Three cases of flush wall injection of helium into supersonic freestreams are simulated using detached eddy simulation with a synthetic Inflow boundary layer used to provide a time-varying boundary condition. The synthetic Inflow boundary layer only resolves the largest structures of the boundary layer and provides statistically meaningful perturbations to the jet plume. Reynolds-averaged Navier-Stokes simulations of each case are used for comparison. Two of the cases involve low-angled injection into a Mach 4.0 freestream, one being a single, circular cross section injector and the other being an array of four circular cross section injectors. The injection in the third case takes place through a circular cross section that is normal to the Mach 3.0 freestream. For the two Mach 4.0 cases, the DES with the synthetic boundary layer is found to reproduce the width of the jet plume well, but overpredict the jet plume height. Mean helium mass fraction contours are compared with experiment at two downstream data planes for the normal injection. At both data stations the DES overpredicts the mean height of the core of the jet plume (location of maximum helium concentration), but captures the overall plume height better than RANS. The DES and RANS are found to predict significantly different jet plume trajectories. For one of the cases, the helium plenum chamber was also modeled. While the inclusion of the plenum chamber had a large effect on the flow within the injector nozzle, it was not found to have significant effect on the far field helium distribution or jet trajectory. It is also qualitatively determined that the magnitude of RMS fluctuations within the synthetic inflow boundary layer have an effect on the mixing of injectant with freestream air, except in a small region.