A detonation wave propagating in a straight tube (detonation tube) was reflected off the end wall of the tube, and the pressure profile produced by the propagation of the reflected shock wave was experimentally investigated. The detonation wave was initiated at the opposite end of the reflection end, and two ignition conditions were tested. First, ignition at the closed end of the tube (called as "closed ignition end condition"), where the fluid motion was negligible, was evaluated. Second, ignition at the open end of the tube (called as "opened ignition end condition"), where the burned gas flowed toward the vacuum tank attached to the detonation tube, was evaluated. Karnesky et al. (2013) suggested the empirical model in order to represent the pressure profile near the reflection end in the closed ignition end condition. In this paper, the empirical model of Karnesky et al. was modified in order to represent the pressure profile in the opened ignition end condition, and the effect of two ignition conditions on the pressure profiles was discussed. In these models, the pressure profile at the reflection end was empirically formulated by using two empirical parameters, and a uniform pressure distribution between the reflected shock wave and the reflection end was assumed. In this paper, the empirical parameters were normalized by the characteristic parameters for the propagating reflected shock wave. These parameters expressed the conditions of the combustible mixture and the length of the detonation tube. In the opened ignition end condition, the model well represented the measured pressure profile created by the propagating detonation wave and reflected shock wave in the entire length of the detonation tube because the rarefaction wave existed in the entire region behind the detonation wave, and the pressure behind the reflected shock wave had an approximately uniform distribution. Conversely, the model was applicable for a limited duration for the closed ignition end condition because a pressure gradient gradually developed behind the reflected shock wave when the reflected shock wave began to propagate in the plateau region behind the rarefaction wave.

There is increasing interest in the use of hydrogen as an energy source in fuel cells, and such cells are expected to find practical applications in the near future. However, the reaction rate of a hydrogen-air mixture is so high that the deflagration wave generated during ignition can easily become a detonation wave, even though only a small amount of energy is supplied to the premixed gas. Such a detonation wave can cause serious damage because of the high-pressure and temperature at the wavefront. Despite such concerns, the onset conditions for producing a detonation wave in a non-uniform mixture of hydrogen and air have not yet been fully clarified. In the present study, these conditions were investigated by changing the concentration of hydrogen to understand the onset condition of detonation wave. A vertical detonation tube was divided into two chambers using a slide valve; the upper chamber was filled with air and the lower chamber with hydrogen. A hydrogen concentration gradient was produced by opening the valve for a specific period of time. A pair of electret sensors was used to determine the concentration of hydrogen and the equivalence ratio by measuring the speed of sound in the premixed gas. The onset conditions for detonation were investigated by changing the overall equivalence ratio, φ , and the elapsed time, t d , from the onset of diffusion. It was found that for φ = 1.67 and t d ≥ 540 s, a detonation wave was produced leading to a large increase in pressure. Furthermore, the results indicated that the local equivalence ratio in the vicinity of the spark plug had an important influence on the initiation of the detonation wave.