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 Dave442 October 17, 2012 11:42

Calculation of Wall Shear Stress

Dear all,

I am trying to understand how wall shear stress components are calculated in CFX. I have carried out a steady-state analysis of incompressible laminar fluid flow over a flat plate and validated the solution against the Blasius solution. As far as I am aware (I could not find a definition in the theory manual) the components and magnitude of the wall shear stress vector are defined as follows:

Tx = [Nx*Mu*(2*Du/Dx)]+[Ny*Mu*(Du/Dy+Dv/Dx)]+[Nz*Mu*(Du/Dz+Dw/Dx)]

Ty = [Nx*Mu*(Dv/Dx+Du/Dy)]+[Ny*Mu*(2*Dv/Dy)]+[Nz*Mu*(Dv/Dz+Dw/Dy)]

Tz = [Nx*Mu*(Dw/Dx+Du/Dz)]+[Ny*Mu*(Dw/Dy+Dv/Dz)]+[Nz*Mu*(2*Dw/Dz)]

T = sqrt(Tx^2+Ty^2+Tz^2)

In CFX-post I have exported the following variables for a sample node located roughly halfway along the length of the plate:

Dynamic Viscosity = 8.90E-04
Normal X = 0.00E+00
Normal Y = -1.00E+00
Normal Z = 0.00E+00
Velocity u.Gradient X = -5.27E-02
Velocity u.Gradient Y = 4.13E+02
Velocity u.Gradient Z = 0.00E+00
Velocity v.Gradient X = -9.79E-06
Velocity v.Gradient Y = 5.93E-02
Velocity v.Gradient Z = 0.00E+00
Velocity w.Gradient X = 0.00E+00
Velocity w.Gradient Y = 0.00E+00
Velocity w.Gradient Z = 0.00E+00

Using these variables and the equations above I calculate the following values for the components and magnitude of the wall shear stress vector:

Tx = -3.68E-01
Ty = -1.06E-04
Tz = 0.00E+00
T = 3.67E-01

Unfortunately, when I compare the calculated values to those exported from CFX I notice some differences:

Tx = 3.67E-01
Ty = -1.21E-19
Tz = -4.84E-25
T = 3.67E-01

Although the magnitude comes out the same I am clearly getting something wrong. If anyone has a better idea of how the wall shear stress components are calculated I would really appreciate some advice.

Thanks,
Dave

 ghorrocks October 17, 2012 17:42

-4.84E-25 = -1.21E-19 = zero with a bit of numerical noise. So your calculation of Ty and Tz are correct within numerical accuracy. You have a sign error in Tx, but the magnitude is correct.

 Dave442 October 17, 2012 19:31

Hi Glen,

Thanks a lot for replying. Your explanation makes sense for Tz = 0 but from my hand calculations should Ty not be slightly greater than zero?

The sign error for Tx occurs because, according to the results exported from CFX, the y-component of the normal vector Ny = -1. As the plate is flat I expected this component to be positive and if it was I guess the calculations would match up. Any ideas why it comes out as negative?

Also, do you think I have the overall methodology correct?

Many thanks,
Dave

 ghorrocks October 18, 2012 05:53

I do not have time to check your methodology. For you sign error check the definition of axes. Are you sure you have the directions correct?

Don't forget that you are returning the value of a volume centred slightly off the wall, and that it is a representative average of the conditions of that volume. So you will always get small errors associated with that.

 Dave442 October 18, 2012 07:26

1 Attachment(s)
Hi Glen,

Sorry, I wasn't asking you to check my calculations or anything. I was just wondering, as I cant find the definition in the theory manual, if the wall shear stress vector is definitely derived in CFX from the dot product of the viscous stress tensor and the unit normal vector as follows:

Tau = T . n

T = viscous stress tensor
n = surface normal vector
Tau = wall shear stress vector

As far as my axes are concerned, I generated my model using the global Cartesian axes. I have attached a picture to illustrate (the red vectors indicate the direction of the surface normal vector).

Thanks again for your input, its much appreciated.
Dave

 mrkmrk May 16, 2014 15:58

Calculation of Wall Shear Stress

Hi all,

I want to calculate wall shear stress on a curved pipe so that
Somewhere in this pipe the wall shear stress due to recirculation zones will become negative.
I should not use "Wall shear" variable in the ansys cfx library
(Because "wall shear=sqrt ((wall shear X^2) + (wall shear Y^2) + (wall shear Z^2))" and this will make positive every negative values)

Can anyone guide me how calculate it by Ansys CFX v14.5?
I have modeled a laminar water flow in straight pipe (which is rotated 45 degree about x axis)
And calculated wall shear stress both analytically and numerically but they are not the same (because tangential WSS and Wall shear Z are not the same)

Analytical solution:
WSS= 5.960229836*e-6 Pa

Numerical solution:
Wall shear Z= 6.1361e-006 Pa
Wall shear= 8.67757e-006 Pa

Hope to see a response.

 ghorrocks May 17, 2014 04:06

Have you covered the basics?

http://www.cfd-online.com/Wiki/Ansys..._inaccurate.3F

 mrkmrk May 18, 2014 05:23

Hi Glenn,

I really appreciate your help, your link was so useful
but I want to calculate tangential wall shear stress, in this way I found that I should use "Normal X/Y/Z" variables in CFX, now the problem is when I probe this variables values at an arbitrary point located on a wall, CFX cannot calculate it, but when i export this variables value on a surface CFX can calculate it for every point that is located on this face (i.e. this wall), please tell me how solve this problem?is there an alternative way?

 ghorrocks May 18, 2014 06:47

Is your problem that you cannot calculate the wall shear stress, or is your problem that your simulation is inaccurate?

The link I gave discusses accuracy, but your question suggests you do not know how to calculate it.

 mrkmrk May 18, 2014 08:49

I cannot calculate tangential WSS on a curved line of a curved wall.

 ghorrocks May 18, 2014 18:17

WSS exists on walls. Walls are surface objects. When you do probes you probe the volume mesh, and WSS does not exist in the volume mesh.

How are you trying to calculate WSS? In the solver or in CFD-Post?

 mrkmrk May 19, 2014 00:40

Calculation of Wall Shear Stress

Hi Glenn,
good night,

In the CFD-Post.

 ghorrocks May 19, 2014 01:23

So can't you export the Wall Shear X, Y and Z values from CFD-Post using the wall surface as the object to export?

 mrkmrk May 19, 2014 01:53

Calculation of Wall Shear Stress

yes, I can, but there is a problem with this,

let me explain what exactly I want to do,

in the CFD-post I can calculate wall shear stress in the directions of global coordinate, but on a curved line which is located on a curved wall non of this directions are not tangential direction, therefore I want to calculate tangential WSS by this method:

tangential wall shear stress vector= T-((T.N)N)

where T is wall shear stress vector and N is normal vector,now CFX can calculate T (by the probe or chart or export method) but cannot calculate N on a line, CFX only can calculate N on a surface, therefore it can only calculate tangential wss contour but I want tangential wall shear stress chart on a line.

thank you for your prompt response.

 ghorrocks May 19, 2014 06:57

In CFD-Post put a line object on the wall you wish to get the WSS from, and following the path you wish to study. I am not sure if there is a variable containing the normal direction of the line (if so this is easy) - but if not you can export the WSS on the line object, then at each point on the line work out the direction vector of the line (can do this with a simple scheme looking at the location of adjacent points). You can then work out the WSS components in the local frame of reference at each point on the line.

 mrkmrk May 19, 2014 10:04

Hi Glenn,

you solved my problem, I really do not know how to thank you?:):):)

GOOD LUCK

best regards,

David

 guxin7005 May 26, 2014 08:08

Quote:
 Originally Posted by ghorrocks (Post 492831) In CFD-Post put a line object on the wall you wish to get the WSS from, and following the path you wish to study. I am not sure if there is a variable containing the normal direction of the line (if so this is easy) - but if not you can export the WSS on the line object, then at each point on the line work out the direction vector of the line (can do this with a simple scheme looking at the location of adjacent points). You can then work out the WSS components in the local frame of reference at each point on the line.
Hi, ghorrocks,

I just try your method to plot the boundary velocity profile for comparison between simulation and experiments. My wall is not parallel to inlet flow, there is an angle of attack. When I plot the velocity profile, such as y vs u/U, for the u, should I should the Velocity u in CFD-POST, or should I calculate the velocity tangential to the wall?

Thank you!

 ghorrocks May 26, 2014 08:45

I did not describe a method for plotting velocity profiles. The method I discussed was for plotting wall shear stress along a boundary.

 brainok August 7, 2014 00:46

Dear Glenn

Dear Glenn
I am a beginner. I want to measure the Wall Shear Stress on the artery (flow is parallel along with artery). I understand that WSS cannot be take from cut plane ROI.

However, Streamline can show the WSS graphically, I want to know the number of WSS on distal or proximal area in the artery. Although your explanation give me some clue, I don't know how am I doing. Could you guide me to me sure WSS?

Many thanks
HyoSuk

Quote:
 Originally Posted by ghorrocks (Post 492831) In CFD-Post put a line object on the wall you wish to get the WSS from, and following the path you wish to study. I am not sure if there is a variable containing the normal direction of the line (if so this is easy) - but if not you can export the WSS on the line object, then at each point on the line work out the direction vector of the line (can do this with a simple scheme looking at the location of adjacent points). You can then work out the WSS components in the local frame of reference at each point on the line.

 ghorrocks August 7, 2014 06:34

There should be no need to do as you say. Have you seen my post #15? That explains how to do it.

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