Flow Calculations for Pulsating One-Dimensional Detonations

Abstract

The nature of the long‐time flow in an idealized one‐dimensional, piston‐supported detonation is investigated by numerical solution of the time‐dependent hydrodynamic equations. The method of characteristics is used, with shocks treated as jump discontinuities. The fluid is an ideal gas of constant heat capacity undergoing an exothermic, irreversible, unimolecular reaction A → B obeying an Arrhenius rate law. The results are consistent with Erpenbeck's linearized analysis of the stability of the steady detonation, which revealed some cases in which the usual steady‐state solution is unstable to infinitesimal longitudinal perturbations. In a typical flow of this type, the shock pressure is found to oscillate about the steady‐solution value with a peak pressure nearly 50% higher and with a period of about 9 steady‐solution half‐reaction times.