Ignition Theory Research Articles

Ignition of porous materials by gas filtration (unsteady downstream filtration)

The wave theory of ignition is used to create an analytic method for calculating the temporal characteristics of ignition in porous samples by a flow of hot gas into the material (unsteady downstream filtration). When classical dimensionless variables are used, characteristic ignition times are found to have an anomalous dependence on the parameter β=RT ign/E: as β is increased, the duration of the ignition stages is reduced and does not increase, as it does for conductive heating of the material. A scale is found for the gas density, such that the temporal ignition characteristics have the customary dependence on β when it is used. It is shown that the equations for isothermal filtration can be used to determine the mass feed rate of the gas. Numerical calculations confirm the validity of the basic assumptions of the theory regarding the existence of stages in the ignition process and the wave mechanism for heating the material. Good quantitative agreement is obtained between an approximate analysis and the numerical calculations. The error in determining the time to develop a zero temperature gradient at the sample boundary and the thermal explosion time is less than 50%.

Estimation of kinetic rate parameters for coal combustion from measurements of the ignition temperature

Combustion reactivity plays a significant role in the development of optimal strategies for the efficient utilization of coal. A promising technique for characterization of combustion reactivity involves measurement of the gas temperatures which lead to the ignition of coal particles of different sizes, and the use of classical ignition theory to extract the relevant reaction rate parameters. This paper examines the influence of the modeling assumptions, within the framework of heterogeneous ignition theory, on the combustion rate parameters calculated from experimental data. It is shown that unequivocal determination of reaction order from ignition data is difficult. Further, the manner in which the rate constant is defined—whether it is based on the external or the internal surface area—exerts a significant influence on the reactivity parameters. The effect of radiation is included in the energy balance and shown to influence the results substantially, for larger particles in particular. Finally, it is shown that combustion reactivity determined from ignition measurements does not differ significantly from other measurement techniques if the effects of radiation and mass transport limitations are accounted for.

Realization of the Three Class A Geometries in Heating Tests on a Cellulosic Material

The three ‘class A geometries’ in ignition theory––the sphere, the infinite cylinder and the infinite slab––are utilized in heating experiments on sawdust, which represents wood waste. Results obtained are shown to be wholly consistent with results for the same material in cubic samples, the shape most commonly used in assessing self-heating. The activation energy is determined and an extrapolation to predict the maximum safe stockpile height is performed. The infinite cylinder results are examined and extended in order to make predictions concerning storage of susceptible materials in cylindrical silos.

Microwave heating of an infinite solid slab and its thermal stability analysis using steady state bifurcation theory

This paper presents an analytical solution of the steady state temperature profiles in a microwave heated slab. The analytical solution has been obtained by taking advantages of the well known Frank-Kamenetskii thermal ignition theory. Both the finite Biot number and infinite Biot number boundary conditions have been considered and their effects upon the critical parameters for the onset of thermal instability evaluated.

Theory of radical-induced ignition of counterflowing hydrogen versus oxygen at high temperatures

Ignition of hydrogen and oxygen in counterflow was studied using asymptotic methods for temperatures above that of crossover. Starting with seven elementary reaction steps, a reduced mechanism was derived using chemical steady-state approximations for the O and OH radicals. An algebraic ignition criterion was derived using this mechanism which predicts the ignition state as a function of the parameters defining the system. This criterion successfully explains the behavior analogous to the “first” and “second” explosion limits observed in homogeneous hydrogen-oxygen mixtures. A bifurcation analysis was then performed to clarify the ignition behavior. This analysis demonstrated that an ignition turning point can occur solely through the interaction of radical species with no contribution from heat release. The source of this turning was found to be the reaction H + HO 2 → 20H, confirming results from numerical calculation. Finally, the regimes in which abrupt or monotonic transition to an ignited state were recalculated including the effect of this reaction.

Multiple solutions in hollow geometries in the theory of thermal ignition

Following Burnell et al., the dimensionless form of the steady state heat balance equation for material undergoing an exothermic reaction over the symmetrical N-dimensional unit sphere is u″(r) + (N − 1)r −1u′(r) + λe −( 1 u ) = 0 . The parameter λ is held constant so that the solution structure is dependent on the bifurcation parameter U appearing in the boundary condition u(1) = U. In previous papers we discussed the existence of multiple solutions for both class A (slab, infinite cylinder, and sphere) and nonclass A geometries and showed that multiple solutions (of multiplicity greater that three) occur for 2 < N < 12. In this paper, we present numerical results for some hollow geometries which indicate that similar solution structure to that of previous cases is preserved and that the multiplicity of solutions does not always depend on the size of the hollow region.

Surface temperature at ignition of wooden based slabs

Up to now, a sufficiently developed ignition theory is not available for wood slabs and other combustible building materials in the form of layers. Very often, the concept of surface ignition temperature as a material characteristic is used, especially when related to fire modelling. Measurements of surface temperature at ignition during cone calorimeter tests for several plywoods and particle board in the horizontal and vertical configurations are presented here. It was found that the surface temperature at ignition depends not only on the material properties but also strongly on the experimental conditions (irradiation, sample configuration). There is evidence that two different mechanisms control ignition in the horizontal and vertical orientations of the samples.

Effect of heating a semi-transparent medium by radiant energy on ignition characteristics in thermal explosion theory

Abstract In ignition theory, there are no volume heat sources in a substance which is being heated through the surface. In most actual cases, ignition occurs under more complex heating conditions. One of these heating conditions is the ignition of a semi-transparent body by the flow of radiant energy. This case is investigated, showing the effect of the presence of volume heat sources of a non-chemical nature on critical and ignition conditions. The Arrhenius heat reaction law and the Frank-Kamenetskii exponential approximation for this law are also used. The ignition characteristics and transition conditions are demonstrated. The transition conditions can be obtained from the condition d θ d θ a = 0 , as well as from d 2 ψ d θ 2 = 0 . The results show that the critical point in the temperature-time plane can be obtained by setting d θ d τ = 0 , d 2 θ d τ 2 = 0 , and d 3 θ d τ 3 = 0 . The non-stationary solutions are also presented.

Effect of a cyclical heat flux on the ignition energy of an explosive in the condensed phase

An analysis of the results of numerical calculations of the ignition of an explosive in the condensed phase showed that the energy density necessary to ignite a material can be decreased substantially by changing the parameters of the cyclicity of the heat flux initiating the effect. The effect is explained qualitatively by the appearance of pre-explosion heating, which is generally ignored when the customary analytical methods of the classical theory of ignition are used.

A Statistical Investigation of Ignition in a Fuel Spray Using a Shock Tube.

In order to determine the general aspect of the spontaneous ignition in a fuel spray injected in compressed air at high temperature, which takes place usually in diesel and pulse jet engines, an experimental method using a shock tube is developed. A shock wave driven by high-pressure He gas propagates in the air in the low-pressure tube and reflects at a shock tube end. Through application of the pressure of the shock wave at reflection, n-octane fuel is injected into the air behind reflected shock waves in the shock tube. The fuel injection space is optically separated into 5 regions in the vertical direction, and the induction period of spontaneous ignition in each region is separately observed. As the induction period fluctuates markedly, the measured results are treated statistically and analyzed on the basis of the stochastic ignition theory.

Adiabatic method in the thermal theory of ignition of metal particles in gases

An approximate solution of the problem of ignition of metal particles in gases, which is mathematically complicated by the nonlinear kinetics of metal oxidation, has been obtained. An analytical expression for the ignition delay, similar to the semiempirical Friedman—Macek dependence, is proposed. The numerical calculations are in good agreement with the analytical solution.

Combustion kinetic parameters of thai lignite char

Kinetic parameters, the pre-exponential factor and the activation energy, of two Thai lignite char of different ash contents and electrode carbon have been experimentally determined based on the Semenov's thermal ignition theory adapted to single particle ignition. Combustion rate constants obtained have been comparatively plotted with those from Field's correlation (1969). Results indicated that the reaction rate coefficient for lignite char approaches value estimated from Field's equation at temperature about 850°C.

Path-following for disjoint bifurcation problems arising in ignition theory

The correct formulation governing the ignition of a solid reactant undergoing slow oxidation gives rise to a nonlinear problem which in symmetrical geometries (infinite slab, cylinder, and sphere) is a two point boundary value problem. The discontinuity in the smallest branch of steady-states is the threshold for ignition. The solution branches are found by modifications of the path-following software (AUTO). Gross multiplicity of steady-states occurs for dimensions greater than two, and in all cases, the diagrams exhibit “disjointedness” for some parameter values which require special redefinition of the nonlinearity.

A crystallization theory of underwater aluminum ignition

The possibility is considered that observed underwater, steam explosion-induced ignitions of low-temperature molten aluminum fragments (microspheres) can be explained by Ostwalds [1] “law of stages” in nucleation processes. That is, it is proposed that the chemical change from molten aluminum to solid aluminum oxide beneath the surfaces of the microspheres proceeds in three distinct stages: (i) chemical reaction between a dissolved species of oxygen and molten aluminum to metastable molten aluminum oxide, (ii) nucleation of solid aluminum oxide crystals within the metastable melt, and (iii) the growth of the crystals into a continuous scale of solid aluminum oxide. During Stages (i) and (ii) the rate at which oxygen is adsorbed by the growing aluminum oxide melt layer is believed to be sufficiently high to support the rapid oxidation of the melt fragments within the steam explosion zone. Because the oxygen adsorption potential in solids is much lower than in liquids, the oxidation rate at the end of Stage (iii) is expected to decrease discontinuously by several orders of magnitude, leading to a final stage of net microsphere cooling. Thus, according to the theory presented herein, underwater aluminum ignition is determined by the outcome of a race between the aluminum chemical reaction rate and the rate of aluminum oxide crystallization. The present theoretical approach, primarily concerned with trends and order-of-magnitude predictions, indicates that, unless the initial temperature of the aluminum melt is well above its melting temperature, a very strong initiator (e.g. blasting cap) is required in order for chemical energy to be released during an aluminum/water explosion. With further development, the reaction/crystallization model may prove useful for guiding future experimental work in this area.

Ignition of a highly exothermic mixture on a steel substrate in an electromagnetic field

Ignition in an electromagnetic field has been examined from theory and by experiment for a highly exothermic mixture on a steel substrate. Various initiation states can occur in accordance with the electromagnetic power. Numerical and approximate analyses are compared with experiment. The proposed mechanism fits within the theory of thermal ignition and enables one to optimize self-propagating synthesis coating.

Critical initial conditions for thermal ignition

In the conductive theory of thermal ignition, there is a practically important region of parameter space where the heat conduction partial differential equation with a nonlinear (Arrhenius) heat generation term displays two attractors. Their basins of attraction (particularly that of the minimal solutions) are of great practical importance. Good estimates for the latter region are obtained by a method of spatial averaging of the nonlinear term which give very small errors for large classes of initial conditions, provided the latter are not too ‘spikey’. For ‘hot spot’ type initial conditions the method still works and gives satisfactory estimates. The bound is focussed on the critical initial energy.

Kinetic and heat transfer-controlled solidification of highly supercooled droplets

An efficient integral profile computational method is used to solve the problem of the solidification of highly subcooled droplets. The effects of surface cooling by radiation and convection, interface crystallization kinetics and fully time-dependent heat conduction are included in the method. Particular attention is focused on the predicted drop surface temperature-time histories as these, together with available experimental luminosity-time traces for solidifying microspheres of Al 2O 3 and ZrO 2, are used to infer the coefficient of the kinetic law for Al 2O 3 crystallization—one of the crucial parameters in a recently proposed theory of underwater aluminum ignition.

Combustion of highly exothermic mixtures based on iron and chromium oxides

The combustion of highly exothermic heterogeneous mixtures containing metal oxides (FeO, Cr2O3) and metallic (Al) or nonmetallic (C) reducing agents has been studied under dynamic conditions. A relation between the temperature of ignition and the ratio of the components of the mixture has been established. The ignition temperature was compared with the theoretical value derived from the quasisteady theory of ignition of condensed systems of hot material with a high thermal conductivity and a variable surface temperature. The theoretical values were in agreement with the experimental results.

Combustion reactivity of rice husk: An experimental and numerical investigation

The combustion reactivity of rice husk from New South Wales, Australia was measured by heating cubical baskets in controlled environment and monitoring the centre temperature.Frank-Kamenetskii’s ignition theory was used to calculatethe activation energy. Results agreed well with tests on other cellulosic materials, Numerical simulations of temperature changes were carried out, using a special technique to deal with non-linearities in the heat conduction equation.The numerical results indicate that tlie time factor should be taken into account when evaluating self-combustion risks.

Experimental studies of ignition behaviour and combustion reactivity of pulverized fuel particles

A pulse ignition technique, whereby a small mass of fine coal or char particles is fed into a drop-tube furnace, was used to evaluate the ignition characteristics of pulverized fuel particles. Combustion rates were estimated from the ignition temperatures and were compared with rates determined experimentally using a fixed-bed reactor, DTG, and an entrained-flow reactor. Three Australian coals, two chars prepared from these coals and a petroleum coke were used. Coal rank and particle size were found to influence the ignition temperatures of the coal and char particles. However, these effects were reduced at high oxygen concentrations. In pure oxygen, the ignition temperatures of the chars and their parent coals were similar. Heterogeneous and homogeneous ignition theories indicated that at low O 2 concentrations ignition was controlled by a homogeneous mechanism, whereas at high O 2 concentrations heterogeneous ignition became dominant. The combustion rates of the chars determined by the four techniques were compared at an oxygen partial pressure of 10.1 kPa. The results of the fixed-bed, DTG and entrained flow experiments were consistent with each other and spanned the range of kinetic control from regime I at low temperature (fixed bed) to regime II at high temperature (entrained flow). The drop-tube experiments indicated consistently higher combustion rates than did the other techniques. The pulse ignition measurements therefore, while providing a valid means of characterizing coal and char ignition behaviour, result in overestimation of the char combustion rate.