[inarus]

Hello,

This question maybe have been asked a 100 times at least, though there are so many posts, so many opinions and debate for a lot of CFD applications.

Many practice CFD since a long time ago and are fixated by the idea that y+ must be at most 1, but viscous solvers have evolved lately and are proposing wall-functions as well, that in my limited experience, diminish cell count of grids, which is not bad when doing a 5 grid dependency study.

I use Hexpress mesh generator and ISIS-CFD flow solver for ship flows with free surface.

Using benchmark data, at least for fine hulls, advancing in calm water at Reynolds numbers in the range of 0.5E+07 ... 1.3E+07, the results are in good agreement with the EFD data, the estimated error is bellow 5% for grids around 2M cells (Y+ = 30 and wall-function) for the whole resistance curve. Again, for fine, slender hull forms.

Numeca's documentation and published papers are describing test cases almost exclusively using wall-functions with a corresponding y+ ranging from 30 for towing tank model sizes, up to 300 for full scale ships.

Someone very experienced told me that the accuracy for viscous drag component of total resistance, obtained with wall-function, might not be in agreement with reality versus the solution obtained by using no-slip (wall resolved turbulence model) BC.

The clicking part is easy, but my theoretical background so far is quite limited, that's why I am asking for a more plain English explanation than what's written in theoretical books.

Thank you very much!

Best regards

[FMDenaro]

You should think about y+ as a local Reynolds number measured by taking the distance from the wall. A cell Re number =O(1) (wall resolved grid) is sufficient to resolved viscous and convective effects (of the momentum) at the same numerical resolution. The wall model introduces a physical model into the viscous term to get the first cell at high y+ plus.

Giving this framework, you could think of a same reasoning in defining similar grid constraint for other equations where different non-dimensional numbers (Peclet, Schimdt, etc.) are in effect.

In principle, the reasoning can be applied also in absence of walls but in presence of different flow layers that appears like a "discontinuity"

[inarus]

Originally Posted by FMDenaro

A cell Re number =O(1) (wall resolved grid) is sufficient to resolved viscous and convective effects (of the momentum) at the same numerical resolution.

Can you please elaborate this one a little further?


Many thanks!

[FMDenaro]

Originally Posted by inarus

Can you please elaborate this one a little further?


Many thanks!

I means that the cell scale h is so small to allow the characteristic viscous time and the characteristic convective time to be the same. That is, a particle of fluid that moves at a velocity U along a distance h in a time h/U diffuses at a time U^2/ni. This is a constraint for a well resolved numerical simulation.

[inarus]

Originally Posted by FMDenaro

I means that the cell scale h is so small to allow the characteristic viscous time and the characteristic convective time to be the same. That is, a particle of fluid that moves at a velocity U along a distance h in a time h/U diffuses at a time U^2/ni. This is a constraint for a well resolved numerical simulation.

Thank you for the hints, I should be able now to look into it a bit more in books, etc.

Thanks again!