Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates II: effect of nonuniform surface properties in the longitudinal direction
Poiseuille flow and thermal transpiration of a rarefied gas between parallel plates II: effect of nonuniform surface properties in the longitudinal direction
复制标题
平行板之间稀薄气体的泊肃叶流和热蒸发 II：纵向不均匀表面特性的影响
DOI：
10.1007/s00033-015-0580-4
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
T. Doi
中科院分区：
文献类型：
--
作者：
T. Doi
研究了两平行平板间稀薄气体的Poiseuille流动和热蒸腾问题，其中一个壁面为麦克斯韦边界，其调节系数在纵向上呈周期性分布。基于Boltzmann方程的Bhatnager-Gross-Krook-Welander模型对流动行为进行了数值研究。在纵向坐标中线性函数和周期函数的叠加中求解。在较宽的平均自由程和表征调节系数分布的参数范围内，给出了数值解。由于纵向表面性质的不均匀，流动是非平行的，气体的压力和温度与常规平行流动的压力和温度有偏差。气体和墙壁之间的能量转移就会发生。气体的质量流量可以用一个由一维流动数据组成的公式来近似，但当调节系数的变化幅度足够大时，Poiseuille流动中观察到了一个不可忽略的不一致。通过对流经长槽的流动的直接数值分析，验证了该方法的有效性。
Poiseuille flow and thermal transpiration of a rarefied gas between two parallel plates are studied for the situation that one of the walls is a Maxwell-type boundary with a periodic distribution of the accommodation coefficient in the longitudinal direction. The flow behavior is studied numerically based on the Bhatnager–Gross–Krook–Welander model of the Boltzmann equation. The solution is sought in a superposition of a linear and a periodic functions in the longitudinal coordinate. The numerical solution is provided over a wide range of the mean free path and the parameters characterizing the distribution of the accommodation coefficient. Due to the nonuniform surface properties in the longitudinal direction, the flow is nonparallel, and a deviation in the pressure and the temperature of the gas from those of the conventional parallel flow is observed. An energy transfer between the gas and the walls arises. The mass flow rate of the gas is approximated by a formula consisting of the data of one-dimensional flows; however, a non-negligible disagreement is observed in Poiseuille flow when the amplitude of the variation of the accommodation coefficient is sufficiently large. The validity of the present approach is confirmed by a direct numerical analysis of a flow through a long channel.