# Flow over a plate

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 June 29, 2018, 10:22 Flow over a plate #1 Member   Vivek Join Date: Mar 2018 Location: India Posts: 54 Rep Power: 8 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!!

June 29, 2018, 11:31
#2
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Filippo Maria Denaro
Join Date: Jul 2010
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Quote:
 Originally Posted by vivek05 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.

June 29, 2018, 12:07
#3
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Vivek
Join Date: Mar 2018
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Quote:
 Originally Posted by FMDenaro 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??

June 29, 2018, 12:33
#4
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Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,763
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Quote:
 Originally Posted by vivek05 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.

 Tags flat plate, sharp corner