The field management for 2D differential viscoelastic simulation!

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yaoshun0727 posted this 07 April 2020

I  am using polyflow to perform a 2D differential viscoelastic simulation of the extrusion die, using the DEVSS and SU methods. In field management, I added the field D DEVSS. Then i obtain the DEVSS results in the cfd-post. But i have a question that what the physical meaning of DEVSS is?

Regards!

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yaoshun0727 posted this 07 April 2020

yaoshun0727 posted this 07 April 2020

bducoeur posted this 08 April 2020

When the EVSS technique is used for solving the viscoelastic constitutive equation, the extra-stress tensor T is written as T = S + 2.η.D, while the constitutive equation is rewritten accordingly. Hence there are two tensors, S and D. Since they are used within the context of the EVSS technique, they have been named S EVSS and D EVSS.
[See also: D. Rajagopalan, R.C. Armstrong and R.A. Brown, Finite element methods for calculation of steady viscoelastic flows using constitutive equations with a Newtonian viscosity, J. non-Newt. Fluid Mech., 36 (1990) 159-192]

When the DEVSS technique is used for solving the viscoelastic constitutive equation, the constitutive equation for the extra-stress tensor T is kept unchanged, it has been named T DEVSS. Only the momentum equation is modified, a viscous term expressed in terms of velocity gradient unknowns is added, while a counterpart expressed in terms of rate-of-deformation tensor unknowns is removed.
A new tensor is thus calculated, the rate-of-deformation tensor. Within the context of the DEVSS technique, it has been named D DEVSS.
[See also: R. Guénette and M. Fortin, A new mixed finite element method for computing viscoelastic flow, J. non-Newt. Fluid Mech., 60 (1995) 27-52]

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yaoshun0727 posted this 09 April 2020

Thanks for your kind reply. And the DEVSS is divided into 4 parts: DEVSS11, DEVSS12, DEVSS22, DEVSS33. So the DEVSS is the sum of these components?

bducoeur posted this 09 April 2020

Those are the component of the tensor.   Lets say a tensor T

 

What is the meaning of the component Tij of a stress tensor?

It is the j-th component of the force applied on an infinitesimal element, whose orientation is along the i-direction. Note that individual components of a tensor are not really relevant, on the same way as individual components of a velocity vector are not really more relevant either...

What is the meaning of T11, T12, T22, T33 in a 2D axisymmetric flow?

The reference frame is (r,z), both directions being referred to as 1 and 2. They are respectively the radial and axial directions. A third direction (theta or t), referred to as 3, is also considered : the hoop, azimuthal or circumferential direction. Hence, T11 refers to Trr, T22 refers to Tzz, T12 refers to Trz, and T33 refers to as Ttt.

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