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mahesh prakash September 1, 1999 05:51

a low Re number model for impinging jets
Dear John ,

I address this question to you because, you had posted a reply to one of the queries in the forum stating that "There are low Re k-e turbulence models fine tuned for different types of flows". I agree with you whole heartedly. I have been working on impinging jet flows for some time now and have not come across any low Reynolds number model which suits such type of flows. All the low Reynolds number models seem to overpredict turbulence levels at the stagnation point. Is there any low Re (k-e) turbulence model which is fine tuned for such flows?.

I am interested in using only a k-e model because I have got several other complications in my system to contend with.

Thanks in advance (P.S. : Any other reader is welcome to reply to this query!!!)



Dr. Hrvoje Jasak September 1, 1999 07:29

Re: a low Re number model for impinging jets

I can only give you some advice coming from high-Re modelling, but if you're corageous enough, you can just extend the argument to low-Re (after all, it's got nothing to do will wall functions). Most k-e models have problems with impingement (k is too high), but two of them fare better than the rest. My first choice would be the RNG model (if you can find the appropriate low-Re extension). The second posisbility is the Kato-Launder model, where the generation term in the k-equation contains the product of the rate-of-strain and vorticity tensors, thus switching off the generation at the impingement point. Now, I know that you can do a two-liner to prove that this model is fundamentally wrong (talk to Launder, not to me) BUT a) it has the desired effect and does not mess up the rest of the flow and b) it is easily extendible to low-Re (you just fiddle the generation term).

Jonas Larsson September 1, 1999 08:17

Re: a low Re number model for impinging jets
Just a note about using the Kato-Launder modification in stagnation flows. My experience, which is mainly limited to turbine blade heat-tranfer simulations, is that the Kato-Launder modification does remove the excessive production of k as desired. However, if you have a high free-stream turbulence level the Kato-Launder model does not give the correct response at all - it does not predict the increase in for example heat transfer. Results obtained with the Kato-Launder fix are close to "laminar free-stream" results, which isn't really surprising since what Kato-Launder does is essentially to turn of the turbulence model in irrotational flows.

I've found that different variants of Shih-Lumley's non-linear realizable stress-strain relation works much better, especially if used in a k-omega framework.

Jonas Larsson September 1, 1999 08:26

Re: a low Re number model for impinging jets
There are a few different low-Re k-epsilon models coming from UMIST which are tuned to stagnation flows - I think one of the cases used to tune the constants is an impingement case. These models are very complex though and my experience from them is not very good - difficult to implement and sometimes gives strange results on for example convex walls. But don't judge too much from my experience here - I've only run one or two cases with one variant (a 3-equation cubic k-epsilon model presented in Suga's PhD thesis).

Look for papers by Craft, Suga, Launder and others for more details.

John C. Chien September 1, 1999 22:23

Re: a low Re number model for impinging jets
(1). Sorry to delay answering your questions, because as you see some people seem to love dancing so I have to take care of them first. (2). First of all, you will have to verify the results of using a particular model yourself. (3). This is important, because there are differences in the solution method used. A general statement may not be applicable to your case. (4). Back to the basic issue of turbulence modeling, it is nothing but the calculation of the variable scaling factor. The scaling factor can be applied at different locations, for example, at the cmu level, at the extra term in the epsilon equation level, or at the length scale variable level. (5). Since this problem has been studied by some researchers, one simple thing you can do is: make the cmu as a function of the velocity gradient near the stagnation point region. This is a general guideline, and it has been used for the round jet modeling. It is a very simple idea to adjust the cmu value to change the flow field. Changing the cmu will change the eddy viscosity. And the prediction of the eddy viscosity is the central issue of the turbulence modeling. If you know the eddy viscosity distribution, there is no need to calculate the TKE and TKE dissipation at all. But don't ask me how, because it is you who are interested in solving the problem. (6). If you don't like this approach, you can always try adding or deleting terms, or modifing the equations.

Paulo Zandonade September 2, 1999 00:43

Re: a low Re number model for impinging jets
Just as a note on the post by Jonas. You can find information on the Lien et al. and Suga models at Professor Lien's homepage at:

At UMIST I think the page you will be most interested in is Dr. David Apsley's at:

especially the turbulence modelling page.

I would also look up the following paper:

Craft, T.J, Graham, L.W. and Lander, B.E., "Impinging jet studies for turbulence model assessment. Part 2: An examination of the performance of four turbulence models," Int. J. Heat Mass Transfer 36, p. 2685.

mahesh prakash September 2, 1999 05:01

Re: a low Re number model for impinging jets
Dear Dr. Hrvoje,

Could you please give me the reference for the Kato and Lanuder model?


mahesh prakash September 2, 1999 05:02

Re: a low Re number model for impinging jets
Thanks for all the replies provided so far!!!


Jonas Larsson September 2, 1999 05:12

Re: a low Re number model for impinging jets
I'm not Dr. Hrvoje, but I can give you the reference:

M. Kato and B.E. Launder, "The modeling of turbulent flow around stationary and vibrating square cylinders" in Proc. 9th Symposium on Turblent Shear Flows Kyoto, pp 10.4.1-10.4.6, August 1993

You really don't need the reference to test this model. As Hrvoje said it is a very simple modification of the production term in the k equation - just replace the square of the strain with a product of stain and vorticity. There are equations describing this in the papers available from my homepage (see for example the Antwerpen paper).

Dr. Hrvoje Jasak September 2, 1999 06:11

Re: a low Re number model for impinging jets
Hi guys,

Now that we have "answered" the original question, maybe I can hijack your attention towards the non-linear k-e models. I have implemented a whole bunch (quadratic model by Shih, cubic model by Lien, similar to Suga's model, quadratic model by Speziale), either with wall functions or with a low-Re treatment. Judging on this experience, I think they are a waste of time and certainly inferior to a decent RSTM closure. The thing that bothers me is that sometimes they show a sign of doing the right thing (bigger secondary vortex on a backward-facing step, secondary flow pattern in square ducts and similar). It seems they are on the right track, but nowhere near the right magnitude of phenomena. BUT, when things go wrong, you get absolute rubbish: recirculation zones become huge, turbulence quantities go haywire (like huge epsilons at lee-slope detachment points), the solution changes like crazy when you change a differencing scheme or mesh resolution (and I'm latking about 100k cells in 2-D!), they flap about and generally cause trouble! Comments? Did anyone try a round jet, or maybe a swirling jet with some of this stuff?

Jonas Larsson September 3, 1999 08:03

Re: a low Re number model for impinging jets
Sure, I've seen bad results with non-linear models, but I've also seen very bad results with standard linear models... For example, you often see turbulence levels explode with standard models if you have regions with large normal strain. If you run external aerodynamic simulations this often results in rising total pressure and incorrect pressure drag and all kinds of problems with things that should be easy to predict.

You mention the quadratic Shih-Lumley model. I haven't used this model exactly. However, I've used a variant that has the same basic stress-strain relation but is based on k-omega instead. I've found this model to be realtively stable - I rarely see this kind of exploding k-regions or huge length scales that you often see with linear models. However, I don't think that the non-linear part is the key to improved stability here. I think that it is the variable Cmu which is improving things - Fluent has the same variable Cmu in their "realizable model", which I also have quite good experience from. In the sentences above I don't mean "numercial stability" with the word "stability", rather "model stability/correctness".

A general observation that I've made is also than k-omega is more stable than k-epsilon (not numerically but model model-wise).

The more complex cubic models from UMIST have, as I said previously, sometimes given me very strange results.

I'd also be very interested in hearing some experience from others on this subject - very few people talk about these problems. Instead your run 10 different models and find one which works well in one case and present that in a paper... I guess we all do the same now and then.

Jonas Larsson September 3, 1999 08:05

Re: a low Re number model for impinging jets
I forgot to ask, what kind of problems did you experience with the Shih type of quadratic model?

John C. Chien September 3, 1999 13:15

Re: a low Re number model for impinging jets
(1). Back in early 80's, I had work on a project to delvelop Navier-Stokes solutions with the standard k-epsilon model and my modification to it for the confined swirl jet flow in a dump combustor with slope wall. The modified model and the results agree well with published data. (2). I think, the standard k-epsilon model is a good platform for modification and extension. It is well-known that a set of universal model constants do not exist. And the modified model can be easily developed for the round jet as well. Modeling is just like an experienced Italian dress maker, it is not mass produced only with s,m,L, and xL sizes. This is something one can not stored it in a code.

John C. Chien September 3, 1999 13:29

Re: a low Re number model for impinging jets
(1). Yes, very few people talk about these problems in turbulence modeling. (2). The turbulence modeling community is small. They tend to be in the upper end of the research. It normally takes 5 to 10 years after the PHD to gain some feeling about the turbulence modeling. (3). What you are saying is true. I think, it is not because K-omega is better, but it is because k-epsilon has something important missing. (4). Turbulence modeling is the only key to the future success of CFD.

Md. Ziaul Islam September 3, 1999 16:40

Re: a low Re number model for impinging jets
I have heard of the public-domain hydrodynamic KIVA codes developed by University of Wisconsin, Madison and Los Alamos National Laboratories to solve hydrodynamics problems. This is a good software for this kind of problem solutions.

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