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calculate y+ and u+ -how to get wall shear stress?

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Old   March 27, 2006, 11:47
Default calculate y+ and u+ -how to get wall shear stress?
  #1
Ralf Schmidt
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Hi!

I guess, that's a beginner question, but how to calculate u+ and y+???

Ok, I know the formula, for both I need the wall shear stress. But how to get this one??? I found some empirical formulas for pipe flow, but how to figure out the wall shear stress for any other kind of flow like flow around a bluff body???

Any help is highly appreciated

Ralf

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Old   March 27, 2006, 15:16
Default Re: calculate y+ and u+ -how to get wall shear str
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Biga
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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 },

where

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.

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Old   March 28, 2006, 02:12
Default Re: calculate y+ and u+ -how to get wall shear str
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Ralf Schmidt
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ok, thats theoretical equations. For all of them, I need the actuall velocity gradient close to the wall.

I want to generate a grid, thats first element in the BL is at about y+ = 5. How to set this distance, when I don't know the velocity gradient a prior??

Ralf

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Old   March 28, 2006, 05:58
Default Re: calculate y+ and u+ -how to get wall shear str
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Christoph
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I'm using the estimation of the Numeca manual: y = 6 (Re/L)^(-7/8) (L/2)^(1/8) y+

Re = Reynolds number L = Length scale y = 1st grid point distance y+ = what you want to reach

Normally that gives useful results.

Christoph

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Old   March 28, 2006, 06:29
Default Re: calculate y+ and u+ -how to get wall shear str
  #5
Ralf Schmidt
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thanks a lot for that!

For a bluff body (cylinder in axial flow), the Re number is made from the free stream velocity and the cylinder diameter D? Is D=L?

The wall shear stress (and therefore y+) depends on x, the distance from the beginning of the body. That's not in the equations...

Can you send me the reference? Maybe as pdf? I can not access the Nemeca manual.

Ralf

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Old   March 28, 2006, 09:33
Default Re: calculate y+ and u+ -how to get wall shear str
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Christoph
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In this case L=D.

I didn't manage to send you an email with attachement, so here's the text I'm refering to (it isn't really that much!):

Regarding your name I suppose that you don't need a translation of it...

-------------------------------

" Die Blasius-Gleichung bietet die Möglichkeit, den Zusammenhang zwischen dem Wandabstand der ersten Netzzelle und dem korrespondierenden y+ Wert vor der Rechnung abzuschätzen:

y = 6 (Re/L)^(-7/8) (L/2)^(1/8) y+

mit: Re Reynoldszahl L einer typischen Referenzlänge y dem Wandabstand der ersten Netzzelle

Größere Wandabstände können vom Löser ohne Probleme behandelt werden, führen jedoch zu einem Verlust an numerischer Genauigkeit. "

Quelle: NUMECA

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Old   October 1, 2012, 22:30
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Naimah
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Quote:
Originally Posted by Biga
;41614
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 },

where

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.

Did it help?

Hi,
Im not really understand about the explanation for 3D case. Can you explain more details for 3D case?

Thank you.

Regards,
Naimah
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