Hello community!!
Today I want to tell about how Y+ is useful in first guess of mesh and also to check quality of mesh.
For this, first user should able to analyze the problem up to which extent he needs accurate results.
“ Y+ ” is one of the parameters which affects the accuracy of our CFD results.
In many applications, study of fluid behavior and its properties has great importance to consider. Let’s consider the same example of airplane wing as in last post.
The drag force is highly influenced by the wall shear stress. So, it is very important to determine the wall shear stress accurately.
We know, almost in all CFD codes the fluid parameters store at center of the cell and they vary linearly between two cells.
As we know, the fluid properties like velocity are not uniform like free stream velocity near the walls.
This is because of boundary layer formation. The velocity gradients are very steep in boundary layer thickness.
In order to attain and trace this nonlinear velocity profile with our piecewise linearly varying behavior in CFD, we should refine our mesh into very thin cells in this boundary layer region or near to the wall which sometimes may lead to reduce mesh quality.
In other case, if we discretize domain with larger cells to reduce computational cost which leads to deviation of results in large extent leads to inaccurate results.
We may get different results for different discretization of our domain.
Out of them how to decide correct or appropriate result??
This can be estimated by plotting Y+ in post processing.
Y+ is the dimensionless distance normal to the wall. This is related to define mesh quality and helps in optimizing the mesh.
People usually say that if Y+ is nearly equal to 1, mesh quality is very good and results can be accurate but it leads to highly refined mesh and obviously increase in computational cost.
So, its always important to make good guess of our first mesh to get closure to appropriate results in less number of simulations. For this we first must know about “Law of the wall.”
Law of the wall is universal plot between dimensionless vertical height (Y+) on logarithmic scale and dimensionless velocity (U+). This plot is applicable irrespective of any fluid and any flow.
The plot has 3 regions as in image attached down depicting regions in boundary layer near the wall.
It is observed that Y+ linearly with U+ in viscous sub layer region and logarithmically in log law region.
*Scale of Y+ is logarithmic because of which we cannot notice linear variation in viscous sublayer zone.
Here we can understand the role of Y+. The CFD code in background ensures to correct the fluid property, velocity at center of the cell attached to the wall with respect to the Law of the wall.
Always remember that the correction of velocity applied only to the cells adjacent to wall after that it follows linear variation between cells as mentioned in beginning and for larger values of Y+ generally where Y+ does not vary linearly with velocity. The range of this Y+ from where to be corrected depends on CFD code.
To predict the first cell size which is adjacent to wall, following relations mentioned in attached image are more often used.
Now people may encounter with a question that as Y+ is correcting velocity with respect to law of the wall, why don’t we consider bigger cell size adjacent to wall which will reduce total cell count??
There are two reasons for it. First one is the CFD code is making correction of velocity and it cannot be always true for all cells adjacent to entire wall.
Second reason is if we go with bigger cell size means bigger Y+ value, the velocity at center of that cell after correction can be true but velocity curve in boundary layer may not match with original value as the velocity gradients are very steep in near to the wall.
In conclusion, we can say that if we require very accurate results, we should try to attain Y+ near to 1 or at least in range where Y+ vary linearly with U+ and if accuracy in results is not essential, we can go with bigger Y+ values like Y+ > 30.
I hope this blog helps you all and mention in comments your suggestions and your way of approach in choosing Y+.
