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# A Simple Model for Calculating Peak Pressure in Vented Explosions of Hydrogen and Hydrocarbons

### Abstract

The authors presented a basic mathematical model for estimating peak overpressure attained in vented explosions of hydrogen in a previous study (Sinha et al. [1]). The model focussed on idealized cases of hydrogen, and was not applicable for realistic accidental scenarios like presence of obstacles, initial turbulent mixture, etc. In the present study, the underlying framework of the model is reformulated to overcome these limitations. The flame shape computations are simplified. A more accurate and simpler formulation for venting is also introduced. Further, by using simplifying assumptions and algebraic manipulations, the detailed model consisting of several equations is reduced to a single equation with only four parameters. Two of these parameters depend only on fuel properties and a standard table provided in the Appendix can be used. Therefore, to compute the overpressure, only the two parameters based on enclosure geometry need to be evaluated. This greatly simplifies the model and calculation effort. Also, since the focus of previous investigation was hydrogen, properties of hydrocarbon fuels, which are much more widely used, were not accounted for. The present model also accounts for thermo-physical properties of hydrocarbons and provides table for fuel parameters to be used in the final equation for propane and methane. The model is also improved by addition of different sub-models to account for various realistic accidental scenarios. Moreover, no adjustable parameters are used; the same equation is used for all conditions and all gases. Predictions from this simplified model are compared with experimentally measured values of overpressure for hydrogen and hydrocarbons and found to be in good agreement. First the results from experiments focussing on idealized conditions of uniformly mixed fuel in an empty enclosure under quiescent conditions are considered. Further the model applicability is also tested for realistic conditions of accidental explosion consisting of obstacles inside the enclosure, non-uniform fuel distribution, initial turbulent mixture, etc. For all the cases tested, the new simple model is found to produce reasonably good predictions.

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