The Dynamics of Unsteady Detonation with Diffusion

The dynamics of one-dimensional detonations predicted by a one-step irreversible Arrhenius kinetic model with the inclusion of mass, momentum, and energy diffusion were investigated. A series of calculations in which activation energy is varied, holding the length scales of diffusion and reaction constant, was performed. As in the inviscid case, as the activation energy increases, the system goes through a period-doubling process and eventually undergoes a transition to chaos. Within the chaotic regime, there exist regions of low frequency limit cycles. An approximation to Feigenbaum’s constant, the rate at which bifurcation points converge, is obtained. The addition of diffusion significantly delays the onset of instability and strongly influences the dynamics in the unstable regime. Because the selected reaction and viscous length scales are representative of real physical systems, the common use of reactive Euler equations to predict detonation dynamics in the unstable and marginally stable regimes is called into question; reactive Navier-Stokes may be a more appropriate model in such regimes.