## 5 Conclusions and Recommendations  
In this study, using the 90\({}^{\circ}\) bend angle of the seawater pipeline of polar ships as the model, and coupled with the CFD numerical simulation method, the pressure drop of the two-phase flow in the pipeline and the wear rate along the pipeline were analyzed in terms of different velocity, ice packing factor (IPF), ice particle size and particle rotation. The following conclusions are obtained:  
* Vibration is the most important factor affecting the pressure drop and wear rate. The pressure drop under vibration is greater than that with the static pipe, while the wear rate under vibration is greater than that under the static pipe at same angle section of the elbow.
* With other conditions remaining unchanged, the wear rate first decreases when the flow velocity is up to 2 m/s, where the minimum wear appears. The wear rate is positively correlated with flow rate at the same angle section of the elbow. It slowly increases until the flow is up to 3 m/s, and the wear degree is more obvious at 30\({}^{\circ}\) and 90\({}^{\circ}\) sections.
* Under vibration conditions, the maximum wear rate has an inflection point that varies with changes of IPF. When IPF is less than 8%, the wear rate only slightly varies, while it greatly increases once IPF is more than 8%.
* Under vibration conditions, the pressure drops significantly when the particle diameter is in the range of 0.1-0.3 mm and tends to stabilize once the particle diameter is over 0.3 mm. The wear rate of the pipe worsens when the particle rotation is considered.  
To sum up, vibration is an important factor that causes pipeline wear. For ships sailing in polar regions, operators should strictly follow the ice-breaking work-flow to avoid local high-frequency vibration caused by improper operation. In the design of a pipeline layout scheme, the pipeline should be arranged in the H-V direction as much as possible. The flow rate should be controlled in the range  
Figure 11: The effect of particle rotation on wear rate along the path.  
Figure 10: Velocity comparison of particle rotation at different cross-sections at the elbow.  
of 2-3 m/s, IPF should be reduced as much as possible, and particle diameter should be controlled at about 0.3 mm. For piping seawater to important equipment, multi-degrees-of-freedom damping support can be used to improve the multi-dimensional damping effect of the pipeline and the service cycle of the pipeline.  
Conceptualization, L.X. and G.-C.L.; methodology, G.-C.L. and Z.-Q.L.; software, G.-C.L. and H.-W.C.; validation, L.X. and J.L.; resources, L.X.; writing--original draft preparation, G.-C.L. and Q.S.; writing--review and editing, G.-C.L.; supervision, L.X. and J.L.; funding acquisition, L.X. and J.L. All authors have read and agreed to the published version of the manuscript.  
National natural science foundation of China project \"study on the mechanism of ice crystals' influence on the heat transfer in polar transport vessel seawater system\" (grant no. 51479152) and projects from Key Lab of Marine Power Engineering and Tech. authorized by MOT (KLMPET2018-01) and the Fundamental Research Funds for the General Universities (WUT: 2019 III046 GX).  
The authors declare no conflict of interest.