The coaxial spray injection and combustion flowfields of a Space Shuttle Main Engine preburner injector element have been analyzed using a three-phase numerical code. The processes of atomization, evaporation, secondary droplet breakup, and multispecies chemistry, as well as turbulent diffusion, are included. The model produced realistic pictures of the complex internal flowfield, including liquid jet length, spray shape, flame-zone size and characteristics, and predicted temperatures that seem to be in agreement with test data envelopes. It predicted an external group combustion type of flame. Salient combustion and mixing features are discussed and sources of uncertainty are pointed out for future studies.