*3.2.1 Speed distribution in different sections*

In the post-processing stage of the simulation, cross sections are defined at certain distances in the flow channel, to analyze the distribution of the velocity vectors in the same section and in each of them (**Figure 15**).

It can be seen that in the central regions of the sections in the feeding zone (conical zone), these velocity vectors have a higher value (celestial zone) than in the contours since, as the flow of the material is close to the inner wall of the flow channel, the velocity is zero (blue zone), this is consistent with what happens in reality when a fluid circulates through a conduit, and the velocity profile will be maximum in the center and tending to zero in regions close to the inside walls of the same.

As the flow of the molten material progresses, velocity vectors can be observed in the central areas of each cross section of greater magnitude (more intense green color), and this is due to the abrupt change of the geometry in the flow channel going from a conical rectangular; in particular, if we analyze the fourth cross section

**Figure 15.** *Distribution of speeds inside and at the outlet of the head.*

## *Design, Simulation, and Analysis of the Extrusion Process of a PVC Thermoplastic Profile… DOI: http://dx.doi.org/10.5772/intechopen.100909*

from the entrance of the flow to the head, it is observed that in the center there is a zone of velocity vectors of even greater magnitudes (red color).

Variations in the velocity vectors at each point of the same section cause the flow channel not to comply with the design principle of "minimum volume" of the heads; that is, the melt must reach all the points at the same time of the cross section or with the same speed.

These differences between the sliding of the fluid in the central zones with respect to those that are closer to the inner wall of the head cause internal shear stresses in the molten material that could later lead to the appearance of failures in service; this becomes more critical in profiles with complex shapes and in the particular case that between width and thickness, there is an important dimensional difference.

#### *3.2.2 Distribution of shear deformations*

In the graph shown below (**Figure 16**), it is observed that in the area where the geometry changes, shear deformations are generated (all colors are very high except blue), and this indicates that in these places, the molten material can get to degrade, especially in our case in which rigid PVC is used, due to the generation of high localized temperatures due to friction and shear.

In order to reduce or prevent this detrimental effect from being generated, it is advisable to modify the geometry of the head flow channel so that the transition between the two zones is smooth.

The simulation results predict in this case the detrimental effects that occur with the current head design, so that if it is necessary to build a new head, the geometry must be modified, so that the shear deformations are low and if possible, their

**Figure 16.** *Distribution of shear deformations.*

values are between 50 and 100 1/s, which is advisable to process this type of material and as described in the rheological test, they are the values where the Power or Ostwald Law is valid.

Another analysis that is carried out is on the contour areas at the entrance and exit of the molten material from the head, in which the shear deformation is zero, especially if a final parallel area of the matrix is left sufficient to have a swelling of the die, minimum fade, and within the recommended parameters [6].
