A Rapid Theoretical Approach for Estimating the Energy Losses Induced by Tip Clearance Jets in Centrifugal Pumps

Abstract The semi-open centrifugal pump plays a critical role in energy conversion and fluid transport. However, the formation of the tip clearance jet (TCJ) complicates the flow pattern, leading to a significant reduction in energy conversion efficiency. In practice, an empirical formula is frequently employed to estimate energy losses at the blade tips, but this method is constrained by single-point predictions and low accuracy. This study proposes a rapid theoretical approach based on fluid element forces to more accurately estimate energy losses associated with TCJ in centrifugal blades. Our results demonstrate the effectiveness of this approach in predicting differential pressure at the blade tip, jet flow rates, and jet energy losses, with average errors of 4.73%, 4.41%, and 5.42% relative to numerical simulations. From a theoretical perspective, we confirm that differential pressure is the primary driving force behind TCJ formation. In engineering cases with gap sizes of 0.5 mm and 1.1 mm, the empirical formula resulted in prediction errors of 20.08% and 16.34%, respectively. In contrast, our theoretical approach achieves a prediction error of less than 4.5% at the design point, with a 72% improvement in accuracy, while maintaining high precision even under off-design conditions. These findings highlight the advantages of our approach, including its multi-point prediction capability and high precision. This study introduces a novel method for estimating energy losses in centrifugal pumps due to TCJ.