Analysis of transient startup characteristics in a two-stage mixed-flow pump using a theoretical prediction model

In large-scale hydraulic engineering projects (such as China's South-to-North Water Diversion Project), the optimization of pumping station control strategies through studying the synchronization between starting flow rate and head can enhance operational efficiency and reduce energy losses during the startup phase. Currently, theoretical prediction models, owing to their computational efficiency and interpretability of underlying mechanisms, represent the most suitable approach for analyzing startup transient characteristics in engineering applications, but the transient prediction theory for multistage mixed flow pumps is overly simplified, making it difficult to accurately analyze the flow and head characteristics during startup, and also have significant errors in predicting multistage coupling losses. To address the above issues, a highly efficient and accurate transient prediction model for the startup process of a two-stage mixed flow pump was developed. A transient head model for the impeller was developed using torque-energy balance theory, incorporating a dynamic slip factor and corrected inflow angle under transient conditions. Subsequently, guide vane losses (diffuser, friction, pressure differential) and inter-stage losses (incidence, friction, pressure differential) were modeled. These components were integrated into a pressure balance equation, enabling iterative computation of transient head and flow rate. Then, the transient characteristics of the two-stage mixed flow pump under varying startup curves were analyzed, with a superior S-shaped curve proposed to minimize hydraulic shock during acceleration phases. Finaly, the transient prediction model's accuracy is validated through recirculation passage experimental during startup, and transient characteristics under different startup curves are analyzed.