## 3 Application
### Spray  
As a typical gas-liquid two-phase flow, the spray process is of great importance in many projects, such as drying, cooling, spraying and dedusting. During the spray process, the liquid is ejected through the high-pressure system with fine particles, forming a mixture of tiny particles suspended in the gas. Spray is also used as an early step in multiphase chemical reaction flow, including spray combustion, gasification and pyrolysis, and its characteristics are of great significance for later behavior. In the numerical simulation of the spray process, CFD-DPM is used to explore the flow law of the gas-liquid mixing flow field as well as the performance evaluation and optimization of the pressure system [36; 37; 38]. [PERSON] et al. simulated the drift and deposition behavior of droplets during UAV spraying. The effects of spray height, nozzle pressure and airflow velocity on droplet drift distance and deposition concentration were predicted, and a correlation model was constructed [39]. [PERSON] et al. studied the fuel injector cavitations process and analyzed the effect of the nozzle spray shape towards the spray characteristic of hybrid biofuel blends [40]. The CFD simulation of UAV chemical application may not fully capture the atmospheric conditions and other environmental factors that can affect chemical dispersion. The cavitation area, droplet size, spray cone angle, spray width and spray tip penetration were compared with circular and elliptical nozzle shapes. This has important positive significance for spray combustion behavior. The numerical analysis of nozzle flow and spray characteristics may not consider all the chemical properties and combustion dynamics of diesel and biofuel blends. Moreover, some scholars determined the airflow pattern using the Euler method and traced liquid particle distribution through DPM to determine the optimal spray conditions [41]. In addition, a technology for the long-distance transmission of a droplet air supply system is called air-assisted spray. This technique pays more attention to the interaction between the flow field and droplets and the dynamic behavior of droplets. [PERSON] et al. studied the motion law of droplet flow under the airflow action of long-range air-blast sprayers [42]. The research provides valuable insights into the droplet flow characteristics and deposition patterns within an airflow field, which is crucial for applications such as agricultural sprays and indoor air quality management. The study by [PERSON] et al. [42] may have limitations in accurately capturing the full range of droplet behaviors in real-world conditions due to the simplifications made in the simulation models. Through the establishment of a monitoring section and bilateral coupling calculation in a three-dimensional flow field, the liquid flow data and deposition results were obtained. It was found that the load of the droplet group interferes with the formation of the airflow field. The numerical simulations conducted by [PERSON] et al [43]. may face challenges in precisely predicting the molten breakup behaviors due to the complex interplay of surface tension, viscosity and aerodynamic forces. This study may also be limited by the range of atomization parameters explored. Due to the secondary fragmentation of droplets, a longer transport distance will be formed after the formation of smaller particles. In general, the computational fluid dynamics-discrete phase method had a later start with few existing applications. Its strength lies in its capability to handle complex geometries and multiphase interactions, which is crucial for optimizing spray systems in various industries, such as agriculture, material processing and combustion engineering. However, the technique also faces challenges, particularly in terms of computational intensity, which can be significant when simulating a large number of droplets or complex spray configurations.