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Shear Stress on Rough Surface

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Old   October 7, 2021, 04:45
Default Shear Stress on Rough Surface
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Boqi Ren
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Hi everyone
I'm writing here to ask some questions about the calculation of wall shear stress on the rough surface.

As we know, the definition of wall shear stress is

\tau_w= \mu (\frac{\partial u}{\partial y})_{y=0}

so for the rough surface, can I calculate the shear stress in the following way?
\tau_w= \mu (\frac{\partial u_t}{\partial n})_{y=0}
Where t means the tangential direction of the local surface, and n means the normal direction.

And, could you recommend some relative reference to me?
THANK YOU VERY MUCH!

Last edited by Sylorn; October 7, 2021 at 04:57. Reason: to correct the formulations
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Old   October 7, 2021, 11:05
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Quote:
Originally Posted by Sylorn View Post
Hi everyone
I'm writing here to ask some questions about the calculation of wall shear stress on the rough surface.

As we know, the definition of wall shear stress is

\tau_w= \mu (\frac{\partial u}{\partial y})_{y=0}

so for the rough surface, can I calculate the shear stress in the following way?
\tau_w= \mu (\frac{\partial u_t}{\partial n})_{y=0}
Where t means the tangential direction of the local surface, and n means the normal direction.

And, could you recommend some relative reference to me?
THANK YOU VERY MUCH!



Since the surface is rough you should evaluate the normal derivative at x=x(s), y=y(s), not at y=0.
The action of the stress can be better see if you write the contribution of the stress tensor on a finite surface:


Int[S] n.Td dS


Td being the deviatoric part having zero trace.
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Old   October 7, 2021, 23:45
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Originally Posted by FMDenaro View Post
Since the surface is rough you should evaluate the normal derivative at x=x(s), y=y(s), not at y=0.
The action of the stress can be better see if you write the contribution of the stress tensor on a finite surface:


Int[S] n.Td dS


Td being the deviatoric part having zero trace.
FMDenaro, Thank you very much!
Yes, as you said, the wall shear stress should be on the wall, so in the second equation, y=0 is not correct.
But I still feel confused with \textbf{T}d. Could you explain this term in more detail?
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Old   October 8, 2021, 11:25
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Originally Posted by Sylorn View Post
FMDenaro, Thank you very much!
Yes, as you said, the wall shear stress should be on the wall, so in the second equation, y=0 is not correct.
But I still feel confused with \textbf{T}d. Could you explain this term in more detail?

It's the tensor form of shear stress. du/dy the way Isaac Newton did it is for 1D.
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