Analysis on Inner Flow Field and Hydrodynamic Force on Flexible Mining Pipeline Under Bending States

To investigate the internal flow characteristics of particles during hydraulic lifting in deep-sea mining risers, this study developed a three-dimensional curved riser multiphase flow model based on the Eulerian–Eulerian framework and the RNG k-ε turbulence model. The effects of particle distribution and pressure loss in the curved section, as well as the influence of curvature radius, were analyzed. Results indicate that particle distributions take concave circular or crescent-shaped patterns, becoming more uniform with larger curvature radii. Pressure on the extrados is consistently greater than on the intrados, with pressure loss increasing in the bend and peaking at the midpoint. A larger curvature radius leads to greater total pressure loss but lower frictional loss. Additionally, the bend experiences a restoring force toward the vertical position, which increases as the curvature radius decreases.