Mass Transfer Related to Heterogeneous Combustion of Solid Carbon in the Forward Stagnation Region - Part 2 - Combustion Rate in Special Environments

Carbon combustion is a research subject, indispensable for practical utilization of coal combustion, ablative carbon heat-shields, and/or aerospace applications with carboncarbon composites (C/C-composites). Because of this practical importance, extensive research has been conducted not only experimentally but also theoretically and/or numerically, and several reviews (Batchelder, et al., 1953; Gerstein & Coffin, 1956; Walker, et al., 1959; Clark, et al., 1962; Khitrin, 1962; Mulcahy & Smith, 1969; Maahs, 1971; Rosner, 1972; Essenhigh, 1976, 1981; Annamalai & Ryan, 1993; Annamalai, et al., 1994) describe the accomplishments in this field, as mentioned in Part 1. Nevertheless, because of the complexities involved, there still remain several problems that must be clarified to understand basic nature of carbon combustion. In Part 1, after describing general characteristics of the carbon combustion, it was intended to represent it by use of some of the basic characteristics of the chemically reacting boundary layers (Chung, 1965; Law, 1978), under recognition that flow configurations are indispensable for proper evaluation of the heat and mass transfer, especially for the situation in which the gas-phase reaction can intimately affect overall combustion response through its coupling to the surface reactions. The flow configuration chosen was that of the stagnation-flow, which is a well-defined, one-dimensional flow, being characterized by a single parameter, called the stagnation velocity gradient, offering various advantages for mathematical analyses, experimental data acquisition, and/or physical interpretations. Specifically, formulation of the governing equations was first presented in Part 1, based on theories on the chemically reacting boundary layer. Chemical reactions considered were the surface C-O2 and C-CO2 reactions and the gas-phase CO-O2 reaction. Generalized speciesenthalpy coupling functions were then derived without assuming any limit or near-limit behaviors, which not only enable us to minimize the extent of numerical efforts needed for generalized treatment, but also provide useful insight into the conserved scalars in the carbon combustion. After that, it was shown that straightforward derivation of the combustion response could be allowed in the limiting situations, such as those for the Frozen, Flame-detached, and Flame-attached modes.