Role of the argon and helium bath gases on the structure of H2/O2 detonations

Abstract

This study investigates the role of two inert mono-atomic diluents, argon and helium, on the detonation structure in order to assess the importance of vibrational non-equilibrium and wall losses. When relaxation effects and wall losses are neglected, the detonation waves in mixtures diluted with either of these gases have the same kinetics, Mach number, and specific heat ratio and hence are expected to lead to the same cellular dynamics. Differences in transport properties and species relaxation rates thus permit to establish the importance of these effects. The experiments were conducted in $2{\text{H}}_2+{\text{O}}_2+7\text{Ar}$ and $2{\text{H}}_2+{\text{O}}_2+7\text{He}$ mixtures in a narrow channel, where boundary layer losses can be controlled by the proximity of the detonations to their propagation limits. The initial pressure was adjusted in such a way that the induction zone length calculated from the ideal ZND model remained constant. This is expected to also constrain the cell size. The experiments revealed differences in velocity deficits and cell sizes despite maintaining a constant induction zone length across the mixtures. These differences were minimal in sensitive mixtures but became more pronounced as velocity deficits increased and cell sizes approached the channel dimensions. Near the detonation limits, the disparity in cell sizes between the two mixtures nearly doubled. We incorporated the boundary layer flow divergence in a perturbation analysis based on the square-wave detonation assumption. This permitted to establish the controlling loss parameter as the product of the induction to channel size and the inverse of the square root of the Reynolds number. The very good collapse of the experimental results with the loss parameter, and further comparison with two-dimensional numerical simulations with account for flow divergence to the third dimension, confirmed the viscous loss mechanism to be dominating. Calculations suggest that the slower relaxation of ${\text{H}}_2$ becomes comparable with the ignition delay anticipated from the ZND model and is slower by 70% in the argon diluted system. Differences possibly highlighting the role of non-equilibrium were not observed. This suggests the vibrational non-equilibrium effect may be less apparent in cellular detonations in the system studied in this work due to the lengthening of the ignition delays owing to the non-steady detonation structure. This study establishes that the large differences between the enlarged cells observed in our experiments and numerical predictions of lossless systems can be entirely attributed to wall losses.

Novelty and significance

This study establishes the relative importance of vibrational non-equilibrium and boundary layer losses in controlling the detonation cellular structure in channels close to the propagation limit. The novel experimental technique consisted of changing the inert mono-atomic diluent in order to change the relaxation rates and transport coefficients, without changing the kinetics. This permitted to conclude that relaxation effects were negligible. A closed form solution for detonations with boundary layer losses was derived in the limit of high activation energy for square wave detonations. This allowed to obtain a new non-dimensional loss parameter that can scale the results obtained experimentally. An improvement over existing 2D formulation for treatment of boundary layer losses was proposed, which enabled very good agreement with experiment.