## 1 Introduction
Moreover, numerical simulation can reduce the experimental cost and overcome the limitations of experimental methods [23], and is widely used in the field of modern engineering technology. Related achievements include use of the k-epsilon turbulence model by [PERSON] [24], who numerically simulated the erosion of two-phase flow in a straight pipe and developed the rule of particle-wall interaction under turbulent conditions. [PERSON] [25] simulated the effect of sand particles on fluids during oil and gas production based on CFD technology and provided a solution for valve manufacturers to reduce the sensitivity of particle corrosion. In addition, [PERSON] [26] used the CFD method, coupling discrete element model (DEM), population balance model (PBM), etc., to study the impact of particle collision frequency and particle velocity on the erosion of the pipeline, which enriched the research on pipeline erosion problems using Numerical simulation methods. In order to further explore the influence of pipe diameter and solid particle diameter on the erosion of pipes, [PERSON] [27] proposed a baseline model suitable for adiabatic bubbles; [PERSON] [28] found that there was a sudden change in particle size; as the particle size increased, the wear rate decreased. [PERSON] et al. [29], in their analysis of the corrosion of oil and gas pipelines, pointed out that small particles can cause more severe erosion of pipelines. In terms of model selection, [PERSON] [30] compared the advantages and disadvantages of the Euler model and the Lagrangian model; [PERSON] [31] compared and analyzed the Lagrangian method and the Euler solution of the Euler equation. Recently, [PERSON] and [PERSON] [32] also predicted the erosion depth of the pipe elbow after being impacted by particles, taking into account the particle rotation characteristics under static conditions; however, they did not consider the influence of vibration conditions; [PERSON] [33] and [PERSON] [34] combined the CFD method and k-epsilon and k-omega models to study the influence of pipeline particle size, pipe diameter, flow rate, carrier viscosity, impact surface materials and other potential factors on pipeline erosion characteristics. Unfortunately, none of their studies considered the effects of vibration conditions. Although [PERSON] et al. [35] studied the wear characteristics of seawater pipes at different vibration frequencies and vibration ranges, they did not study coupling factors such as particle size and particle rotation. Therefore, it is necessary to continue to study the influence of different potential factors on pipeline erosion when coupled with vibration. In this study, the seawater pipeline of polar ships was selected as the research object, and the effects of solid particles and vibration conditions were taken into account. The DPM discrete model and erosion wear model were used for the numerical analysis of pipeline erosion, where the amplitude and vibration frequency were set in the range of 0.5-1.5 mm and 0-80 Hz, respectively [36]. Factors such as sea ice particle diameter, two-phase flow velocity, particle rotation characteristics and ice packing factor (IPF) were coupled with the natural vibration of the ship's hull. The wear of the pipeline under static conditions was compared, and the erosion law of the seawater pipeline was analyzed. Finally, the optimal measures for pipeline vibration protection were proposed.