## 2 Materials and Methods
### Jet-Cleaning 3D CFD Modeling
#### 2.1.3 Selection of Parameters for Jet Cleaning  
In the field of nozzle structural optimization, many scholars usually select key structural variables based on engineering experience or a local analysis [19; 29], and such a parameter-selection method relying on subjective cognition may lead to the omission of important variables or the redundancy of non-essential parameters, and the empirical parameter selection is easily limited by the knowledge boundary of the researcher. Therefore, to break through the limitations of the traditional optimization methods and to obtain the optimal nozzle-cleaning performance with relatively few key structural variables, this study carried out a study on the identification of the significance of the influence of the main structural parameters of the nozzle before the optimization of the jet-cleaning performance and selected the parameters that have a significant influence on the evaluation indexes (maximum shear stress on the wall surface, action area, and water consumption) for optimization to achieve the reduction of the complexity of the related work and the improvement of the work. By selecting the parameters with a significant influence on the evaluation indexes (peak wall shear stress, action area, cleaning water consumption), the optimization is carried out to reduce the complexity of the related work and improve the efficiency. To comprehensively study the influence of nozzle structural parameters on the evaluation indexes, after relevant measurements of the nozzle structural parameters, six relatively independent structural parameters, such as the inlet section diameter \(D\), incident section diameter \(d\), inlet length \(L_{1}\), incident length \(L_{3}\), shrinkage segment angle \(\alpha\), and V-groove half-angle \(\beta\) are selected in this study, which are usually included in the parameters used in previous references [17; 18; 29]. An orthogonal test is a statistical experimental design method based on orthogonal tables, which can efficiently analyze the effects of factors on the results and determine the optimal parameters with a minimum number of experiments through the balanced allocation of multi-factor combinations at each level. The core of the orthogonal test is the orthogonal table, which can cover the balanced matching of factor levels in a limited number of experiments, avoiding redundancy while maintaining the comparability of results. The design needs to first define the target factors and their levels, choose the appropriate orthogonal table to arrange the experimental combinations, and then identify the key factors and the optimal level combinations through extreme deviation or ANOVA. This method is widely used in engineering optimization, manufacturing processes, agriculture, and other fields and can significantly reduce the cost and time of experiments. In the study, the number of levels of each factor (relevant cleaning parameters) was determined to be 3. The orthogonal test factors and the levels set are shown in Table 1.  
Combined with the knowledge of orthogonal tests, the L\({}_{18}\) orthogonal test table was chosen for the above 6-factor, 3-level orthogonal test. In the L\({}_{18}\) orthogonal test table, 18 combinations of design factors were obtained; each combination represents an independent parameter design scheme, and the orthogonal test table is shown in Table 2.  
Therefore, on the basis of the orthogonal tests described above, the independent parameters of the jet-cleaning model selected in this study were the nozzle incident section diameter \(d\), V-groove half angle \(\beta\), incident target distance \(s\), incident angle \(\theta\), incident pressure \(p\), and gas doping volume \(r\). The ranges of the relevant parameters are shown in Table 3.