I've been looking for information about cfd work done in supersonic jets submerged in liquid bath, like gas injection in metal converters, but nothing came up. I think that maybe this case is too complex for cfd so that's why I've found nothing. Even steady flow with bubbles is quite complex, with these high speeds it's very difficult to resolve all equations. How could be modelled an interphase between supersonic gas and (initialy) steady liquid? Maybe it's not possible yet, please let me know, thanks.

Hmmm, I see that very complex to compute. To add my ignorance to the pool, the only thing I can advice you is the continuity of the stress force vector and heat flux (if you're considering these terms in your equations). Perhaps if you neglect the heat diffusion and viscuous terms you don't have any BC.

Good luck.

I have heard of people doing work in this area. You might contact CFX development in Harwell (UK). Either they have done it, are developing it or have turned it down.