Using RANS in transient simulations
 

Hello everyone,

my question is with regards to RANS turbulence models used in transient simulations. Is it true that the turbulence timescale has to be much smaller than the timestep because RANS is based on statistical averages? If so, how do I calculate the turbulence timescale?

Here is some background to my question. During my PhD I was using the k-omega SST model when modelling the Pelton turbine. All the available publications in the field use RANS turbulence models (k-epsilon or k-omega based). Now during my Viva examination the usage of RANS turbulence model was questioned. The argument was that I am using RANS, which is a statistical model, in a transient simulation. One examiner said that the turbulence timescale must be much smaller than the timestep to make sure that the statistical model is appropriate. I am trying to find a way of how to calculate the timescale using the Reynolds number but had no luck. Any thoughts? BTW, the examiner thought that it was not enough to simply say that all previous simulations used RANS (k-ε or k-ω).

I would really appreciate your comments on this.

Best wishes,
Audrius

Time Scale = Length Scale / Velocity Scale;
LS = k^1.5 / e, e - turbulent dissipation;
k = 0.5 * (u'^2 + v'^2 + w'^2) - turbulent kinetic energy;
VS = k^0.5;
Re_t = LS * k^0.5 / nu;

I agree with the examiner. You do need to show this as it is an inherent assumption of the RANS approach. If there is not a clear separation of turbulence and flow time scales then you have to go to LES style models.

Thank you both for your responses and comments.

What still confuses me is whether it is possible to estimate the turbulence timescale before running a simulation? So that I could check if there is a clear separation of turbulence and flow time scales and determine what turbulence model to use. For instance to calculate k I would need to know the turbulent fluctuations u', v' and w'. Is there a way to estimate these?

Surely, I can get k and ε values by running a simulation, but are these values then correct and can I trust them if the simulation was based on wrong assumptions in the first place?

Sorry to be bothering you with what might be trivial but I am really confused right now.

You can use a k-e simulation to estimate the time and length scales. If the time and length scales work out to be OK then the simulation is good. If the time and length scales are not good then the simulation has shown itself to be invalid and so should not be trusted.

Thanks, Glenn!

That clarifies it all.