This is really a question to the turbulence gurus at Fluent (Paul Malan, Sung-Eun Kim ...) concerning the implementation of the Realizable k-epsilon model. However, I think that the implications are of general interest to all Fluent users so I'll post the question here.

The realizable k-epsilon model that is available in Fluent has a variable Cmu. This variable Cmu works very well in the main flow and this model is my favourite model in Fluent. It avoids a lot of problems that you have with the standard k-eps model (overproduction of k etc.). However, it is not that self-evident how to handle the variable Cmu near walls. I think that Fluent just uses the variable Cmu in wall-laws, two-layer models and low-Re models. This might be okay, but I'm far from convinced. Recentely I have seen some anomalies in certain solutions that I think might be related to this. None of the wall-treatments available in Fluent were designed for a variable Cmu and using the variable Cmu can make them invalid. In the two-layer model for example, using the variable Cmu (dependent on k and epsilon) will create a strange mix of two models that were not originally intended to be used together. As far as I know the Realizable k-epsilon model was originally just a high-Re model and it did not include any low-Re treatment. The rapid-distortion theory used to derive the realizable model is also only valid in the high-Re case.

My question to Fluent is if you have validated the Realizable k-epsilon model for use together with all your near-wall treatments (wall-laws, two-layer, low-Re)? What kind of validations have you done? Are there any near-wall models that I definitely should avoid when using the Realizable k-epsilon model?

(1). Very good questions, and also serious questions. (2). Here, I can only share with you my experience in using Fluent codes a couple of years ago. (3). At that time, the hybrid mesh to cover the wall layer with fine mesh was not invented or available yet. This make it not practical to use the so-called low Reynolds number model. So, there was no low Reynolds number k-epsilon model in the option list. (4). Based on the old mesh (pure tri- or tet- mesh) system, it seems to me that the RNG k-epsilon two-layer model provides better results. It was hard to draw a positive conclusion , because of the limitation on the near wall mesh. (you have to see for yourself, to convince yourself) (5). So, in this case, my experience was limited to the difference between the coarse-mesh high Re k-epsilon solution and that of the fine-mesh RNG k-epsilon results. (6). With the new hybrid mesh introduced, the prediction of results was improved. But only very limited cases was carried out in 3-D, because the generation of the fine mesh next to the wall was carried out numerically in the code. The generation of the mesh was slow. (7). So, I think, the low Re modeling part is missing from the code options. (8). Along the same line, I have been checking out another code with similar option lists. Still, only the two-layer, RNG k-epsilon model is available. But, since this code is using structured mesh, I can easily control the very fine mesh next to the wall. This is required to eliminate the mesh requirement in the first place. (9). Currently, I have been getting converged results from this code, and I was able to draw some important 3-D flow features inside the boundary layer and the formation of the secondary flows. (10). Since I have not been able to get good results in terms of the total pressure loss, there is no way to address the accuracy of the turbulence model (Rodi's two-layer model on RNG k-epsilon two-equation model). My feeling is that this code I am running has high diffusion effect in it, probably coming from the numerical method side. (10). So, I think, in order to address that part of the turbulence model, one needs to first fix the mesh problem, and also the numerical method problem first. (11). It would be very interesting to look at the turbulence eddy viscosity distribution in the flow field first. Because, even in this code I am running, I am getting funny eddy-viscosity distributions, which may not be a problem when coupled with the velocity field gradients. (12). Also, because of the slow convergency in the turbulence variables, strict convergence criterion is required. (13). I think, this is a difficult problem, because I am dealing all the time with real 3-D problems. (14). Validation of turbulence models in 2-D cases could be a better starting point. ( I hate to quote that my colleague once said to me that his results using Star-CD code agreed better with his test data. ) (15). So, I think, it is still wide open in the turbulence modeling and validation. Perhaps, a true low Re , two-equation k-epsilon model is required to provide a reference solution. (The problem is, sometimes you will run into convergence problem in using a low Re model.) (16). That is all I can say right now. Perhaps, the developers would like to add some comments to this important question.

As far as I know, the realizable model as implemented by Fluent is based on the paper by Tsan-Hsing Shih et al. In that paper Cmu was assumed to depend on a variable, say A, that was assumed to be constant. This constant was determined by calibrating it using boundary layer flow. The calibration was done so that recovery of the famous coefficient Cmu=0.09 in the inertial sublayer was attained. So in a way the Low Reynolds number region is taken into account in the Realizable model. The slight deviation that Fluent made was that they used a number slightly more than A=4.0 as was used by Shih. This constant of course depends on the type of flow used for calibration. May be in your problem this constant should be something else.

The validation flow models used were: (1) rotating homogeneous shear flow (2) boundary-free shear flows (planar and round jet)(3) channel flow and boundary layers with and without pressure gradients (4) the famous backward-facing step flow. These details are given in the Computers & Fluids journal Vol. 24, No.3, pp227-238, 1995. You probably have the paper any way, but someone else may wan to read it.

I think the model is capable of handling Low Re flows provided Fluent did the implementation correctly.

I hope we get a comment from our friends at Fluent.

I don't think that this model is a Low-Re model that can be solved through the viscous sublayer down to the wall. I even remember discussing this with Shih at a workshop in 1995. I specifically asked him about low-Re extensions of his new range of Realizable models and he didn't mention this model then. Also note that the rapid-distortion theory that Shih used to derive the stress-strain relationship and the Cmu depenency on k and epsilon is not valid close to the wall.

The fact that Fluent does not mention this model as a Low-Re model in the manual also indicates that you need some kind of additional low-Re treatment. Anyway, it doesn't matter, since the model in Fluent is used together with other types of wall-treatment, for example the Wolfstein two-layer model, which does not have a varibale Cmu.

Btw, there is also an interesting non-linear extension of Shih's model that I'd really like to see implemented in Fluent, but that is another story.

Could you post the reference to this new non-linear model?

Thanks

I'm not sure about the latest reference... I haven't followed this lately. The best reference I have is Shih's chapter in "Turbulence and Transition Modelling", ERCOFTAC Serios, Kluwer Academic Publishers, 1995. If you want the latest things Shih can surely help you - he is at NASA Glenn (formerly Lewis) and you can find his email there.