Shock-induced Ignition for Simplified Chemical Kinetics
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AbstractThe scenario of ignition behind a shock moving into reactive mixture is relevant from the perspective of safety (i.e. storage and handling), because it plays an important role in deflagration to detonation transition, for instance following shock reflections. Numerical simulation of ignition between a contact surface or a flame, and a shock moving into combustible mixture is difficult because of the singular nature of the initial conditions. Indeed, initially, as the shock starts moving into reactive mixture, the region filled with shocked fluid has zero thickness. Thus, on a fixed grid, the number of grid points between the shock and the contact surface increases as the shock moves away from the latter. Due to the initial poor resolution in this region staircasing may occur, leading to amplification by the chemistry of these numerical artifacts, and ultimately to unreliable results. To overcome these difficulties, the problem formulation is transformed from using space and time as the independent variables to space over time and time; coupled with a closed form short time asymptotics solution which is used as initial conditions. The former provides for a finite domain at t=0, and the latter effectively reduces the size of the computation without compromising resolution. The transformed problem is integrated using an essentially non-oscillatory algorithm, which adequately captures the entire ignition evolution, from slow formation and rapid growth of the hot spot, to appearance of a secondary shock and subsequent transition to detonation. A parametric study is performed for single step Arrhenius and three-step chain-branching chemistry. The entire ignition evolution is explained by means of pressure, temperature, and mass fractions profiles. Additionally, the validity of the constant volume assumption in shock tube experiments is assessed. The induction times are found to depend upon the ignition criteria used and the location where the measurement is made; also they may differ from spatially uniform values by a significant margin, depending upon the heat release.
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