A numerical study of the longitudinal pulsed detonation (LPD) is conducted in the present paper. The occurrence mechanism of the LPD, called shock wave amplification by coherent energy release, is verified preliminarily in this study. To be specific, upstream propagating shock waves, which originate from the outlet, induce a specific gradient of reactant distribution, and then detonation waves are ignited and evolve along the gradient in close succession. It is worth noting that the occurrence of LPD does not mean that the LPD will necessarily be sustained. The low injection pressure ratio PR (i.e., the ratio of inlet pressure to outlet pressure) = 1.3 is found to be conducive to the sustenance of the LPD instability in the baseline model. A lower PR (PR ≤ 1.2) or a slightly higher PR (1.4 ≤ PR ≤ 1.8) shall lead to an unstable detonation or quenching of detonations, while a much higher PR (PR > 1.8) contributes to the formation of stable canonical rotating detonation waves. In addition, the combustion regimes of five combustors of different heights at different PR are explored. As the combustion chamber height increases, the PR of the sustainable LPD is nearly linearly increasing, and its operating frequency decreases gradually. The calculation formula between the sustainable LPD propagating frequency and the natural acoustic resonance frequency of the combustor is employed and discussed, but in consideration of its imperfection, further investigation is required.
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