Numerical Study of the Motion of a Freely Falling Sphere in Fluid

Liu, Lei (Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration) | Lu, Haining (Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration) | Yang, Jianmin (Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration) | Peng, Tao (Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration) | Tian, Xinliang (Shanghai Jiao Tong University, Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration)

OnePetro 

ABSTRACT

Numerical study of the free-fall of a single sphere at different Reynolds numbers has been conducted with Computational Fluid Dynamics(CFD) method based on the engineering concerns of the dynamics of ore particles in vertical pipes in deep sea mining. A combination of Detached Eddy Simulation (DES) and the six-degree-of-freedom (6-DOF) motion solver was adopted. The sphere motion, the hydrodynamic forces on the sphere and the characteristics of the surrounding flow field were analyzed in detail. Different falling trajectories of the sphere were observed. The surrounding flow field gradually lost the symmetry with the increase of Reynolds number. The results of this article would provide a basic reference for the further investigation on motion of the multiple ore particles.

INTRODUCTION

As the increasing demand of the natural sources in the world, deep sea deposits are considered as the most valuable alternative sources. Deep sea mining applications has been proposed since 1960s (Mero, 1965; Willums and Bradley, 1974; Chung, 1999; Chung, 2005; Chung, 2009). One of the most important issues in deep sea mining is the ore transportation from seafloor. Typically, ore particles can be transported vertically to the support vessels in the upward flow of water in a riser. Significant efforts have been dedicated to the vertical hydraulic transport system in deep sea mining (Engelmann, 1978; Bournaski et al., 2001; Xia et al., 2004; Chung et al., 2007; van Wijk, 2016).

Engelmann (1978) conducted experimental investigation on the hydrodynamic behaviors of ore particles in a vertical tube, and established the empirical equations for designing the hydraulic transport system in deep sea mining. Chung et al. (1998), Chung et al. (2001) and Chung et al. (2007) had a thorough investigation on the vertically upward transport in deep sea mining, including the transportation of spherical bead and non-spherical particles, the effects of particle shape and size, different particle behaviors over a wide range of Reynolds number in both Newtonian fluid and non-Newtonian fluids. Yoon et al. (1999), Yoon et al. (2001) and Yoon et al. (2008) studied the flow characteristics of the solid-liquid two-phase mixture in both vertical tubes and flexible hoses. Bournaski et al. (2001) and Xia et al. (2004) studied the hydraulic gradient caused by the fluid, the coarse particles and the collisions in the vertical pipes. Parenteau (2010) carried out numerical simulations to investigate the transient behaviors and pressure predictions for the risers by using Computational Fluid Dynamics (CFD) methods. Talmon and Rhee (2011) designed a close-loop system in the laboratory to conduct experiments on ore transport over large vertical distances. Sobota et al. (2013) experimentally investigated the velocities of ore particles and carrier liquid to determine the slip velocities for the artificial nodules in the vertical pipe. Vlasak et al. (2014) studied the influence of pipe inclination, solid concentration and mixture velocity on the characteristics of particle-water mixtures by using a pipe loop system. van Wijk (2016) carried out a study into flow assurance of the hydraulic transport system in deep sea mining and proposed a onedimensional flow model to investigate the mechanisms leading to the riser blockage.