# y+ and y*

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 August 13, 2008, 10:00 y+ and y* #1 Hink Guest   Posts: n/a i would really be grateful if someone can explain to me when do i need to use y+ and y*, what the importance of using them when modelling wind profiles. i have tried to read about it but cant get to understand it. thanks

 August 13, 2008, 15:10 Re: y+ and y* #2 Louis Guest   Posts: n/a y+ is the distance away from a noslip surface normalized by y*. It is useful in that it gives you an idea of where in the boundary layer you are. For instance, for a flat plate turbulent boundary layer (no pressure gradient) 0 < y+ < 5 is in the viscous sublayer, 5 < y+ < 50 is the buffer region and y+ > 50 is the log law region. The upper limit of the low law region depends on the Reynolds number. Things become a little hazier when you have flows with pressure gradients and separation, etc, but y+ still gives you some bearing. When building a mesh for a CFD model with noslip walls, it is important to make sure the grid spacing normal to the wall is sufficient to resolve the boundary layer. Typically, if no wall function is used (i.e., the noslip condition is applied), the first off wall grid point (if using finite difference) or cell center (if using finite volume) needs to be at approximately y+=1. Also, you need to control the grid stretching to make sure there are enough points through the viscous and buffer regions (a geometric growth factor of 1.1-1.2 is typically recommended). If a wall function is used, then the first point or cell center can be placed in the log region (i.e., y+=100). This depends on the wall function. But you still need to control the stretching. There are a few expressions out there that help you to figure out what your wall spacing needs to be given the desired y+ resolution, Reynolds number and a length scale. Once you have obtained a solution, you need to check to make sure the y+'s of the first grid point or cell center are acceptable. Hope this helps.

 August 14, 2008, 18:23 Re: y+ and y* #3 pankaj saha Guest   Posts: n/a Hi, Louis, you are absolutly correct. Before to set grid, you can calculate , and set the grid dimension. There is a relation of y+ with Re. So, for a given Re, you can get the value of grid point for maintaining y+ =1. Louis, can you expalin that, if anyone set the 1st grid point at y+=6,and take no-slip b.c, then what are possible error encounter? Also, how many grid point one needs within y+=11. Also, for presure gradient and separation do we need, more resolution near the wall.? wait for your comment. thanks

 August 15, 2008, 06:53 Re: y+ and y* #4 Louis Guest   Posts: n/a The typical error for not having appropriate resolution is that you will underpredict the drag. I also understand that convective heat transfer calculations are very sensitive to wall resolution. I typically don't look at the number of points I have by a certain point in the bl. I try to keep the grid stretching ratio between 1.1 and 1.2. This would put around 5-6 points through to y+=11. No, you don't need more resolution for pressure gradient and separation. In an adverse gradient (leading to separation), your spacing requirement actually decreases because the bl is getting thicker. It goes in the opposite direction for a favorable gradient but the difference shouldn't be so much that the spacing set using zero gradient becomes unreasonable.

 August 16, 2008, 05:28 Re: y+ and y* #5 pankaj saha Guest   Posts: n/a hi, Louis , nice to discuss with you. Hope you did excelent piece of work on this. right now , i am also working on LES chanel flow. i have set my first grid around y+=2 and took 5-6 points within y+=11. i am getting friction velocity right...but my mean velocity is overprectied by 30%. AS, my case , it should be 1.0 , but i am getting 1.36. So, every result is overeprected by some margin. Could, you face this type of situation. Please, tell what is the remedy?

 August 18, 2008, 06:50 Re: y+ and y* #6 Louis Guest   Posts: n/a It's been a while since I've looked at channel flow. If I recall correctly, you can't place too much stock in getting the friction velocity correct because that has to balance the pressure gradient that you are specifying. So, it is a check that you are properly conserving momentum but not an indicator that you have proper resolution. One thing to bare in mind with LES when you are not using a wall function is that you need to accurately resolve the near wall streaky structures. The size of these things are typically cited in inner units (i.e., x+ and z+ defined analogously to y+). I think these are O(100) but you need to look it up. If your mesh/code does not resolved these you will not get the right answer.

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