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Can anyone explain y+ ?

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Old   February 22, 2022, 16:22
Default Can anyone explain y+ ?
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qutadah
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Hi everyone,


so I am a little confused about the y+ in our meshes, and its relationship to the turbulence model used and all other factors. Now I understand that y+ is dependent on wall shear stress, element distance to the nearest wall and local kinematic viscosity. And y+ is defined as the dimensionless distance of the first cell in our infiltration layer in the mesh near wall.


My questions are:


1- do we use this y+ value in other further away cells or only in the cells where wall functions are used, (in case a wall function is used)


2- in case a fully resolved flow, this y+ has no meaning, does it? In which cases is the y+ viable? Laminar flow, turbulent, wall roughness, use of wall functions. I cant connect the dots.



3- I do not understand the relationship between the turbulence model used and the y+ value to be chosen, a lot of suggestions of what values to use where and with which turbulence model, but no explanation to the why these values and how they were calculated or derived for these turbulence models.


4- Does y+ value change for different wall roughness?



I am a beginner in CFD if there are any stupid questions or questions that overlap



If you have any good reads or books on the subject that explain this well, please advise!


Thanks !
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Old   February 22, 2022, 17:38
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1) In the code, y+ is used only in the first cell near the wall. In more general terms, y+ is typically used as coordinate along a wall normal direction for plots (in which case you still use the same tau at the wall along the whole coordinate)

2) y+ has meaning wherever you have a flow along a wall. It is a Reynolds number. In a code, you use it only for near wall cells because it is the variable trough which most wall functions are parameterized.

3) The question is very simple: it depends from the validity of the turbulence model at the wall and the suitability of the available wall function to cover certain y+ ranges. Most k-epsilon models do not work at the low y+ values near a wall; they require a y+ in the log range. Spalart-Allmaras and most k-omega models work also at the low y+ values close to a wall, but also with wall functions at high y+; if the particular wall function in use allows it, they also (kind of) work at intermediate y+ values. Most of these reasoning are however based on the equilibrium boundary layer flow.

4) y+ does not depend from the wall roughness. What happens with roughness is that y+ won't anymore work as correct nondimensional coordinate near a wall. When properly adjusted for the roughness it will be again (profiles for different roughnesses will collapse again in terms of the adjusted y+)
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Old   February 22, 2022, 21:27
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I would add that y+ is the inner coordinates in the method of matched asymptotic expansions and the related discipline of asymptotic expansions. If you read the notes of Blasius, you find such a technique being used. In other words, someone didn't just roll dice and one day decide to normalize velocity by the wall shear stress. Prandtl had buddies in the math department of his school and was very familiar with it. The math gives you the procedure for determining what the normalization should be and it falls right out of the physical parameters. It's not just a turbulence modeling tool, CFD tool, or just a fluid dynamics tool either. You find it in the analysis of any boundary layer phenomenon in physics and boundary layers arises whenever you have two or more distinct length scales (in fluids this is the inertial scale and viscous scale). There's also electric boundary layers and magnetic boundary layers in E&M for example.
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