Ignition Analysis of Adiabatic, Homogeneous Systems Including Reactant Consumption

Ignition of reactants initially at some moderate temperature, with reactant consumption effects included by introducing the adiabatic flame temperature and an effective specific heat into a First Law analysis, is analyzed using a thermal model, for firstand second-order reactions. After the normal Zel'dovich expansion of the Arrhenius term, the approximate equation so obtained is analytically solvable using a Poincare expansion method. The resulting solution, in the form of a truncated series, is in excellent agreement with numerical integration of the approximate equation. Applying the Poincare method to an extended Zel'dovich type expansion yields a solution for first-order reactions that is acceptably close to that obtained by numerical integration of the governing differential equation before transformation. A method is developed for obtaining approximate thermal theory activation energy and pre-exponential factor values for a system of reactants, using experimental data and this solution.