An experimental method for introducing carbon dioxide as a means of stabilizing a hypervelocity boundary layer over a slender bodied vehicle is investigated through the use of numerical simulations. In the current study, two different test bodies are examined. The first is a five-degree-half-angle cone currently under research at the T5 Shock Tunnel with a four cm porous wall insert used to transpire gas into the boundary layer. The second test body is a similar cone with a porous wall over a majority of the cone surface. Computationally, the transpiration is performed using an axi-symmetric flow simulation with wall-normal blowing. The effect of the injection and the transition location are gauged by solving the parabolized stability equations and using the semi-empirical eN method. The results show transition due to the injection for the first test body and a delay in the transition location for the second test body as compared to a cone without injection under the same free-stream conditions. The mechanism for the stabilizing effect of carbon dioxide is also explored through selectively applying non-equilibrium processes to the stability analysis. The results show that vibrational non-equilibrium plays a role in reducing disturbance amplification, however, other factors also contribute.