## 3 Results and Discussion
### Air Duct Hole Diameter  
Contour and arrow plots in the air density separator were plotted to investigate the effect of the duct hole diameter on the separation process of the plastics. As Figure 3 shows, airflow particles move with a ballistic trajectory from the air inlet to the trash outlet. Recirculation zones formed on the vibrating bed, because the minimum flow is essential for the separation process, as the plastic material is collected in this region [23]. The introduction of duct hole at the upper wall of the density separator has clearly improved the ballistic trajectory of the air stream. Increasing the air duct hole diameter in the positive direction from the reference position increased the velocity magnitude. By contrast, increasing the air duct hole diameter in the negative direction reduced the velocity magnitude. Light plastic materials (PVC) are easily carried away with higher velocity magnitude and are fed upward on the vibrating bed, which in turn improves the separation process. Heavier PET materials fall on the small guide, which directs the materials to the outlet for recycling. Separation process is less effective when the air ballistic trajectory does not possess higher kinetic energy (velocity magnitude). Therefore,  
Figure 2: Comparisons of velocity magnitudes at point 1 for different (**a**) turbulence models and (**b**) mesh sizes at an air inlet velocity of 35 m/s and bed slanting angle (\(\theta\)) of 0\({}^{\circ}\). density separation cannot easily separate PET and PVC materials from each other. Moreover, the \(+4D\) separator model exhibited higher velocity magnitudes than other models (Figure 3c). These results show that increasing the duct hole diameter in the positive direction enhanced separation. Moreover, the results indicate that the \(+4D\) separator model is more suitable for separating the PET and PVC material because of the higher velocity magnitude. The kinetic energy (velocity magnitude) of the ballistic trajectory significantly varies at the leading and trailing edges of the vibrating bed (Figure 3). Therefore, two points have been selected at the vibrating bed to estimate flow properties. The effect of air duct hole diameter was further investigated  
Figure 3: Contour and vector plots of velocity magnitude inside (**a**) basic, (**b**) \(+2D\), (**c**) \(+4D\), (**d**) \(-2D\), (**e**) \(-4D\), (**f**) \(-6D\), and (**g**) \(-8D\) separator models at an air inlet velocity of 35 m/s and bed slanting angle (\(\theta\)) of \(0^{\circ}\). by computing the velocity and pressure magnitudes at points 1 and 2 (Figure 4). Velocity magnitude significantly increased with the installation of the air duct, which in turn enhances the separation process (Figure 4a). The velocity magnitude shows a minimum value near the vibrating bed and a maximum near the air duct hole. The minimum value near the vibrating bed indicates that the plastic materials are gathered on the bed. The +4\(D\) separator model shows the maximum velocity magnitude among all models. Increasing the duct hole diameter in the positive direction increases velocity magnitude. Velocity magnitude dropped remarkably when the duct hole diameter was increased in negative direction. Similar velocity magnitude results were obtained in the case of point 2, as duct holes with positive diameters show higher values of velocity (Figure 4b). This result implies that the +4\(D\) separator model enhances the separation process, because the model uses the kinetic energy of the ballistic trajectory more effectively in comparison with other models. The effect of various duct hole diameters on pressure distributions was observed by calculation at point 1 (Figure 4c). The basic model resulted in the highest pressure magnitude, whereas the +4\(D\) separator model produced the lowest. An inverse relation was found between pressure and the plastic separation process. Higher pressure reduces the screening process by decreasing the velocity magnitude of the ballistic trajectory.