Theoretical model on transient performance of a centrifugal pump under start-up conditions in pumped-storage system

Startup and shutdown are quite common processes in the operation of fluid machinery. Therefore, it is of great significance to clarify the mechanism of pumps during start-up periods for their safe and stable operations. To this end, the transient performance of a centrifugal under start-up conditions is investigated experimentally and theoretically. A theoretical prediction model is established based on the pipeline balance between the transient pump head and pipeline resistance, combined with the corresponding time -stepping algorithm for solving the pipeline balance equation. The independence test of the transient time step for the prediction method is conducted to determine a proper value. The predicted results show that sufficient prediction accuracy can be achieved, with an average relative error of 11.13 % compared with experimental results. A thorough mathematical analysis is performed to demonstrate the convexity of the characteristics of the transient pump head according to its second derivative from the pipeline balance equation. Then, a unified hyperbolic sine function with a normalized transient pump head and normalized time is established, which works well for the same pump under start-up conditions with various acceleration time.