If the turbulence model of a CFD code is not 1- or 2-equation but a simple one, can I get more accurate result if I increase the number of the grids near to the wall? Or, this is not true in all cases?

Another question is, how can I get an estimate for the required number of the grids (within the boundary layer) to predict the separated flows in internal flows? And, does it matter which turbulence model is used?

Thanks, Sue

Dear Sue,

The use of turbulence models for fluid dynamics problems has a great dependence on the problem to solve. In fact ther is no universal model, that works the best on all cases. And as for your questions, here are my suggestions.

1. For any given turbulence model, increasing the grids near to the wall would mean better resolution of the boundary layer, and it is expected that the results are better. However, note that for certain models like k-epsilon, near-wall corrections may be necessary. Just increasing the grids, without looking at the capabilities of the model could result in erroneous conclusions and confusion. And you could always start off with a zero-equation algebraic model like Baldwin-Lomax and hope to improve your accuracy by increasing the near wall resolution.

2. The number of grid layers to have an adequate resolution of the turbulent boundary layer is not fixed, and could vary from 20-50. The important point to note is the y+ - which is like Reynold's number based on friction velocity should be lesser than 1, though for B/L model, y+ < 5-7 everywhere is good enough. The y+ is also a measure of how close the first gridline is to the body and is crucial in resolving the laminar sub-layer. In general for 2D problems I have simulated, which are external flow cases a spacing of 1e-4 was used, and around 25-35 layers in the BL. The same ideas apply even for internal flows, you need to have the y+ sufficiently small(~5) in order to get your results accurately. For external aerodynamic flows, S/A is the best choice, while for internal flows k-w or Menter SST would be fine. I am not very confident of performance of zero-equation models for separated flows, and for massive separtion none of the developed models would work satisfactorily.

Hope it helps

Regards,

Ganesh

Thank you Ganesh for your helpful information. I would still like to know what you meant by "massive separation", and how do you think you can predict those areas? LES, or DNS? In other words, at what condtions we should say that RANS models are not useful?

Regards, Sue

Dear Sue,

By "massive separation", I am precisely referring to those cases, where RANS models perform poorly. This generally happens at very high angles of attack, in case of airfoil, for example. Separation is mild for AoA around 7-8deg., moderate for around 10-12 and massive for 15-20 deg. You could refer to the following paper for details on the fact that even a 2-equation model is not good enough to predict massive separation successfully.

Techinical note AIAA Jl. Vol 35(7)

Computation of unsteady separating flows over an oscillating airfoil, Ko and McCroskey

And if you are looking for a way out, I think it has to be DNS/LES/DES and the like. The major deficiency of most RANS models are that they have parameters that come out of experiments and hence the "coverage zone" or "Range of applicability" of these models are limited. Even in case of LES, there does exist some modelling, but possibly the errors are lesser. Most commonly used models also depend on the Boussinuesq hypothesis, which also limits their applicability. Models like the Reynold's Stress Models (RSM) or Non-linear Eddy Viscosity Models, would possibly be a better choice compared to the common k-w or S/A and the like, but the problem of constants determined from experiments still pose a limit on the applicability. RANS are popular because there are situations where the hypothesis is valid and for which the constants are tuned to and more importantly the effort is comparitively lesser compared to LES/DNS. Yes, the obvious choice for "massive separation" would then be LES/DNS, but DNS is limited drastically by computational power available. In fact the number of nodes, N ~ Re^2. Thus the number of nodes would increase as square of Re, and only lower Re has been computed with DNS. Under these circumstances, I would prefer to go for a LES/DES simulation, for cases involving "massive separation".

Hope this helps

Regards,

Ganesh

Y+ value is Reynolds no dependent. Y+ of say 1000 can be quite acceptable in some cases. Y+ of less than 1 is not always easier to achieve without imposing millions of nodes. This criterion is not particularly useful if you expect a large separation in your flow...

RSM can be worse than two equation model if the boundary condition is not known exactly. It's really case depedent.

In some problems, it's really hard to measure the flow condition precisely and you really need to think about what information you have before you choose a model.

Hi,

Y+ of 1000 acceptable in some cases, I would like to know which ones ... For this value of y+, you do not resolve the boundary layer at all. Regarding the pertinence of the y+ criterion when we expect a large separation, how can you predict precisely a separation point without computing correctly the boundary layer ?

Dear TB,

y+ of 1000 being acceptable in certain cases, seems surprising. The basic reason being the fact that y+ is like the Reynold's number ( Re = VL/nu, y+ = yU*/nu) and the laminar sub-layer which is essential to be resolved has prominent viscous effects that leads to low Re. True that y+ ~ 1 is not easy to achieve, but as I had mentioned in my earlier mail, you really need not achieve 1, anything of the order of 5-10 is fine enough. y+<1000, seems to be too far away and does not come anywhere near resolving the laminar sublayer. Possibly for laminar flow, if you make a definition of y+, 1000 is fine enough, but for turbulent flows, I never encountered a situation where this was right. Also, from my personal experiences, I have started form a grid of y+ around 1000 and even less, but the results of skin friction distribution are comfortably far off and unless I adapt the grids near the BL, effectively reducing my y+ to acceptable values, I never achieve the correct result.

Regards,

Ganesh

Sorry... I mean 100, not 1000... keep the eyes sharp, guys.

I have done some internal turbulent flow problem with max Y+ of around 200. It's quite close to the experimental results anyway. Besides, if max Y+ is far from the domain of interest, it will be fine. Any different idea?

Y+ can be very small at separation zone, which can be misleading if you only look at the results quantitatively. Any thoughts about this?