Solution of Gas Phase Equations

Analytical solutions for the simplified gas equations above have been published only for limiting values of large and small activation energy, Eg l 

The classical large activation energy ( 1) solution obtained by activation energy asymptotics [5] is 

This solution defines a flame stracture analogous to the condensed phase an inert, convective-diffusive preheat zone of thickness Xg, followed by a thin, reactive- 

In the reaction B + M C + M, species-M is any species, which in this binary gas system formally means B or C. The gas reaction is interpreted as thermal decomposition of species-B by high-energy collision with either itself or species-C. Reaction is initiated by collision between two molecules that are relatively unreactive chemically (compared to radicals) only a tiny fraction (exp(- )) of the collisions that occur lead to reaction, those involving the most thermally energetic molecules. This is consistent with the assumption of the reaction rate being second order overall, but first order with respect to reactant species-B. The mass fraction of the other collision partner, species-M, which does not appear in the reaction rate expression, is implicitly taken to be constant at a value of unity. 

as obtained by matching measured regression rates, which agrees with kinetic theory. For NC/NG double base propellant combustion, species-B would represent the reactants of the primary flame, such as NO2 and CH2O, while species-C would represent the products of the primary flame, NO, CO, and H2O. The secondary flame, which produces final thermodynamic products N2 and CO2, does not occur close enough to the propellant surface to contribute to the regression rate below 10 MPa, and is not included in the model. The assumed final flame temperature corresponds to the dark zone temperature of around 1300 to 1600 K. 

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