气体中椭球颗粒受力特性研究

Study on Force Characteristics of Ellipsoids in Gas

摘要

颗粒在流体中的受力决定了其动力学行为,气体中悬浮的颗粒通常为非球形颗粒,其受力特性与颗粒形状、取向和动量适应系数等因素密切相关。椭球颗粒的长径比和气体分子的入射角(椭球颗粒极轴与流体流动方向的夹角)是导致其受力特性与球形颗粒不同的关键因素。该文基于直接蒙特卡罗模拟的方法,对椭球颗粒的受力进行分析,并计算了其曳力系数和升力系数,直接蒙特卡罗模拟结果与理论计算结果吻合较好。结果表明,在克努森数不同时,连续介质区内的理论计算式同样适用于自由分子区和过渡区,并且曳力系数和升力系数在不同的克努森数下随入射角变化的趋势相同。长椭球颗粒的曳力系数在入射角90°时为最大值,扁椭球颗粒曳力系数的变化与长椭球颗粒相反,在入射角90°时为最小值。长椭球颗粒和扁椭球颗粒的升力系数均在入射角45°时为最大值。气体分子入射角相同时,椭球颗粒的曳力系数和升力系数随速比的增大而减小。在自由分子区,椭球颗粒的曳力系数和升力系数与颗粒表面的动量适应系数成线性变化。

Abstract

The dynamic behaviors of particles are mainly affected by forces exerted on the particles in fluid. The particles suspended in gas are typically nonspherical. Forces on nonspherical particles depend on shape, orientation and momentum accommodation coefficients. The aspect ratio of ellipsoids and the incident angle of gas flow (the angle between the polar axis of an ellipsoid and the direction of gas flow) are the key factors, which lead to the transport dynamics of nonspherical particles different from spherical particles. In this study, we analyzed the forces on ellipsoids and calculated the drag and lift coefficients using the direct simulation Monte Carlo (DSMC) method. The results obtained by the DSMC method are in agreement with theoretical predictions. Across various Knudsen numbers, the variations of drag and lift coefficients are analogous. It is found that the theoretical formulae in the continuum regime can be extended to the transition and free molecular regimes. There is a maximum of drag coefficient where the incident angle is 90° for prolate ellipsoids. However, the drag coefficient is a minimum in the condition of 90° for oblate ellipsoids. Lift coefficients of prolate and oblate ellipsoids increase to a maximum at 45° and subsequently decrease. At the same incident angles, drag and lift coefficients decrease with speed ratios in the free molecular regime. For a particle suspended in the free molecular regime, the drag and lift coefficients are proportional to the momentum accommodation coefficients of ellipsoids.

关键词

气体 / 直接蒙特卡罗模拟 / 椭球颗粒 / 曳力系数 / 升力系数 / 非球形颗粒

Key words

gas / direct simulation Monte Carlo / ellipsoid particles / drag coefficients / lift coefficients / nonspherical particles

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基金资助

国家自然科学基金面上资助项目(12472268)