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

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Abstract
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 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.

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