## 2 Materials and Methods
### Numerical Model
Consequently, the final computational model adopted approximately 1.6 \(\times\) 10\({}^{6}\) elements to effectively balance computational accuracy and efficiency. The MRF method addressed rotor-stator interaction, with velocity inlet (Equation (6)) and constant pressure outlet boundary conditions:  
\[v_{in}=\frac{Q}{A} \tag{6}\]  
where \(Q\) is flow rate and \(A\) denotes inlet area. The working fluid was an oil-water mixture with a volumetric ratio of 1:9, and the impeller rotational speed was set to 3500 r/min. Near-wall turbulence was resolved using standard wall functions. Solution convergence was defined by residuals below 10\({}^{-5}\). Given the study's focus on near-wall flow control--rather than multiphase interactions--and the  
Figure 4: Pump head and efficiency at varying mesh densities. Figure 3: Mesh discretization. applicability of approximating the mixture as a homogeneous fluid under the high water-cut condition (90%), a single-phase model was adopted to achieve a compromise between computational efficiency and engineering accuracy. Multiphase flow models would be necessary for future scenarios involving gas presence or high oil-cut conditions. Specific boundary condition configurations are detailed in Table 1. This modeling framework effectively characterizes the influence mechanisms of non-smooth structures on blade surface flow dynamics. Building upon the findings of [PERSON] et al. [25] regarding the optimal placement of bio-inspired non-smooth structures on centrifugal pump blades, this study posits that arranging non-smooth structures in peak shear stress regions under fixed dimple unit quantities maximizes drag reduction effectiveness. To validate this hypothesis, a quantitative analysis of shear stress distribution on the impeller surface was performed through numerical simulations. Numerical results under typical operating conditions (flow rate: 100 m\({}^{3}\)/d, oil-water volumetric ratio: 1:9) are illustrated in Figure 5. The impeller surface exhibits significant spatial heterogeneity in shear stress distribution, with pronounced stress concentration observed at the leading edge of the suction surface and the trailing edge of the pressure surface. Based on this flow field characterization, these two shear stress extremum regions were selected as optimization zones for non-smooth structures. The topological arrangement of dimple-type units is shown in Figure 6. This targeted placement strategy aims to maximize flow characteristic improvements through localized drag reduction effects. Guided by the geometric similarity criterion established by [PERSON] et al. [29], which asserts optimal drag reduction when the ratio of dimple diameter to blade chord length reaches 2%, the theoretically calculated optimal dimple diameter for this study's impeller (chord length: 48.5 mm) is \(d=0.97\) mm. To investigate size sensitivity, three comparative parameter sets were designed: suboptimal diameter (\(d=0.6\) mm), near-optimal diameter (\(d=0.9\) mm), and supra-optimal diameter (\(d=1.2\) mm). These dimples were arranged in the shear stress peak regions identified in Section 3.1 (Figure 5) with circumferential spacing governed by \(m=n=d+0.1\) mm, where \(m\) and \(n\) denote axial and radial spacing, respectively. This configuration systematically characterizes the nonlinear relationship between dimple dimensions and flow behavior.