自由分子区内不规则颗粒的热泳力计算

doi:10.11949/0438-1157.20250166

摘要/Abstract

摘要：

在气固两相流动中，悬浮在气体中的实际颗粒大多为非球形颗粒。基于气体动理论的方法，建立了一种较为简便的计算模型，推导得到了颗粒在自由分子区内所受热泳力的通用表达式，并进一步得到了球体、圆柱体颗粒所受热泳力的具体表达式。考虑到颗粒在自由分子区内的高速布朗旋转，在宏观时间尺度上可以认为颗粒在各个方向上为等概率分布，由此推导得到了任意形状颗粒所受均向热泳力的表达式，结果表明非球形颗粒的均向热泳力正比于颗粒表面积，且比例系数与颗粒形状无关。此结果得到了直接Monte Carlo模拟的验证，为简化颗粒输运特性研究及其应用提供了新思路。

关键词: 气溶胶, 多相流, 非球形颗粒, 热泳力, 动力学理论, 直接Monte Carlo模拟

Abstract:

In a gas-solid two-phase flow, the particles suspended in the gas are mostly non-spherical, whose geometric shape and orientation have a significant impact on particle transport. Non-spherical particles are usually simplified as sphere particles, but this may cause serious errors. While the specific expressions for non-spherical particles are too complex to be employed for practical applications. In this paper, we derived a general expression for the thermophoretic force of non-spherical particles in the free molecular regime. Then specific expressions for the thermophoretic force on sphere and cylinder can be obtained. Considering the high-speed Brownian rotation of particles in the free molecular region, a uniformly random distribution of the particle orientation can be assumed in the case of weak potential field. Based on this, the expression of the orientation-averaged thermophoretic force on particles of any shape can be derived, which is found to be proportional to the surface area of the particles, and the proportion coefficient is independent of the particle size or shape. This result is verified by direct simulation Monte Carlo, providing a new idea for simplifying the research on particle transport characteristics and its application.

Key words: aerosol, multiphase flow, non-spherical particle, thermophoretic force, kinetic theory, direct simulation Monte Carlo

中图分类号:

O 356

常心泉, 张克学, 王军, 夏国栋. 自由分子区内不规则颗粒的热泳力计算[J]. 化工学报, 2025, 76(8): 3944-3953.

Xinquan CHANG, Kexue ZHANG, Jun WANG, Guodong XIA. Thermophoretic forces on irregular particles in the free molecular regime[J]. CIESC Journal, 2025, 76(8): 3944-3953.

图/表 13

图1 自由分子区内颗粒受力分析模型示意图

Fig.1 The coordinate systems for particles in the free molecular regime

图2 球形颗粒受力分析模型图

Fig.2 The reference systems for spheres

图3 圆柱体颗粒受力分析模型图

Fig.3 The reference systems for cylinders

图4 椭球体颗粒受力分析模型图

Fig.4 The reference systems for spheroids

图5 直接Monte Carlo模拟计算模型图

Fig.5 Direct simulation Monte Carlo model

图6 模拟域内温度分布剖面图

Fig.6 Temperature distribution profile in the simulation box

图7 Y=0处温度分布路径图

Fig.7 Temperature distribution path diagram at Y=0

图8 半径为1 μm球形颗粒所受热泳力随温度梯度的变化

Fig.8 Thermophoretic force of spherical particle with a radius of 1 μm versus the temperature gradient

图9 不同壁面温差下球形颗粒所受热泳力随其表面积的变化

Fig.9 Thermophoretic force on spherical particle versus the surface area with varying wall temperature

图10 椭球体颗粒所受均向热泳力随颗粒表面积的变化

Fig.10 Influence of the surface area on orientation-averaged forces acting on spheroid particles

图11 圆柱体颗粒所受热泳力的方向特性依赖曲线

Fig.11 The orientation dependence of the thermophoretic force for cylinders

图12 椭球体颗粒所受热泳力的方向特性依赖曲线

Fig.12 The orientation dependence of the thermophoretic force for spheroids

图13 不同形状颗粒所受均向热泳力随颗粒表面积的变化

Fig.13 Influence of the surface area on orientation-averaged forces acting on different shape of particles

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