# Talk:RNG k-epsilon model

Hello I'm quite new in CFD

What does RNG mean?

I know that the difference between K-epsilon and RNG k-epsilon models are the constants in the transport equations but what is the purpose to change these variables and when we used each model?

Thanks

RNG means Renormalization Group Theory. It is a mathematical theory which can be used to derive a turbulence model which is similar to the k-epsilon model. When this was first done it was a kind of revolution that a mathematical theory could be used to derive this kind of turbulence model. It was done by Yakhot and Orzag. The exact formulation and constants in the RNG k-epsilon model is not the same as in the old k-epsilon models though. The RNG models have not been that much of a revolution though and they are not that frequently used today. Some people claim that for rotating flows RNG models are superior. I have tested a RNG k-epsilon model a few times and the only application where I noticed better results with it was in rotating cavities, but then it turned out to be more interesting to run transient and even DES/LES simulations. --Jola 03:33, 7 June 2007 (MDT)

The RNG model was developed using Re-Normalisation Group (RNG) methods to renormalise the N-S equations, to account for the effects of smaller scales of motion - in the stadard k-e model the eddy viscosity is determined from a single turbulence length scale, so the calculated turbulent diffusion is that which occurs only at the specified scale, whereas in reality all scales of motion will contribute to the turbulent diffusion. The modified production of the dissipation rate attempts to account for the contribution from other scales of motion. For a reference see Yakhot, V., Orszag, S.A., Thangam, S., Gatski, T.B. & Speziale, C.G. (1992), "Development of turbulence models for shear flows by a double expansion technique", Physics of Fluids A, Vol. 4, No. 7, pp1510-1520.. I think the RNG model gave better results for turb flow over a backward facing step - discussed in the paper. I've tried it for modelling vortex evolution which is quite tricky due to the strong rotation and didnt see any better performance than with the standard k-e model. --Si 03:47, 7 June 2007 (MDT)

This may be a little late in coming, but isn't this (the above two paragraphs) exactly what the main article needs? Could someone reformat this and move it to the main article? Incidentally, the RNG k-epsilon model is apparently favored for indoor air simulations - just found that out recently (have a ref if there is interest). --Jasond 11:00, 8 June 2007 (MDT)

I've done quite a major edit to the article, using the above paragraphs and some other details I'm familiar with. I've got a few thoughts on what the turbulence modelling section should be - see the item in the discussion forum. I'm quite interested in the section that said "turbulent viscosity is modelled as" and had the following in (the section that I've taken out!)

$d \left(\frac{\rho^2 k}{\sqrt{\epsilon \mu}} \right) = 1.72 \frac{\hat{\nu}}{\sqrt{{\hat{\nu}}^3-1+C_\nu}} d{\hat{\nu}}$

$\hat{\nu} = \mu_{\rm eff}/\mu$

and

$C_\nu \approx 100$

and the $R_{\epsilon}$ term as I've not seen either of those before. Anyone got any pointers? --Si 07:42, 11 June 2007 (MDT)