The present paper deals with the unsteady compressible (Ma > 0.3) reacting flows of hydrogen-air mixture in pulse detonation combustor. In order to achieve the potential thrust gain from PDE combustor, the shrouded ejector is placed at exit section of detonation tube. In this analysis, core diameter and ejector length effect on vortex generation has been investigated. Furthermore, the propagation of detonation combustion wave is analyzed for three equivalence ratio (ER) of lean, stoichiometric and rich (phi < 1, phi = 1, phi > 1) in multiple pulse time. Not only the reacting flow structure but also the propulsive performance of pulse detonation combustor has been investigated. Moreover, this numerical simulation is carried out to minimize the fuel consumption in instantaneous pulse time for fully developed detonation wave. The eddy dissipation combustion model with a single-step Arrhenius chemical kinetics model is used to simulate the fuel-air reacting mixture in Ansys fluent platform. The contour plot clearly shows formation number of 2.39 has more significance role for vortex core generation with shortest possible time of 0.033 s. The pickup flame propagation speed of 2310 m/s is obtained, and this magnitude is higher than C-J velocity. The result also indicates that minimum pollutant number is released from lean and rich mixture combustion; even, marginal thrust is generated with magnitude of 35 N and 37 N, respectively, from equivalence ratio of phi = 0.64 and phi = 1.4 at pulse time of 0.033 s. Although the maximum pollutant number of 0.0489 is found from phi = 1.0, strong thrust is obtained from stoichiometric H-2-air mixture.