[dshawul]

What is the difference between them ? I read that RANS is time averaged and can be used only for steady flows, while URANS is ensemble average. Where does this difference in averaging manifest itself in the equations. I read general statements in this forum that URANS has the time-derivative term but not RANS. So if I add that term to the RANS equations , will it become URANS ? What is confusing me is that the RANS equations I see in text books f.i Versteeg has the time derivative term in it. Or does that subtle difference in averaging has some other implications to the final equations?
I can not find a description of URANS in text books so I appreciate any links.

Thanks in advance