[challenger85]

Good Morning

I would like to ask some questions about a air-water two-phase flow problem which I have to treat for a dimploma thesis.

For a short description: the task is about the simulation of the flow in a test rig of a fuel rod bundle in a nuclear power plant with rectangular rod array. For the simulations, a quarter section of one subchannel is used, means it contains a quarter rod as a wall and four straight planes as symmetry boundary conditions.

Several simulatinos was carried out so far. The approach is a RANS simulation with a two fluid model. For turbulence, a Reynolds Stress Transport Model is used (this was found to be necessary for a flow containing many walls). We started to investigate the infulence of the different non-drag forces for our case. For this purpose, we set a low void fraction of 0.05 (air volume fraction of course), to simulate a dispersed bubbly flow. You can imagine, that the non wall forces are quite important for this case. The results without any non-drag forces and only lift force activated caused no problems (at least in the simulation point of view). Now, to avoid a steep void fraction concentration in the near wall regions, we tried to activate Franks Wall Lubrication force. Now, the solution divereges away just after a few iterations.

For a better understanding: The following models were used for the forces:

- Schiller Naumann Drag (this will be changed to Grace Drag model, which
was said to be better for air-water two phase flow)
- Tomiyama Lift force
- Frank Wall lubrication force

The initial bubble diameter was choosen 2.5mm

I looked for this force in the ANSYS CFX manual, because I somehow expected problems of this nature for this flow. My question is now:

- What is the correct way to avoid these convergence problems?

My problem is, that I have almost no experience on this type of simulation at all. Now, three parameter can be chosen for the Frank wall lubrication model. For the first run, the default values for these coefficient were used. Do you have some experience on this issue? Do you think, that just the wall lubrication force is the reason for this behavior, or is it possible, that there are other effects, which are just amplified by activating the wall lubrication force?

Do you need any further information on the problem itself?

[ghorrocks]

For turbulence, a Reynolds Stress Transport Model is used (this was found to be necessary for a flow containing many walls).

Sounds like you are kidding yourself here. The RSM model is MUCH harder to converge than k-e or SST. RSM is really of use when you have a rotating flow or something to generate anisotropic turbulence. And even if you do have anisotropic turbulence then the massive simplifications inherent in multiphase turbulence modelling make the simplification of assuming isotropic turbulence seem minor in comparison.

Also the "number of walls" is no impediment to a 2-equation model.

And finally RSM models are of dubious benefit in multiphase models. Don't kid yourself that the extra equation gives you any extra accuracy over a normal 2-equation model.

Can you explain why you think you need RSM? I think you will find things much easier and probably more accurate if you go to a k-e or SST turbulence model.

[challenger85]

Thanks first for the reply.

For the turbulence choice, I have to cite two articles out of the Nuclear Engineering and Design journal, namely:

Technical note on turbulence models for rod bundle flow computations, Gabor Hazi, Annals of Nuclear Energy 32 (2005)

and

CFD analysis of flow field in a triangular rod bundle, S. Toth, A Aszodi, Nuclear Engineering and Design 2008

You have to know first about the geometry and flow specification of rod bundles I think. Measurements on this topics has shown, that near the rods, swirling secondary flow motions are likely to arise, which could be responsible for mixing processes inside such a bundle (one is not certain about this topic up to now). Mixing processes are a key issue of fuel rod bundle flows. Now, Toth and Aszodi mentioned in their paper, that "the k-epsilon and the SST models could not predict the secondary flow, whereas the Reynolds stress models were able to calculate them.". This has also a reason, which was treated by Hazi: about these circulating motions near the rod wall, he wrote: "There is no sign of such circulation using the k-epsilon model. The question arises: Why does the computation using the k-epsilon model fail to predict this phenomenon?". Furthermore, he mentioned the following: "Based on (this) hypothesis, secondary flow develops in channels when the normal Reynolds stresses are anisotropic and there is a strong gradient in the lateral mean velocity due to, e.g., wall effects. Since measurements show that both criteria are satisfied in case of rod bundles, consequently a suitable turbulence model should respect these observations". Furthermore, he stated that: "... Indeed, this model (means the standard k-epsilon) is based on the turbulent-viscosity hypothesis..."
I will not repeat the equations here. So, furthermore:
"The introduction of this term (in the equation for the Reynolds stresses using the turbulent-viscosity hypothesis) implies an isotropic assumption for the normal stresses and accordingly, this model should not be applied for the problem in question."
Of course, also the SST Model will fail, because it is finally based on the same hypothesis.
Also previous simulation I did showed this fact.


My explanations about the "many walls" was not that accurat. But, i thought that this will support people which did not need a correct physical and geometric background, but had the same problems as I have right now.

Therefore: I need convergence for this problem, with the BSL (or any other Reynolds stress transport model) Reynold stress model and activated Wall Lubrication Force by Frank.

OK, briefly, these are the reasons why I think I have to choose a Reynolds stress transport model.

Thanks again for the answer

Best regards
Torsten Betschart

P.S.: I am not that good in english language, therefore you have to apologize my question... You said, that

Sounds like you are kidding yourself here.

Did you mean that I am brainless or fatuitous? Or have you been just amused by the "strange" setup or the choice of the Turbulence Model? Or Did you mean that I just (by mistake then of course) assumed, that the solution of the additional Reynolds stress Tensor equations will improve my results just by the fact that some additional equations will give more dedicated results (which is, by the special case of the flow here, finally the case)? I personally think, you meant the last one... I really just ask about that.

[ghorrocks]

Thanks for the additional detail. I am no expert in nuclear modelling but am I correct in saying both the references you cite are for single phase flows? Yes, in single phase flows RSM models will capture flow features 2-eqn models cannot.

But in turbulence modelling in multiphase flows there are far more significant influences on turbulence in the multiple phases compared to whether you use a RSM or 2-eqn model.

So I still think you are making things hard for yourself by using RSM models in a multiphase flow. I will be very surprised if the RSM gives you a more accurate result than a 2-eqn model, and certainly the additional difficulty in convergence of a RSM model will cause problems.

Did you mean that I am brainless or fatuitous?

Neither - I just wanted to do a bit of a stir to see if you could justify your choice of turbulence model. A lot of people just use the RSM model because it is "the best one" and really have no idea of where it is useful and where it is not.

[challenger85]

Hmm. It is true, that these papers are for single phase flows. The problem (at least I found that) is, that there were not many simulations carried out on these fuel rod bundle using two phase flow, and therefore literature is sparse. But you made a very important point to me.
I will check other sources in literature (or at least search for some more, what will be not that easy). And parallel, one could run a simulation similar to the described by using a 2eqn turbulence model.
Which of these two do you think would be the better choice here, the SST k-omega turbulence model by menter or the k-epsilon model?

Thanks a lot for your explanations and your help.

This was fast. I tried to set up a simulation using the SST model. The problem is now, that the simulation divereged away after approximately the same number of iterations. Therefore, the problem should be found in the wall lubrication force model more than in the turbulence model. Do you have any idea? Could the grid resolution have an influence on the behavior of the simulation?

Best regards

[ghorrocks]

To resolve the convergence issue I would start with a simple single phase flow and hopefully that should be easy to converge. Then, using the previous simulation as an initial condition add the physics one bit at a time. First add the multiphase, then in the next simulation the wall lubrication then the lift force. Finally, if everything is behaving itself then add the RSM turbulence model and see if that improves accuracy.

I would definitely add the RSM model last as it is going to be hard to converge and you need everything else sorted before it even has a hope of converging.