[Halle]

Hi there!

I'm doing a 2D-Simulation of an Airfoil. When I checked the results for mesh dependency, I found out that the solution depends greatly on the mesh size. My Target Parameters are the maximum shear strain rate on the airfoil and the total pressure loss from inlet to outlet. The mesh dependency for shear stress is a lot bigger, than for the pressure.

When I started, my maximum Yplus was around 1 - Now It's less than 0,1. I increased the the mesh density by factors 2, 4, 8 and 12 referring to the original mesh, resulting in an increase of max. shear strain rate of 79%. From 8 to 12, the shear strain increased by 2,2%. Even if I accept this as accurate enough, this would mean I'd have to simulate the 3D-Case with this resolution, which is not acceptable.

My mesh quality regarding angles and volume change is very good. I tried do a transient simulation of this case, but had the same results as in the steady state solution. I also checked that my target parameters are converged.

Is this dependency normal? If not, do you have any ideas how to fix it?

[ghorrocks]

Have you looked at the SSR contours? Please post an image.

What Re is the flow? What turbulence model? Laminar to turbulent transition? Separations? Anything else we should know about?

[Halle]

Thanks for your reply.

It's a turbulent flow with a Re number of 1.25*10^5. I used the SST model and had no separation at this angle of attack.

[ghorrocks]

Why is convergence of SSR important for you? Most people care about lift, drag and things like that, and if the SSR is not fully converged then that is OK.

[Halle]

Because the airfoil is from a blood pump and SSR is an important factor in determining hemolysis (rupturing of red blood cells).

[flotus1]

I suggest you check convergence for the wall-normal and the streamwise cell size independently.

Unless you are using a Reynolds-stress turbulence model, Y+ around 1 should be sufficient and the solution should not change if you refine the mesh further in wall-normal direction.

Do you run your case in double precision? This is recommended with low Y+ values.
How did you judge the convergence of your target calues with respect to the number of iterations?

[Halle]

Thanks for your reply!

I used double precision for the calculation and monitor points to observe the convergence of my target parameters.

For my convergence check I refined in wall normal direction only.

[flotus1]

About the velocity vectors in the background, is this one vector per face center?
In this case mesh expansion rate in streamwise direction is quite high ( and the resolution could be better for the high accuracy aims you have)

This could cause a cross-dependency with the wall-normal resolution.

[ghorrocks]

Alex's points are important, but so is this:

Shear strain rate is a derivative quantity, and is therefore more sensitive to noise then normal quantities. This means it is much harder to achieve convergence on SSR than velocity or pressure. I think you will find you will probably have to relax your allowable tolerance on SSR accuracy.

Additionally, converging on the maximum of a value is more challenging than converging on the average of that value over a range. The maximum is sensitive to little spikes and bumps and wiggles caused by any noise source. A bit of averaging will help here to reduce the effect of the noise. This has some physical validity as if the peak of SSR is only a nanometer across, then it probably does not cause any damage to the blood cells. It needs to be big enough to actually cause damage - I will let you work out what "big enough" is for a red blood cell .

So, in summary:
* Do not expect the same level of convergence on SSR as other variables
* Use a volume average of SSR rather than max value.

And taking the max value of an inherently noisy signal (like SSR) is always going to be very tough.

[Halle]

Thank you guys! I really appreciate your thoughts on this!

I think this will be enough to justify my results.