引用本文: 周锟, 张权. 椭球体绕流阻力数值模拟研究. 力学与实践, 2024, 46(1): 28-40.
Zhou Kun, Zhang Quan. Numerical investigation of drag of a spheroid. Mechanics in Engineering, 2024, 46(1): 28-40.
 Citation: Zhou Kun, Zhang Quan. Numerical investigation of drag of a spheroid. Mechanics in Engineering, 2024, 46(1): 28-40.

## NUMERICAL INVESTIGATION OF DRAG OF A SPHEROID

• 摘要: 颗粒在无界均匀流场中的阻力是颗粒多相流领域最基本的问题之一。在相关的工程应用与科学研究中，颗粒基本都是非球形。早期基本以相同体积的圆球阻力来近似非球颗粒的实际阻力，近来则提出了多种基于实验数值拟合的非球颗粒阻力经验公式。本文通过高精度的计算方法，系统模拟了从扁平到细长的回转椭球颗粒，在常见的颗粒雷诺数范围内（0.1~1000），对于各种来流攻角条件下的阻力，数值模拟结果得到了已知理论解的充分验证。在不存在理论解的大多数条件下，将数值结果与多种流行的经验公式结果进行了系统比较。一般而言，当颗粒以最大迎风面积置于来流中时，其所受阻力最大。但是数值模拟发现了特例，在流动进入牛顿阻力区时（雷诺数1000），扁平的椭球在回转轴与流向一致时（此时具有最大迎风面积），其阻力反而小于倾斜置于流场中的结果。对流动结构的分析表明，这是因为在非轴对称条件（颗粒倾斜）下，流动更容易失稳，造成紊乱的尾流，使得压差阻力上升。综合分析表明，对于给定的颗粒形状，数值模拟相对于通过各种实验数据拟合得到的适用于一般非球颗粒的经验公式具有更高的精度。累积更大量的高精度数值模拟结果，有望给出具有更高精度、更具适应性的阻力公式。

Abstract: The flow drag of a particle in unbounded uniform incoming flow is one of the fundamental problems in particulate multi-phase flow. Particles in relevant flows are generally non-spherical. Earlier investigations used the drag of a volume-equivalent sphere as a first approximation. Recently more empirical formulas, mostly derived from data fitting of measurements, have been developed. In this paper, high precision numerical simulations are carried out for a fixed oblate/prolate spheroid in a flow with varying particle Reynolds number from 0.1 to 1000, where different spheroid orientation has been taken into account. The simulation model and method have been verified against known analytical solutions. For more general flow conditions without known analytical solutions, numerical results have been compared with those from various popular empirical formulas. Generally speaking, a spheroid experiences the highest drag when it is located in the flow with the broadest side against the flow. However, numerical simulation at Reynolds number 1000 reveals an exception, i.e., an oblate spheroid experiences higher drag when put slanted in the flow than when put crosswise. This is because the flow around the spheroid is more stable in an axial-symmetrical setting than in the asymmetrical setting when the wake becomes chaotic and hence the form drag increases substantially. Overall, the numerical simulation is believed more precise in predicting the drag of a particle of specific shape than empirical formulas which aim to apply for a broad range of shapes. Through accumulating more high precision numerical data, it is promising to develop a more precise and broadly applicable drag formula.

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