随着陆地资源的减少以及国家深海战略的持续推进，深海固态矿产资源开发成为满足人类经济和社会发展需求的重要途径。经过几十年的不断探索，深海采矿技术及设备得到了长足发展，衍生出众多的开采和输送方式。其中，公认的最具商业化开采前景的方式为采矿车-提升管道式的采矿系统。然而，在复杂的深海环境中，长达几千米的提升立管受到海浪和洋流的影响会产生运动响应。并且，提升立管内矿石颗粒直径大、密度高，对管内流体的跟随性较差，因此运动立管中的矿石颗粒易与管壁发生碰撞，这会导致矿石颗粒的运动行为更加复杂，进而影响矿石提升效率，甚至加剧立管内固液两相流的堵塞风险。因此，对运动立管内矿石和海水形成的粗重颗粒固液两相流运动开展深入的研究，可以为深海采矿系统的安全设计和矿石输送效率的提升提供科学的依据，具有重要的科学意义和工程应用价值。

以往国内外学者多聚焦于研究静止立管中单颗粒或颗粒群的沉降和上升运动，且主要关注细颗粒或低密度颗粒的运动。本文则主要关注横向运动立管中粗重矿石颗粒的沉降和上升运动。该问题与以往研究较多的情形相比，立管内的矿石颗粒的直径和密度都很大，因而伽利略数高。另外，立管的横向振动和较高的管内上升流速度导致矿石颗粒所处流场条件复杂。因此，矿石颗粒的运动行为更加复杂。本文通过分析立管振动幅度和频率、颗粒与立管直径比、颗粒与流体密度比、立管内上升流速度以及颗粒-管壁碰撞等对球形颗粒运动的影响规律，为深海采矿系统关键参数的设计提供科学依据。本文主要的创新性研究如下。

首先，鉴于目前并未有成熟的软件或数值方法完全适用于横向运动立管中粗重颗粒固液两相流问题的研究，本文发展了两种数值计算方法。一方面，本文所研究的问题中，立管存在横向运动，管内颗粒直径大，且在立管中做长时间、长距离的运移，颗粒横向运动范围也较大。针对研究对象的这些新特征，本文在开源软件OpenFOAM中进行算法和模型植入，开发了适用于本文研究问题的数值模拟方法。该数值模拟方法借鉴欧拉-拉格朗日方法，通过N-S方程和刚体六自由度运动方程，分别计算立管内流场和颗粒运动，结合移动计算域和重叠网格技术，实现粗重颗粒在立管中长时间、长距离和大范围运动的模拟，并采用硬球碰撞模型计算颗粒-管壁碰撞。另一方面，鉴于上述数值模拟方法计算效率较低，本文基于任意流场中的颗粒运动方程和软球碰撞模型，另行发展了一种高效数值计算方法。通过与无界振荡流场中颗粒运动的数值计算结果、硅油中钢球沉降及其与管壁碰撞的实验结果、以及球形颗粒在立管中沉降的数值模拟结果进行对比，验证了本文发展的两种数值方法的正确性。

其次，基于上述开发的数值模拟方法，对横向振动立管中球形单颗粒的沉降运动进行了研究。讨论了立管振动幅度和频率，以及颗粒-管壁碰撞对横向振动立管中球形单颗粒的运动轨迹、横向速度和沉降速度的影响，并通过分析颗粒周围的流速和压强分布，给出了颗粒与流体相互作用的新机制。

然后，采用上述开发的高效数值计算方法，先后研究了横向振动立管上升Poiseuille流和指数速度分布流中的单颗粒运动。通过分析立管振动幅度和频率、颗粒与立管直径比、颗粒与流体密度比以及颗粒-管壁碰撞等对上述两种速度剖面流动中颗粒运动的影响，总结了颗粒横向速度与立管振动速度的相位差、两者相对速度的幅值、颗粒垂向速度的平均值和波动幅值以及颗粒-管壁碰撞时刻所在的相位等随上述参数的变化规律。得到了横向振动立管内颗粒运动的5种轨迹类型，并给出了不同直径比下，颗粒-管壁“完全碰撞”（每个立管振动周期内，颗粒-管壁碰撞两次）时，立管振动幅度和频率所满足的临界条件。

最后，自主设计并搭建了横向振动立管水力提升矿石颗粒的实验装置，并开展了横向振动立管中粗重颗粒运动的实验研究。基于上述数值计算结果，设计了立管振动幅度和频率、颗粒直径以及立管内上升流速度等实验工况条件。通过实验，分析了立管振动幅度和频率、颗粒与立管直径比对颗粒沉降运动的影响，以及上升流中颗粒横向和垂向速度随立管内上升流速度的变化。同时，将实验结果与数值计算结果进行对比，进一步验证了本文所发展的数值计算方法的鲁棒性，以及数值结果的合理性。

With the depletion of terrestrial resources and the emphasis on strengthening maritime capabilities, attention has been shifted towards exploring the deep sea as a potential reservoir for mineral resources. This exploration has become an important avenue for meeting economic and social development goals. Over several decades, significant progress has been made in deep-sea mining technology and equipment, leading to various methods of the mining and transportation. Among these methods, the collector-lifting riser system has emerged as the most commercially viable approach. However, in this mining system, vibrations can be induced when the lifting risers with thousands of meters are subjected to ocean waves and currents. In addition, ores with larger diameters and higher densities have a weaker ability to catch up with the vibrating riser, leading to collisions between the riser and ores. The presence of collisions not only fatigue the riser, but also complicate the behavior of the ores. More importantly, collisions between the riser and ores impact the efficiency of ore lifting, even exacerbate the blockage of the solid-liquid two-phase flow within the riser. Therefore, it is crucial to investigate the behavior of solid-liquid two-phase flow containing coarse and heavy particles in order to ensure the safety and transportation efficiency of mining systems.

It should be noticed that previous studies primarily focus on the motion of a particle in a stationary riser, and the Reynolds number of the particle inside is relatively low, which indicates that the density ratio ρ_r = ρ_p/ρ_f approaches to 1.0 or the particle diameter is very small. However, in deep-sea mining, the effect of the ore diameter cannot be ignored because of the large ratio of its value to the riser diameter, and the density of the ores is also large. Consequently, both the values of Galileo number G and Reynolds number Re are high. In addition, the flow inside the riser becomes more chaotic due to the vibration of the riser and large vertical velocity of the internal fluid. As a result, the particle trajectory might be more chaotic. Therefore, during the study, the ore and the lifting riser are simplified as a sphere and a vertical riser, respectively. The main focus of this study is to analyze the movement of spherical particle inside a riser with transverse vibration under the influences of riser vibration amplitude and frequency, diameter ratio of the particle to riser, density ratio of the particle to the ambient fluid, and collisions between the particle and the riser wall. The findings of this research can provide valuable insights for the design of deep-sea mining systems. The main aspects covered in this paper are as follows:

Firstly, since there is no existing software or numerical simulation method suitable for studying coarse and heavy particle solid-liquid two-phase flow in a transversely vibrating riser, two numerical calculation methods are developed. For one method, a moving computational domain, overset mesh, and a hard-sphere collision model embedded in OpenFOAM-v2006 are utilized, which is suitable for the simulation of the long-time and long-distance transportation, and large lateral migration of the particle within the riser. Based on the Euler-Lagrange method, the flow field and particle movement can be calculated by employing the Navier-Stokes equation and the rigid body six-degree-of-freedom equation respectively. Besides, another method based on the particle motion equation suitable for arbitrary fluid field and the soft sphere collision model is proposed to address the low computational efficiency of the previous simulation method. These two numerical methods are verified through comparisons with numerical results of particle motion in unbounded vibrating flow fields, experimental results of steel sphere sedimentation and collision with a vessel bottom in silicone oil, and numerical results of a spherical particle settling in the riser, proving their accuracy.

Secondly, using the developed numerical simulation method, the sedimentation of a spherical particle in the riser with transverse vibration is studied. The effects of riser vibration amplitude and frequency, as well as collisions between the particle and the riser wall, on the trajectory, lateral velocity, and settling velocity of the particle in the transverse vibrating riser are discussed. Moreover, the interaction mechanism between particle and fluid is explained by analyzing the flow velocity and pressure distribution around the particle.

Next, the movement of a spherical particle in Poiseuille flow and exponential distribution flow within a transversely vibrating risers is investigated using the efficient numerical calculation method. By discussing the effects of riser vibration amplitude and frequency, diameter ratio, density ratio, and collision between the particle and the riser wall on a particle movement in these two upward flows, the variations of particle lateral velocity and vertical velocity, as well as the phase difference of the collision moment with various parameters are summarized. Five types of particle movement trajectories in the vibrating riser are presented, and the critical conditions for “complete collision” (Two times of collision occur in each vibration period.) between the particle and the riser wall are obtained.

Finally, experiments on the movement of coarse and heavy particles in the riser with transverse vibration are conducted. Referring to the results obtained from numerical calculations regarding to particle sedimentation and rising movement in the vibrating riser, experimental conditions such as riser vibration amplitude and frequency, particle diameter, and vertical velocities of the internal fluid are designed. The influences of riser vibration amplitude and frequency, as well as diameter ratio, on particle sedimentation are analyzed based on experimental results. In addition to the above parameters, the variations in lateral and vertical velocities of the particle with the vertical velocity of the lifting riser are discussed. Furthermore, the experimental results are compared with the numerical calculation results to validate the developed numerical calculation methods in this study.