## 2 Materials and Methods  
### Jet-Cleaning 3D CFD Modeling  
#### 2.1.1 Model Description  
The core technology of the jet-type self-cleaning screen filter lies in its highly efficient jet cleaning, in which the fan-shaped nozzle is the core execution unit, its unique geometric structure enables the cleaning water flow to form a wide-angle fan-shaped water curtain, and through the impact of the water flow to effectively strip the sediment and other impurities adhering to the screen mesh [17; 18]. The prototype of the filter is shown in Figure 1a, including the water inlet, water outlet, nozzle, drive motor, control screen, etc.; the cross-section of the filter is shown in Figure 1b, which shows in detail the relative arrangement of the nozzle and the screen; Figure 1c shows the specific structure of the fan-shaped nozzle and the precise measurement of its internal structure under a high-definition microscope (WO-HD228S, AOSVI, Shenzhen, China). As shown by [PERSON] et al. [17], the self-cleaning performance of this filter is primarily limited by the internal structure of the nozzle, operating pressure, and other factors. Therefore, to investigate the self-cleaning performance of the filter and optimize it, the key is to accurately describe the effect of the nozzle structure on the jet's impact on the target surface.  
The jet-cleaning model mainly consists of the nozzle inlet section, contraction section, incident section, and nozzle outside the flow field, the target surface, and these five parts of the jet-cleaning geometric structure are shown in Figure 2. Figure 2a shows the schematic diagram of the jet-cleaning model, where the water flow is directed to the target surface through the nozzle to achieve the effect of cleaning; Figure 2b shows the detailed structural diagram of the inside of the nozzle, which describes the structure of the three parts of the inside of the nozzle, which are the inlet section of the nozzle (I), the contraction section (II), and the incidence section (III); and Figure 2c describes the inlet, the outlet, the target surface, etc., of the jet-cleaning model. Under the action of external operating pressure, the fluid (pure water or water mixed with gas) from the nozzle inlet section, after the contraction section of the compression of the development of the fluid in the nozzle through the kinetic energy and other energy exchanges, to reach the incident section of the time, the mixed flow has been a larger velocity of the impact of the fluid; the development of the external flow field, and ultimately reached the target wall, the kinetic energy of the jet is transformed into a target surface (screen) of the pressure of the potential energy, to achieve the cleaning of the target surface (screen).  
In computational fluid dynamics (CFD) modeling, reasonable assumptions are a key means of simplifying complex flow problems [28; 29]. The following assumptions were adopted to simplify the modeling and computational processes [35]:  
Figure 1: Structure of jet-type self-cleaning screen filter. (**a**) overall structure of the filter, (**b**) section structure of the filter, (**c**) jet cleaning nozzle and related detail structures. (1: electrical machinery; 2: outlet; 3: pressure gauge; 4: inlet; 5: self-cleaning controller; 6: sewage discharge outlet; 7: clean water inlet; 8: special-shaped filter screen; 9: jet pipe; 10: nozzle; 11: loose joint).  
Figure 2: Schematic of the jet-cleaning model: (**a**) jet cleaning process and nozzle configuration, (**b**) nozzle geometry parameters, and (**c**) jet cleaning model boundary setting. (\(D\): inlet section diameter; \(d\): incident section diameter; \(\alpha\): shrinkage segment angle; \(\beta\): V-groove half angle; \(\theta\): incident angle; 5: incident target distance).  
Both gas and liquid phases are incompressible media, immiscible with each other;
* The temperature remains constant throughout the flow process;
* All wall surfaces are smooth with no-slip conditions;
* Gravitational effects in the flow field are negligible.