Theory and applications of ignition with variable activation energy (original) (raw)
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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)
Characterisation of reaction propagation from auto-ignition
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Finite supplies of fossil fuels and their current dominance in energy production and usage make their efficient usage and the search for viable alternatives of critical importance. A large part of this is the understanding of the combustion of fuels, both existing and novel and of the engines in which they are consumed. One fundamental parameter that is not sufficiently understood is excitation time, the almost instantaneous heat release period at the end of an ignition delay period. A reduced thermokinetic model is applied to an attempt to simulate excitation without a large comprehensive model. The failure of the model in this task indicates differences in chemistry between excitation and ignition delay periods that are too large for a simple scheme to overcome with a single set of rate parameters. This work will present a full and fundamental characterisation through the use of two complimentary diagrams, one an existing diagram for the identification of developing detonation, th...
Thermokinetic modeling of the combustion of carbonaceous particulate matter
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The scope of this study was to determine the kinetics (conversion model, preexponential factor and activation energy) of the combustion of two diesel sootlike materials (Printex XE-2B and Flammruss 101) in the presence of an excess of oxygen by dynamic thermogravimetry. A composite kinetic analysis procedure was applied to evaluate the full kinetic triplet from nonisothermal kinetic data. First, the activation energy values were obtained from the Kissinger–Akahira–Sunose isoconversional method. The values were 129 kJ mol−1 (Printex XE-2B) and 144 kJ mol−1 (Flammruss 101). The higher reactivity of Printex XE-2B material was attributed to its markedly greater surface area. The activation energy was found to depend slightly on conversion, suggesting that the combustion was a single-step process for both materials. Second, a comparison of the theoretical masterplots deduced by assuming various conversion models with the experimental masterplots obtained from the kinetic data allowed the selection of the appropriate conversion model of the process. Both materials were found to follow a mechanism based on surface nucleation with subsequent movement of the resulting surface, which was consistent with the penetration of oxygen through the porous structure of the solid samples. Also, the preexponential factors and exact kinetic exponents were evaluated on the basis of predetermined activation energies and conversion models. The adequate consistency of the kinetic triplet was assessed by comparing both experimental and calculated thermoanalytical curves at constant heating rate.