Understanding the cyclic boundary condition
 

Dear foamers,

I need to solve problems with cyclic BCs 'all around the place'. To be clearer, this is the geometry I am considering:
https://www.dropbox.com/s/amuzikceam...nder_array.png

On this screenshot, the colouring is the velocity (U) magnitude, U being obtained using the simpleFoam solver and a uniform inlet BC on the x = 0 face. What I want to do is simply simulate the flow in the (6,4) cell using periodic boundary conditions:
https://www.dropbox.com/s/v5nz4mvx6user06/6-4_cell.png

Firstly, let's have a look at what we want to reproduce. Here are the velocity magnitude and orientation in the (6,4) cell (let's call this the reference problem):
https://www.dropbox.com/s/8eivt2e1ai...eference_U.png
This velocity field seems periodic. If we subtract a periodic field from this one, we should get another periodic field, maybe better as an evidence. So we do that and plot the so-called deviation field, UTilde, obtained by subtracting the volume average of U (which is constant over the cell) from U:

UTilde = U - UAverage

Here is what we get:
https://www.dropbox.com/s/8gnccd1pzy...nce_UTilde.png
This deviation field is periodic 'x-wise' and 'y-wise'.

I tried to simulate the flow in the (6,4) cell using the simpleFoam solver (though if might not be the best, AFAIK; anyway, this is not the worst problem here). I therefore simply applied cyclic patches at the boundaries of the cell. Although this insufficiently constraints the problem, the SIMPLE algorithm converges to a solution which only depends on the initial condition, yielding the following velocity field:
https://www.dropbox.com/s/rufn5k53mf...periodic_U.png

Given that image, we can doubt that this field is periodic. The deviation field gives a clearer proof:
https://www.dropbox.com/s/nf81rnnj4h...dic_UTilde.png
UTilde is not periodic, while it should be.

So here is my question: Is there any reason why the periodic BC wouldn't be satisfied in the cyclic problem? Did I do something wrong?

The associated OpenFOAM cases come attached. Screenshot gallery:
https://www.dropbox.com/sh/hmq2qx6jcvjc6lx/LFKCB1X32b

Update
 

I ran an additional simulation with a correctly constrained problem, replacing the inlet and outlet cyclic patches with regular inlet and outlet patches.

Inlet: zeroGradient pressure, fixedValue uniform velocity
Outlet: fixedValue uniform pressure, zeroGradient velocity
https://www.dropbox.com/s/38s9ap0ev5...periodic_U.png

The 'y-wise' periodicity is not satisfied either.

hi,

something in cyclic patch in your original case is wrong.
checkMesh shows some error.

Using createPatch fixed this problem.
a modified case with createPatchDict and modified Allrun is here,
Attachment 28671

Periodic fields is obtained with this case. tested with OF222.

Problem solved
 

Thank you very much! It seems like patch orientation is much more of a big deal than I expected.

Dear foamers,

I have an additional question about the cyclic boundary condition: what does it actually do? Does it ensure equality of fields and derivatives at the associated boundaries? Or does it only ensure equality of fields?

Hi, I was also searching for some doc which contains the details of the cyclic bc but unfortunately there isn't enough. Did you get the answer to this? If so are you willing to share your understanding here?

That is a simple idea. It recycle the quantity between two patches or planes! What is complex with the b.L.

Thanks for responding to my concern. Can you please elaborate with an example if possible?

yes, sure. For example the velocity on the outlet will be exactly mapped to the inlet. In other word, the length of the domain will be assumed infinity. You can see the channel395 tutorial for more details.

Yaa I understood that in cyclic boundary condition the patches have same physical behavior but specifically for this channel 395 case why do we need cyclic bc and why not some other kind of boundary condition?

Because you do not have entrance length in the channel. you want to have fully developed flow inside the channel. As I said before, you making the length infinity when you use cyclic bc.