Results from 3D, compressible, unsteady Favre-averaged calculations of transverse injection into a supersonic cross flow are reported. Four injector geometries, namely, circular, wedge, diamond, and chevron, have been investigated. The effectiveness of the chevron injector is demonstrated by comparing performance metrics, such as degree of mixing and total pressure loss, against those of the other injectors. The results show that the chevron injector provides better mixing and spreading compared to other injectors, with almost the same total pressure loss. Furthermore, for the operating conditions studied, the chevron-penetration angle is shown to have a minimal impact on the mixing and the total pressure loss.