The Effects of Natural Convection and the Consumption of Reactant on the Occurrence of Thermal Explosion in a Reacting Gas Contained inside a Closed Spherical Vessel (original) (raw)

On the occurrence of thermal explosion in a reacting gas: The effects of natural convection and consumption of reactant

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.

Effects of kinetic and transport phenomena on thermal explosion and oscillatory behaviour in a spherical reactor with mixed convection

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...

Thermal explosion analysis of a strong exothermic chemical reaction with variable pre-exponential factor in a spherical vessel

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.

A comparison of measured temperatures with those calculated numerically and analytically for an exothermic chemical reaction inside a spherical batch reactor with natural convection

Chemical Engineering Science, 2007

When any exothermic chemical reaction occurs inside e.g., an unstirred spherical vessel, the heating effect of the reaction often induces temperature gradients and consequently natural convection. This work sets out to compare previously measured temperatures at different positions inside such a batch reactor with values computed numerically and analytically. It is the first such study for a reaction with an order greater than zero, occurring in a spherical reactor. The main reaction considered is the thermal decomposition of the gas, azomethane, which has often been used in experimental studies of thermal explosion. Other experimental results for the reaction between nitric oxide and oxygen, as well as between hydrogen and chlorine are also considered here. The measured temperatures at the centre of the vessel are first compared with analytical scales, derived by inspecting the governing equations. It is found that the temperature rise when diffusion is the dominant transport mechanism (i.e., at small values of the Rayleigh number) is directly proportional to the ratio of the characteristic timescales for diffusion and for the reaction. Similarly, when natural convection is the dominant transport mechanism, the temperature rise is proportional to the ratio of the timescales for convection and reaction.

The influence of the flow of the reacting gas on the conditions for a thermal explosion

Proceedings of the National Academy of Sciences, 1997

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computationa...

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.

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...

Thermal decomposition analysis in a sphere of combustible materials

In this article, we look at spontaneous combustion due to exothermic chemical reaction taking place within a stockpile of combustible material. The model includes mass and energy balance equations in a spherical domain. The complicated chemical reaction is simplified by considering a one-dimensional process. The differential equations governing the problem are solved using semi-implicit finite difference method. The effects of kinetic parameters embedded within the system are analyzed and the results are expressed graphically and discussed accordingly.

Thermal explosion in a stirred medium

Russian Journal of Physical Chemistry B, 2013

The critical conditions of a thermal explosion in a cylindrical chemical reactor with several sym metrically positioned agitators for creating a forced convection of the reaction mixture are examined. The analysis is carried out for an arbitrary Peclet number on the assumption that the flow of the fluid is laminar. The critical value of the thermal explosion parameter (Frank Kamenetskii parameter) is determined as a function of the number of agitators, Peclet number, and the distances between the axes of the agitators and the reactor axis. In contrast to the previous studies, the dependence of the thermal explosion parameter on the rate of stirring of the medium is considered. Calculations show that, as the number of agitators and mixing rate increases, the thermal explosion probability decreases, so that the critical value of the thermal explosion parameter can be several times greater than its classical value. It is demonstrated that, depending on the values of the parameters, the problem can have four stationary solutions, two of which are stable.