Christopher Romick

The dynamics of unsteady detonation with diffusion

Here we consider an unsteady detonation with diffusion included. This introduces an interaction between the reaction length scales and diffusion length scales. Detailed kinetics introduce multiple length scales as shown though the spatial eigenvalue analysis of hydrogen-oxygen system; the smallest length scale is {approx} 10{sup 7} m and the largest {approx} 10{sup -2} m; away from equilibrium, the breadth can be larger. In this paper, we consider a simpler set of model equations, similar to the inviscid reactive compressible fluid equations, but include diffusion (in the form of thermal/energy, momentum, and mass diffusion). We will seek to reveal how the complex dynamics already discovered in one-step systems in the inviscid limit changes with the addition of diffusion.

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 2/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.

Dynamics of Unsteady Inviscid and Viscous Detonations in Hydrogen-Air

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. A series of shock-fitted calculations was performed in which the overdrive was varied in the inviscid limit. The 0.97 MHz frequency of oscillation predicted for a f = 1.1 overdriven detonation agrees well with the value of1.04 MHz observed by Lehr in the equivalent shock-induced combustion experiment around a spherical projectile. As the initial overdrive is lowered, the long time behavior of the system becomes more complex, causing the amplitude of pulsations to increase and oscillations at multiple frequencies to appear. When the viscous analog of these detonations was simulated, it was found that viscous effects slightly alter the structure of a stable detonation and can significantly decrease the amplitude of pulsations in an unstable detonation.