One-dimensional model predictions for the detonation diffraction critical tube diameter

Detonation diffraction leads to either successful transmission of the detonation or quenching wherein the propagation mechanism is attenuated. The transmission behavior is governed by competing effects of energy release, curvature, and unsteadiness. There is a potentially unique critical diameter that will determine the diffraction outcome for every combustible mixture composition at each set of initial conditions. The critical diffraction diameter has been correlated to several detonation parameters to date; however, these correlations all have limitations. Analytical or quasi-analytical solutions to the diffraction problem, specifically those able to predict the critical diameter, are scarce. The present work develops several critical diameter models by uniting previous work on diffraction phenomena and the critical initiation energy problem. Curvature, decay rate, and energy-based models are established, and their critical diameter predictions are compared against a wide range of experimental critical diameter data. While detonation diffraction is a complex multifaceted phenomenon, a curvature-based one-dimensional model in this work is shown to accurately reproduce empirical critical diameter behavior at relatively low computational cost.