Numerical simulations are performed to study the process of flame propagation through a small orifice and transition to detonation in a confined pre-chamber/main-chamber system. The numerical model solves the fully compressible Navier-Stokes equations by a high-order numerical algorithm on a dynamically adapting mesh, coupled with a single-step chemical-diffusive model for a stoichiometric ethylene-oxygen mixture. Four successive stages, namely laminar flame propagation, jet flame formation, flame distortion by shock waves, and transition to detonation, are observed. Parametric studies with varying nozzle diameters and initial temperatures are tested to investigate the effect of nozzle size and the stochasticity of deflagration-to-detonation transition (DDT). The results suggest that the case with a smaller nozzle size, d = 1.5 mm, requires a longer time for the flame to evolve and transition into a detonation. A small change in the initial temperature results in clear fluctuations of flame surface length in the turbulent flame regime. In addition, the case with the smaller orifice size is shown to be more sensitive to the initial temperature. Due to the stochastic nature of DDT, the time and location for detonation initiation vary in all cases. Nevertheless, the detonation mechanism remains the same and is independent of the small variations in the initial temperature or the orifice size.
Numerical simulations are performed to study the mechanism of deflagration to detonation transition (DDT) in a pre-/main- chamber combustion system. The fully compressible Navier-Stokes equations, coupled with a chemical-diffusive model in a stoichiometric ethylene-oxygen mixture, are solved with a high-order numerical algorithm on a dynamically adapting mesh. The two-dimensional simulation shows that a laminar flame grows in the pre-chamber and then develops into a jet flame as it passes through the orifice. A strong shock forms immediately ahead of the flame, reflecting off the walls, and interacting with the flame front. The shock-flame interactions are crucial for the development of flame instabilities, which trigger the subsequent turbulent flame development. The DDT arises due to an energy-focusing mechanism, where multiple shocks collide at the flame front. A chemical explosive mode analysis (CEMA) criteria is developed to study the DDT ignition mode. Preliminary one-dimensional computations for a laminar propagating flame, a fast flame deflagration, and a Chapman-Jouguet detonation are conducted to demonstrate the validity of CEMA on the chemical-diffusive model, as well as to determine the proper conditioning value for CEMA diagnostic. The two-dimensional analysis with CEMA indicates that the DDT initiated by the energy focusing mechanism can form a strong thermal expansion region that features large positive eigenvalues for the chemical explosive mode and dominance of the local autoignition mode. Thus, the CEMA criterion proposed in this study provides a robust diagnostic for identifying autoignition-supported DDT of which emergence of excessive local autoignition mode is found to be a precursor.
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