## 1 Introduction
[9], a numerical study on the performance of a multistage centrifugal pump for different Radial diffuser shapes is performed. It is found that the differential head is lower when the return channel Outlet angle is 60 deg instead of 90 deg because of the pre-swirl at the diffuser Outlet. The turbulence model SST k - \(\omega\) is used; however, no information is provided concerning the computational grid. Thus, it is not clear whether the results obtained are compared with the experimental data. In Ref. [10], a numerical study of unsteady flow and time variation of pressure within a complete double-blade centrifugal pump is presented. For this purpose, a SST k - \(\omega\) turbulence model is used, and the results obtained are validated using experimental data provided by the same authors. As a result, it is found that the rotor-stator interference between the impeller and solute is the main source of pressure pulsation. A study in which five types of solute structures are designed is presented in Ref. [11]. FLUENT is used to determine the steady and unsteady calculation of the five volute structure models. It is found that the static pressure gradient distribution of the double-tongue volute centrifugal pump under various operating conditions is improved to varying degrees, and the low-speed region of the diffusion section is reduced. The numerical results obtained are then validated with experimental data. The impact of leakages and balance holes on the performance of a multistage centrifugal pump has also been studied experimentally, as well as using CFD, in Ref. [12]. The relative difference between the CFD and experimental results is in the range of 1-10%. It is found that balance holes reduce the hydraulic efficiency of the pump by increasing the leak flow, although it is important to reduce the axial forces of the pump shaft. The impacts of wall roughness, impeller blades, and diffuser vanes on the performance of a one-stage centrifugal pump is studied in Refs. [13; 14]. The studies are performed numerically, and the results are validated using experimental data. A turbulence model of the type \(\mathrm{k}-\varepsilon\) is used for this purpose. Thus, it is found that the pump stage head and brake horsepower increased as the height of impeller blades and diffuser vanes and the number of impeller blades increased. In addition, the higher wall roughness heights of the impeller and diffuser negatively affected the pump stage head, brake horsepower and efficiency. The impact of the surface roughness on the performance of a two-stage centrifugal pump is also studied in Ref. [15]. The study is performed using CFD simulations, and the numerical results are validated using experimental data obtained by the authors. It is found that surface roughness has the greatest impact on disk friction losses. In this regard, the authors in Ref. [15] recommend that the outer impeller surfaces, as well as the pump casing part surfaces, should be manufactured with the minimum possible values of roughness. For this aim, a standard \(\mathrm{k}-\varepsilon\) turbulence model and surface roughness of 1 \(\mathrm{\SIUnitSymbolMicro m}\) is used. In Ref. [16], a study concerning the development of a centrifugal pump for operation at high head and high flow rates is conducted. The first stage of the pump consists of a double-suction impeller. A twin volute is installed after the first impeller, and an inducer-type guide vane is installed between the first and second stages (ITGV). Numerical studies used to determine the pump operation by using ANSYS CFX are performed. In this case, a SST \(\mathrm{k}-\omega\) turbulence model is used. As a result of the numerical experiments performed, it is found that using the ITGV leads to a decrease in the circumferential velocity of the fluid but also improves the overall performance of the pump by diminishing the losses obtained in the second stage. The authors in Ref. [16] emphasize that the experimental validation of the results obtained is pending.