Hi guys,

I am working on on a transonic turbulent channel flow. The simulation is 3D and fully unsteady. The symmetrical domain consists of one non-slip floor, two sidewalls and one upper wall. My professor wants to know the difference on the flowfield if we use periodic BC and slip BC for the sidewalls respectively. All other settings are identical for the two simulations. We also want to explore some difference in acoustic characteristics.

I think mathematically we are just solving N-S equation using two similar kinds of boundary settings. It's hard for me to find the difference in instant flow field. And for a time-average domain, they should be the same. I even wonder if this topic is really meaningful. Any opinion?

BTW, is the slip wall BC exactly the same with symmetry BC?

Thank you very much.

Bearcat

Your professor is rightly curious about the difference between periodic and slip conditions. Those are completely different conditions, mathematically and physically, but they can give you the same result, under certain flow conditions (a zero gradient normal to the boundary, for example, can be consistent with both symmetry and periodicity).

I can't comment on the implementation of your slip condition, but typically it's equivalent to a symmetry condition. They are not the same as a periodicity condition!.

Actually my professor is interested in the acoustic difference for these two BC. She thought the pressure wave reflection from the sidewall may be different under these two BC.

You would expect so.

Mathematically, both are same.

Periodic BC, e.g. dv/dx = 0 on the wall. This will give v(n) = v(n-1); where n is the grid number at the wall.

Slip BC is put in the form: v(n) = v(n-1) at the wall.

Both are same from my point of view.

Wrong. A periodic boundary condition enforces "periodicity" over the domain, not "symmetry". Periodicity means that the flow variables at one boundary are transferred to the variables at the corresponding point on the opposing boundary, for example if you have a "left-hand" boundary at j=1 and a "right-hand" boundary at j=jmax, then the periodicity conditions says v(1) = v(jmax), for scalar quantities (vectors may have to be rotated in the case of rotational periodicity).

Let's keep these terms straight: Periodicity/Symmetry/Slip are three concepts. The latter two are usually identical (inviscid wall). The first one is completely different.

Hi,

it's not a channel flow problem but I have performed subsonic LES of cavity located within a channel with either periodic or slip lateral BC. Results were quite different, even looking at the time-averaged flowfields: with periodicity, the flow was almost homogeneous in the spanwise direction (only small perturbations of short wavelength) whereas with slip BC there was a strong asymmetry due to a bifurcation (see http://journals.cambridge.org/action...22112006004502 if you're interested in details)

I do not expect such a dramatic alteration for a "simple" channel flow because there is no separated region in it but if acoustic waves are at play, lateral BC surely matters.

Regards,

Lionel

Thank you for your paper, Lionel. Actually my simulation is close to your application with a groove on the channel floor.

For your case, I think a symmetry time-averaged flow field should be the theoretical result from symmetrical BC. But it's quite unstable. And asymmetry is easily excited due to the computation error and order.

I came to an idea that both slip and periodic sidewall are kind of constraints on the flow field. Slip sidewall set the span-wise velocity to zero and periodic BC set all three velocity components on one sidewall identical to the other sidewall. In the perspective of velocity vectors attached to grid points, periodic BC is losing more degrees of freedom or adding more constraints to the flow field. So cavity flow with periodic sidewall will have a lower sound pressure level(SPL) than the slip sidewall case.