Numerical Simulations of a Marginal Detonation: Wave Velocities and Transverse Wave Structure

Abstract

Two-dimensional numerical simulations are presented of detonations propagating in a low-pressure (50 Torr), Argon-diluted (by 70%), stoichiometric H₂-O₂ mixture. For such a mixture, the system is experimentally close to the detonability limit and so may be considered a marginal detonation. Comparisons are made between simulations that use two different models to simulate the chemical reactions and heat-release: (1) a two-step reaction model, and (2) a model that integrates a full set of elementary chemical reactions. In addition, qualitative and quantitative comparisons are made to experiments. Comparisons are made of the detonation velocity and the transverse-wave structure, two properties for which marginal detonations have distinctive features. The result is that all of the simulations show features of both marginal and ordinary waves. There is general agreement in the pressure field and in the decay of the leading shock velocity along the axis of the cell. For both chemical models, the average computed velocity of the wave along the entire structure (1625 m/s) is very close to the Chapman-Jouguet velocity (1619 m/s), leading to the conclusion that the computed detonation wave is an ordinary detonation. This is not consistent with the fact that the experimental detonation is close to the detonability limit. Close to the origin of the detonation cell, the computed transverse-wave structure is a single Mach reflection, which later develops into a double and complex Mach structure. This behavior is typical of a marginal detonation wave. We speculate that the experiments performed close to the detonability limit show strong effects of wall losses. Thus the physical model used, an Euler solution with chemical reactions, does not properly model the detonation when the effects of viscous boundary layers and heat transport to the walls are important.