基于Boltzmann矩方程的扩展速度滑移边界条件

摘要

An extended velocity slip boundary condition for half space gas flow was derived theoretically from R13 moment equations based on the fact that the correction effect of Knudsen layer beyond the Knudsen layer is almost zero.The slip coefficients of extended velocity slip boundary condition was not fixed,which was not only related to the Knudsen number,but also the wall accommodation coefficient.Micro Poiseuille gas flow was considered to analyze the validity of extended velocity slip boundary condition.The research shows that the extended velocity slip boundary condition is superior to the existing velocity slip boundary conditions in literatures and the mass flow rate calculated according to the extended velocity slip boundary condition is more closer to the results from linearized Boltzmann-hard sphere molecular model equation in the early transition flow regime.When the Knudsen number equals to 1,the velocity profile of micro channel flow still shows a large discrepancy from the results of direct simulation Monte Carlo (DSMC) method.%针对半空间流,从R13矩方程出发,基于壁面附近Knudsen层外Knudsen层的修正效应近似为零的条件,理论推导得到等温情形下扩展的速度滑移边界条件.该速度滑移边界条件的滑移系数是不固定的,不仅与气流的努森数有关,还与壁面适应系数有关.以微Poiseuille流为例,分析扩展的速度滑移边界条件的适用性.研究表明,在近过渡流区,扩展的速度滑移边界情形下的质量流率与基于Boltzmann-硬球分子模型方程的结果更为接近,优于现有文献中的速度滑移边界条件.当努森数为1时,扩展的速度滑移边界条件情形下的气流速度与直接模拟Monte Carlo(DSMC)模拟结果之间的差别仍然较大.