Tip leakage vortex has an important influence on the performance of semi-open centrifugal pumps. Simulations based on the three-dimensional Reynolds-Averaged Navier–Stokes were conducted to study the structural characteristics of tip leakage vortex and its effects on the internal flow field, and the Shear Stress Transport k-ω turbulence model was used to simulate the whole flow passage of centrifugal pumps with tip clearances of 0 mm and 1 mm. Then, the tip leakage vortex was analyzed using the relative vorticity transport equation. The numerical data and experimental results agreed well. The leakage vortex formed in the tip clearance led to 18.7% and 14.4% decrease in head and efficiency under design condition, respectively, and the bigger the flow rate, the fast the performance decreased. Tip leakage vortex formed at the leading edge of the blade moved along the suction surface. Whereas the tip leakage vortex formed near the middle of the blade extended to the pressure surface of the adjacent blade. This phenomenon deteriorated the flow field and induced passage vortex, thereby reducing the static pressure and blade load and changing the static pressure distribution law. The formation and development of leakage vortex could be attributed to the relative vortex stretching the term. The Coriolis force term could reflect the change of vorticity caused by leakage flow, and the viscous diffusion term served as the vorticity source.

Semi-open centrifugal pumps are widely used in various fields. However, the tip leakage vortex (TLV) has a malign effect on the impeller flow field. The structure and trajectory of a TLV under different discharge conditions were simulated and are discussed herein. Then, the characteristics of the TLV were analyzed using a new omega vortex identification method. The external characteristic and pressure fluctuation of the simulation and experiment were consistent. A secondary leakage vortex near the blade outlet was formed under the high-discharge condition. A leading-edge overflow phenomenon under the low-discharge condition and led to the formation of a reverse-flow vortex. The interface between the main flow and tip leakage flow moved toward the impeller upstream with decreased discharge. As a result, the peak of the entropy production curve moved upstream, and leading-edge overflow and reverse flow occurred. The tip leakage flow changed the blade pressure distribution, resulting in a decrease in the blade load.

Vibration characteristic is an important factor in evaluating operation stability of centrifugal pump. The vibration of main shaft was measured using a laser vibrometer, internal flow field was simulated via the shear stress transport turbulence model, and distribution law of vibration and pressure fluctuation in the impeller were analysed to explore the induction factor of vibration and the inherent relationship with pressure fluctuation in a semi-open centrifugal pump under low flow rate condition. Results of the numerical simulation are consistent with the experimental data. In addition to rotation frequency caused by impeller rotation, vibration frequency also includes characteristic frequency with high amplitude induced by unstable flow. The complex vortex in the impeller is composed of tip leakage vortex (TLV), reverse flow vortex, passage vortex and tip separation vortex. The primary tip leakage vortex (PTLV) formed by the streamline spills from 0 to 0.2λ where λ is the dimensionless distance from leading edge to trailing edge collides with tip leakage flow, the leading edge overflow and reverse flow vortex at the frequency of 1.6 f_n ( f_n is the rotating frequency) and 2.2 f_n appear, respectively. The tip separation vortex formed in the tip clearance induced a frequency of 1.2 f_n. The frequency of unstable flow phenomenon was consistent with the vibration frequency of main shaft, which induced the vibration of centrifugal pump.

The inlet elbow pipe of a double-suction pump in solid–liquid two-phase flow can easily lead to a variety of unstable flow conditions, such as flow asymmetry, turbulence intensity, and vortex formation. Additionally, the inertia and aggregation effects of particle movement complicate this phenomenon further, significantly affecting energy performance and causing erosion damage. This study explores the relationship among elbow curvature, solid–liquid two-phase flow characteristics, entropy production distribution, and wear patterns in a double-suction centrifugal pump. The interaction between inlet vortex evolution and particle movements is elucidated, followed by an exploration of the spatial energy performance and erosion distribution within the double-suction pump. The results indicate that a rise in elbow curvature has a significant effect on the flow field, intensifying flow asymmetry, enhancing turbulence and vortex formation, which, in turn, leads to greater energy loss and entropy production rate, while diminishing pump efficiency. The influence of elbow curvature on energy loss is determined through the entropy production theory. In solid–liquid two-phase flow, the inertia and aggregation effects of the particles intensify wall friction and turbulent dissipation, resulting in a greater localized wear intensity. Under conditions with greater curvature, the effects of particle aggregation are enhanced, resulting in a more pronounced erosion intensity. This study offers a comprehensive insight into the pump performance in terms of the interplay of inlet vortex characteristics and the particle migration process.