基于简化Boltzmann方程的超声速流稀薄效应分析

从近连续流到近自由分子流,计算分析超声速流场的稀薄效应。模型Boltzmann方程先后经简化分布函数和离散速度坐标变换后,采用一个隐式通量修正二阶迎风TVD格式差分求解。壁面取漫反射气体分子模型。在Knudsen数为0.001,0.01,0.1,1.0,10等5种情形下,数值模拟二维圆柱氩气体绕流,观察到了不同的波系及尾迹结构。总阻力系数计算值同实验数据基本吻合,碰撞项Shakov动力学模型反映的流场细节略好于修正BGK模型。稀薄效应趋于弱化激波等超声速流动结构,物体影响域增大。

Rarefaction Effect Analysis of Supersonic Flows Based on Reduced Boltzmann Equations

Rarefaction effect on supersonic flow fields in the transition from near continuum to near free-molecule flow is analyzed numerically. The model Boltzmann equations, which are derived from the transformations of reduced distribution function and discrete velocity ordinate together, are solved through using an implicit flux-corrected second-order upwind TVD (Total Variation Diminishing) scheme. Gas molecule diffuse reflection model is implemented on the wall. For five cases, namely that Knudsen numbers are 0.001, 0.01, 0.1, 1.0 and 10 respectively, the Argon gas flows around a two-dimensional cylinder are simulated numerically, and different wave systems and wake structures are investigated. The calculated total drag coefficients can agree qualitatively well with the experiment data. Flow details obtained by employing Shakov kinetic model for collision term are a little better than by modified BGK model. Rarefaction effect tends to make supersonic flows move smoothly, and to enlarge the influence domain of cylinder.