the governing equations. The paper deals with uniform temperature and concentration (Semenov problem). It is well known that the results can be applied to the distributed temperature and concentration case by the use of correction factors. It is shown that criticality can be defined in the temperature-time plane as accepted by most authors. However, using our definitions of criticality in the temperature-concentration plane confirms the previous findings of Adler and Enig. They showed that the classically defined critical state in the temperature-time plane is always a subcritical state in the temperature-concentration plane. At the same time, the critical state in the temperature-concentration plane is always a supercritical state in the temperature-time plane. However, the critical state in the temperature-concentration plane is in agreement with that in the Semenov number (~)-temperature plane. It is shown that the critical states in all planes coincide only when n = 0 or B = oo and agree with the well known results neglecting reactant consumption. The difference between the critical and ignition temperatures is discussed. It is shown that as B approaches infinity, the solution for • as a function of r for any value of n approaches the solution for n = 0. Hence for B = oo, substituting for n = 0 in Alder and Enig results produces the classical Semenov result. This resolves the objections expressed against these results before. At the same time the locus of the critical states for n = 0, with finite B is determined. The effect of the degree of reaction on the induction time for adiabatic systems is demonstrated. The conditions required for ignition of subcritical systems is demonstrated. The conditions required for ignition of subcritical systems are discussed as well as the effect of initial conditions on criticality. NOMENCLATURE Nondimensional Variables and Parameters a 1/'~ = hSRTsZ/QVA,,C~Ee-E/RT~ A. frequency factor (s-~) B QCoE/pc~RTs 2 C concentration of reactant (molm-3) C O initial concentration of reactant (mol m-3) C~ specific heat (J K-tkg-l) E activation energy (J mol-~) h convection heat transfer coefficient (J K-1 m-2s-1) n order of reaction Q heat of reaction (J mol-l) R universal gas constant (J K-~mol-~) V volume (m 3) T temperature (K)
Physical chemistry chemical physics : PCCP, 2014
Thermal explosions are often influenced by the complex interaction between transport and reaction phenomena. In particular, reactant consumption can promote safer, non-explosive operation conditions of combustion systems. However, in liquids or gases, the presence of forced convection can affect the behaviour of a system, instigating oscillations in the temperature, reactant concentration and velocity fields. This work describes the effect of reactant consumption on a simple, one-step, exothermic reaction occurring in a spherical reactor with both forced and natural convection, by means of numerical simulations. Regime diagrams characterised by ratios of timescales for each transport and reaction phenomena are presented and the explosion boundary is represented for several forced convection and reaction consumption intensities. Special attention is given to the oscillatory behaviour observed for moderate forced convection and oscillatory regions are represented on the regime diagram...
This study is devoted to investigate the analysis of thermal explosion of a strong exothermic chemical reaction with variable pre-exponential factor in a spherical vessel. The steady state solutions for strong exothermic decomposition of a combustible material uniformly distributed in a heated spherical vessel under Bimolecular, Arrhenius and Sensitised reaction rates. Analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type of Hermite-Padé approximants and important properties of the temperature field including bifurcations and thermal criticality are discussed.
Effect of geometry on the analysis of thermal explosion of a strongly exothermic chemical reactions
This study is devoted to investigate the effect of geometry on thermal explosion of a strong exothermic chemical reaction with variable pre-exponential factor under Bimolecular, Arrhenius and Sensitised reaction rate, neglecting the consumption of the material are examined. Analytical solutions are constructed for the governing nonlinear boundary-value problem using perturbation technique together with a special type Hermite-pade approximation and important properties of the temperature field including bifurcations and thermal criticality are discussed. It is shown that temperature field is highly influenced by the geometry.