Propagation of gaseous detonation waves in a spatially inhomogeneous reactive medium

Detonation propagation in a compressible medium wherein the energy release has been made spatially inhomogeneous is examined via numerical simulation. The inhomogeneity is introduced via step functions in the reaction progress variable, with the local value of energy release correspondingly increased so as to maintain the same average energy density in the medium, and thus a constant Chapman Jouguet (CJ) detonation velocity. A one-step Arrhenius rate governs the rate of energy release in the reactive zones. The resulting dynamics of a detonation propagating in such systems with one-dimensional layers and two-dimensional squares are simulated using a Godunov-type finite-volume scheme. The resulting wave dynamics are analyzed by computing the average wave velocity and one-dimensional averaged wave structure. In the case of sufficiently inhomogeneous media wherein the spacing between reactive zones is greater than the inherent reaction zone length, average wave speeds significantly greater than the corresponding CJ speed of the homogenized medium are obtained. If the shock transit time between reactive zones is less than the reaction time scale, then the classical CJ detonation velocity is recovered. The spatio-temporal averaged structure of the waves in these systems is analyzed via a Favre averaging technique, with terms associated with the thermal and mechanical fluctuations being explicitly computed. The analysis of the averaged wave structure identifies the super-CJ detonations as weak detonations owing to the existence of mechanical non-equilibrium at the effective sonic point embedded within the wave structure. The correspondence of the super-CJ behavior identified in this study with real detonation phenomena that may be observed in experiments is discussed

Detonation modelling of non-ideal high explosives

High explosives (HE) are used in many fields where the energy liberated by the combustion process is used to perform useful work. High explosives normally burn via a detonation; a supersonic wave consisting of a shock wave coupled to chemical energy release. Detonations in conventional HE (CHE) propagate with a typical velocity of 6 - 8 km/s. Insensitive HE (IHE) and non-ideal HE (NIHE) are of particular interest as they are harder to initiate and thus safer to store and transport. Detonations in IHEs and NIHEs are characterized by longer reaction time and length scales than detonations in CHE. NIHEs are typically characterized by their porous, granular structure. Detonations in NIHEs have lower detonation velocities (4 - 6 km/s) than those in CHEs or IHEs due to their lower initial densities. The short time scales (O(ns ??? ??s)), length scales (O(??m ??? mm)) and the opaque nature of HEs and their products make experimental observations, required to calibrate detonation models for reaction flow modelling, challenging. Currently used reactive burn models assume a two component, mechanically equilibrated mixture of reactants and products. Individual components are modelled with an empirical equation of state (EOS). The set of relations which uniquely determine the mixture-averaged state in terms of the states of the mixture constituents, the mixture closure conditions, are also often of a pressure-temperature equilibrium form. The chemical reaction rate law(s) are mostly based on preconceptions of how a detonating HE burns. Typically, such engineering style models are complex and contain a large number of fitting parameters that are calibrated in some form to a limited set of experimental data. Minimal attention has been devoted to the physical and mathematical implications of the fitting process and reactive burn model structure (such as the choice of closure condition) to issues such as detonation stability and interacting oblique shock structure. For a well-posed reactive burn model, such properties should be understood. A majority of this thesis research is devoted to formulating and studying the shock and detonation properties of reactive burn models based on the use of stiffened-gas (SG) equations of state. A SG model allows an appropriate initial sound speed of a material to be set, an important improvement over ideal gas models when applied to condensed phase reactive burn models. Due to its relative simplicity, a semi-analytical understanding of reactive burn models based on the use of SG EOS models for its constituent components can be obtained. Furthermore, changes in physical aspects of the reactive burn model, such as detonation stability and interacting oblique shock structure, with changes in calibrated fitting parameters, can be better understood. In this context, we establish the ability of SG EOS models to reasonably formulate a reactive burn model for the IHE PBX 9502. The model is designed to capture the fast and slow reaction stages inherent in PBX 9502 detonation using a two-stage reaction model. Different mixture closure conditions are examined, namely the classical pressure-temperature equilibrium assumption and a constant solid entropy closure condition. The stability characteristics of SG EOS based detonation models are examined in the context of varying EOS properties of the reactants and products, as well as closure conditions. The SG EOS based structure of oblique shock and detonation waves are also examined. Finally, in a separate exercise, the implemetation and results of a series of large cylindrical rate-stick experiments with the NIHE ammonium nitrate-fuel oil (ANFO) is reported. A detonation-shock-dynamics calibration to the detonation front curvature data obtained from experiments is also presented

Numerical simulations of cellular detonation diffraction in a stable gaseous mixture

In this paper, the diffraction phenomenon of gaseous cellular detonations emerging from a confined tube into a sudden open space is simulated using the reactive Euler equations with a two-step Arrhenius chemistry model. Both two-dimensional and axisymmetric configurations are used for modeling cylindrical and spherical expansions, respectively. The chemical parameters are chosen for a stable gaseous explosive mixture in which the cellular detonation structure is highly regular. Adaptive mesh refinement (AMR) is used to resolve the detonation wave structure and its evolution during the transmission. The numerical results show that the critical channel width and critical diameter over the detonation cell size are about 13±1 and 25±1, respectively. These numerical findings are comparable with the experimental observation and confirm again that the critical channel width and critical diameter differ essentially by a factor close to 2, equal to the geometrical scaling based on front curvature theory. Unlike unstable mixtures where instabilities manifested in the detonation front structure play a significant role during the transmission, the present numerical results and the observed geometrical scaling provide again evidence that the failure of detonation diffraction in stable mixtures with a regular detonation cellular pattern is dominantly caused by the global curvature due to the wave divergence resulting in the global decoupling of the reaction zone with the expanding shock front