In response to the multi-physical processes of the actual air-breathing ramjet detonation engine,high-resolution numerical simulation is adopted to simulate injection mixing,flame acceleration,deflagration-to-detonation transition(DDT),detonation propagation and diffraction,expansion and blowout in detail.Naiver-Stokes equations with adaptive mesh refinement method are adopted with considering a detailed 11 species and 27 steps hydrogen-air chemical reaction mechanism,and the complete ramjet engine working process under the subsonic incoming flow,mixing,and injection are obtained.Multiple groups of transverse air jets are utilized in a smooth tube to obtain speedy DDT.The results show that with the mixing and injection conditions,the equivalence ratio distribution of the mixture is extremely uneven.Multiple groups of transverse jet obstacles enhance the mixture's uniformity and stimulate the occurrence of DDT.During the expansion process of combustion products,the secondary expansion phenomenon is detected.Under the interaction between exhaust gas and the atmospheric environment,a flow instability structure appears in the flow field.The simulated results also demonstrate that mixing and purging occupy most of the time of the entire detonation engine.