In order to improve the efficiency and safety of vertical hydraulic transport systems for non-spherical particles, a new pipeline transport system with a tangential jet inlet is adopted in this study, and a modified non-spherical drag coefficient model is used to analyze the liquid–solid flow characteristics based on the CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) coupling method. The focus of the study is on the influence of different tangential flow proportions in terms of the velocity distribution, the vorticity, the total pressure, the concentration and drag force of particles of various shapes. The conveying efficiency is measured according to the fluid velocity distribution and the particle concentration, and the safety of conveying is evaluated according to the flow structure and drag force of the particles. The result shows that the velocity of the swirling pipes is significantly higher than the straight pipe. With the increase of the tangential flow proportion, the swirling number and the vorticity magnitude increase, and the vortex core is broken and merged more quickly. Furthermore, the concentration gap and axial drag force gap between particles of various shapes are reduced with the effect of swirling flow, the particle concentration increases, and the particles of each component are uniformly mixed and transported.