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December 17, 2011, 12:01 |
1D Stress Tensor
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#1 |
Senior Member
Join Date: Jun 2010
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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! |
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December 17, 2011, 12:10 |
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#2 |
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cfdnewbie
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well, just set all the derivatives wrt y and z to zero, so sth like div(v) will become du/dx...
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December 19, 2011, 07:32 |
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#3 |
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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! |
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December 21, 2011, 04:01 |
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#4 |
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