Instability of steady and quasi-steady detonations

The stability properties and dynamic behavior of steady and quasi-steady detonation theories are investigated through linear stability analysis and numerical simulation. A general, unsteady, three-dimensional formulation of the reactive Euler equations in a shock-fitted reference frame is derived. The formulation is specialized to three configurations: planar one-dimensional detonation, radially symmetric one-dimensional detonation, and two-dimensional detonation in a rectangular channel. High-order convergent numerical simulation schemes for these configurations are derived and used to study the linear and nonlinear stability of detonations. Shock-fitted numerical simulation is used to study the two-dimensional instability of steady solutions to the Zel'dovich, von Neumann, and Doring (ZND) model of detonation. It is demonstrated through several methods of analysis that the dependence of instability growth rates and oscillation frequencies on the initial disturbance wavelength, as predicted by linear stability theory, is quantitatively reproduced by shock-fitted simulations. Agreement with the theorized temporal and spatial structure of the instability is demonstrated by a functional expansion of the solution perturbations, obtained from simulation data, in terms of the linear stability eigenfunctions. Three regimes of unstable behavior - linear, weakly non-linear, and fully non-linear - are explored and characterized in terms of the power spectrum of the normal detonation velocity. Using solutions obtained from Detonation Shock Dynamics (DSD) theory, the behavior of cylindrically and spherically expanding symmetric detonations is studied by one-dimensional shock-fitted numerical simulation. We consider idealized models of gaseous and condensed phase detonation, as well as a realistic model calibrated for the high explosive PBX-9501. We study the behavior of detonations initialized with solutions of DSD as they expand radially. The various models and calibrations exhibit regimes of hydrodynamic stability, in which the detonation evolves slowly in time and agreement with DSD theory is good, and regimes of instability, which in some cases leads to failure of the detonation wave