Influence of Cross-Sectional Curve Equation on Flow Field Evolution and Particle Separation in the Spiral Concentrator of the First Turn

The flow field evolution in the first turn of the spiral concentrator is decisive for the separation efficiency of solid particles. A laboratory-scale Φ300 mm spiral concentrator was employed as the study subject. The fluid phase was simulated using the RNG k-ε (Renormalization Group) turbulence model and the VOF (Volume of Fluid) multiphase model, while the particles were calculated with an Eulerian multi-fluid VOF model that incorporates the Bagnold effect. The influence of the cross-sectional curve equation on the evolution of flow field parameters in the first turn and on the separation behavior of hematite and quartz particles was systematically investigated. The results indicated that the evolution characteristics of fluid parameters, such as the depth of flow film, the tangential velocity of surface flow, the velocity of secondary circulation, and radial flux, were similar. All parameters were observed to undergo an initial decrease or increase, eventually stabilizing as the longitudinal travel progressed. A negative correlation was identified between the index of the cross-sectional curve equation and both the depth of flow film and the tangential velocity of surface flow in the inner half of the trough, whereas an inverse relationship was noted in the outer half. With an increase in the index of the cross-sectional curve equation, the outward circulation velocity in the initial stage and its radial flux in the outer zone were enhanced, while the fluctuations in the evolution of local fluid parameters were suppressed, with more active fluid radial migration observed at the indices of the cross-sectional curve equation of 2.5 and 3. As the flow field evolved, axial separation between hematite and quartz particles was progressively achieved by gravity due to their density difference. In the middle and inner-outer zones, the migration directions of hematite and quartz were observed to become opposite in the later stage of evolution, while the difference in their migration magnitudes was also found to be widened. With an increase in the index of the cross-sectional curve equation, the disparity in the axial separation and movement between hematite and quartz was enhanced, albeit with a diminishing rate of increase. The maximum separation efficiency between hematite and quartz particles was significantly improved with increased longitudinal travel, reaching over 60% by the end of the first turn; higher indices were determined to be more favorable for achieving this performance. Based on the previous research, the variation in separation indices in the third turn was investigated under both independent adjustment of the index of the cross-sectional curve equation and its combined adjustment with the downward bevel angle. Relatively high and stable separation performance was achieved with the indices of the cross-sectional curve equation of 2.5 and 3, where a maximum separation efficiency of 82.02% was obtained, thereby validating the high efficiency and suitability of the selected spiral concentrator profile. This research elucidated the decisive role of the flow field evolution through the first turn in particle separation behavior from the perspective of quantitative description of hydrodynamic parameters, providing beneficial references for the cross-sectional structure design of spirals and the prediction of the separation index of specific feed.