Pulse Detonation Engine (PDE) is considered to be the propulsion system of future air and space vehicles because of its low cost, light weight, and high performance. Hybrid PDE is a relatively new concept where a turbine is integrated with a PDE. This hybrid system is expected to operate under fuel-rich conditions during take-off (stoichiometric), and fuel-lean (φ = 0.44) conditions during cruise. Hence, the objective of the present study is to simulate the external flow field of a stand alone PDE system and study its variation during the above mentioned operating conditions. In order to study Hybrid PDE systems, the underlying concept of the working of a stand alone PDE, namely, detonation, has to be simulated first. For this purpose, the one-dimensional reactive Euler equations are solved. Since a propagating detonation wave is the result of chemical reactions in a very small region, flow adaptive grids are used for the one dimensional detonation simulations. The global chemical mechanisms employed predicted all the detonation quantities for both stoichiometric and lean mixture of hydrogen-air with the least error. The results from the global chemical mechanism for both mixtures are used in the two-dimensional PDE simulations. Analyses of the axial pressure and temperature distribution in the external flow field show the nature of the blowdown process and its variation for different operating conditions. Flow exergy analysis shows that there is 25% loss in available work when a turbine is placed at one tube length away from the exit of the PDE. One of the important outcomes of this study is the information that can guide in the placement of the turbine downstream of the PDE to achieve lower blowdown time.