AN EXTENSION TO THE NAVIER-STOKES-FOURIER EQUATIONS BY CONSIDERING MOLECULAR COLLISIONS WITH BOUNDARIES
AN EXTENSION TO THE NAVIER-STOKES-FOURIER EQUATIONS BY CONSIDERING MOLECULAR COLLISIONS WITH BOUNDARIES
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DOI：
10.1115/icnmm2008-62222
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发表时间：
2008-07
期刊：
影响因子：
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通讯作者：
E. Arlemark;S. Kokou Dadzie;J. Reese
中科院分区：
文献类型：
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作者：
E. Arlemark;S. Kokou Dadzie;J. Reese
本文提出了一个由具有固体边界的分子碰撞描述和不连续速度滑移和温度跳跃边界条件扩展的Navier-Stokes-Fourier方程（NSF）组成的微气体流动模型。通过考虑气体流动中分子与固体边界的碰撞，我们捕捉到了一些具有线性应力/应变率和热通量/温度梯度关系的传统NSF似乎无法描述的近壁效应。我们提出的模型将具有固体边界的分子碰撞作为传统定义的扩展，扩展了分子在经历分子间碰撞之前的平均移动距离（平均自由程）。通过考虑这两种类型的碰撞，我们得到了一个有效的平均自由路径表达式，它随到表面的距离而变化。提出了利用有效平均自由程来获得有效粘度和有效导热系数的新定义，将NSF方程的适用性扩展到更高的Knudsen数。我们展示了使用该扩展的NSF模型求解的简单流例的结果，并讨论了由于各种假设对模型的限制。我们还提到了基于更详细的气体描述进一步开发模型的有趣想法。
In this paper we propose a model for micro gas flows consisting of the Navier-Stokes-Fourier equations (NSF) extended by a description of molecular collisions with solid boundaries and discontinuous velocity slip and temperature jump boundary conditions. By considering the molecular collisions with the solid boundaries in gas flows we capture some of the near wall effects that the conventional NSF with linear stress/strain-rate and heat-flux/ temperature-gradient relationships seem to be unable to describe. The model that we propose incorporates the molecular collisions with solid boundaries as an extension to the conventional definition of the average travelling distance of molecules before experiencing intermolecular collisions (the mean free path). By considering both of these types of collisions we obtain an effective mean free path expression, which varies with distance to surfaces. The effective mean free path is proposed to be used to obtain new definitions of effective viscosity and effective thermal conductivity, which will extend the applicability of NSF equations to higher Knudsen numbers. We show results of simple flow cases that are solved using this extended NSF model and discuss limitations to the model due to various assumptions. We also mention interesting ideas for further development of the model based on a more detailed gas description.