Approximations to the Structure of a Laminar Detonation Wave by the Method of Matched Asymptotic Expansions

The method of matched asymptotic expansions is used to develop higher-order approximations to the Zeldovich-von Neumann-Döring theory for the structure of a laminar detonation which is supported by an irreversible unimolecular chemical reaction. The Arrhenius rate expression is replaced by the Hirschfelder strong ignition temperature approximation so that analytical solutions are obtainable for the shock and the reaction zone. The perturbation parameter δ is the ratio of the molecular collision time to the chemical reaction time (evaluated at the hot boundary). The solutions are correct to O(δ) for the shock zone and to O(δ2) for the reaction zone. The strong ignition temperature approximation is shown to overestimate the effects of chemical reaction in the shock zone and to give erroneous estimates of the effects in the reaction zone. More realistic rate expressions may be treated by the method of matched asymptotic expansions at the expense of additional numerical computations, if a more accurate description of the laminar detonation structure is desired. However, the results for the strong ignition temperature approximation may be useful as the basis of a stability analysis.