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Old   April 26, 2004, 04:25
Default wall function and grid dependency
  #1
Bob
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Hi I am new at modelling

I have question about turbulence modeling and mesh independency.

I am using k-epsilon and wall functions to resolve the flow. Now I have to optimize the mesh for my case.

How can I attin the gris independency

Can someone help me out.

Pratap
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Old   April 26, 2004, 04:49
Default Re: wall function and grid dependency
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Jonas Larsson
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Grid independency and wall-functions is a bit extra tricky. You can not just refine your grid more and more without any care. Wall functions only work when the first node has a certain distance from the wall. This non-dimensional distance, y+, should be around 50, or at least not below 15 or above 300).

To do a grid-dependence study on a wall-function grid you have to make sure that you do not refine the grid close to the wall so much that your y+ distance becomes too small for wall-functions. When you reach y+ around 50 you should stop refining the normal wall-distance of the first node and instead refine your grid in other regions and in the direction parallell to the wall.
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Old   April 26, 2004, 06:12
Default Re: wall function and grid dependency
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Bob
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thank you jonas, Now I have another simple question whether this applies to all the walls. when you have flow over a sphere while the sphere is in channel so now you have channel walls and sphere walls.

Thanks bob
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Old   April 26, 2004, 06:40
Default Re: wall function and grid dependency
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Jonas Larsson
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Yes, in theory it applies to all walls where you use wall-functions. However, depending on the case some walls will of course be more critical. Typically the walls where viscous effect are important for your overall flow field will be most critical.
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Old   April 27, 2004, 03:30
Default Re: wall function and grid dependency
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Bob
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Another question,

Let us suppose you perform simulations and take some mesh and check y+ plus values for all the walls after some iterations(let us say 5 iterations).le us say they are in the range now you continue the simulations till it reaches the steady state now you calculate the y+ plus values again. and suppose that they are not in the range (above 300). Does it mean that simulations is wrong so do I have to check y+ plus values at every iterations.

Bob
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Old   April 27, 2004, 11:57
Default Re: wall function and grid dependency
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noName
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I don't quite understand why wall functions won't work when your value of y+ is too small? I thought, in most codes, the wall functions come into action only when the y+ values are large (say >15) and no extrapolation is done when y+ values are small. Is there some text where this is well described?
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Old   April 27, 2004, 13:41
Default Re: wall function and grid dependency
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Bob
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Hi Does anybody know ofsome paper where refinement of near wall grid is discussed for recirculating flows.

Bob
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Old   April 27, 2004, 13:48
Default Re: wall function and grid dependency
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Jonas Larsson
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You will only get correct y+ values when your solution is converged. You need a fully developed boundary layer in your solution before you can compute y+. Hence, you have to let the simulation converge, then check your y+, and if necessary re-mesh and re-run the case. Checking y+ after a few iterations will not produce anything useful.

Btw, there is a small tool on the net which you can use to guess the y distance of the first node based on the desired y+. You can find a link to it in the Resources/Calcs/Misc section here at CFD Online.
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Old   April 27, 2004, 13:59
Default Re: wall function and grid dependency
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Jonas Larsson
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The problem is that most turbulence models do not work well when y+ goes below 15 or so and you come close to the viscous sublayer. k-epsilon in particular does not produce correct results if used in this region and in order to get it to work you need to add damping-functions etc. to make it a low-Re model.

k-omega works down through the viscous sublayer.

However, it is not at all trivial to automatically switch between a wall-function approach and a fully resolved low-Re approach based just on your local grid resolution - you need to match two different types of wall treatment and that creates a whole range of new problems. There are such models that can switch between low-Re and wall-functions though.

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Old   April 27, 2004, 15:55
Default Re: wall function and grid dependency
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Hrvoje Jasak
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I was hoping I'd be able to avoid this discussion In my PhD work I had to do mesh refinement with wall functions and I've hit some limitations mentioned before. if you carry on refining (especially in 2-D where you've got the chance of producing enough mesh resolution), you end up with an unfortunate situation where the numerical error is localised in the cells next to the wall and the wall functions rules won't allow you to touch those cells. The reference (if you fancy having a look) is:

@PhdThesis{Jasak:PhD,

author = {Jasak, H.},

title = {Error analysis and estimation in the Finite Volume method with applications to fluid flows},

school = {Imperial College, University of London},

year = 1996 }

As for the second issue (why wall functions go wrong), it is quite straightforward. Consider a fully developed boundary layer on a flat plate. Near the wall k changes with wall distance squared and epsilon with wall distance cubed. This, obviously, requires a LOT of mesh to resolve. Secondly, the standard k-epsilon model without the wall function treatment does NOT reproduce this behaviour: low-Re models (which do) use a bunch of damping functions and sufficient mesh resolution near the wall (otherwise they blow up!).

What wall functions do is simply switch off the correction on turbulent viscosity for the wall face for y+ < 11.6 (that's the famous cross-over). Thus, you end up with laminar viscosity on the wall and the bulk k-epsilon model that does not reproduce the near-wall physics at all. In otherwords, the result is wrong.

Hope this is clear,

Hrv
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Old   April 28, 2004, 02:15
Default Re: wall function and grid dependency
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Bob
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So Based upon the suggestions I am conlcuding the following I have to first mesh the geometry and then run the case let the flow developed its boundary layer(when steady state is reached). then check the y+ plus values if they are under 30-300 then its is okay other wise I have to correct the mesh and re run the case till I get the yplus values of 30-300.

When you simulate wall bounded flow and recirculating flows and use standard k-epsilon turbulence model this restriction is big problem I guess. Do somebody have this paper where mesh refinement in recirculating flows is discussed ? From this disscussion mesh refinement in reciruclting flows is notorious task. Correct me if I am wrong somewhere.

bob

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