Numerical Study of the Propagation of Non-ideal Gas Detonations in High-Activation-Energy Mixtures Within Pipe Systems

Abstract

The focus of this study was to examine the behavior of a gas detonation wave in a non-ideal environment, where detonation deviates from ideal behavior due to external factors like friction. A one-dimensional modeling approach based on the Euler equations was adopted, incorporating friction as a source term in the momentum equation. The chemical kinetics follow a single-step Arrhenius law. The Piecewise Parabolic Method (PPM) was applied to simulate fluid flow and solve the governing equations. To refine the mesh at the shock front, a conservative shock-front tracking algorithm was employed with Adaptive Mesh Refinement (AMR). The impact of friction on detonation behavior was parametrically investigated in mixtures with high activation energies, where detonation becomes highly irregular. Results show that increasing friction intensifies the competition between energy release from chemical reactions and energy loss by friction, leading to instability. For the studied activation energy, exceeding a critical friction limit causes detonation waves to decay. The decay mechanism varies with the level of activation energy. The simulations reveal that for a mixture with an activation energy of 29.5, detonation decays when the friction coefficient exceeds 0.02. Furthermore, the shock wave velocity drops by more than 30% compared to the ideal case, and the dimensionless separation between the reaction front and the shock increases markedly, from 3.65 in the frictionless case to over 150 when the friction coefficient reaches 0.07. These findings underscore the significant sensitivity of detonation dynamics to dissipative effects, offering quantitative insights into detonation stability and decay in non-ideal environments.