## 3 Application  
### Transportation  
As a technology of transporting solid materials through the flow of fluid in closed pipes, transportation plays an important role in the solid processing industry. The key to reducing transportation loss is to explore the law of internal flow in the pipeline and carry out transportation design, control and optimization. The CFD-DPM/DDPM method has been applied to evaluate the performance of dilute/dense phase transportation process.  
In the transportation of the gas-solid dilute phase, DPM which used to predict particle motion ignores the collision between particles and regards particles as massless particles, so it can barely be used for fine particles [16; 17] and cannot be used for large particles (diameter \(>5\) mm) [18]. When the volume fraction is less than 10% and the particles are small enough, DPM can calculate the following characteristics of particles in the fluid. In dense phase transportation, real particles invariably have various sizes and particle collision. DDPM is capable of considering the polydispersity of particles with the help of a size distribution model (Rosin-Rammler model). Based on the study of particle polydispersity in the transportation of drilling cuttings in annular bends [19], it was found that ignoring the size difference in the system may lead to overestimation of the particle deposition trend and overall pressure drop, resulting in inaccurate predictions. [PERSON] et al. used Euler-Euler, DEM and DDPM methods to simulate particle transport in a small-scale circulating fluidized bed (CFB) and compared the results. It showed that DDPM can be used to measure the change in the particle size distribution (PSD) and the interaction between particles in dilute and dense areas, and can then be used to predict particle transport in a fluidized bed. Meanwhile, the chemical interaction between the two phases should also be considered as a factor [20].  
For solid-liquid two-phase flow transportation, DPM is able to simulate millions of particles suspended in turbulence and effectively consider particle deposition. As shown in Figure 2, [PERSON] et al. studied the transport of passive pollutants injected from time periodic sources in free surface channel flow by combining with the fluid volume model (VOF) method [21]. It is considered that the CFD-DPM method can capture the physical characteristics of sediment movement [21]. However, in a complex turbulent environment,the discrete phase method is merely effective in fine particles with the following superior characteristics, while the motion of large particles still displays strong randomness [22].  
Due to the convenient calculation method of the computational fluid dynamics-discrete phase method, it has enormous potential in the application of long-distance large-scale transportation processes. However, the study of particle fretting mechanics in the process is a short board of the discrete phase method. Multi-dimensional modeling and experimental validation could enhance the accuracy and applicability of the model. What's more, the transportation calculation of non-spherical particles is also a limitation due to the existence of a large number of irregular particles in modern industrial transportation. Therefore, the computational fluid dynamics-discrete phase method is more suitable for macro transportation to explore the overall law of multiphase flow.