The pressure time-history associated with a propagating detonation within a pipe can be reasonably well described using a one-dimensional model. These models describe the advancement of the detonation front and the expansion wave behind the detonation front, over which the pressure decays. The length of the expansion wave, and the corresponding pressure decay period, is a function of the distance the detonation wave has traveled. One-dimensional detonation models typically assume an isentropic expansion behind the detonation front. The consequence of this assumption is that the expansion wave will grow infinitively long in an infinitely long pipe. The loss of energy due to heat transfer, however, has been observed to result in a natural limit in the length of the expansion wave, and corresponding pressure decay.
The implication of this limit on piping design for gaseous detonations is that there is a limit on the pressure-impulse that is applied to the system. When a detonation propagates through a piping system, the detonation pressure produces unbalanced loads at the bends, tees, reducers, and closed-ends. These transient loads are a function of both the peak pressure and the details of the pressure decay. In long piping systems, the decay period of the expansion wave can become sufficiently long that very high loads are imposed on the system. Crediting a natural limit of these loads may have significant implications for the design of the pipe and its supports.
Although the existence of an expansion wave limit has been previously observed, consensus on its length does not currently exist in the literature. This paper describes detonation tests that were performed in both 2-inch and 4-inch 36.6m long pipes using mixtures of hydrogen and nitrous oxide. Pressure transducers were installed at periodic locations along the pipe. The slope of the initial pressure decay of the detonation was used to characterize its shape. The slope of the initial pressure decay was found to exponentially approach a limiting steady state value, and this limiting value was achieved after the detonation had propagated approximately 120 pipe diameters.