## 4 Simulation Study of De-Bonding Performance of Composite In Situ Separator
### Results and Discussion  
1. Pitch  
1. Axial Displacement  
Figure 6 shows the relationship between the axial displacement and time for GHBS particles under different helical flow channel pitches. By comparing these results with those in the literature [10], it is evident that the addition of the helical flow channel effectively extended the residence time of GHBS particles in the cylindrical section of the separator, from approximately 0.12 s in the classic hydrocyclone separator to about 0.45 s. Although the residence times of particles in the cylindrical section were roughly the same, around 0.45 s, for different pitches, a rapid decrease in the axial velocity was observed near the exit of the helical section. According to the subsequent particle trajectory results (Figure 7), this turning point occurred because the particles' high axial velocities overcame the boundary layer effect and caused collisions with the flow channel, indicating that the total residence time of particles in the separator was not linearly related to the pitch. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **1 st** & **2 nd** & **3 rd** & **4 th** & **5 th** \\ \hline Helical Section Pitch (mm) & 17.1 & 20 & 24 & 30 & 40 \\ Inlet Type & Tangential & Circular & Involute & Oblique & \\ Particle Diameter (\(\upmu\)m) & 10 & 20 & 30 & 40 & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation plan. Moreover, since the helical flow channel reduced the axial velocities of GHBS particles in the cylindrical section, it also affected their axial movement in the conical section. When the pitch was 17.1 mm, the residual axial velocities of the GHBS particles upon leaving the cylindrical section were insufficient to overcome the axial separation in the conical section, preventing movement toward the underflow outlet within 2 s of the simulation. 2. Particle Trajectory  
In Figure 7, it can be observed that under the influence of the helical flow channel, the GHBS particle trajectories transitioned from a dispersed state at the inlet section to moving along the flow channel, eventually aligning with the flow channel. The smaller the helical pitch, the sooner the particle trajectories aligned with the flow channel. For  
Figure 6: Relationship between axial displacement and particle residence time for different pitches. Figure 7: Particle trajectories with different pitches. instance, when the pitch was 17.1 mm, the particle trajectory aligned with the flow channel at approximately one-third of the cylindrical section, whereas when the pitch was 40 mm, most particles did not align with the flow channel before leaving the cylindrical section. 3. Cementing Bond Load  
Figure 8 shows the relationship between the load on the cementing bonds of GHBS particles and the axial displacement within the separator under different helical flow channel pitches. As shown in the figure, compared with the classic hydrocyclone separator [10], the designed composite separator also exhibited a large bond load value at the inlet section for GHBS particles. This peak value was not significantly affected by the flow channel pitch, which remained at around 20 kPa across all five pitches, with a standard error of approximately 4 kPa. However, in the classic hydrocyclone separator, this maximum load appeared only at the inlet and then quickly decreased, whereas in the composite separator, the cementing bond load decreased more slowly with increasing axial displacement and showed a resurgence and a second peak toward the middle and rear sections of the cylinder. Based on Figures 6 and 7, it can be inferred that the second peak occurred due to the particles overcoming the boundary layer and colliding with the helical flow channel. This also explained why the axial position of the second peak shifted further from the inlet as the pitch increased.