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 引用本文: 常心泉, 张克学, 王军, 夏国栋. 自由分子区内的非球形颗粒曳力计算. 力学学报, 2024, 56(5): 1251-1260.
Chang Xinquan, Zhang Kexue, Wang Jun, Xia Guodong. Drag forces on non-spherical particles in the free molecular regime. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1251-1260.
 Citation: Chang Xinquan, Zhang Kexue, Wang Jun, Xia Guodong. Drag forces on non-spherical particles in the free molecular regime. Chinese Journal of Theoretical and Applied Mechanics, 2024, 56(5): 1251-1260.

## DRAG FORCES ON NON-SPHERICAL PARTICLES IN THE FREE MOLECULAR REGIME

• 摘要: 基于气体动理论方法, 推导得到非球形颗粒所受曳力的通用表达式, 并针对球形颗粒、圆柱体颗粒、椭球体颗粒和圆锥体颗粒等几种常见的非球形颗粒, 得到其所受曳力的具体解析计算式. 该模型适用于气体分子与颗粒表面仅发生一次碰撞的凸面体, 假设气体分子与颗粒间的相互作用符合Maxwell镜面反射-漫反射模型, 计算气体分子与颗粒碰撞过程中的微元动量传递, 进而在颗粒表面积分得到非球形颗粒所受曳力的通用表达式. 计算结果表明, 颗粒所受曳力与其自身的几何形状和在流场中的取向有关. 但是, 基于非球形颗粒得到的计算式较为复杂, 不便于实际应用. 考虑到在自由分子区内, 当外势场较弱时, 颗粒的高速布朗旋转运动会使其取向分布近似为均匀的随机分布, 文章推导得到了不同形状颗粒在均向分布下所受均向曳力的计算式, 结果表明非球形颗粒所受均向曳力正比于颗粒表面积, 且比例系数与颗粒形状无关. 此算法避免了求解具体非球形颗粒受力计算的繁琐计算过程, 更便于实际应用.

Abstract: The evaluation of the drag force on non-spherical particles is of great importance in a wide range of areas. In the present paper, a general analytical expression for the drag force on non-spherical particles in the free molecular regime is obtained based on the gas kinetic theory. The obtained expression is applicable to rigid convex non-spherical particles suspending in a diluted gas, wherein multiple collisions between the gas molecules and the particle are ignored. Based on the Maxwellian scattering model, i.e., specular and diffusion collisions between gas molecule and the particle, the general analytical expression for the drag force on particles can be derived by evaluate the momentum transfer between the gas molecules and the particle upon gas-particle collisions. As examples, the expressions for drag force on several common non-spherical particles, such as spheres, cylinders, ellipsoids and cones, are also presented, which are consistent with the results in open literatures. It is found that the drag force on non-spherical particles depends on the geometric shape and orientation. However, the specific expressions for drag force on non-spherical particles are mathematically too complex to be employed in practical application. Considering that the particle is expected to undergo a rapidly rotation in the case of weak potential field in the free molecular regime, so the distribution of the particle orientation should be a uniformly random distribution. Then, the expression of the orientation-averaged drag force on non-spherical particles can be derived by introducing the random orientation distribution of the particle. It is found that the orientation-averaged drag force is proportional to the surface area of the non-spherical particle, and the corresponding coefficient is independent of the particle size or shape. The findings in the present paper can be employed to simplify the calculation of the drag forces on non-spherical particles in the free molecular regime.

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