1D Stress Tensor

Hooman · December 17, 2011, 12:01

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, 12:10

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, 07:32

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, 04:01

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

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

December 17, 2011, 12:01	1D Stress Tensor	#1
Hooman Member Join Date: Jun 2010 Posts: 94 Rep Power: 4	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 +2muD- 2/3mudiv(v) where D = the rate of strain deformation = 1/2*(grad(v)+grad(v)^T) Thanks in advance!

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December 17, 2011, 12:10		#2
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 444 Rep Power: 7	well, just set all the derivatives wrt y and z to zero, so sth like div(v) will become du/dx...

December 19, 2011, 07:32		#3
Hooman Member Join Date: Jun 2010 Posts: 94 Rep Power: 4	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!

December 21, 2011, 04:01		#4
cfdnewbie Senior Member cfdnewbie Join Date: Mar 2010 Posts: 444 Rep Power: 7	http://www.jstor.org/pss/2157934 not sure if this is what you are looking for, though....