## 1 Introduction  
Surface water systems supplied by glacial meltwater, which often have high concentrations of particulate impurities, like sediment and algal biomass, are the main source of irrigation water in Xinjiang [1, 2, 3]. Drip irrigation systems are extremely vulnerable to serious clogging because of these suspended solids. As a core component of drip irrigation systems, filters effectively remove over 95% of suspended impurities from water sources through multi-stage interception [4, 5, 6]. Their filtration efficiency and self-cleaning capability critically determine the long-term stability of system operation, the service life of emitters, and the irrigation efficiency [7, 8]. Conventional self-cleaning screen filters (e.g., backwashing type, steel brush type) currently exhibit limitations, including inadequate contaminant-removal efficiency, incomplete cleaning performance, low operational effectiveness, and susceptibility to screen deformation and damage [9; 10]. In contrast, the jet-type self-cleaning screen filter introduces an innovative high-efficiency jet mechanism commonly used in industry [11; 12; 13; 14; 15; 16] during its self-cleaning cycle, demonstrating significant advantages in reduced water consumption, enhanced cleaning capability, and broad applicability [17; 18]. Preliminary experiments have demonstrated that its self-cleaning performance surpasses that of conventional self-cleaning filters. However, its commercialization faces challenges due to an undetermined optimal jet-cleaning pattern. Excessive operational pressure may damage the filter screen, while suboptimal nozzle configurations could compromise cleaning effectiveness [19]. Optimizing the jet-cleaning pattern of the self-cleaning screen filter is imperative to improve the overall operational efficiency of drip irrigation systems and mitigate redundant expenditures, thereby accelerating commercial adoption. Jet-cleaning technology efficiently utilizes nozzles to generate high-velocity fluid jets (e.g., water, air) to remove surface fouling, such as contaminants and sediments, from substrates like filter screens. The effectiveness of jet-cleaning processes is directly governed by the structural parameters of the nozzle, operating parameters, and operating conditions [20; 21]. Some researchers [22; 23] have adopted experimental approaches to investigate cleaning parameters in jet-cleaning technology. Representatively, [PERSON] et al. [24] evaluated wall shear stress during jet-impact descaling, utilizing oil-film interferometry to quantitatively map its spatial distribution. Their experimental results revealed a linear correlation between the contaminant removal efficiency and peak wall shear stress magnitudes. The above related physical experiments can obtain more accurate results and phenomena, but they have many limitations in the optimization process of parameters or patterns, such as a long experimental observation period, being time-consuming and labor-intensive, and the inability to exhaustively explore the range of variables. This has prompted researchers to increasingly try to optimize jet cleaning parameters through numerical simulations instead of experiments [25; 26; 27]. For example, [PERSON] and [PERSON] [28] employed computational fluid dynamic (CFD) simulations to determine the critical shear stress required for the effective jet-cleaning of flat contaminated surfaces. [PERSON] and [PERSON] [29] conducted a three-dimensional numerical simulation of the hydrodynamic performance in ultra-high-pressure waterjet descaling nozzles, revealing that the standoff distance and jet impingement angle exert the most significant influence on the wall shear stress. While the numerical simulation approach in the above study may provide an alternative to physical experimentation by reducing labor-intensive time requirements, it requires high-performance computational resources; insufficient computational power may result in computations that are too slow or even unable to solve complex model problems.