## 1 Introduction  
Centrifugal pumps are broadly employed in the process industries (e.g., coal, metal-lurgical and chemical processes) to transport solid-liquid slurries. The two most frequent challenges encountered during the transportation of slurries are a decline in the performance of the pumps and erosion of the wetted surfaces [1]. The components most subjected to high erosion rates are the impeller, liners, and pump casing [2]. Along with all the modules mentioned above, pump casing is the element that receives the greatest damage from erosion. This leads to frequent replacements of the casing, making it the most expensive component of the pump's assembly [3]. Impact and sliding of the solid particles along the wall are two major contributors to erosion while slurry flows through pumps [4,5]. The impact of the particle will be a major concern if slurries are sufficiently dilute [6]. Moreover, it will be multidirectional in case of turbulent flow.  
Numerous techniques have been utilized in the literature to assess erosion rates in the centrifugal pumps computationally. Employed computational methods in the literature are based on two-dimensional models, three-dimensional models, and a component-by-component approach. Methods utilizing 2D geometrical models have been employed by [7,8] to assess the erosion trends in the casing of the centrifugal pump. In this methodology, however, the viscous force term is overlooked. Moreover, particles with a size greater than 1 mm stimulate unpredictably in the solution.  
Consequently, this technique limits the analysis to small particles. [PERSON] et al. [9] used 3D RANS simulations to calculate the erosion wear in the casing of a dilute slurry flow. The prospective interpretation was used by [PERSON] and [PERSON] [10] to solve the transport phase. They resolved particle speeds by weighing the forces employing the Lagrangian approach. [PERSON] et al. [11] applied finite element calculations to forecast the erosion characteristics based on RANS solutions. They discovered that their results were in close agreement with the particle image velocimetry (PIV) results of [PERSON] et al. [12].  
The prediction of wear and tear in centrifugal pump casing is a complex phenomenon that depends on many parameters such as particle velocity, particle impact angle, turbulence flow field, surface texture, and inlet flow conditions. Many of these parameters depend on the geometry of the specific pump design; thus, predictions made for one particular pump do not apply to other pump geometries.  
It can be deducted from the literature review that the working life of the pump's casing can be determined by examining the collective effects of erosion characteristics on the component using experimental or numerical methods. Experimental procedures are incredibly costly and time-exhausting. Therefore, in the current work, erosion characteristics associated with the pump's impeller and the casing are evaluated by employing 3D RANS simulations. A parametric study based on four parameters, i.e., the concentration of solid particles, size of the solid particles, exit head, and cavitation, has been conducted. A set of commercial codes ANSYS-CFX, ICEM CFD, and turbo grid in an environment of the ANSYS workbench are employed to resolve the 3D RANS using the Eulerian-Eulerian method. The shear stress turbulence model (SST) is implemented to achieve better accuracy in the rotating domain of the impeller.