Kenneth P. Coffin, Richard S. Brokaw
A system with general equations has been devised for computing the burning rates of small particles burning as diffusion flames; the equations account for the effects of diffusion and dissociation with a high degree of rigor. Two types of solutions are carried out: (1) a numerical integration of considerable complexity, and (2) a somewhat less complicated and less rigorous analytical solution involving stepwise iteration across the temperature profile. The direct results of the calculation are partial pressures as a function of temperature. Simple additional calculations produce the burning rate and the flame structure. Both solutions were obtained for carbon burning in air; the differences are slight. For boron, because of the greater number of equilibria involved, only the analytical solution was undertaken; a special treatment for a solid reaction product, boric oxide, was required. A number of of ambient temperatures and ambient oxygen concentrations were examined in the case of boron; as an example, three graphs rapidly yield burning rates for a wide range of ambient conditions. The general equations presented here reduce to the much simpler equations used by the previous investigators. The simplified equations were also applied to boron, and yielded results in general agreement with the more detailed analytical solutions. Earlier results from the simplified equations for isooctane and magnesium are included for comparison. The simplified equations appear to be sufficiently accurate for many purposes. For a series of substances covering a wide range of volatility, relative heat-release rates are in the order: hydrocarbon > magnesium > carbon approximately equal to boron.
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