## 3 Application
### Tracking  
In industries, such as metallurgy, chemical engineering, and pharmaceuticals, CFD-DPM is used to track and control the product quality in multiphase flow [87; 88]. By simulating the flow of metal and the movement of inclusions, the production process is monitored and controlled to improve the consistency and quality of the final product.  
Initially, [PERSON] et al. and [PERSON] et al. conducted studies on particle distribution and separation in continuous casting tundishes, refining the numerical models for predicting the motion of particles [89; 90], which is crucial for the optimization of steel production processes. Furthering this line of research, [PERSON] et al. focused on the measurement and modeling of molten steel velocity near the surface in continuous casting tundols, providing foundational insights into the transient fluid flow behavior and its impact on the quality of the cast product [91]. The application of CFD-DPM was then expanded to include more complex scenarios, such as the simulation of bubble transport during a steam generator tube rupture accident in a lead-cooled fast reactor, as investigated by [PERSON] et al. [92] (Figure 7). [PERSON] et al. employed Large Eddy Simulation (LES) combined with DPM to study transient flow, particle transport and entrapment in slab molds with electromagnetic braking. This research not only enhances the control over the solidification process but also contributes to a reduction in defects in the final steel product [93].  
In the context of vacuum treatment, [PERSON] et al. explored steel alloy homogenization during vacuum treatment using both conventional and recurrence CFD methods. The integration of plant observations with simulation results is a strength, but the study may be limited by the specific conditions of the treatment process. Future work could involve broader applications and comparisons with other metallurgical processes [87]. [PERSON] et al. applied a coupled CFD-DPM approach to simulate multiphase flow in autoclaves [94]. A potential limitation could be the complexity of the multiphase interactions, which may require further validation. [PERSON] et al. and [PERSON] et al. utilized CFD modeling to study combustion processes in fluidized bed combustors and the behavior of plumes and free surfaces resulting from sub-sea gas releases, respectively [95; 96]. These studies highlight the method's role in improving energy efficiency and understanding environmental impacts. [PERSON] et al. and [PERSON] et al. focused on particle erosion under multiphase bubble flow conditions, which is critical for designing durable equipment and minimizing maintenance costs in industrial processes [97; 98]. The erosion mechanism under multiphase bubble flow conditions is primarily due to the impact deformation and micro-cutting effects of solid particles on the pipe wall. The presence of gas bubbles alters the motion state of the solid particles and increases their deposition on the bottom of the elbow, leading to severe erosion. Their research contributes to the understanding of material degradation and the development of more robust industrial equipment. However, the universality of simulation needs to be improved.  
In summary, the progressive application of CFD-DPM in tracking metal inclusions and bubbles has led to a deeper understanding of multiphase flows, enabling the optimization of industrial processes, enhancing safety measures and informing the design of more efficient and environmentally friendly technologies. Its key strength lies in its comprehensive modeling of particle interactions with the continuous phase. The method's flexibility in managing different particle sizes and flow conditions is particularly valuable for optimizing product quality and process efficiency. However, the high computational cost associated with simulating numerous particles and the dependency on accurate turbulence models present challenges that can affect the simulation's precision.