Can a flow which is initially supersonic, become subsonic without a shock wave? I am doing my college project in which air is first accelerated to supersonic  conditions in a nozzle. Then it is added into slow moving subsonic air. I see that my flow becomes supersonic and then subsonic but I don't see a shockwave. All this is done on Fluent using various 2 equation models.
Yes, it is possible . The shockless transition from supersonic to subsonic. It has been tested both experimentally and numerical solution. Read this AIAA Paper.

But in your case I would suggest you to be a bit cautious and recheck your mesh and boundary condition in CFD solver.