Linear stability properties and nonlinear dynamics of self-sustained detonations is investigated by means of asymptotic analysis and numerical simulations. The normal-mode linear stability analysis is carried out for gaseous detonations propagating in cylindrical tubes. By comparison of the stability predictions with experiments, it is shown that the instability plays a fundamental role in the onset of spin detonation. We derive far-field closure conditions for unsteady and multi-dimensional detonation waves in arbitrary explosive media as intrinsic properties of the reactive Euler equations in the embedded sonic surface, which is a characteristic surface. The conditions generalize previously known sonic conditions for self-sustained detonations. We investigate the nature of the sonic conditions numerically with a new numerical technique for solving the Euler equations and demonstrate that the sonic locus is a characteristic surface and an information boundary that isolates the reaction zone from the far-field flow. Starting with the general formulation, we derive an asymptotic evolution equation for self-sustained detonations in the limits of slow-time variation and weak curvature and find that the equation predicts ignition and failure of detonations. Based on the evolution equation, we formulate a theory of direct initiation of gaseous detonation that can predict critical conditions from first principles. The ignition theory is also extended to explosives with arbitrary equation of state. With the general conditions at the sonic locus available, we formulate the stability problem for high-explosive detonations described by non-ideal equation of state and calculate stability characteristics of detonation in PBX-9502 and nitromethane.
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