[user2296]

Hi,

for laminar flows in a channel flow, there are formulas for the inlet velocity which show a parabolic profile. Are there also formulas for the inlet velocity for a turbulent channel flow such that the velocity is zero at top and bottom walls?

Thanks

[LuckyTran]

There are approximate formula, not exact ones. The most popular is the 1/7-th power law profile.


If this accuracy is not enough for your needs, then simulate it yourself and map the profile over.

[sbaffini]

There is no closed exact formula but, an addtional crude approximation is to use the wall distance as y value in any wall function formula (Musker, Reichardt, Spalding, Mixed Linear-Standard) and assigning a Cf, tau_Wall or Re_tau (from which u_tau can be derived, given the remaining case/fluid parameters).

If you really don't like the cusp at the channel center (altough, for very high Re, it is quite ininfluent), you can maybe use a pressure gradient sensitized wall function, one that gives you du/dy=0 at the channel half height. Or maybe use a composite function with some part for the outer layer.

[FMDenaro]

Just to add that all previous answers are correct and valid if you use the RANS formulation. For LES/DNS the generation of the inflow profile is a different matter.

[user2296]

@LuckyTran:

Thank you. Do u mean by 'map over' that I perform a first simulation with the 1/7 law as my inlet velocity profile and then take the resulting velocity values (e.g. from the outlet) and put them to the inlet for the second simulation?

[LuckyTran]

Yes you run a case that somehow gets you the velocity profile that you need. It can be 1/7, it can be uniform inlet. If you want the fully developed profile then I recommend to use a periodic BC in the streamwise direction. Then you take the now correct turbulent velocity profile and map it to the inlet to your case. But this is what you would do if you had a channel as part of a more complex geometry. You have a channel...


Can you not just extend the inlet upstream or just use the periodic BC if you want a fully developed profile?

[user2296]

Thanks again for your answer. I think that should work, I will try to use periodic BC and extend the inlet upstream, thank you.