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Flow over a plate

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Old   June 29, 2018, 10:22
Post Flow over a plate
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Vivek
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Hi everyone,
I have one clarification about flow over a flat plate. I had searched in online but i am not clear till now.
Why the leading edge of flat plate has sharp corner in the simulation of flow over a flat plate ?
Why not other shapes?

Thanks in advance!!
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Old   June 29, 2018, 11:31
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Quote:
Originally Posted by vivek05 View Post
Hi everyone,
I have one clarification about flow over a flat plate. I had searched in online but i am not clear till now.
Why the leading edge of flat plate has sharp corner in the simulation of flow over a flat plate ?
Why not other shapes?

Thanks in advance!!



In the theory of developing boundary layer (Prandtl equations), the point x=0 is a point of singularity in the solution. When we solve numerically, the spatial discretization cannot distinguish exactly on a node where the origin is.


If you want to consider a smooth body describing the leading edge, this is developed in a different theory for the BL.
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Old   June 29, 2018, 12:07
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Originally Posted by FMDenaro View Post
In the theory of developing boundary layer (Prandtl equations), the point x=0 is a point of singularity in the solution. When we solve numerically, the spatial discretization cannot distinguish exactly on a node where the origin is.


If you want to consider a smooth body describing the leading edge, this is developed in a different theory for the BL.
Thank you FMDenaro .. what i understood from your reply is ,to locate a node numerically we are using sharp corners because if we used curved leading edge then its difficult to locate a node numerically. is it correct??
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Old   June 29, 2018, 12:33
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Thank you FMDenaro .. what i understood from your reply is ,to locate a node numerically we are using sharp corners because if we used curved leading edge then its difficult to locate a node numerically. is it correct??



No, what I mean is that the BL theory over a flat plate consider really a semi-infinite plat with zero thickness.

On the other hand, on a numerical grid of size h, you can set the first node with no-slip condition but owing to the discretization that does not determine exactly the singular point in the origin.
If you want to describe a slender flat with a rounded leading edge, the standard theory of Prandtl should be modified by the developing boundary layer over the rounded leading edge. If I am right, that theory was developed by Hinze who described an exact solution for small values of x.
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