# Confusion Over Navier-Stokes, RANS and URANS in a Flow With Laminar-Turbulent Transition [closed]

I have been working on a transient simulation, using the SST k-w turbulence model in Fluent(TM). An unsteady boundary condition is used: at the beginning of the simulation the flow is laminar and gradually becomes turbulent.

This is where I am getting a bit confused. When describing the numerics of my model, should I give the Navier-Stokes equations (conservation,momentum and energy), RANS equations or URANS equations?

Are the equations used throughout the simulation or does the solver switch to them from NS only when the flow becomes turbulent? Would RANS work just fine in a laminar flow?

• You are solving RANS or URANS, depending on whether you are doing a transient or steady-state simulation. You should be writing down the SST $k-\omega$ equations if that is what you are solving. Also, I think this question should be closed since it's not likely to be helpful to others. – Jed Brown Aug 5 '13 at 3:38
• I am running a transient simulation. Does that mean that the fluid flow is decribed by the URANS equations? As far as I understand SST k-w just gives an extra two equations (the turbulence model), but a set of 3 main equations (conservation, momentum, energy) are the modified form of Navier-Stokes equations (URANS). Am I correct? – A.L. Verminburger Aug 5 '13 at 8:56
• "Main equations" can be a misleading way to think about this. It is a coupled set of equations, URANS with closures provided by the SST $k-\omega$ model. – Jed Brown Aug 5 '13 at 11:55

## 2 Answers

You are solving the RANS equations. It just so happens that people apply the RANS equations so often to steady problems that people inexplicably think of URANS as some different beast. It's not. You wouldn't call them the UNS equations so don't call them the URANS equations.

• I get what you're saying, but there's enough literature out there that does distinguish between RANS and URANS (and defines Reynolds averaging as being over all time) that I don't think it's a bad idea to specify URANS. If your audience is strictly CFD-savvy then just "RANS" is fine, but I've run into plenty of non-CFD fluids researchers that think "RANS" means only steady, time-averaged solutions. The original RANS equations derived by Reynolds in fact were fully steady, and a lot of the literature reflects that. Even the wikipedia RANS article is strictly steady. – Aurelius Aug 6 '13 at 4:56
• Am I solving RANS even when the flow is laminar? – A.L. Verminburger Aug 6 '13 at 7:29
• RANS comes from taking the expectation of NS across the space of turbulent solutions. Ergodicity assumptions are what permits exchanging averaging over all turbulent solutions to averaging temporally over one turbulent solution. In a statistically-stationary problem the resulting moments are independent of time and hence the temporal state derivatives drop out. As you point out, "Reynolds averaging" is mistakenly used to describe time averaging in this setting. Don't propagate the mistake. – Rhys Ulerich Aug 6 '13 at 15:52
• You're solving RANS anytime you've got nonzero Reynolds stresses. When it's laminar there are no fluctuations and therefore no Reynolds stresses. – Rhys Ulerich Aug 6 '13 at 15:55

It seems to me that this is a question you can easily figure out on your own - at least partially. A cursory search leads to the following links that should help clarify NS, RANS, and URANS:

http://www.os-cfd.ru/cfd_docs/chalmers/urans.pdf?PHPSESSID=e16a72bf68c8e833e522b3120bd6ee4b

http://www.iaeng.org/publication/WCECS2011/WCECS2011_pp673-678.pdf

Of course, you will most likely only be able to figure it out partially because you cannot know for sure what's going on inside Fluent...

• In my simulation the speed of the flow increases gradually (an unsteady boundary condition is used). The flow is initially laminar and only towards the end of the simulation becomes turbulent. The turbulence model is set at the beginning of the simulation. Does that mean that URANS is used throughout the simulation? – A.L. Verminburger Aug 5 '13 at 17:03