Decay of plane detonation waves to the self-propagating Chapman–Jouguet regime

A theoretical study of the decay of plane gaseous detonations is presented. The analysis concerns the relaxation of weakly overdriven detonations toward the Chapman–Jouguet (CJ) regime when the supporting piston is suddenly arrested. The initial condition concerns propagation velocities ${\mathcal{D}}$ that are not far from that of the CJ wave ${\mathcal{D}}_{CJ}$, $0<({\mathcal{D}}/{\mathcal{D}}_{CJ}-1)\ll 1$. The unsteady inner structure of the detonation wave is taken into account analytically for small heat release, i.e. when the propagation Mach number of the CJ wave $M_{u_{CJ}}$ is small, $0<(M_{u_{CJ}}-1)\ll 1$. Under such conditions the flow is transonic across the inner structure. Then, with small differences between heat capacities (Newtonian limit), the problem reduces to an integral equation for the velocity of the lead shock. This equation governs the detonation dynamics resulting from the coupling of the unsteady inner structure with the self-similar dynamics of the centred rarefaction wave in the burnt gas. The key point of the asymptotic analysis is that the response time of the inner structure is larger than the reaction time. How, and to what extent, the result is relevant for real detonations is discussed in the text. In a preliminary step the steady-state approximation is revisited with particular attention paid to the location of the sonic condition.

Mechanical Changes in Materials Caused by Explosive Precompression Shock Waves and the Effects on Fragmentation of Exploding Cylinders

Explosive driven rapid fracture in a structural body will be preceded by a compression process, and the compression effects on mechanical properties of the materials are clearly important to understand shock-induced failure such as spall or fragmentation phenomena. In this study, incident shock waves in plate specimens of aluminum A2017-T4 and 304 stainless steel are generated by plane detonation waves in the high explosive PETN initiated using wire-row explosion techniques, and the compressed specimens are successfully recovered without severe damages due to the reflected expansion waves with use of momentum trap method. A hydro code, Autodyn-2D is applied to determine test conditions: thicknesses of explosives, attenuators, specimens and momentum traps and to evaluate experimental results, simulating time-histories of stress waves in the layers of the test assembly. Microhardness distributions in cross-sections, tensile strength, fracture ductility and yield stress are measured for the recovered specimens, using miniature tensile and compression test pieces machined from them. They are compared with those of virgin specimens, showing significant increase of hardness, tensile and yield strength and remarkable reduction of elongation and ductility for shocked specimens. The results are taken into consideration for evaluation of experimental fragmentation energy in cylinder explosion tests.

Low-frequency two-dimensional linear instability of plane detonation

An analytical dispersion relation describing the linear stability of a plane detonation wave to low-frequency two-dimensional disturbances with arbitrary wavenumbers is derived using a normal mode approach and a combination of high activation energy and Newtonian limit asymptotics, where the ratio of specific heats γ→1. The reaction chemistry is characterized by one-step Arrhenius kinetics. The analysis assumes a large activation energy in the plane steady-state detonation wave and a characteristic linear disturbance wavelength which is longer than the fire-zone thickness. Newtonian limit asymptotics are employed to obtain a complete analytical description of the disturbance behaviour in the induction zone of the detonation wave. The analytical dispersion relation that is derived depends on the activation energy and exhibits favourable agreement with numerical solutions of the full linear stability problem for low-frequency one- and two-dimensional disturbances, even when the activation energy is only moderate. Moreover, the dispersion relation retains vitally important characteristics of the full problem such as the one-dimensional stability of the detonation wave to low-frequency disturbances for decreasing activation energies or increasing overdrives. When two-dimensional oscillatory disturbances are considered, the analytical dispersion relation predicts a monotonic increase in the disturbance growth rate with increasing wavenumber, until a maximum growth rate is reached at a finite wavenumber. Subsequently the growth rate decays with further increases in wavenumber until the detonation becomes stable to the two-dimensional disturbance. In addition, through a new detailed analysis of the behaviour of the perturbations near the fire front, the present analysis is found to be equally valid for detonation waves travelling at the Chapman–Jouguet velocity and for detonation waves which are overdriven. It is found that in contrast to the standard imposition of a radiation or piston condition on acoustic disturbances in the equilibrium zone for overdriven waves, a compatibility condition on the perturbation jump conditions across the fire zone must be satisfied for detonation waves propagating at the Chapman–Jouguet detonation velocity. An insight into the physical mechanisms of the one- and two-dimensional linear instability is also gained, and is found to involve an intricate coupling of acoustic and entropy wave propagation within the detonation wave.