I am tagging the @PowerUsers_CFD here who might give you some good input to your problem.
Input from my side would be:
Using a cyclic boundary condition for inlet and outlet
Using a non uniform boundary condition at inlet for U for example U=U0*(1- (r/R)^2). Either upload it as a CSV or type it in as a formula. Never tried that one before to be honest.
Actually simulate the whole pipe
I am sure there are some more methods you can use but I think those are the ones that are commonly used imho.
Documentation page for turbulent pipe flow: Turbulent Pipe Flow - Doc