Modeling of vibrational non-equilibrium in detonation with global kinetics

Abstract

One-, two-, and three-step global kinetic models that include thermal non-equilibrium were developed for detonation simulations using the open-source software Cantera and the Shock and Detonation Toolbox (SDToolbox). The rate coefficients and thermodynamic parameters of these models were calibrated against steady detonation characteristics obtained from a detailed H/O/N model for a stoichiometric H 2 -air mixture initially at 300 K and 101 kPa. The calibration methodology is discussed in detail. All three models are shown to reproduce the steady structure predicted by the detailed model. The present three-step model accurately captures the thermicity profile. Thermal non-equilibrium effects were modeled by incorporating an additional vibrational energy conservation equation and a distinct vibrational temperature. The impact of non-equilibrium effects was studied by adjusting the parameter 𝜏 ∗ , defined as the ratio of the induction time at thermal equilibrium to the characteristic vibrational relaxation time (evaluated at the post-shock plane). Pathological behavior is observed in the presence of vibrational non-equilibrium. The relationship between the degree of pathological behavior and the intensity of vibrational non-equilibrium is investigated. Three regimes representing increasing non-equilibrium intensities are identified for 𝜏 ∗ = 1 0 , 2, and 0.5. The three-step model developed in this work is a suitable alternative to one- and two-step global models for multidimensional numerical simulations, with the added advantage of capturing the chain-branching process. Novelty and significance statement: The present study provides a methodology for developing global kinetic models of varying complexity for detonation simulations with vibrational/thermal non-equilibrium. One-, two-, and three-step reaction mechanisms were developed and their main features were characterized, with the three-step mechanism being proposed for the first time. We identified, for the first time, the pathological behavior as a general feature of detonation under strong thermal non-equilibrium. The present study also introduces a simple approach for incorporating vibrational/thermal non-equilibrium in global kinetic models. This approach will facilitate the inclusion of more realistic global kinetics in simulations of both laboratory- and large-scale detonation. The newly developed global kinetic mechanisms and the vibrational non-equilibrium model were implemented using Cantera and the Shock and Detonation Toolbox (SDToolbox), providing, for the first time, an open-source framework for studying vibrational/thermal non-equilibrium.