# Relationship between element height and Reynolds number

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 April 16, 2013, 10:29 Relationship between element height and Reynolds number #1 Member   Join Date: Apr 2011 Posts: 43 Rep Power: 8 Hello, I have a question regarding the relationship between the height of an element (dy) and the Reynolds number of a flow (Re). From any of the standard element height estimating scripts, such as here (http://www.cfd-online.com/Tools/yplus.php), or even just estimating dy by solving the y+ equation, I see that my dy is smaller for smaller Re. For flow along a flat plate, my dy would be smaller at an earlier section of a plate than it would be farther along the plate, as the Re increases with the length of the plate. Does this mean then, that in generating a mesh for a turbulent boundary layer flow over a flat plate, that I am under-meshed if I take the dy from the end of the plate, with the highest Re? I can see perhaps growing the size of the elements along with the growth of the boundary layer, so my dy grows naturally with increasing Re, however when I look at other studies (such as here: http://turbmodels.larc.nasa.gov/flatplate.html ) I see that they use a constant dy height along the wall. I am looking at LES of flow over a flat plate (so my dy and y+ are quite important), what seems a standard computation. Do I base my dy on the Re at the end of the plate, as I would think? If I do, am I not resolving turbulence at the earlier sections of the plate? Am I misunderstanding the issue completely?

 April 16, 2013, 11:25 #2 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 For a fixed y+ value, the required dy value will decrease as the Re is increased. For something like a flat plate, standard practice is to use the largest value of Re (typically at the end of the plate) and grid based on the dy for that value. This typically leads to grids that have more than enough resolution near the leading edge of the plate.

April 16, 2013, 11:52
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Filippo Maria Denaro
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Quote:
 Originally Posted by agd For a fixed y+ value, the required dy value will decrease as the Re is increased. For something like a flat plate, standard practice is to use the largest value of Re (typically at the end of the plate) and grid based on the dy for that value. This typically leads to grids that have more than enough resolution near the leading edge of the plate.
I agree, if you are constrained by a structured grid is better to evaluate your minimum dy based on the most critical situation, which happens at the end of the flat plate.
However, a lot of grid points are used without necessity, therefore would be better to use a multi-block grid ...

April 16, 2013, 12:59
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Quote:
 Originally Posted by agd For a fixed y+ value, the required dy value will decrease as the Re is increased. For something like a flat plate, standard practice is to use the largest value of Re (typically at the end of the plate) and grid based on the dy for that value. This typically leads to grids that have more than enough resolution near the leading edge of the plate.

Forgive me if I'm wrong, but calculating it out, or even just using the dy calculator in the OP, it appears that dy increases with Re, not decreases. Thus, with a higher Re you have a larger element size near the wall. Which seems odd to me.

Actually I wrote it out, and keeping everything else the same (viscosity, density and free-stream velocity), the element height dy grows with length to the 1/14 power. Is this correct?

 April 16, 2013, 14:47 #5 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 Just using the calculator you linked to, simply dropping the viscosity by an order of magnitude results in a larger Re and a smaller dy. I'm not sure what you are calculating, but the requisite wall spacing drops as Re increases. To FM Denaro - I agree with your assessment, although most people don't want to put much effort into grid generation. Of course, good grids beget good results, while bad grids beget Powerpoint presentations...

 April 17, 2013, 01:22 #6 Senior Member   Martin Hegedus Join Date: Feb 2011 Posts: 494 Rep Power: 12 dy is a function of both x and Re_x. dy will get smaller as x gets smaller (assuming a constant y+, constant freestream velocity, constant kinematic viscosity, and turbulent flow over the entire surface). Also, as Re_x gets larger at a given x, due to larger velocity or lower kinematic viscosity, dy decreases. It is important to get an appropriate dy over a good portion of the surface so the skin friction is calculated accurately. In general, dy, (for a given y+, velocity, and kinematic viscosity), is mildly sensitive to x.

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