Abstract
In order to examine sustainability of carbon combustion, an attempt has been made to obtain its critical condition for a hot particle, being immersed in a cold environment, situation of which is also encountered in an air-breathing rocket-engine. Main concern has been put on particle combustion in the lower limit, less than ca. 100µm in diameter, although not only the lower limit but also the upper limit of the critical conditions has been obtained. By conducting asymptotics, with focusing on a plateau stage in which particle temperature keeps its initial value, an analytical expression has been obtained for the lower limit of the particle diameter, as functions of the pressure ratio, oxygen mass-fraction, and/or initial temperature. An approximate expression is also obtained from the analytical solution. It is found that both the analytical and approximate expressions can fairly represent the numerical results, as far as the trend and approximate magnitude are concerned. In addition, use has been made of the Arrhenius plot of a comprehensive parameter, consisting of the particle diameter and pressure ratio, in order to identify regions for the particle combustion to be sustained. Comparisons have also been conducted by use of experimental data in the literature, with presenting a fair degree of agreement, as far as the trend and approximate magnitude are concerned. It has been confirmed that the formulation has captured the essential feature, that the reduction in particle size does not necessarily favor the particle combustion, and that the surface reaction ceases to be activated when the particle diameter is reduced to the critical value.
Published Version
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