The effect of Knudsen layers on rarefied cylindrical Couette gas flows
The effect of Knudsen layers on rarefied cylindrical Couette gas flows
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DOI：
10.1007/s10404-012-1019-2
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发表时间：
2013-01-01
影响因子：
2.8
通讯作者：
Reese, Jason M.
中科院分区：
文献类型：
--
作者：
Dongari, Nishanth;Barber, Robert W.;Reese, Jason M.
我们研究了幂律概率分布函数来描述非平面几何中稀薄气体分子的平均自由程。通过考虑边界限制对凹凸曲率表面分子平均自由程的影响，导出了一个新的曲率相关模型。基于该幂律模型，通过平均自由程的输运性质表达式对Navier-Stokes本构关系和速度滑移边界条件进行了修正，得到了等温圆柱Couette流的速度分布，并与直接模拟Monte Carlo（DSMC）数据进行了比较.我们证明，我们的模型是更准确的比经典的滑移解决方案，我们能够捕捉到重要的非线性趋势与非平衡物理的努森层。此外，我们建立了一个新的临界调节系数，导致速度反演的非直观现象的标准。幂律模型预测的临界调节系数显着低于使用经典滑移解计算的临界调节系数，并且与现有的DSMC数据非常一致。我们提出的非平面表面的本构缩放是基于简单的物理参数，可以很容易地实现在传统的流体动力学代码的任意几何配置的微流体系统。
We investigate a power-law probability distribution function to describe the mean free path of rarefied gas molecules in non-planar geometries. A new curvature-dependent model is derived by taking into account the boundary-limiting effects on the molecular mean free path for surfaces with both convex and concave curvatures. The Navier-Stokes constitutive relations and the velocity-slip boundary conditions are then modified based on this power-law scaling through the transport property expressions in terms of the mean free path. Velocity profiles for isothermal cylindrical Couette flow are obtained using this power-law model and compared with direct simulation Monte Carlo (DSMC) data. We demonstrate that our model is more accurate than the classical slip solution, and we are able to capture important non-linear trends associated with the non-equilibrium physics of the Knudsen layer. In addition, we establish a new criterion for the critical accommodation coefficient that leads to the non-intuitive phenomenon of velocity inversion. The power-law model predicts that the critical accommodation coefficient is significantly lower than that calculated using the classical slip solution, and is in good agreement with available DSMC data. Our proposed constitutive scaling for non-planar surfaces is based on simple physical arguments and can be readily implemented in conventional fluid dynamics codes for arbitrary geometric configurations of microfluidic systems.