A model of micro lubrication between two walls with an arbitrary temperature difference based on kinetic theory
A model of micro lubrication between two walls with an arbitrary temperature difference based on kinetic theory
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DOI：
10.1063/5.0004994
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发表时间：
2020-05
影响因子：
4.6
通讯作者：
T. Doi
中科院分区：
文献类型：
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作者：
T. Doi
基于玻尔兹曼方程的 Bhatnagar-Gross-Krook-Welander 模型，研究了具有任意温差的两个壁之间气体的微润滑。应用缓慢变化的近似，解析研究了当基于间隙尺寸的努森数较大时的动力学方程。本应是非线性传热问题解的主阶近似被其自由分子解所取代。由于这种粗略的近似，以封闭形式导出了雷诺型方程的宏观润滑模型。为了评估模型，还对动力学方程进行了直接数值分析。在温度比为 0.75 到 2 之间、努森数 Kn 为 0.1 到 10 的范围内，使用我们的模型计算的升力近似于直接数值分析的升力，统一误差在 4% 以内。当 Kn 足够大时，移动壁的加热会减小作用在另一壁上的升力，而当 Kn 足够小时，则会增强。
Micro lubrication of a gas between two walls with an arbitrary temperature difference is studied on the basis of the Bhatnagar–Gross–Krook–Welander model of the Boltzmann equation. Applying the slowly varying approximation, the kinetic equation is studied analytically when the Knudsen number based on the gap size is large. The leading order approximation, which ought to be the solution of the nonlinear heat transfer problem, is replaced by its free molecular solution. Due to this crude approximation, a macroscopic lubrication model of Reynolds-type equation is derived in a closed form. For an assessment of the model, a direct numerical analysis of the kinetic equation is also conducted. The lift calculated using our model approximates that of the direct numerical analysis within the error of 4% uniformly in the range of the temperature ratio between 0.75 and 2 and the Knudsen number Kn between 0.1 and 10. A heating of the moving wall reduces the lift acting on the other wall when Kn is sufficiently large, whereas it is enhanced when Kn is sufficiently small.