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Journal of Combustion
Volume 2013, Article ID 790672, 22 pages
Research Article

Combustion Rate of Solid Carbon in the Axisymmetric Stagnation Flowfield Established over a Sphere and/or a Flat Plate

1Aerospace Research and Development Directorate, Japan Aerospace Exploration Agency, 7-44-1 Jindaiji-Higashi, Chofu, Tokyo 182-8522, Japan
2Department of Mechanical Engineering, Numadu National College of Technology, 3600 O-oka, Numadu 410-8501, Japan

Received 29 November 2012; Revised 4 February 2013; Accepted 4 February 2013

Academic Editor: Yiguang Ju

Copyright © 2013 Atsushi Makino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Carbon combustion in the forward stagnation flowfield has been examined through experimental comparisons, by conducting aerothermochemical analyses, with the surface C-O2 and C-CO2 reactions and the gas-phase CO-O2 reaction taken into account. By virtue of the generalized species-enthalpy coupling functions, close coupling of those reactions has been elucidated. Explicit combustion-rate expressions by use of the transfer number in terms of the natural logarithmic term, just like that for droplet combustion, have further been obtained for the combustion response in the limiting situations. It has been confirmed that before the establishment of CO flame, the combustion rate can fairly be represented by the expression in the frozen mode, that after its establishment by the expression in the flame-attached or flame-detached modes, and that the critical condition derived by the asymptotics can fairly predict the surface temperature for its establishment. The formulation has further been extended to include the surface C-H2O and gas-phase H2-O2 reactions additionally, so as to evaluate the combustion rate in humid airflow. Since those expressions are explicit and have fair accuracy, they are anticipated to make various contributions not only for qualitative/quantitative studies, but also for various aerospace applications, including propulsion with high-energy-density fuels.