| Previous experiments demonstrated that the accidental release of high pressure hydrogen into air can lead to the possibility of spontaneous ignition. It is believed that this ignition is due to the heating of the mixing layer, between hydrogen and air, caused by a shock wave that is driven by the pressurized hydrogen during the release. Currently, this problem is poorly understood and not amenable to direct numerical simulation. This is due to the presence of a wide range of scales between the sizes of the blast wave and the very thin mixing layer. The present study addresses this fundamental ignition problem and develops a solution framework in order to predict the ignition event, for given hydrogen storage pressures and dimension of the release hole, using a two stage model. The key physical processes in the problem are identified to be the mixing of the two gases at the mixing layer, the initial heating by the shock wave, and a cooling effect due to expansion of the mixing layer. First, a multi-dimensional non-reactive compressible flow solver is used to determine the expansion rate of the gas. Next, the mixing layer between the hydrogen and air is considered in a high resolution, one-dimensional model. The mixing layer, at the jet head, is advected as a Lagrangian fluid particle. Results indicate that for every storage pressure, there exists a critical hole size below which ignition is prevented during the release process. This limit was found to depend on the competition between the heating provided by the shock wave and the cooling due to expansion. Furthermore, the limiting ignition criteria were found to be well approximated, to leading order, by the Homogeneous Ignition Model of Cuenot and Poinsot, supplemented by a heat loss term due to expansion. Therefore, turbulent mixing occurring in reality is not likely to affect the ignition limits derived in the present study. |
