POLYFLOW - a simple model for viscoelastic coextrusion (encapsulation) ?
How can one define a simple viscoelastic flow model for coextrusion, in order to detect possible viscoelastic effects, originating e.g. from second normal stress difference.
Let us consider a situation as described in the figure below. One can probably identify an angular sector for the flow, whose channel exhibits some level of symmetry. In the figure, on guesses the entry at the back, planes of symmetry, a wall (below), and the exit (at the front).
<a target=_blank href="http://www.fluentusers.com/support/solutions/1572/viscoelastic.gif">http://www.fluentusers.com/support/solutions/1572/viscoelastic.gif</a>http://www.fluentusers.com/support/solutions/1572/viscoelastic.gif
A viscoelastic flow is defined (single mode Giesekus model), together with a transport variable or species (named here "colour"). Two parameters of the Giesekus model depend on that transport variable via a PMAT function: presently, the relaxation time and the non-linear parameter alpha depend on the "colour". For this dependence with respect to the transport variable, the smoothed ramp is used, and defined in such a way that the function is close to 0 when the "colour" is close below 0, and the function is close to 1 when the colour is above 0. In other words, parameters a, b, c and d are respectively equal to -0.05, 0, 0.05 and 1. There is a Clarify solution for the smoothed ramp parameters.
The boundary conditions for the "colour" variable, defined at the entry of the computational domain, are such that the colour is initially positive on half the entry and negative on the other half. One may imagine here that one fluid is represented with a positive colour, while the other one is represented with a negative colour. This is seen at the entry, in the figure below. The flow transports that colour, and the distribution is possibly altered with the secondary motions intrinsic to the Giesekus model (second normal stress difference). If one adds a dependence of the relaxation time and of the non-linear parameter alpha with respect to the "colour", one gets an interesting mechanism, where a layer displaces the other.
Eventualy, when incorporating an evolution on the flow rate, one sees that the effect described is enhanced with increasing flow rate. This is in a way in qualitative agreement with some user`s question.
Of course, this is not the eighth wonder on Earth: it is a model, quite simplified, defined for a possible qualitative description of an observed mechanism. For the time being, it is difficult to decide whether it suffices for describing a mechanism. In particular, all details of the actual physics or not necessarily known.
Interestingly, this calculation can be achieved with the standard version of POLYFLOW. It however invokes a former version for viscoelastic routines, which are made available with the use of the keyword OLD_VISCOELASTIC in the .p3rc file for the POLYDATA session, in order to have access to former version of routines. Files for calculation are also available here below
<a target=_blank href="http://www.fluentusers.com/support/solutions/1572/viscoelastic.tar.gz">http://www.fluentusers.com/support/solutions/1572/viscoelastic.tar.gz</a>http://www.fluentusers.com/support/solutions/1572/viscoelastic.tar.gz