Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures
Comparative study of the Boltzmann and McCormack equations for Couette and Fourier flows of binary gaseous mixtures
复制标题
DOI：
10.1016/j.ijheatmasstransfer.2015.12.068
复制
发表时间：
2016-05
影响因子：
5.2
通讯作者：
M. Ho;Lei Wu;I. Graur;Yonghao Zhang;J. Reese
中科院分区：
文献类型：
--
作者：
M. Ho;Lei Wu;I. Graur;Yonghao Zhang;J. Reese
我们评估的准确性的麦科马克模型通过比较其解决方案的Couette和傅立叶流动的二元气体混合物的线性化玻尔兹曼方程的结果。针对不同摩尔浓度值，对Ne-Ar和He-Xe混合气体从滑移到近自由分子流状态进行了数值模拟。我们的数值计算结果表明，虽然只有很小的差异，在Couette流和傅立叶流的热通量，计算从两个动力学方程的剪切应力，在其他宏观量的差异可以是非常大的，特别是在自由分子流制度。此外，从两个模型的结果之间的差异增加的分子质量比和较重的物种的摩尔浓度。最后，McCormack模型，这是来自线性化的流动只，通过比较其解决方案与玻尔兹曼方程的傅立叶流与大壁温比的适用性进行了研究。
We evaluate the accuracy of the McCormack model by comparing its solutions for Couette and Fourier flows of binary gaseous mixtures with results from the linearized Boltzmann equation. Numerical simulations of Ne–Ar and He–Xe gas mixtures are carried out from slip to near free-molecular flow regimes for different values of the molar concentration. Our numerical results show that while there are only small differences in the shear stress in Couette flow and the heat flux in Fourier flow, calculated from the two kinetic equations, differences in other macroscopic quantities can be very large, especially in free-molecular flow regime. Moreover, the difference between results from the two models increases with the molecular mass ratio and the molar concentration of the heavier species. Finally, the applicability of the McCormack model, which was derived for linearized flows only, is investigated by comparing its solutions with those from the Boltzmann equation for Fourier flow with large wall-temperature ratios.