## 4 Results and Discussion  
### Effects of Flow Velocity  
The effects of velocity change on pressure drop in the static state and vibration state were explored under the H-H direction velocity. The simulation results showed that the pressure drop in the straight pipe increased proportionally with the flow velocity, which was consistent with those of [PERSON]'s study [43]. After further analysis, it was found that when the inertial force of the particle was much less \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Part** & **Description** & **Boundary Condition** & **Setting Mode** \\ \hline Fluid & The fluid domain & FLUID & – \\ Inlet & Pipe inlet & Velocity Inlet & 3 m/s \\ Outlet & Export pipeline & Out Flow & Escape \\ Wall & Straight pipe and corner wall & WALL & Reflect \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial boundary conditions in FLUENT. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Working Condition** & **Velocity (m/s)** & **Flow Direction 1 ** & **Grain Diameter (mm)** & **IFF (\%)** & **Rotation 2 ** \\ \hline
1 & 3 & 1 & 0.5 & 5\% & 0 \\
2 & 1 & 0 & 0.5 & 5\% & 0 \\
3 & 2 & 0 & 0.5 & 5\% & 0 \\
4 & 3 & 0 & 0.5 & 5\% & 0 \\
5 & 4 & 0 & 0.5  
than the buoyancy force at the velocity of 1 m/s, the particles floated on the top of the pipe and flowed in layers (Figure 6A). Once vibration was introduced, the pressure drop curve significantly changed when the velocity was over 3 m/s. By comparing the variation of wear rate with and without vibration, it could be determined that the pipeline vibration played a major role in flow resistance within the velocity range of 0-3 m/s, while the velocity began to play a major role once velocity exceeded 3 m/s. At the same flow rate, the pressure drop under vibration was always greater than that of the static pipe. In the static state, the abrasion increased with the increase of velocity when the speed was less than 3 m/s. The growth rate of abrasion was not high, possibly because at this point, ice particles had poor follow ability, and buoyancy played a major role. The accumulation of ice particles on the top of the pipe could affect wear on the top of the pipe. As the flow continued to increase, the ice particles pulled by the water were strongly pulled into the flow and gradually formed a mixed and even suspension. The greater the flow velocity, the greater the direct impact strength on the outer wall of the pipe and the higher the wear rate (Figure 6B). Then, the relationship between the curve of maximum wear rate at different angle sections of the 90\({}^{\circ}\) elbow with flow rate was further explored. At the same angular section, the wear rate increased with the increase of the flow rate. It increased slowly at velocities under 3 m/s and began to increase significantly after exceeding 3 m/s (Figure 6C). Moreover, after exceeding 3 m/s, the wear rates of 30\({}^{\circ}\) and 90\({}^{\circ}\) sections at the same velocity were higher than those of other angular sections. Combined with Figure 6B, C, it can be seen that, within a certain velocity range (1-3 m/s), the wear of the bend was relatively low, and vibration was the main factor that affected the erosion of the wall of the pipe by sea ice particles. When the velocity of flow exceeded this range, the inertia of sea ice particles increased, gradually overcoming the floating lift and vibration rebound force, and the impact cutting amount on the pipe increased, and the abrasion increased accordingly. The 30\({}^{\circ}\) cross-section and 90\({}^{\circ}\) cross-section were affected by the direct impact of ice particles and the effect on secondary flow, respectively, leading to these two sections having the most serious wear and tear. Particles at a velocity of 1 m/s had very disordered trajectories under the influence of vibration in the pipeline and collided back and forth with the wall surface, resulting in a large wear rate at this velocity (Figure 7).