Understanding Y+ for CFD Simulations (2024)

Yplus is an important parameter to be considered in any CFD simulation for good results. Here is formulae for Y+ and related terms:

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But what I see that people around are blindly following some guidelines which are not applicable for their cases. And they end up with problems in solution convergence and accuracy etc.

1. For example if one situation is applicable for some cases, but may not be on the cases he or she is solving. For example if you are solving the flow over the blunt body, then in this case, major drag is coming from pressure rather than the skin friction or boundary layer. So fine tuning boundary layer mesh will not give you much advantage.
2. For very high Reynolds number flows, where boundary layer becomes very thin and effects of it are not important.
3. For high Mach number flow, consequently Reynolds number is also very high, again boundary layer is thin and results are dependent on shock wave resolution rather than boundary layer resolution.
4. Flow with no separation, and still you are trying with Y+ of order 1 or less. In this case you are increasing round off error. This will be counter productive as you are not understanding flow physics.
5. When you are not interested in drag coefficient and still you are trying for high resolution in boundary layer. In this case you are not getting much advantage as the flow parameters you are interested are not dependent on boundary layer flow. But rather flow physics outside the boundary layer. For example lift coefficient.

Now I want to point out you guys to the article on the hybrid wall functions, also known as universal wall function which are valid in all zones of boundary layer (viscous sub-layer, buffer layer and log layer)

Hybrid Wall Functions

In above article you will see that now new hybrid wall function is applicable for all Y+ values. But keep in mind that these hybrid wall functions are designed for SA and K-Omega type models (SST included). However, K-Epsilon type models are designed for wall functions i.e. Y+ >30. But with one equation treatment for K-Epsilon models you can integrate them to viscous sub-layer. In this case K-Epsilon type models requires Y+<0.2. This is also known as enhanced wall treatment.

Now based on the above article you can see that, strict value of Y+ < 2 for SST model and Y+ < 1 for SA model is now not must. So keeping Y+ upto 10 will give you same results as of mesh with Y+ ~ 1.

Also note that for transition modeling (laminar to turbulence transition) you need mesh with Y+ < 1 everywhere along with the requirement of fine mesh in stream-wise direction.

Based on above discussion I would like to give you some guidelines / best practices:

1. Keep Y+ below 10 for viscous dominate flows with separation.
2. Use Y+ < 1 for the transition prediction and heat transfer calculations.
3. Use Y+ < 10 for SST model (omega based models in general)
4. Use K-Epsilon model with scalable wall functions (default option in new version of Fluent). It will keep the Y+ above 11.06 so that it does not suffer the limitation of old standard wall functions. Moreover now you can carry the successive refinement of mesh, which was not possible with standard WFs.

Now I would like to give you some results which I ran on Ahmed Body with Hexa Mesh with Y+ < 1 and Y+ ~ 10.

Here is picture of Mesh:

Zoomed view in boundary layer (For Y+1 mesh):

Zoomed view in boundary layer (For Y+10 mesh):

Here is the plot of experimental velocity profiles at various locations. We will compare velocity profile at X = -123 mm for two Y + values i.e. 1 and 10. You can get experimental profiles from Experimental velocity profiles at different axial locations

Here are the results for K-Epsilon realizable mode at X = -123 mm:

See the location of X = -123 and corresponding mesh for Y+ = 1 and Y+ = 10 Mesh.

View of Y+ =1 mesh with line for XY plot at X = -123 mm,

Zoomed view of Y+ =1 mesh with line for XY plot at X = -123 mm,

View of Y+ =10 mesh with line for XY plot at X = -123 mm,

Zoomed view of Y+ =10 mesh with line for XY plot at X = -123 mm,

And here is the Drag Coefficient comparison:

You can see difference between Y+ = 1 and Y+ =10 is around 2.5%. And keep in mind that K-Epsilon type models do not use imply hybrid wall functions, rather they work on enchanted wall treatment. And according to Fluent user guide, the value of Y+ should not exceed 3 to 5.

Here is velocity profile for the SA Model:

And here is the Drag Coefficient comparison:

Which shows less than 1.5% error between Y+1 and Y+10 results.

Here is velocity profile for SST model:

And drag coefficient comparison shows the 2% error between Y+1 and Y+10 meshes.

Here is the contour plot of Y+ for Y = +1 and Y = +10 grids.

Y+1 Mesh:

Y+10 Mesh:

Based on above we can conclude it is not necessary to always use the Y+ <1 mesh for better results. With hybrid wall functions you can use mesh up to Y+ 10 without much problems. This will also reduce aspect ratio and number of mesh counts. This will ensure the good convergence in less time. While maintaining the same accuracy to that of Y+ = 1 mesh.

Here is the Y+ calculator for calculating Y+ value for first cell height based on first cell distance and Reynolds number and for calculating first cell height based on given Y+ and Reynolds number. This is designed in excel so you can use it very easily.

Y+ calculator

Some common mistakes made by CFDers are:

1. Creating mesh with required Y+ but then putting next cell outside the boundary layer. Please keep in mind that boundary layer cannot cannot be resolved with just one point. You need to put atleast 10-15 points for Y+ ~ 10 mesh and up to 40 nodes for Y+ ~ 1.
2. Trying to create very fine mesh with Y+ ~ 1 for supersonic flows where boundary layer contribution is negligible.
3. Creating meshes of Y+ = 1 for all turbulence models. Different turbulence models have different requirements for Y+ values. Even the Y+ values varies between two turbulence models for same mesh. It is because the way friction velocity is calculated for different turbulence models.
4. For transition flows creating mesh with maximum Y+ < 1, but not providing enough points in stream-wise direction. This will calculate the wrong location of transition point and hence increasing or decreasing the frictions effects due to turbulence.
5. Not putting sufficient points in viscous sub-layer. This means that we are not resolving velocity profile properly in viscous sub layer. For some cases this can critical. So try to atleast put 3-5 points in viscous sub-layer. Here is the XY plot for velocity profile for K-epsilon with Realizable model with less number of nodes in viscous sub layer. this will not resolve the sub laye properly and you will be able to get the negative values of velocity in boundary layer.