Hydrogen flames in tubes: Critical run-up distances

The hazard associated with flame acceleration to supersonic speeds in hydrogen mixtures is discussed. A set of approximate models for evaluation of the run-up distances to supersonic flames in relatively smooth tubes and tubes with obstacles is presented. The model for smooth tubes is based on general relationships between the flame area, turbulent burning velocity, and the flame speed combined with an approximate description for the boundary layer thickness ahead of an accelerated flame. The unknown constants of the model are evaluated using experimental data. This model is then supplemented with the model for the minimum run-up distance for FA in tubes with obstacles developed earlier. On the basis of these two models, solutions for the determination of the critical run-up distances for FA and deflagration to detonation transition in tubes and channels for various hydrogen mixtures, initial temperature and pressure, tube size and tube roughness are presented.