Mechanism of tip clearance leakage vortex evolution and energy loss characteristics in gas–liquid multiphase pumps based on vortex dynamics theory

In the extremely complex environment of offshore extraction, the stability and reliability of the helical–axial multiphase pump have become a critical focus in both practical engineering and theoretical research. The tip clearance leakage flow induced by the tip clearance between the impeller blades and the pump casing is one of the key factors constraining the performance of multiphase pumps. Building upon existing research, this paper proposes the Reynolds-averaged transport equation for the enstrophy of the rigid vorticity based on gas–liquid two-phase flow. This equation is coupled with the mean kinetic energy transport equation to systematically analyze the energy loss mechanisms and vortex dynamics characteristics caused by the generation and dissipation processes of the tip clearance leakage vortex. The study found that the tip clearance region exhibits a high turbulence kinetic energy generation rate, accounting for 34% to 44% of the total flow loss within the impeller, due to the strong shear interaction between the leakage flow and the main flow. Vorticity diagnostics revealed that the liquid phase continuously dominates the flow in this region due to centrifugal gas–liquid separation, intensifying viscous dissipation. Analysis based on the Reynolds-averaged transport equation for the enstrophy of the rigid vorticity indicates that the evolution of rigid vorticity in the main flow passage is dominated by the Coriolis Force Term; the generation of shear vorticity is controlled by the Vorticity Stretching Term; and the Baroclinic Torque Term couples with the gas–liquid density gradient to synergistically influence the vortex structure. The application of this equation effectively elucidates the gas–liquid two-phase regulation laws governing Tip clearance flow within multiphase pumps. The research results provide an important theoretical basis for optimizing the structural design of the tip clearance in multiphase pumps and enhancing their hydraulic performance and operational stability.