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March 27, 2006, 11:47 
calculate y+ and u+ how to get wall shear stress?

#1 
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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 

March 27, 2006, 15:16 
Re: calculate y+ and u+ how to get wall shear str

#2 
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Wall shear stress = u_tau = sqrt{ tau_wall / rho }.
For a 2D flat plate flow, you can assume tau_wall = tau_xy = mu du/dy_wall. For a 3D flow, you need to compute tau_wall from the stressstrain 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? 

March 28, 2006, 02:12 
Re: calculate y+ and u+ how to get wall shear str

#3 
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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 

March 28, 2006, 05:58 
Re: calculate y+ and u+ how to get wall shear str

#4 
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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 

March 28, 2006, 06:29 
Re: calculate y+ and u+ how to get wall shear str

#5 
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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 

March 28, 2006, 09:33 
Re: calculate y+ and u+ how to get wall shear str

#6 
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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 BlasiusGleichung 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 

October 1, 2012, 22:30 

#7  
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Naimah
Join Date: Nov 2011
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Quote:
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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