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Hooman December 17, 2011 13:01

1D Stress Tensor
 
Hi,

What does the second and third terms of the stress tensor reduce to when dealing with the 1D compressible and viscous flow? (So only the pressure term remains)

stress tensor = -P +2*mu*D- 2/3*mu*div(v)
where D = the rate of strain deformation = 1/2*(grad(v)+grad(v)^T)

Thanks in advance!

cfdnewbie December 17, 2011 13:10

well, just set all the derivatives wrt y and z to zero, so sth like div(v) will become du/dx...

Hooman December 19, 2011 08:32

Hi, Yeah I think I know how to get it mathematically:
stress tensor = -P +1/3*du/dx
I needed to check this as I was not sure what happens physically in a 1D case where a force is applied in the same plane as the fluid velocity (say x-direction).

Also the equation originally involves two viscous stress: the dynamic viscosity which relates stress two linear deformations and the second stress which relates stress to volumetric deformations. And I was not sure if the second one will be present in a 1D case.

I would appreciate any references to 1D shear stress equations. I have found one but I can't quite derive the same equation they have so not sure if its correct.

Thank you in advance!

cfdnewbie December 21, 2011 05:01

http://www.jstor.org/pss/2157934

not sure if this is what you are looking for, though....:confused::confused:


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