Numerical simulations of transverse injection through low-angled injector ports into a supersonic freestream are performed using a hybrid, unstructured solver. Two cases are investigated: air injected into a M=2.9 air freestream with a 25° injection angle, and heated helium injected into a M=4.0 air freestream with a 30° injection angle. Simulations were run in RANS and DES modes. A set of the DES simulations were run with an unsteady inflow boundary layer, where the perturbations are a statistically meaningful representation of a series of randomly placed hairpin eddies. This boundary condition was fed periodically into the domain, and was reused multiple times over the course of a simulation. The RANS and DES simulations are found to capture the salient features of the flow, though discrepancies with experimental data are found. While the DES simulations were found to give steady-state solutions for the flow fields, the addition of the unsteady inflow boundary layer was found to greatly impact the downstream flow field and to improve the overall agreement with experiment. In the case of the helium injection, it was found that the predicted mass fraction distributions of the DES simulations with the unsteady inflow boundary layer was far less dependent on the value of the turbulent Schmidt number. This result shows that the mixing found in DES simulation with the unsteady inflow boundary layer is a result of the large-scale turbulent motion of the flow, rather than because of the gradient diffusion term. However, the 'box of eddies' used to create the unsteady inflow boundary layers were not long enough to ensure that no bias was introduced into the flow field, and future simulations will be run with larger boxes. The results of the study show a great deal of promise for the use of DES simulations in conjunction with unsteady inflow boundary layers for simulation of SCRAMjet fuel injection.