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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.

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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.

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