This paper introduces a simplified approach for analyzing local elastic hoop response of piping to reflected gaseous detonations and deflagration-to-detonation transitions (DDT). A consequence associated with gaseous explosions is the potential for DDT to occur near the end of a closed pipe or gas pocket. As an accelerating deflagration flame approaches a closed end, the unburned fuel ahead of the flame front is compressed to an elevated initial pressure. This process is often referred to as pressure piling or pre-compression, and the combination of detonation reflection with the elevated initial pressure, can produce extremely high peak pressures and large values of impulse. In this paper, the event where DDT occurs immediately ahead of the reflecting surface is referred to as a reflected-DDT (R-DDT).
In addition to gas mixture and initial conditions, the peak pressure and shape of the pressure time-history associated with a reflected detonation or DDT is a function of the detonation propagation distance prior to reflection and the relative distance between the ignition location, the DDT location, and the reflecting surface. An empirical pressure time-history has been developed using pressure data from approximately 190 explosion tests using hydrogen and nitrous oxide mixtures in 2-inch and 4-inch pipe to describe events ranging from fully-developed reflected detonations to R-DDTs. The empirical model of the pressure time-history was validated by comparing measured elastic hoop strains to finite-element model predictions using the pressure time-history model. Part 2 of this paper compares the methodology to plastic response data.