## 1 Introduction
performed experiments using laser-manufactured microstructures to obtain optimal texturing parameters for positive displacement pumps and found that pumps designed with these parameters exhibited significantly improved wear performance [19]. [PERSON] et al. studied the effects of sediment concentration in Brazil's Acre River on fluvial water pump impellers and performed ball-catering microscale abrasive wear tests to determine the erosive power of the sediments. Their results indicate that impeller wear increased almost linearly with an increase in sediment concentration [20]. [PERSON] studied the wear characteristics of slurry pumps under a variety of working conditions using a mathematical model of erosive wear in slurry pump impellers and performed tests to experimentally validate their approach [21]. [PERSON] et al. presented a numerical method for predicting the wear depth distribution on the blade of an impeller and validated the proposed method using experimental data [22]. The numerical methods and erosive wear models used in studies focused on pump wear can vary depending on the study parameters, and the models also differ in their range of applicability. [PERSON] used the discrete phase model (DPM) to analyze the wear caused by different flow rates and solid particle diameters in flow-passing parts and consequently obtained the wear rates of all flow-passing parts [23]. [PERSON] used the dense discrete phase model (DDPM) to analyze the transient wear characteristics of centrifugal pumps, focusing on how each particle-related characteristic affected the wear of flow-passing parts in a centrifugal pump [24]. Eulerian multiphase flow models are frequently used to analyze pump wear characteristics associated with the transportation of solid-liquid two-phase flows, and their use has produced many useful insights [25; 26; 27; 28]. [PERSON] et al. used an Euler-Euler model to analyze the effect of changes in the particle size distribution (PSD) on particle motion characteristics and the performance of centrifugal slurry pumps. Their results indicate that changes in the PSD affect the motion of particles in the pump flow channel, as an increase in the proportion of fine particles results in a decrease in the intensity of granular pressure, maximum granular viscosity, and head loss [29]. [PERSON] et al. used the particle Eulerian-Eulerian multiphase model to study impeller wear in slurry pumps [30]. Further, [PERSON] et al. employed the Mixture and Eulerian-Eulerianmultiphase flow models to study the wear performance of centrifugal slurry pumps during the transportation of solid-liquid two-phase flows and found that the experimentally observed effects of solids on pump performance were better predicted using the Eulerian-Eulerian model than the Mixture model [31]. In certain studies, particle and heterogeneous models were used to analyze the flows of slurry-pump rear impellers of various shapes and thus predict the wear characteristics of slurry pumps [32; 33]. [PERSON] et al. employed particle and heterogeneous models to study the effects of rear impeller shape on the wear characteristics of slurry pumps and thus predict the wear of slurry pumps [34]. [PERSON] et al. used a two-phase particle flow model to analyze the effects of sand-particle size on the wear of impeller surfaces [35]. [PERSON] et al. used the Particle two-phase and Finnie models to conduct a comparative analysis of the wear characteristics of pulp pumps; the former exhibited severe erosion of the front cover and impeller blade when the pump was operated at the rated flow, whereas the pump casing was severely eroded at low flow rates in the latter [36]. [PERSON] et al. used the Finnie wear model to analyze the wear characteristics of the flow-passing components of deep-sea lifting pumps, which yielded the wear rates of each flow-passing component [37].