Fast deflagration waves

Activation energy asymptotics are used to formulate an approximation for combustion occurring at a high Mach number. Assumptions of a one-step reaction, Arrhenius kinetics, perfect gases, Newtonian fluids, Fick's diffusion law, equal specific heats, equal molecular masses, and constant material properties are employed in formulating governing equations of the mass, momentum, energy, and species balances. Three separate perturbation expansions are defined for the structure of the deflagration wave, and the propagation speed is shown to a function of the ignition temperature, which is not higher than the adiabatic flame temperature. It is found that an exponentially long tail is present, indicating that a small quantity of reactant escapes and burns slowly. The existence of a Mach layer behind the reaction zone is proven, although the approximation does not describe its characteristics.