Research on Reduced-order Prediction of Multi-dimensional Centrifugal Pump under Variable Rotational Speed Condition

Variable-speed operating conditions are ubiquitous in the practical operation of centrifugal pump systems, which induce intense unsteady flow variations, sophisticated fluid-rotor interactions, and abrupt fluctuations in hydraulic performance. These dynamic behaviors readily lead to system instability, mechanical vibration and operational efficiency degradation, thereby imposing great challenges to the real-time condition monitoring, active control and intelligent operation of centrifugal pump equipment. Traditional CFD resolves internal flow details via high-precision iterative computation but suffer from excessive computational costs and long calculation cycles, which severely limit their applicability in real-time prediction, dynamic optimization and online fault early warning. Conventional reduced-order models (ROMs) exhibit notable limitations in strongly transient and non-periodic operating scenarios, as they fail to accurately characterize the spatial-temporal evolution of complex flow fields under variable-speed and variable-flow conditions. To effectively mitigate these technical bottlenecks and improve the transient response performance and prediction accuracy of centrifugal pump systems, this study aims to develop a high-precision and high-efficiency framework for transient flow field prediction of centrifugal pumps under variable-speed transient operations. In this study, the dynamic transient operating characteristics of centrifugal pumps under variable rotational speeds were investigated. High-fidelity large eddy simulation (LES) was implemented by adopting a high-order flux reconstruction method coupled with an immersed boundary technique, through which a high-quality transient flow field database covering multiple initial flow rate conditions and complete temporal evolution processes was established. Based on the refined simulation dataset, a novel dynamic ROM was constructed by integrating proper orthogonal decomposition (POD) and Gaussian process regression (GPR). The POD algorithm was employed to extract dominant spatial flow modes and realize efficient dimensionality reduction of high-dimensional flow field variables. Meanwhile, the GPR algorithm was introduced to establish the nonlinear mapping relationships between modal coefficients, time variables and operating parameters, enabling the high-precision prediction of temporal evolution characteristics of POD modal coefficients under diverse working conditions. Two sets of validation tests, including single-dimensional prediction using one initial flow condition and multi-dimensional prediction of unseen case with six training flow rates, were implemented. The results demonstrate that the proposed POD-GPR dynamic ROM delivers superior predictive performance for strongly transient flow behaviors in centrifugal pumps. In single-dimensional prediction, the model accurately predicts transient hydraulic parameters and fine-scale flow field details at arbitrary intermediate time instants, with mean absolute percentage error (MAPE) of 2.71% for pump head and 4.82% for flow rate. Specifically, the computational time of conventional GPU-accelerated CFD simulations is shortened from 36 hours to only one minute on a single CPU core. For multi-dimensional prediction of unseen case, the model presents reliable predictive capability, yielding MAPE values of 3.21% for pump head and 7.42% for flow rate. Furthermore, the prediction accuracy of pressure fields is consistently higher than that of velocity fields. Velocity fields contain abundant high-wavenumber small-scale flow components beyond the Nyquist frequency, which cause aliasing effects and Gibbs oscillations during POD reconstruction and further deteriorate velocity prediction accuracy. In contrast, pressure fields possess smoother spatial distributions, which well comply with the smoothness hypothesis of the GPR algorithm. POD energy spectrum analysis further verifies that high-order flow modes contain abundant small-scale velocity structures, posing inevitable challenges to mode truncation and dimensionality reduction accuracy. With extremely low marginal computational costs, the developed model supports rapid transient flow field reconstruction and high-precision hydraulic performance prediction for arbitrary initial operating states. This work provides an efficient and reliable technical approach for the real-time monitoring, dynamic performance prediction and intelligent control optimization of centrifugal pump transient operating processes. It can be extended to the transient flow prediction and state evaluation of other rotating fluid machinery, and provides a meaningful reference for the efficient reduced-order modeling of unsteady flow fields in fluid engineering research.