A Model for Hydrogen Detonation Diffraction or Transmission to a Non-confined Layer

One strategy for arresting propagating detonation waves in pipes is by imposing a sudden area enlargement, which provides a rapid lateral divergence of the gases in the reaction zone and attenuates the leading shock. For sufficiently small tube diameter, the detonation decays to a deflagration and the shock decays to negligible strengths. This is known as the critical tube diameter problem. In the present study, we provide a closed form model to predict the detonation quenching for 2D channels. This problem also applies to the transmission of a detonation wave from a confined layer to a weakly-confined layer. Whitham’s geometric shock dynamics, coupled with a shock evolution law based on shocks sustained by a constant source obtained by the shock change equations of Radulescu, is shown to capture the lateral shock dynamics response to the failure wave originating at the expansion corner. A criterion for successful detonation transmission to open space is that the lateral strain rate provided by the failure wave not exceed the critical strain rate of steady curved detonations. Using the critical lateral strain rate obtained by He and Clavin, a closed form solution is obtained for the critical channel opening permitting detonation transmission. The predicted critical channel width is found in excellent agreement with our recent experiments and simulations of diffracting H2/O2/Ar detonations. Model comparison with available data for H2/air detonation diffraction into open space at ambient conditions, or for transmission into a weakly confined layer by air is also found in good agreement, within a factor never exceeding 2 for the critical opening or layer dimension.