## 3 Results and Discussion  
### Flow Characteristics in the Differential Motion Assembly  
The viscous effect is significant, and it is of great concern to the dynamic response of structures. Thus, in this study, the flow characteristics in the differential motion assembly with different fluid viscosities were studied first. The velocity streamlines in the differential motion assembly with different fluid viscosities are shown in Figure 4. It can be seen that a vortex area appeared in the differential motion assembly, and that the size of the vortex area increased as the viscosity of the fluid decreased from 1000 mPa\(\cdot\)s to 1 mPa\(\cdot\)s. To quantify the effect of the fluid viscosity on the flow velocity, we extracted the velocity at a monitoring line 220 mm away from the flow inlet, as shown in Figure 5. As seen in Figure 5, the maximum velocity in the monitoring line increased with the increase in the fluid viscosity, and the maximum in the monitoring line was 68 m/s for a fluid viscosity of 1000 mPa\(\cdot\)s. These results demonstrate that increased fluid viscosity can increase the local velocity of the flow and decrease the size of the vortex area. Figure 3: Grid independence study. Figure 2: Mesh and boundary conditions of the flow domain in the differential motion assembly. For the real working condition of the differential motion assembly, the fluid viscosity is usually about 100 mPa-s. Thus, we set the fluid viscosity as 100 mPa-s to study the effect of the flow rate and the inner structure. The flow characteristics of drilling fluid in the differential motion assembly, such as flow velocity and pressure distribution, directly affect the operational reliability and life of the assembly. Figure 6 shows the velocity streamlines in the differential motion assembly for different inlet flow rates. As the inlet flow rate increased, the velocity of the fluid in the differential motion assembly increased remarkably. The maximum velocity of 65 m/s appeared at the inlet of the ball seat for an inlet flow rate of 0.04 m\({}^{3}\)/s. Although the diameter of the flow domain increased abruptly from 30 to 90 mm after the drilling fluid flowed through the ball seat, the drilling fluid near the axis still flowed a distance of about 200 mm at a relatively large velocity (e.g., at approximately 64 m/s when the inlet flow rate was 0.04 m\({}^{3}\)/s) before the velocity of the fluid gradually decreased. However, due to the abrupt increase in the diameter of the flow domain at the outlet of the ball seat, a severe vortex was present near the wall of the differential motion assembly. The size of the vortex area showed almost no change for different inlet flow rates, which may be attributed to the same inner hydraulic structure. A vortex is a harmful flow characteristic that causes drilling fluid, which carries particles such as barite, to continuously impact and severely erode the inner wall of the differential motion assembly. Unfortunately, the inner wall with a diameter of 90 mm is a motion surface, and after the ball is dropped to trigger the differential motion assembly, this wall moves upward under hydrodynamic pressure to realize in situ pressure preservation. The erosion  
Figure 4: Velocity streamlines in the differential motion assembly with different fluid viscosities; the flow rate was 0.04 m\({}^{3}\)/s. Figure 5: Velocity distributions at the monitoring line with different fluid viscosities; the flow rate was 0.04 m\({}^{3}\)/s. of this wall causes sticking when the differential motion assembly moves upward and leads to the failure of the IPP-Coring system.