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value of k for atmospheric wind

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Old   June 24, 2021, 15:10
Default value of k for atmospheric wind
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Adrian Main
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Hello everyone. I am quite new to OpenFOAM and I would like to know if I could please get the advise from any of you related to the next topic:

A bit of context: I am running a Atmospheric Wind simulation, within the field of civil engineering, sort of what we do with wind tunnels tests. I have a structure imported from STL format, in the middle of a quadrilateral blockMesh and I am subjecting it to a wind. I have successfully snapped the geometry with SnappyHexMesh. I want to obtain surface pressures and pressure coefficients on my object (a building).

I am using simpleFoam to solve the model with realizableKE turbulent model. The boundary conditions are quite critical. I have used the ones from here, based on the paper from Hargreaves and Wright (2007):

I have implemented these boundary conditions. Are they correct/advisable for my study? I had to cancel the “Top” wall shear since it was making my model to diverge but I don’t think this is critical. Is it?

I am experiencing some troubles to define the internalField value for “k”, in the “k” input file. My results are super sensitive to this input value and completely dependent on it (despite I thought this was just an initial setup and then the analysis is to work its way towards the right k it needs…). But no, it is critical to get this number right. From the equation k = friction velocity^2 / Cmu^0.5 I get a big number (k=8.57 obtained with rho=1.184, kappa=0.42, z0=0.03, zref=10 and Uref=22.2) leading to what I deem unrealistically huge vortices and very bad convergence. By trial and error I’ve found that the results I consider about-right are for an internalField close to k=0.1.

Can anyone make sense of all this? Which is the “k” I should be using (and why)?

Many thanks for your help. Adrian
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Old   June 25, 2021, 04:45
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Uwe Pilz
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There is something wrong if your results depends on initial k in a strong way. The simulation should find the adequate value by itself. An unfavorable starting value may lead to an exploding simulation. But if that not happens, the final result should not depend on the starting point.

I assume that something is wrong with you model. A hint for this is that you had to remove b.c. for the top.

Some proposals:
1) build a simple geometry with the same physics (and all boundary conditions) and look what happens. Blockmesh should be sufficient for that.
May be, your model is unphysical.
BTW, you get a realistic value for k from this.

2) run checkmesh. Look first at non-orthogonality which should be less than 50 or 60 for rather physical complicated models.
Look if there are elements with large non orthogonality in the near of the areas where you need the solution.
Improve the mesh. If that is not possible, rather simplify the geometry instead of using a bad mesh.

3) Use robust methods for discretization and solving instead of very accurate ones. If you get decent results with that you may proceed with more accurate ones.
Uwe Pilz
Die der Hauptbewegung überlagerte Schwankungsbewegung ist in ihren Einzelheiten so hoffnungslos kompliziert, daß ihre theoretische Berechnung aussichtslos erscheint. (Hermann Schlichting, 1950)
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Old   June 25, 2021, 10:02
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The Hargreaves and Wright paper applies what are called "Surface Layer Approximation" profiles to the lower part of the ABL. These are essentially the same as a constant stress approximation, and are a high Re# asymptotic state for the log law region. In other words, they are a basic approximation for the lower 50m or so of the ABL, and are a pretty poor representation of anything above this.

For some reason, this H&W paper has been taken as a manual, and these boundary conditions seem to be being used widely across the CWE industry, even by consultancies who are also doing wind tunnel modelling (who should know that the idea of a constant k profile across the ABL is nonsense!).

A more physical k profile would have the values decaying with height; a linear decay usually gives a good fit to wind tunnel data (ignoring Coriolis effects and wind shear).

Once you have your profile, do as piu58 suggests - pass it through an empty (2d) domain, and see if your profiles develop. If they do develop significantly, then your inlet BCs are not in balance with your ground BC, so check the details again.
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atmboundarylayer, realizableke

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