Hypersonic aerodynamics is gaining interest in the research community due to raising need in the areas like space missions, enhanced performance of missiles or rockets etc. Wave drag being the major obstacle for success of such mission, various drag reduction techniques are considered for studies in the literature. Among those techniques, injection of gas from the stagnation point is one of the most promising active drag reduction technique. Therefore, in the present studies, emphasis is given to numerical studies for dynamics of counter-flow injection and its dependence on the free-stream stagnation enthalpy. It has been noticed that wave drag reduction results from the splitting of a strong shock wave into multiple oblique shocks. As jet total pressure increases, bow shock moves away from the body and recirculation region becomes larger. Further, present computational investigations revealed that the increase in enthalpy from 0.2959 MJ/Kg to 0.5918 MJ/Kg leads to reduction in potential of this technique in reducing in the wave drag for same injection pressure ratio.