Unraveling the drag crisis of large spheres in vertical turbulent pipe flow for deep-sea mining: a 6-DOF CFD investigation

Accurate modeling of large-sphere motion in vertical turbulent pipe flow is pivotal for designing efficient and safe deep-sea mining operations. In this study, we perform a six-degree-of-freedom (6-DOF) computational fluid dynamics (CFD) analysis to investigate the terminal velocity and drag characteristics of single spheres in fully developed turbulent flow. The sphere's terminal velocity is validated against experimental data, demonstrating good agreement with an average systematic error of 6.6 %. A key finding is that traditional drag models relying on the particle Reynolds number fail to predict the abrupt decrease in drag—known as the drag crisis—observed in the experiments. Instead, the pipe Reynolds number emerges as a more effective descriptor, capturing the sudden dip in drag coefficient and subsequent rise. Further analysis of the flow field and sphere velocities reveals that the onset of drag crisis correlates with freestream turbulence in the pipe. Additionally, we explore the effects of transport parameters such as the fluid velocity, particle diameter, pipe diameter, particle density, and fluid density on terminal velocity. Overall, this work advances the understanding of drag behavior and sphere dynamics under real-world deep-sea mining conditions and underscores the importance of considering pipe-scale turbulence effects.