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Theory Behind Calculating Wall Shear Stress
Posted 28 janv. 2015, 16:33 UTC−5 Fluid & Heat, Computational Fluid Dynamics (CFD), Parameters, Variables, & Functions Version 4.4 1 Reply
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So I'm fairly new to Comsol and still don't know much about the theory behind somethings and I wanted to know what is the proper way to derive shear stress in a two-dimensional model.
For a while I have been using this equation: spf.mu*(uy+vx)
Basically calculating the shear rate by finding the gradient of Vx in the y direction adding the gradient of Vy in the x direction
However recently I realized that Comsol has an variable for shear rate called spf.sr
I get similar results but the spf.sr gives me only positive values.
Did I miss something in my equation? Which way do you think is correct?
Thanks,
Chris
For a while I have been using this equation: spf.mu*(uy+vx)
Basically calculating the shear rate by finding the gradient of Vx in the y direction adding the gradient of Vy in the x direction
However recently I realized that Comsol has an variable for shear rate called spf.sr
I get similar results but the spf.sr gives me only positive values.
Did I miss something in my equation? Which way do you think is correct?
Thanks,
Chris
1 Reply Last Post 29 janv. 2015, 10:22 UTC−5
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Posted:
10 years ago
Hi
I am not the greatest theorist the world and if someone wants to correct me please do, but I can try and help with what I know. But to start with the succinct answer to your problem is to use the spf.mu*(uy+vx).
To explain why, the way you work out what the shear stress on a surface is you need to find the "surface traction" which is basically the force acting on the surface. You find this by multiplying the stress tensor with the normal vector to your surface.
Once you have the surface traction, and as you want the shear stress i.e. the force tangential to the surface, you dot your surface traction with the tangential vector. There you have it, the shear stress.
Now if your wall is parallel to the x or y axis and you go through the above you find that the shear stress comes out as mu*(uy+vx). If its not then I think you probably have to scale by the tangential and normal vectors manually, but thankfully there already pre-built into COMSOL, (the normal vector components are nx,ny and tangential vector tx,ty) .
Not to get too distracted from your question but from my understanding the shear rate is second invariant of velocity gradient tensor and is often used in Non-Newtonian fluids where your viscosity is shear rate dependent.
Hope this helps
I am not the greatest theorist the world and if someone wants to correct me please do, but I can try and help with what I know. But to start with the succinct answer to your problem is to use the spf.mu*(uy+vx).
To explain why, the way you work out what the shear stress on a surface is you need to find the "surface traction" which is basically the force acting on the surface. You find this by multiplying the stress tensor with the normal vector to your surface.
Once you have the surface traction, and as you want the shear stress i.e. the force tangential to the surface, you dot your surface traction with the tangential vector. There you have it, the shear stress.
Now if your wall is parallel to the x or y axis and you go through the above you find that the shear stress comes out as mu*(uy+vx). If its not then I think you probably have to scale by the tangential and normal vectors manually, but thankfully there already pre-built into COMSOL, (the normal vector components are nx,ny and tangential vector tx,ty) .
Not to get too distracted from your question but from my understanding the shear rate is second invariant of velocity gradient tensor and is often used in Non-Newtonian fluids where your viscosity is shear rate dependent.
Hope this helps