The complex, dynamic shock-detonation structure formed by the glancing interaction of a primary detonation with a secondary explosive is studied by using time-dependent two-dimensional simulations and related experiments. The materials considered in the simulations are stoichiometric and lean mixtures of hydrogen and oxygen diluted with argon. Related experiments have used undiluted hydrogen and oxygen as well as other gases. For the conditions simulated: (a) the primary mixture is stoichiometric and the secondary inert; (b) both the primary and secondary mixtures are the same and stoichiometric; (c) the primary mixture is lean and the secondary is stoichiometric; and (d) the primary mixture is stoichiometric and the secondary is lean. In addition, for cases (b) and (d) , comparisons are made between simulations in which the primary mixture is overdriven and when it is a Chapman-Jouguet detonation. For the overdriven stoichiometric primary detonation interacting with the lean mixture, a complex detonation structure forms and quickly asymptotes to the detonation velocity of the primary mixture. For this same case, but when the primary detonation is initially at Chapman-Jouguet velocity, the detonation appears to die but then reignites due to a series of shock reflections and then propagates as a complex structure. The lowest velocity of the complex structure is always greater than the Chapman-Jouguet velocity of the lean mixture and it increases in time, appearing to approach the Chapman-Jouguet velocity of the stoichiometric mixture. The dynamics of this decay and reignition process are described and discussed in detail.

Numerical simulations of detonation transmission

In this study, we revisit the problem of detonation diffraction in mildly irregular ethylene-oxygen mixtures using high resolution numerical simulations. In particular, we focus on the re-initiation of diffracted waves in the critical regime and the role of transverse detonations on the re-establishment of the detonation. This problem is significant for characterizing detonation wave propagation as well as for the development of next-generation detonation engines. A thermochemically derived four-step combustion model that responds appropriately to the thermodynamic state behind the complex shock wave dynamics was adopted in an Euler framework. While past attempts using simplified combustion models have largely failed to predict the onset of transverse detonations near the critical limit, our simulations demonstrate that the four-step model can capture these features. Our results reveal that transverse triple point collisions are fundamental for triggering the re-initiation of the detonation and that multiple modes of re-initiation exist in the critical regime. The transverse detonation initiation distance and wall reflection lengths are then compared with experimental measurements and found to be in agreement. We also demonstrate that the incident wave re-establishes at the Chapman-Jouguet speed when re-initiation occurs through the diffraction process. However, if re-initiation of a quenched detonation occurs by a transverse detonation following the reflection of the expanding wave at the boundary, the re-initiated detonation becomes overdriven along the Mach wave. Finally, it was found that the transverse detonations are Chapman-Jouguet detonations that travel in the shocked but unreacted gas.

Detonation wave diffraction in stoichiometric C2H4/O2 mixtures using a global four-step combustion model

The interactions of mildly irregular detonation waves with sharp interfaces separating combustible mixtures from inert gas were modeled numerically using the Compressible Linear Eddy Model for Large Eddy Simulation (CLEM-LES) approach. In past experiments of Lieberman and Shepherd [Phys. Fluids 19, 096101 (2007)], such interactions resulted in a Transmitted Shock-Turbulent Mixing Zone complex as the reactive wave traveled through the interface separating fuel rich ethylene-oxygen mixtures and nitrogen: Kelvin-Helmholtz (K-H) instability was proposed as the main mechanism contributing to the formation of the Turbulent Mixing Zone (TMZ). This work aims to determine to what extent K-H plays a role, and whether or not other sources of instability contribute to the observed evolution of the TMZ. Results show that full-scale simulations using the CLEM-LES reproduce well (qualitatively and quantitatively) the experimental flow features. Upon recasting the simulations in the frame of reference of the node (i.e., location where the detonation wave meets the interface), and by removing the cellular instability from the front, the growth rates of the TMZ only due to K-H instabilities originating from the velocity difference across the mixing layer were found to be insignificant. Conversely, the addition of controlled perturbations to the detonation front pressure, resulted in significant growth of the TMZ. This outcome suggests that the TMZ formation and evolution is heavily influenced by instabilities originating at the front. In this regard, transverse waves associated with the detonation front cellular structure are likely to provide the bulk of TMZ growth through additional Richtmyer-Meshkov instabilities.

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Origins of instabilities in turbulent mixing layers behind detonation propagation into reactive-inert gas interfaces

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On the role of transverse detonation waves in the re-establishment of attenuated detonations in methane–oxygen

This study reports the Mach reflection of gaseous detonation on porous wedges experimentally, in which the porous wall is consisted of equidistant inline square columns. The smoked foil technique was utilized to monitor the evolution of the triple-point trajectory and detonation cells in Mach stem region. In addition to the wedge angle and initial pressure of gaseous mixture, this paper also focuses on the effect of porosity and pore size on Mach reflection and its mechanism. The results show that the strength of the Mach stem is significantly weakened by the porous media compared with that on smooth wedge, which is ascribed to the diffraction and reflection waves generated by the interaction of the Mach stem front with the pore. Further, the onset of the triple-point trajectory is delayed and the angle of which is decreased. The porosity and pore size present distinct influence on the Mach stem height. With the increase of the porosity and the decrease of pore size, the Mach stem region is attenuated more dramatically and the Mach stem is harder to be formed or even could not be observed. Furthermore, the triple-point trajectory on the porous wall exhibits local self-similarity, and satisfies the frozen limit in the near field and the equilibrium limit in the far field. However, the lengths of the existence of the frozen limit and the transition to the equilibrium limit on the porous wall are found to be much shorter than the hydrodynamic thickness.

Mach reflection of detonation wave on porous wall

Two-dimensional simulations of detonation interaction with gravity-driven diffuse interfaces, separating reactive mixtures and inert gas, were performed using the CLEM-LES methodology. The dynamics of the interactions were characterized and detonation failure and re-initiation mechanisms were described. Triple point transmission seems to be a characteristic feature of these configurations, and is responsible for both, quenching and re-ignition, within the diffuse interface. Results show that regions where the interface is thicker yield lower critical cell size gradients and vice versa. The average critical gradient found for the cases considered is 0.54, higher than the value of 0.1 reported in literature. The extension of the limit appears to be a direct consequence of the cellular dynamics within the diffuse interface.

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M. Peswani

Papers

Detonation wave diffraction in stoichiometric C2H4/O2 mixtures using a global four-step combustion model

Detonation-diffuse interface interactions: failure, re-initiation and propagation limits

Combustion properties of a simple and efficient four-step model

On the role of transverse detonation waves in the re-establishment of attenuated detonations in methane–oxygen