Detonation engines are expected to be included in a number of aerospace thrusters in the future. Several types of detonation engines are currently under examination, including the rotating detonation engine. In this work, the feasibility study and design of a laboratory sample RDE which has an annular geometry with diameter of 76 mm has been performed. In this sample, hydrogen and standard air are separately injected into the combustion chamber of detonation engine. The injection of fuel and air flows are in the axial and radial directions, respectively. First, numerical studies are validated comparing the FLUENT results with the experimental ones. Then, the geometry and equivalence ratio of injection mixture are investigated parametrically. Considering the negligible variations of thermodynamics parameters in the radial direction of flow field and to reduce the computational costs, a 2D model is used for numerical simulations. Using three different equivalence ratio, it is found that detonation speed, pressure, and temperature behind detonation front, at the equivalence ratio of 1.2 is more than the equivalence ratio of 0.8. Also maximum detonation speed and pressure behind detonation is taken place in stoichiometric condition. The coefficient 0.5 and 2 are used in order to evaluate the effects of chamber length. Because the chamber outflow is semi-subsonic, chamber length change has a significant effect on the engine performance and flow field. The results point out that increasing the chamber length in low injection pressure and high injection pressure leads to increasing and decreasing the height of detonation front, respectively.