Compressible flow through a branched duct and the motion of a sphere through a high blockage ratio pipe are two important and engaging topics throughout the years. The results of studies on these topics are of practical relevance to many fields such as the gas pipeline technology, air transport systems in gas turbines technology, and tube transportation, etc. However, studies on the motion of a sphere in a branched duct are scarce. Studies of the motion of a sphere in a near-vacuum tube could contribute to the development of a branched Hyperloop system in the future. In this study, we investigated the effect of the tube curvature radius and angle on the aerodynamic characteristics of a sphere during its motion in a branched tube. We examined, quantified, and compared the variation of the drag, side force, and pressure waves for the cases where a sphere enters a branch considering six curvature radii (from 500 to 3000 m), three angles (10°, 15°, and 20°), three speeds (100, 200, and 300 m s-1), and two initial pressures (1/1000 and 1 atm) in simulations. The results indicated that the drag and side force vary only in the intersection region (region where the straight tube and branched tube intersect); before and after the intersection region, they are similar. With an increase in the curvature radius, the rate of drag reduction ($F_D$/max($F_D$)) decreases, while the changes in the angle do not affect variation of drag and side forces. Furthermore, we compared the motion of a sphere in straight and branched directions and found out that the flow in front and behind the sphere was similar for both directions.

多年来，通过支管的可压缩流和球体通过高阻塞比管道的运动是两个重要且引人入胜的主题。这些课题的研究成果对输气管道技术、燃气轮机技术中的空气输送系统、管道输送等诸多领域具有实际意义。然而，关于球体在支管中运动的研究却很少. 对近真空管中球体运动的研究可能有助于未来分支超回路列车系统的发展。在这项研究中，我们研究了管曲率半径和角度对球体在支管中运动过程中的空气动力学特性的影响。我们检查、量化并比较了阻力、侧向力的变化，以及球体进入分支的情况下的压力波，考虑了六个曲率半径（从 500 到 3000 米）、三个角度（10°、15° 和 20°）、三个速度（100、200 和 300 m·s- 1), 以及模拟中的两个初始压力 (1/1000 和 1 atm)。结果表明，阻力和侧向力仅在交叉区域（直管和支管相交的区域）发生变化；交叉区域之前和之后，它们是相似的。随着曲率半径的增加，减阻率（结果表明，阻力和侧向力仅在交叉区域（直管和支管相交的区域）发生变化；交叉区域之前和之后，它们是相似的。随着曲率半径的增加，减阻率（结果表明，阻力和侧向力仅在交叉区域（直管和支管相交的区域）发生变化；交叉区域之前和之后，它们是相似的。随着曲率半径的增加，减阻率（$F_{丁}$/最大限度（$F_{丁}$))减小，而角度的变化不影响阻力和侧向力的变化。此外，我们比较了球体在直线方向和分支方向上的运动，发现球体前后的流动在两个方向上都是相似的。