Shock focusing ignition techniques can avoid deflagration-to-detonation transition (DDT), which make pulse detonation engine (PDE) more efficient. Numerical simulations of an idealized pulse detonation engine consisting of axial inlet and circumferential inlet are presented in this paper. Using detailed hydrogen-air mixture chemical kinetic model, investigation on detonation direct initiation by shock focusing is done. Studies indicate that in initial static flow field, the regions of high temperature and pressure created by shock focusing can produce detonation at the condition of circumferential inlet Mach 2.4. The temperature and pressure of the focusing region is nearly 3000K and 6.3MPa. But in dynamic flow field, the high temperature and pressure created by shock wave focusing for an incident Mach number of 2.4 decrease to 1027K and 4.5MPa which cannot produce detonation. When the incident Mach number increases to 3.5, the transient temperature and pressure of the focusing region is nearly 3000K and 30MPa, which capable of initiating a detonation wave.

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