On the modelling of isothermal gas flows at the microscale
On the modelling of isothermal gas flows at the microscale
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DOI：
10.1017/s0022112008001158
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发表时间：
2008-05
影响因子：
3.7
通讯作者：
D. Lockerby;J. Reese
中科院分区：
文献类型：
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作者：
D. Lockerby;J. Reese
本文提出了关于微尺度稀薄（非平衡）等温气流建模的两个新命题。第一个是一个新的测试用例，用于对这些流动的高阶或扩展流体动力学模型进行基准测试。这种时变剪切波问题不需要在固体表面指定边界条件，因此对于评估流体模型是否可以捕获整体流动中的稀疏效应非常有用。我们评估了许多不同的提出的扩展流体动力学模型，我们发现 R13 方程在这种情况下表现最好。我们的第二个命题是一种简单的技术，用于将固体表面的存在引起的非平衡效应引入计算流体动力学框架。通过将滑移边界条件的新模型与纳维-斯托克斯本构关系的近壁缩放相结合，我们获得了一个在更高努森数下比传统二阶滑移模型更准确的模型。我们表明，这为组合库埃特/泊肃叶流提供了良好的结果，并且该模型可以预测分子模拟中显而易见的应力/应变率反演。通过检查微球周围的低速流动，证明了该模型对非平面几何形状的通用性。尽管对于其在最高克努森数下的稳定性存在一些疑问，但与球体阻力的传统预测相比，它显示出显着的改进。
This paper makes two new propositions regarding the modelling of rarefied (non-equilibrium) isothermal gas flows at the microscale. The first is a new test case for benchmarking high-order, or extended, hydrodynamic models for these flows. This standing time-varying shear-wave problem does not require boundary conditions to be specified at a solid surface, so is useful for assessing whether fluid models can capture rarefaction effects in the bulk flow. We assess a number of different proposed extended hydrodynamic models, and we find the R13 equations perform the best in this case. Our second proposition is a simple technique for introducing non-equilibrium effects caused by the presence of solid surfaces into the computational fluid dynamics framework. By combining a new model for slip boundary conditions with a near-wall scaling of the Navier--Stokes constitutive relations, we obtain a model that is much more accurate at higher Knudsen numbers than the conventional second-order slip model. We show that this provides good results for combined Couette/Poiseuille flow, and that the model can predict the stress/strain-rate inversion that is evident from molecular simulations. The model's generality to non-planar geometries is demonstrated by examining low-speed flow around a micro-sphere. It shows a marked improvement over conventional predictions of the drag on the sphere, although there are some questions regarding its stability at the highest Knudsen numbers.