Chequerboard oscillations

[Gareth Gretton]

Hello,
I've been working on "2D" airfoil simulations in Code_Saturne for a while now and I have unfortunately now realised that I'm getting chequerboard oscillations (at least in one direction) along the wall. This is quite a long post, but hopefully it will provide anyone reading with all of the information required to appreciate what’s going on.
 
A few relevant details are as follows:
Profile: NACA 6 series
Alpha: 0 deg
Re: 3e6
Grid: 284 x 90 cells C-grid, with 98 cells on each of the top and bottom surfaces, and Delta y_1^+ ~ 0.5 (more on this later).
Turbulence model: k-omega SST
 
Attached to this post are a number of graphs:
geometry.pdf - this shows the geometry of the 'top' i.e. suction side of the airfoil
cp.pdf - this shows the pressure coefficient with oscillations visible but not dominant
cf_Vinf.pdf - this shows the friction coefficient (but note that the velocity used to non-dimensionize is the free-stream velocity rather than the boundary layer 'edge' velocity). Oscillations are dominant.
UVW.pdf - this shows the velocity in the cell nearest to the wall in the global XYZ coordinate system. X is aligned with the chord-line, while the gird is one cell thick in the Z direction.
U_Sxieta.pdf - this again shows the velocity in the cell nearest to the wall, but the coordinate system is now as follows: S is normal to the wall, xi is parallel to the wall and in the XY plane, and eta is parallel to Z.
yplus.pdf - shows Delta y_1^+ based on the distance from the wall to the cell centre. The values are a bit low because the mesh was originally 'designed' for a higher Reynolds number and for Delta y_1^+ = 1 at the first node.
 
I've tried a couple of things to get rid of the oscillations. First, I tried increasing the spacing normal to the wall, whilst keeping the number of cells the same (and all details in the direction normal to this the same). I doubled the distance, then doubled again, then doubled a third time, so Delta y_1^+ ~ 0.5, 1, 2, 4 for this sequence. I did this because a) I though my values were a bit low, and b) because I thought reducing the cell aspect ratio might help matters. Unfortunately this just made matters worse.
 
Second, I tried switching 'back' to IMRGRA = 0. I say 'back' because I had been working with IMRGRA = 3 for some time. Again, this made matters worse, as will be seen in the graphs. I also ran simulations on all of the aforementioned grids using IMRGRA = 0 but again matters were worse.
 
It might be worth pointing out here that the lift and drag values are what you'd expect, so it's not like the 'global' flow field is being affected by these problems at the wall.

Finally, I've attached a zip file with all of the files necessary to re-run this case.

[Gareth Gretton]

Three more attachments . . .

[Gareth Gretton]

And the final one . . .

[Mickael Hassanaly]

Dear M GRETTON,
Could you send me your post process method?
I'm trying to take a look to your case.
Best regards.
Mickaël Hassanaly

[Gareth Gretton]

Hello Mickaël,
My post-processing is done in Matlab from CGNS files (by using the mexcgns library). I can certainly send these files if they would be helpful. I think I also have some Ensight files which show the same results.
Something which I might add is that I've recently tried using different convective schemes (first order upwind and the "second order linear upwind" method). Using either of these upwind methods eliminates the oscillations (see attached graph for the friction coefficient), but the first order method gives a poor prediction for the drag.
Best regards,
Gareth