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July 20, 2009, 12:51 
assymetric solution: why?

#1 
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Franz Roman
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Hi all,
I am running some 3D simulations with a perfectly symmetric geometry, grid and boundary conditions. However I get most of the time an asymmetric solution. My geometry includes a sudden expansion or a diffuser in its instead. I have read in several threads already that asymmetric solutions in completely symmetric problems occur frequently, even that this is how it physically happens, and apparently important examples are sudden expansions and difussers. However, it seems that in reality this is caused by very small perturbations of the flow, like a small scratch on one wall or something. But is the asymmetry also possible when the physical system is absolutely 100% symmetric, down to the last scratch or without any at all? Can somebody explain me how this is so? When I run the same simulation several times, I get the asymmetry always to the same side. If in the physical system such asymmetries occur, should it not be 50% to one side and 50% to the other? I mean, I just dont get it. I was thinking of just simulating one half of the geometry and use the symmetry BC on the symmetry plane. That way I can avoid the asimmetry, but it feels like cheating somehow. Can the asymmetry have something to do with the order in which the grid elements are taken to solve the equations? Causing an accumulation of numerical error to one side? Please tell me if I am talking bullshit here, I am no expert. And please someone explain me how assymetry can occur in reality for a perfectly symmetric system. Thanks a lot Franz 

July 21, 2009, 02:35 

#2 
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Shyam
Join Date: Apr 2009
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Hi,
Yes. Perfectly symmetric problem definitions can produce asymmetric solutions. In experiments, as you mentioned, the roughness of the walls, the initialization of the flow etc. can affect the bias of the solution towards one side or other. The asymmetric nature of the flow can be a resultant of the shock interactions with the flow causing it to choke or create more mixing/turbulence, or two or more interacting vortices. Formation of the Lambda shock in a converging diverging nozzle is one such example. Now coming to the numerics, a perfectly symmetric problem (with symmetric grid) should theoretically give a symmetric solution. But, again, even the smallest disturbance might result in the solution to shift towards asymmetric condition. This can be seen in the flow past a circular cylinder. Many times, an external perturbation is used to start the vortex shedding, which might not ever occur otherwise. In case of strong shocks, due to the high density/pressure gradients involved, even the smallest of the error, such as the precision of representation of grid points (0.9999999 instead of 1 etc.) would influence the solution. Even the direction of the solver sweeps might affect the solution. Most of the time, these errors are suppressed by the numerical dissipation that tends to make the solution symmetric and smooth. But, this is not necessary in all the cases. It is thus not advisable for one to solve the problem with symmetry BC for those problems that are known to have asymmetric results. In such cases, that flow physics might not be fully represented. Hope it helps, Shyam 

July 21, 2009, 05:15 

#3 
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Franz Roman
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Hi Shyam,
thanks for your reply. A question though: You said: "Now coming to the numerics, a perfectly symmetric problem (with symmetric grid) should theoretically give a symmetric solution" and "Even the direction of the solver sweeps might affect the solution". So, if this was the cause of the asymmetry, if the asymmetric result is a numerical issue and not physical, wouldnt using the symmetry BC help instead of damaging? If not, what could you recommend? is unsteady simulation an option? I just read in a thread that maybe depending on the ratio of entrance area to expansion area (in the case of a sudden expansion) the solution can be symmetric or asymmetric. In any case, if in reality (assuming an idealized perfectly symmetric problem) the flow should be symmetric, then that is what I would like to get. What I am looking for is testing different geometries to find the one with the most uniform flow distribution, in the case of a simple food dryer. So for me a symmetric solution would be nice, if it is possible. Thanks a lot Franz 

July 21, 2009, 06:12 

#4 
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Rami BenZvi
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If you wish to have a symmetric solution, of course using symmetry and solving only the symmetric portion of the domain will rule out the asymmetric solution.
If  on the other hand  you suspect that asymmetry is physical and you wish to retain this as possible numerical solution, then solve for the full domain without symmetry BC. Similar argument holds for the time dependence. If you are sure that a steady state is feasible and you are only interested in that steady solution, you may drop the transient term. However, if you suspect that there is no steady state or if you wish to see transient effects  then you should solve the nonsteady problem. 

July 21, 2009, 06:15 

#5 
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Shyam
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Yes, it is true that some expansion ratios in certain nozzle shapes might result in asymmetric solution. Even such cases would be symmetric if there is absolutely no disturbance. If the flow is inherently stable, any disturbance to the solution would be convected downstream and the flow would revert back to the symmetric profile. But, if the flow (that is originally symmetric) is very unstable, especially when it gets chocked by a shock, even a slight disturbance might topple the flow and it can become asymmetric. In reality, no perfectly symmetric conditions can exist as there would be some minute disturbances in space. So, for cases where the flow has a stable asymmetric solution, one would not be able to find an experimental result that has a symmetric profile. The disturbances would spoil that fun!
For numerical solutions, as I mentioned before, the truncation and approximation errors would result as disturbances in the flow. In many cases these might be enough to kick the flow from a symmetric profile to asymmetric one. Since this would be closer in comparison with the actual flow, I would suggest that you take these asymmetric results as it is. When you apply symmetric BCs, you force the solution to be symmetric and end up solving a different problem. You can do a grid refinement test to check if the flow structures are reproduced correctly. In the case of planar nozzle flow, the asymmetry can be biased to either side. In that situation, you may mirror the results to have a consistent comparison. The refinement study is one of the best method to identify numerical errors in the solution. 

July 21, 2009, 15:22 

#6 
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Franz Roman
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Hi,
thanks for the answers. I have realized that pretty much all the simulations I run will have an asymmetrical solution if let to run until the residues go horizontal. For one I had obtained a nice symmetric solution when the residues got to 1e6. Then I let it run several thousand iterations more, and the residues ultimately went horizontal, a little short of 1e7. The solution then was asymmetric. BUT: a little after reaching 1e6 (when I initially had taken the solution to be good enough) theres is an inflection in the residues´curves and they start to increase slowly and for a long time, to later slowly start to drop again and go horizontal. It is during this weird inflection of the residues that the solution starts to get asymmetric. Can someone explain in case this observation is correct? I have not so much problem with moderately asymmetric solutions, but in one case (a diffuser instead of a sudden expansion), again with a symmetric everything, the flow attaches itself strongly to one side of the diffuser, giving a strongly asymmetric solution. I certainly wish the physical world were more symmetric. More help and comments are extremely welcome , Thanks 

July 26, 2009, 01:57 

#7  
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fateme chegini
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Quote:
One of my friends had a similiar problem when simulating an estuary. He found out that the direction of the solver sweeps affect the solution and gives assymetric results. So what he did was this: He sweeped half of the in xy direction and the other half in yx direction and he got symetric results. Although this isn't a fundamental solution but at least it proves that the assymetric results were due to numerical errors. Another solution is to sweep in both directions and calculate the mean, but this would consume too much time. So what should we do in these circumstanses? Any Idea? 

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