## 4 Conclusions  
In this study, CFD simulations were performed to investigate the flow characteristics in a differential motion assembly during the IPP-Coring process with different flow rates. The effects of the diameter of the ball seat and the structure of the ball seat outlet on the fluid status, velocity, and pressure distribution were thoroughly investigated. Thus, the hydraulic structure of the differential motion assembly was improved. The specific conclusions are presented as follows:  
1. There was a severe vortex area in the differential motion assembly due to the presence of the ball seat. Increased fluid viscosity can increase the local velocity of the flow and decrease the size of the vortex area. In addition, as the inlet flow rate increased from 0.01 to 0.04 m\({}^{3}\)/s, the vortex velocity near the wall and the pressure drops between the inlet and outlet of the differential motion assembly increased by 3.8- and 14-fold, respectively.
2. With the increase in the ball seat diameter from 30 to 40 mm, the maximum velocity in the differential motion assembly decreased to 0.55 times that of the original assembly. The axial length of the vortex area and the vortex velocity near the wall decreased to 0.85 and 0.67 times the values of the original assembly. In addition, the pressure drop decreased to 0.2 times that in the original assembly with a 30 mm ball seat diameter.
3. Compared with the cone and original right-angled structures, the arc structure at the ball seat outlet of the differential motion assembly showed the best hydraulic properties. Its axial vortex length and vortex velocity near the wall in the differential motion assembly decreased, respectively, to 0.7 and 0.4 times the values for the system with the original right-angled structure at the ball seat outlet. The pressure drop was only 0.33 times that of the system with the original right-angled structure at the ball seat outlet.
4. Considering the above results, the ball seat with a 40 mm diameter was selected for the differential motion assembly, and the outlet of the ball seat was set as the arc structure. The calculated results of the particle trajectories and the erosion show that the improved structure has lower particle velocity and less impact on the wall, and the average erosion rate decreased to 0.42 times the original structure. Due to the  
Figure 17: Photographs showing the outlet of the ball seat of the original and improved differential motion assemblies after the experiments.  
lower pressure drop and erosion rate, the improved differential motion assembly may have better promise for field performance.  
Conceptualization, D.G. and J.L.; methodology, D.G., D.W. and Y.Z.; software D.G. and X.F.; validation, D.G., J.L. and D.W.; formal analysis, D.G. and X.F.; investigation, D.G. and Y.Z.; resources, H.X.; data curation, D.G.; writing--original draft preparation, D.G.; writing--review and editing, D.G., J.L. and H.X.; visualization, D.G.; supervision, H.X.; project administration, H.X.; funding acquisition, H.X. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful for the financial support from the National Natural Science Foundation of China (No. 51827901), the National Science Fund for Distinguished Young Scholars (No. 52225403) and the Sichuan Science and Technology Program (2023 NSFSC0780).  
Not applicable.  
Raw or processed data required to reproduce these findings cannot be shared at this time, as the data also form part of an ongoing study.  
The authors declare no conflict of interest.