## 3 Application
### Erosion  
In the process of pipeline transportation, the solid particles contained in the fluid will wear down the pipeline due to repeated collision. Therefore, erosion prediction and process protection are particularly significant. The simulation of the erosion process based on CFD-DPM is a low-cost and effective method [23]. The modeling process mainly includes three steps: flow modeling, particle tracking and associating particle impact information with erosion damage. The existing erosion models mostly rely on theoretical or empirical methods and mainly consider the role of solid particles [24]. In two-phase flow erosion, scholars mainly focus on the effects of fluid parameters, particle characteristics, pipeline structure and operation on erosion. In a great quantity of studies (numerical simulation or experiment) in the past few decades, the accurate influence of almost all effective parameters (such as material, particle velocity, incident angle, fluid phase viscosity, density, etc.) on pipeline mass loss is now very clear [25; 26; 27; 28; 29]. However, particle-fluid, particle-particle and particle-wall interactions are not included in the influencing factors of erosion. In the numerical study of partial erosion and wear of 90\({}^{\circ}\) elbow by CFD-DPM, it was found that in addition to the drag force between particles and fluid, the saffman force is also an important force affecting particle motion. Furthermore, in the curved part, the secondary collision between the particles and wall in circular and square pipes led to the difference in the wear phenomenon between particles with different particle sizes [30]. Due to the multiple repetitiveness of interparticle forces, the DDPM used may not fully capture the intricacies of particle-particle interactions, particularly at higher solid concentrations. [PERSON] et al. compared DPM (one-way coupling) and DDPM (four-way coupling) on simulating the effect of particle load on erosion. According to the erosion rate under a high particle load, DDPM can calculate the critical particle load compared with DPM (Figure 3), which is in better agreement with the experimental data [31]. The reasonable optimization of the pipeline structure plays a positive role in reducing erosion. Due to a great deal of parameters in the pipeline structure, [PERSON] et al. constructed the objective function with the throttle valve bonnet length, the bonnet  
Figure 2: Particle tracks compared to flow streamlines [21]. external radius and the chamber inner radius as variables and the mass loss as a dependent variable. Combined with the response surface method and genetic algorithm, the valve body structure was optimized. The average erosion mass loss was 30.2% lower than the original cavity size [32]. In addition to the direct optimization of the structure, adding ribs at the elbow to reduce the one-time collision of particles can also effectively reduce the overall erosion of the pipeline, but the ribs themselves are also eroded [33]. It is certain that the application of CFD-DPM/DDPM in two-phase flow erosion prediction and protection has matured. The optimization design based on CFD erosion simulation may not fully account for the dynamic changes in operations, potentially limiting the practical applicability of the findings. Compared with the erosion of two-phase flow, the erosion modeling of multiphase flow is more complex because more phases are involved in the erosion process. [PERSON] et al. studied and compared the effects of gas-solid two-phase flow and gas-solid-liquid three-phase flow on erosion and displacement by using the combined model of fluid-structure interaction (FSI), CFD and DPM [34]. By setting up a control group, it was found that a change in the discrete phase content has little impact on pipeline displacement, but the concentration has a notable effect on erosion. Droplets of the same size have less momentum, resulting in droplets that have less effect on erosion than sand.