On the Resolution Necessary to Capture Dynamics of Unsteady Detonation

The dynamics of one-dimensional, overdriven, hydrogen-air detonations predicted in the inviscid limit as well as with the inclusion of mass, momentum, and energy diffusion were investigated. The effect of resolution was studied for both shock-capturing and shockfitting in the inviscid limit, and it was found that shock-capturing required four times the amount of resolution of shock-fitting to predict the essential dynamics. Harmonic analysis was used to examine how the long time dynamics changed as the overdrive was varied in both the inviscid limit and the viscous analog. As the overdrive is lowered, the pulsation’s fundamental frequency shifts smoothly from 1.03 MHz at an overdrive of f = 1.12 to 0.71 MHz at an overdrive of f = 1.035 before making a sudden jump to 0.11 MHz at an overdrive of f = 1.029, where overdrive is f = D o/D 2 CJ , Do the initial detonation velocity, and DCJ the Chapman-Jouguet velocity. It was found that viscous effects reduce the magnitude of the pulsations. As the strength of the inherent instability grows, due to interaction of the hydrodynamics and chemical reactions, the effect of viscosity is reduced.