K-epsilon vs. k-omega turbulence modelling
 

Hello,

I am currently working on a heat transfer model involving strong vortical cooling effects in the pressure based solver. To reduce computational expense, the turbulence models of choice are the realisable k-epsilon and SST k-omega two equation models, with the aim to fully resolve the boundary layer with a suitably defined fine mesh density.

These two models have returned sizeable numerical differences. I am trying to understand why this could be. Could anyone give any information regarding these turbulence models for this particular case?

Cheers

Tom

The SST k-omega model reduces to a standard k-epsilon model away from walls.

Near walls, the SST k-omega uses the the omega formulation whereas the realizable k-epsilon uses the epsilon formulation.

The two models differ in their approach both near walls and away from walls.

The SST k-omega model is generally thought to be better near walls, but because it reduces to the standard k-epsilon model away from walls and not the realizable k-epsilon model, it also has weaknesses.

The two models are very different and it should be no surprise that significant differences in results can be obtained from each model (this should be considered the norm rather than unusual).

Thank you for your input.

You have alerted me to one point regarding the turbulence models I have used; that being the SST k-omega model which has a blending function to reduce the model to the standard k-epsilon model.

I overlooked this feature, and was expecting that the solutions provided would support the application of the SST k-omega model, given its suggested superiority in the near wall flow regions.

It would be good to gauge what turbulence models other users of Fluent have adopted to capture steady state heat transfer, particularly when flow characteristics such as separation, reattachment, and recirculation have a strong presence.

Hi,
I have used SST k-omega model, Realizable and RNG k-epsilon models for a similar problem involving heat transfer in a duct (internal flow) with a lot separation, reattachment and re-circulations at near-wall regions. Significant differences in wall temperatures are seen between the turbulence models.
Unfortunately very high temperatures are obtained with the usage of SST k-omega model compared to the k-epsilon models, which has resulted in bad-comparison with the results from the literature. This finding is contrary to other numerical simulation papers. The re-circulation size in case of SST k-omega model is also very different from the k-epsilon models.
y+ less than 1 was maintained for all the cases.

The reason for high temperatures with the usage of SST k-omega model evades me. Please let me know of your suggestions, as to what can be wrong.

Regards
Avinash

Hi,
did you find the reason for the wrong behavior of the SST?
I recognized the same behavior when applying the SST in separated flows (although in OpenFoam) getting to high wall temperatures and a significant underestimation of the Nusselt number respectively.

Regards,
Pascal

I have the very same issue, I compared the two models k-eps (real)and k-w SST on the same mesh .

1. Nu is poor (k-w SST ) ||| good ( k-epsilon (real) )
2. Friction excellent (k-w SST ) ||| poor ( k-epsilon (real) )

I understand why everyone would like to compare Nu and f for two models, because it feels like a low hanging fruit.

For separated flows, k-epsilon and k-w SST models can and generally do give wildly different results. Don't just compare Nu and f. To appreciate the difference, just compare the separation patterns of the two models. Generally, k-epsilon predicts a much weaker separation than k-w model. In some cases, k-epsilon predicts no separation and k-w model predicts a VERY large separation bubble.

Flow separation is considered by many (to be a primary flow pattern, as opposed to secondary flow). When your simulation is missing something as important as a separation (or contains a separation bubble when it shouldn't), then it should be no surprised to anyone that it also predicts the wrong Nu and f.

Dear Lucky,

Thank you for your kind remarks. You are right that separation is well captured in case of k-w SST but my geometry is a bit complicated. Its a pipe with grooves in its thickness. Those grooves are helically extruded into the pipe thickness. I have modelled 1/10 th of geometry with periodic conditions side wise. There are total 10 grooves.
Since I was getting a lot of difference from experiment in case of k omega at high Re. I checked the model constants, I modified the Energy Prandtl number and Wall Prandtl number from 0.85 to 0.35 and got my results very close to experiment. It seemed logical to me because its the wall Pr number that controls the thermal boundary layer.

So decreasing this value will not increase the wall temperature much which should be logical because at high Re the flow conduction time is not much as compared to the flow velocity and so the fluid is not well heated and the delta T , the conduction temp and the bulk temp diff should be less.
Therefore, h will be more and hence the Nu will be higher. I hope you will agree with me.

Dear Lucky,

I can check the separation but the issue is that the geometry is not consistent in axial direction (z drn) all the way long. cutting a plane at a particular location may/may not give true separation region.

I agree that if you change some model constants that shouldn't be changed, that it can can an effect on the results. Yes.

Yet again there is no surprise that you can change the turbulent Prandtl number and force Nu to make your experimental result. Remember von Neumann's infamous statement.

With four parameters I can fit an elephant, and with five I can make him wiggle his trunk.

Interestingly, you set the turbulent Prandtl number to ~0.3 when many experiments suggest that typical turbulent Prandtl number in ribbed/grooved pipe flow is closer to 0.9. You can tune any number of parameters to get a desired surface result but they are all meaningless from a CFD perspective unless you consider, verify, and validate the entire flowfield result. I can also tune a random number generator to give me any desired number.

A lot of people also tend to miss a very important problem. The fact that there is a turbulent Prandtl number. There is also a closure problem on the energy equation (just like the momentum equation) that needs additional models. If you dig into it, you'll realize how little development has been done on the closure model for the energy equation. I.e. what models can you use to predict the correct local turbulent Prandtl number, the same way we try to predict the local eddy viscosity. For ribbed flows, the work at ITLR Stuttgart comes to mind with rather impressive results. At the end of the day, why is anyone surprised that you predict the wrong heat transfer when there is this magical missing model to close the energy equations in the first place?

thanks Tran

Could you please give me the reference for turbulent Pr of 0.9 for ribbed flows? I am now worried a lot because my supervisor has asked me to publish a paper and now I do not have results matching with experiment (with 0.85 Pr) , in some cases kepsilon is good. But how do I justify because globally k-epsilon is not recommended for such flows. [:(]

Hi, I am assuming you are working with air.

The laminar or molecular Prandtl number for air is 0.7.

If turbulence enhances heat transport (via turbulent fluctuations) then how can the turbulent Prandtl number be less than 0.7? Although this argument is not perfect (it assumes Boussinesq hypothesis roughly holds), any turbulent Prandtl number less than 0.7 is non-physical. Even where the Boussinesq hypothesis does not hold exactly, everyone can appreciate that advection does not decrease the total rate of heat transfer to below that of pure conduction. The exception is the extremely rare case when the velocity fluctuations are perfectly out of phase with the turbulent fluctuations (which generally occurs only if there is a forcing function).

Hi there,

1. No, I am working with water and solid material is Stainless Steel. It seems a bit harder to absorb your point of advection that it does not decrease the total rate of heat transfer to below pure conduction. Do you mean that the ratio of Pr is related to adv/cond, and you may be referring to that?

2. Could you please provide reference for your statement, that
"many experiments suggest that typical turbulent Prandtl number in ribbed/grooved pipe flow is closer to 0.9."