4.1 Geometrical configuration

Six screws with same length and diameter (designated by alphabetical A to F as shown in Figure 3) were employed in this work to verify the synergic effect of

The geometrical configuration of various screws (with screw elements and torsion elements).

Multi-Field Synergy Process for Polymer Plasticization: A Novel Design Concept for Screw… DOI: http://dx.doi.org/10.5772/intechopen.89616


Table 1.

(FEM), and present results of computational fluid dynamics (CFD) simulations of the flow and heat transfer of a viscous polypropylene (PP) melt in the screw with torsion elements to confirm this field synergy method and compared them with the

The geometrical configuration of the proposed torsion element is shown in Figure 2. The torsion channels are divided into N parts along the circumferential direction by torsion flights. Between every two adjacent torsion flights, there are two surfaces twisted by 90°along the axial direction. When polymer flows over the torsion channel, it is expected to undergo a torsional rotation (tumbling) under the forces generated from viscous friction with barrel wall and with the steering between two 90° twisted surfaces. As a result, spiral-shaped or torsional-shaped flow may occur in the torsion channel. In consequence, the intersection angle between the velocity and the heat flux will decrease to less than 90° compared with that in the standard screw channel, and then the synergic effect between the

Six screws with same length and diameter (designated by alphabetical A to F as shown in Figure 3) were employed in this work to verify the synergic effect of

velocity vector and the temperature gradient will be improved.

The geometrical configuration of various screws (with screw elements and torsion elements).

conventional screw in common use today.

The geometrical configuration and flow line of particles for a torsion element.

Figure 2.

Thermosoftening Plastics

Figure 3.

22

4.1 Geometrical configuration

Geometric parameters of simulation models.

torsion element. Screws were constructed of two kinds of polymer plasticization elements: the torsion element and the screw element. Screws A to D had six torsion elements with regular arrangement in different orders. As control subjects, screw E is a conventional screw without torsion element and screw F is a torsional screw without screw elements. Table 1 presents a summary of the geometric parameters of simulation models.

#### 4.2 Governing equations and boundary conditions

In this case, we assumed that the polymer fluid had non-isothermal transient laminar flow and was incompressible. No-slip conditions were adopted at the boundary. Polypropylene (PP) was chosen to be the model polymer due to its common use in polymer processing. Compared with viscous force, the inertial force can be neglected due to the high viscosity of PP. Therefore, the governing equations representing the flow field in this situation are shown in the form of Eqs. (11)–(13).

Continuity equation:

$$\frac{\partial u\_i}{\partial \mathbf{x}\_i} = \mathbf{0} \tag{11}$$

Momentum equation:

$$
\rho \frac{\partial u\_{\text{i}}}{\partial t} + \frac{\partial P}{\partial \mathbf{x}\_{\text{i}}} = \frac{\partial}{\partial \mathbf{x}\_{\text{j}}} \left( \eta \frac{\partial u\_{\text{i}}}{\partial \mathbf{x}\_{\text{j}}} \right) \tag{12}
$$

Energy equation:

$$
\lambda \rho \mathbf{x}\_{\rm p} \left( \frac{\partial T}{\partial t} + u\_{\rm i} \frac{\partial T}{\partial \mathbf{x}\_{\rm i}} \right) = \lambda \frac{\partial^2 T}{\partial \mathbf{x}\_{\rm i}^2} + \rho \tag{13}
$$

The apparent viscosity of PP was described by the Carreau-approximate Arrhenius model (Eq. 14), which match most polymers, to consider the factors of both temperature and shear.

$$\eta = \eta\_0 \left( 1 + t^2 \dot{\gamma}^2 \right)^{(n-1)/2} \exp\left[ -B(T - T\_0) \right] \tag{14}$$

The physical characteristics of the PP and screw material are listed in Tables 2 and 3, respectively. The choice of the polymer affects only the constants in the constitutive equation (Eq. (14)). Moreover, the Carreau-approximate Arrhenius model has been already validated for most polymer melts (e.g., polystyrene,
