Abstract
Centrifugal pumps are critical across various industrial sectors, yet their complex, three-dimensional, and unsteady turbulent flows pose significant challenges for traditional empirical design methods. This review aims to systematize modern research on the mathematical modeling of centrifugal pumps, emphasizing the application of advanced turbulence models and artificial intelligence (AI) to identify current trends and future prospects. A comprehensive analysis of over 70 peer-reviewed articles indexed by Scopus database, published between 2010 and 2026, was conducted. The methodology focuses on evaluating Reynolds-Averaged Navier-Stokes (RANS), Large Eddy Simulation (LES), hybrid RANS-LES approaches, and the integration of machine learning algorithms. The results reveal a fundamental paradigm shift from isolated computational fluid dynamics (CFD) simulations to integrated, AI-driven methodologies. While RANS and its unsteady (URANS) form remain the industry standard for evaluating baseline performance due to computational efficiency, LES and hybrid models (such as DES and SST-SAS) are increasingly utilized to achieve benchmark accuracy for complex transient phenomena like boundary layer separation and cavitation. Furthermore, high-fidelity CFD calculations are now predominantly used to generate training databases for deep neural networks. This synergy enables near-instantaneous multi-criteria geometry optimization, virtual sensor deployment, and predictive equipment diagnostics.