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wanna88 September 26, 2012 06:38

WSS and normal velocity gradient for the slanted pipe
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Hi all,

I have question regarding the wall shears stress and the velocity gradient in the slanted pipe

Based on Fluent user guide:
In a laminar flow , the wall shear stress is defined by the normal velocity gradient at the wall

There will be no problem to calculate the normal velocity gradient for the case in the straight pipe. For example the axial flow is in z direction, the velocity gradient can be calculated by find the difference of the adjacent z velocity to the 0 velocity at the wall then divide by the distance from the adjacent z velocity to wall.

How about in the slanted pipe when there is flow in the y and z direction? Which velocity need to be taken to calculate for the velocity gradient? attached figure

I have this problem since my geometry is an irregular shape. It have difference direction of the velocity.
I need to verify why I have the high WSS at certain region. The only way is by using the velocity gradient. But in this case, Im not sure which velocity should be taken.

Hope someone can help me.

Thank you so much.


skyblue_mech September 26, 2012 15:00

Hi ,
I am having the same problem for calculating the WSS for complicated boundary shapes. Did you get the answer ?
Please let me know if u did.

wanna88 October 1, 2012 22:34


Do you find any answer for this?
I found out that there are different ways to calculate the WSS for 2D and 3D case.

Wall shear stress = u_tau = sqrt{ tau_wall / rho }.

For a 2-D flat plate flow, you can assume tau_wall = tau_xy = mu du/dy_wall.

For a 3-D flow, you need to compute tau_wall from the stress-strain tensor (tau). You can do this by:

tau_wall = sqrt{ Rx^2 + Ry^2 + Rz^2 },


Rx = tau_xx * nx + tau_xy * ny + tau_xz * nz and so on...

Here, {nx; ny; nz} is the face normal direction attached to the wall.

But, Im not really understand the above explanation

I found out in 1 paper
wall shear stress = 2*miu*(strain rate tensor.normal vector on the wall)

Strain rate tensor + 1/2 (dui/dxj + duj/dxi)

Can you help me to take a look also on this?:)

Thank you.


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