## 4 Conclusions  
The present study numerically investigates the flow characteristics in the air-based density separator to optimize the separation process. The study proposes a new density separator design  
Figure 9: Effect of air inlet velocity on the (**a**) velocity magnitude of +4\(D\) duct hole diameter at point 1, (**b**) shear stress with different duct hole shapes and (**c**) vorticity magnitude with different duct hole shapes at a bed slanting angle (\(\theta\)) of 0\({}^{\circ}\).  
by installing air duct holes with different diameters and shapes to improve the ballistic trajectory of the airflow. The present study considers a 2D model of the density separator to optimize the air ballistic trajectory and the inclination angles of the vibrating bed by computing the flow properties in the separator model. Various inlet air velocities, duct hole diameters and shapes, and slanting angles of the vibrating bed are employed to determine the effects of the parameters on velocity magnitude, pressure distribution, shear stress, and vorticity magnitude.  
The air duct hole installed at the upper wall of the density separator improves the ballistic trajectory of the air stream. The recirculation zone formed on the vibrating bed is necessary for the collection of separated plastic material. Increasing the air duct hole diameter in a positive direction from the reference position increases the kinetic energy of the airflow. An increase in the fluid pressure negatively affects the plastic separation process. The +4\(D\) separator model increased the separation of PET and PVC material due to higher velocity and less pressure magnitudes. The introduction of triangular or round-shaped duct holes increased the kinetic energy of the ballistic trajectory. The increase in the slanting angles of the vibrating bed improves the ballistic trajectory but reduces the efficiency of the separation process by decreasing the recirculation zone on the vibrating bed. Shear stress and vorticity also increase with an increase in the bed inclination angles. The increasing air inlet velocity also increases the kinetic energy of the ballistic trajectory. An optimized value of the bed slanting angle and air inlet velocity must be selected to increase the plastic separation process. The separation process increases with the air duct hole diameter of +4\(D\), the triangular duct hole shape (diameter of 1.5_D_), the low bed slanting angles (less than 4\({}^{\circ}\)), and the inlet air velocity of 35 m/s. Consideration of the plastic is recommended in future studies to address the real physical phenomenon in the density separator. Therefore, a numerical study is proposed to examine the effects of the interaction between air flow and plastic waste to increase the separation process.  
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B2005515) and a grant from the Priority Research Centers Program through the NRF, as funded by MEST (No. 2010-0020089).  
[PERSON] conceived and designed the simulations and paper structure; [PERSON] performed the simulations; [PERSON] designed the model and analyzed the results; [PERSON], [PERSON] and [PERSON] provided the data; [PERSON] gave suggestions and made corrections in the paper; [PERSON] wrote the paper.  
The authors declare no conflict of interest.