On the nature of transverse waves in marginal hydrogen detonation simulations using boundary layer loss modeling and detailed chemistry

Historically, it has been a challenge to simulate the experimentally observed cellular structures and marginal behavior of multi-dimensional, thin-channel hydrogen detonations in the presence of losses, even with detailed chemistry models. Very recently, a quasi-two-dimensional inviscid approach with a calorically perfect gas and two-step chemistry was pursued, where losses due to viscous boundary layers were modeled by the inclusion of an equivalent mass divergence in the lateral direction using Fay's source term formulation with Mirels' compressible laminar boundary layer solutions. A similar approach was adopted for this study, but with the inclusion of thermally-perfect detailed chemistry in order to capture the correct ignition sensitivity of the gas to dynamic changes in the thermodynamic state behind the detonation front. In addition, the strength of transverse waves and their impact on the detonation front was investigated. Here, the detailed San Diego mechanism was applied. For marginal cases, where the detonation waves approach their failure limit, quasistable mode behavior was observed where the number of transverse waves monotonically decreased to a single strong wave over a long enough distance. The strong transverse waves were also found to be slightly weaker than the detonation front, indicating that they are not overdriven relative to the shocked gas in which they propagate, in agreement with recent studies. Numerical experiments at lower pressures close to the quenching limit also suggest the existence of additional longitudinal waves formed through wall-collisioninduced autoignition of unburned gas pockets. These waves could potentially be stronger than the transverse waves and help stabilize and even sustain the detonation. Novelty and Significance This work extends previous numerical investigations of hydrogen detonations in thin channels by including thermally-perfect detailed chemistry and advection of the shock time scalar in Fay's mass divergence source term formulation with Mirels' constant. This work is accurately able to recover experimental observations and also applies the mass divergence formulation to mixtures and conditions closer to the quenching limit than has been done before. The methodology used efficiently allows important details of marginal behavior found behind the detonation front to be resolved and quantified clearly. These numerical results suggest the existence of additional longitudinal waves behind the shock front which are found to play an important role in sustaining detonations at marginal conditions.