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YPlus value for SST

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Old   January 26, 2009, 13:18
Default YPlus value for SST
  #1
Ed Mueller
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Hello all,

I am fairly new to CFX and I have a question about the y-plus value of my mesh. I am using SST turbulence model with automatic wall function. I am wondering what y-plus value to use.

I have searched the forums and I see people who have recommended varyin values for Y+--anything from under 2 to under 200. The CFX help suggests DELTA Y+ of less than 2--how can I relate delta Y+ to Y+?

Also, when it suggests minimum number of nodes is at least 10, does this mean I need 10 prisms on my boundary layer?

Finally, is there an easy way to get an estimate on Y+ without creating a contour plot of it after my model has solved?

For what it's worth, my application is to study cavitation in a water pump.

Any help anyone can give will be greatly appreciated.

Thanks, Ed
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Old   January 26, 2009, 13:58
Default Re: YPlus value for SST
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LKF
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Being a fairly new user to CFX myself, I found the following references in the documentation quite useful.

Pg. 107 - 112 in the Solver Theory Guide Pg. 125 - ... in the Solver Modeling Guide Pg. 129 - 132 in the Solver Modeling Guide Also, Fluid Mechanics 5th Ed. Ch 6.5 - Frank M. White, McGraw Hill

My memory is a bit foggy, but I seem to recall that with the above references and a bit of algebraic subsitution, you can convince yourself that delta y+ is equivalent to y+ . . . with delta y being equivalent to 'n' - the spacing of the first node from the wall.

There is a method derived near pg. 131 (in the third reference above) that provides a means to approximate the required near wall mesh spacing to acheive a target y+ value. It is based on flat plate BL correlations . . . but will point you in the right direction.

As recommended to me previously, the best approach is to conduct a sensitivty analysis on the y+ parameter; vary your near wall spacing while maintaining a consant inflation layer thickness and see how it impacts your results.
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Old   January 27, 2009, 19:15
Default Re: YPlus value for SST
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CFDcarpe
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Ed,

Most of the time, experience indicates you what y+ you are going to get. y+ is the normal distance from the wall to the first cell in wall distance coordinates. Therefore, for a particular flow, a geometric distance y (i.e. the height of the first row in the boundary layer - prism layer in ICEM) will give you a particular y+.

If it is the first time that you are doing the kind of analysis you are attempting to do, then you will definitely need to create a referential grid to understand how your y+ behaves.

then, the manual probably says 10 cells within the boundary layer, because the "automatic wall functions" operate in the sub-viscous region of the boundary layers. The sub-viscous region is between 0 < y+ < 5. So you have to place at least 10 cells in that region. If you keep the growth factor in the prism layer at a reasonable number say, less than 1.5, it should be no problem (given that your first cell height is shooting for a y+ less than 1).
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Old   January 28, 2009, 11:41
Default Re: YPlus value for SST
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CycLone
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An equation is provided in the manual to estimate the near wall spacing based on your desired Y+, the Reynolds Number and your characteristic lenght. Both the CFX-Mesh method in Workbench Meshing and ANSYS TurboGrid provide an option to set the near wall spacing based on these parameters.

As for what Y+ you need, it depends on the flow of interest and the accuracy you require. It is commonly thought that the SST model requires a small Y+ ( <=1 ), but this is not the case. The SST model is just as accurate as k-epsilon when large Y+ (above 11) are used, in which case it uses a logarithmic wall function to calculate the shear stress at the wall. The advantage to SST is that as you refine the mesh to get closer to the wall, it will transition to a linear wall function and yield more accurate results.

The problem with a wall function is that it assumes the boundary layer profile is stable. This assumption may be OK in accelerating flows (such as a nozzle, turbine or the pressure side of an aerofoil), but is not reasonable in diffusing flows (such as a diffuser, pump, compressor, or the suction side of an airfoil).

When the boundary layer is unstable, the details of the velocity distribution in the viscous portion of the boundary layer (Y+<11) become important and determines where a boundary layer will separate. So to accurately predict separation in a diffusing flow one must use a model that can integrate all the way through to the wall (generally Y+ <= 1), hence SST is better for these situations.

Integration to the wall is also important for heat transfer at the wall. Again, this is because at small Y+ values the SST model uses a linear wall function and the boundary layer profile must be determined to accurately predict the rate of heat transfer between the wall and the fluid.

So, you may not need SST, but it doesn't hurt (I always run it by default). If heat transfer is important or you are dealing with diffusing flows, then you probably want to refine the near wall mesh as well.

Also, you should see from this explanation that it is not just that you need a node close to the wall, but also several elements through the boundary layer (hence the recommendation of at least 10). In general, if you use an expansion ratio of 1.2 to 1.3 and keep expanding the inflation (prism) layers to smoothly meet the volume elements (i.e. the final layer should have an aspect ratio (height/base) of ~0.7 up to 1.0), you'll end up with 25 to 50 layers.

-CycLone
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