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Y+ for viscous sublayer 2D airfoil

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Old   October 27, 2019, 15:11
Default Y+ for viscous sublayer 2D airfoil
Ferruccio Rossi
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Hi all,

I am trying to verify the correctness of my 2D airfoil NACA 0012 simulation by verifying my Y+ value. In particular, I am interested in solving the forces acting on the walls of my airfoil (drag, lift), therefore I am using a k-w SST turbulence model, which the literature says it's ideal for solving forces at the wall in detail.

Since I want a precise result for the forces acting on the airfoil, I want to solve the viscous sublayer, rather than using wall functions. From the literature I was able to find, I understood that by solving the viscous sublayer I can get a more precise result for the forces at the walls compared to using wall functions. Therefore I am aiming for a Y+ < 5. Is this assumption correct for the viscous sublayer? I found cases where the literature was saying that Y+ needs to be around 1, and other cases where the literature says it is acceptable to use Y+ < 5, so I am not really sure which one should I aim for if I want to solve the viscous sublayer.

This said, I refined my structured 2D mesh and ran simulations until I got my Y+ to be between 0.5 and 2 (see picture of Y+ plot), which I believe is sufficient for solving the viscous sublayer.

But I still have the following doubts:
1) See the Y+ plotted along the airfoil chord length (attached picture). Why are there local valleys (local mins) around x=0 and x=0.05? I would expect the plot to be more linear, in the same way as the section from x=0.1 to x=0.2.

2) The residuals are converging down to 1E-06, but as you can see in the attached residuals plot, some of them start oscillating (continuity - black line & y-velocity, green line) even though they don't diverge. Is this acceptable, and if so, what does it mean? I can't figure it out. I don't believe this is an issue, since I think residuals at 1E-06 are sufficiently converged, but please correct me if I am wrong.

3) In light of all these considerations, would you say that my Y+ analysis is correct, and I successfully resolved the viscous sublayer?

I would like to hear your opinions and/or suggestions.
Thank you all for your support!

P.S. I attached pictures of my structured 2D mesh in case you want to have a look.
Attached Images
File Type: png y plus.PNG (25.9 KB, 16 views)
File Type: png residuals.PNG (60.0 KB, 16 views)
File Type: jpg Mesh 1.jpg (77.3 KB, 14 views)
File Type: jpg mesh 2.jpg (141.7 KB, 13 views)
File Type: jpg mesh 3.jpg (86.7 KB, 13 views)
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Old   October 27, 2019, 17:12
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Glenn Horrocks
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You appear to be using Fluent and this is the CFX forum. For comments specifically on Fluent you should use that forum, but your question is really a generic CFD question which is relevant to any CFD software.

Firstly, you should not assume that running in the integration to the wall mode (y+ =~1) is more accurate that wall functions. Wall functions work by modelling the effect of the thin layers of the boundary layer without resolving it in the mesh - there is nothing inherently inaccurate about that. If the boundary layer model is accurate then the wall function is accurate.

Rather than target a y+ value you should do a sensitivity analysis to determine if you mesh is fine enough. Not only will this let you know how fine your mesh needs to be to achieve the accuracy you require, but it also gives you an estimate of the error you currently have. To do a sensitivity analysis do another simulation with the mesh significantly changed (I recommend doubling or halving the edge length in all directions) and see what difference it makes to your results. If the difference is an unacceptable error to you then refine the mesh further and continue until you achieve convergence - also known as mesh independence.

Your comment about the convergence flat lining is an FAQ - see:
Note: I do not answer CFD questions by PM. CFD questions should be posted on the forum.
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convergence, mesh, sublayer, viscous, y plus

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