Ratio of eddy viscosity to molecular viscosity : Laminar or turbulent flow?
 

I'm stuck between a rock and a hard place.

I'm modelling a differently heated cavity, which induces density variations and causes the fluid to recirculate.

I've tried laminar and turbulent models but I'm not getting the results I expect.

Using a laminar model when I post process the Reynolds number it indicates the flow may be turbulent. When I switch to a turbulence model (SST) the Reynolds number indicates the flow may be laminar. :confused:

I've read somewhere (I can't recall where!) that the ratio between eddy viscosity to molecular viscosity will truly tell me if my flow is laminar or turbulent. But how can this be true for laminar flow as laminar flow won't have an eddy viscosity?

So I guess what I'm asking is: is the ratio of eddy viscosity to molecular viscosity a good indicator of laminar or turbulent flow? Is it a simple case of going into CFD Post and checking the ratio between these two viscosities?

My guess is that if the ratio is < 1 molecular viscosity dominates and the flow is laminar. If the ratio is > 1 eddy viscosity dominates and the flow is turbulent. And if the ratio = 1 the flow is transitional? Of course I may be wrong (I suspect I am!) and I am happy to be corrected!

Are there any papers or books that you can recommend that'll lead me to the correct path?

Thank you! :)

From first principle, it would be fair to say that while any laminar flow would have shear stress owing to its viscosity and velocity gradients, the reason of "turbulence" is the additional shear stresses (Reynolds stresses) that arise due to random fluctuating velocity components, which are realized through the definition of turbulent viscosity.

Essentially, the ratio of turbulent to molecular viscosity gives an indication about how strong the Reynolds stresses are, as compared to molecular stresses. So it sounds reasonable too use this ratio as a measure of turbulence. Typically, eddy viscosity ratio of more than 100 to 1000 indicates turbulent flow. Although, the evolution of turbulence models has revolved around definition of eddy viscosity and hence for different models you may have different values of it. Try using the best 2-eqn model for your flow (say kw-SST or RNG for high circulation etc).

Also, it wouldn't hurt to go for transition gamma theta model.
Have you observeed other obvious parameters like turbulent kinetic energy etc?

OJ

I would not use the turbulence transition model for a buoyancy driven flow. It is so far removed from where it was developed that I would not trust it without very careful validation.

OJs comment is a good summary of the situation - the only thing I would add is that for bouyancy driven flows (especially in differentially heated cavities) the Rayliegh number is a better judge of whether the flow has gone turbulent than the Re number.

I agree with you oj.bulmer and ghorrocks.

I am monitoring the Rayleigh number. As a general rule of thumb anything below 10^8 is laminar, anything above 10^10 is turbulent. My flow sits at 10^9!

Bummer.

Are you referring to the Reynolds number from the solver output? It is based on the average velocity of the domain and the cube root of the domain volume, and may not the be Reynolds number for your particular problem...

Hi, thanks - but I knew that the solver Re is a red herring! I physically went into CFD post and calculated my Re and Ra numbers based on the post processed data.

I'm sorry for the late reply, OJ. Do you have a source for the bit I've bolded above?

Naturally I've tried to search through the theory guides, and text books to no avail.

In a drive to improve the much-ignored turbulence BCs, I had done a bit of search earlier. The bits I mentioned come from here and here.

Cheers
OJ