Hydrodynamics of Toroidal Vortices in Torque-Flow Pumps

This study investigates the role of toroidal vortex formation in torque-flow pumps and its influence on pump performance. A mathematical model of viscous fluid motion in toroidal coordinates was developed to describe the two-stage energy transfer mechanism, in which the impeller drives the toroidal vortex and the vortex subsequently imparts momentum to the main throughflow. The model identifies vortex deformation as a primary source of hydraulic losses. The theoretical framework was validated by computational fluid dynamics (CFD) simulations of a torque-flow pump. Analysis of the axial, circumferential, and vertical velocity components revealed a closed three-dimensional toroidal circulation loop within the free chamber, confirming the predictions of the mathematical model. A parametric study was conducted to assess the influence of impeller extension into the free chamber (Δb₂) on pump performance. Three characteristic regimes were identified. At Δb₂ ≈ 6 mm, the shaft power decreased to 120.3 kW (an 8.1% decrease compared to the baseline), with efficiency improving to 39.2%. At Δb₂ ≈ 10 mm, the pump achieved its best balance of parameters: efficiency increased from 34.0% to 42.8% (+8.7 percentage points), while head rose from 32.8 m to 38.5 m (+17.4%), with moderate power demand (122.3 kW). At Δb₂ ≈ 70 mm, the head reached 45.6 m (+39%), but power consumption rose to 146.9 kW (+12%), and the design shifted toward centrifugal-type operation, reducing reliability for abrasive fluids. Overall, the results provide both a validated mathematical description of toroidal vortex dynamics and practical guidelines for optimizing torque-flow pump design, with Δb₂ ≈ 10 mm identified as the most rational configuration.