激波结构内流动问题的气体运动论描述  

Gas-kinetic description of shock wave structures by solving Boltzmann model equation

作　　者：李志辉[1] 张涵信[2] 

机构地区：[1]中国空气动力研究与发展中心,四川绵阳621000 [2]国家计算流体力学实验室,北京100083

出　　处：《空气动力学学报》2007年第4期411-418,436,共9页Acta Aerodynamica Sinica

基　　金：国家自然科学基金面上项目(90205009)资助

摘　　要：从介观Boltzmann速度分布函数理论出发,发展计及分子粘性碰撞截面与扩散碰撞截面,可描述各流域一维气体流动问题的Boltzmann简化速度分布函数方程及其气体运动论数值计算方法。通过对不同Knudsen数下非定常激波管流动及不同马赫数定常正激波结构问题数值模拟,研究分析不同流区的激波突跃变化过程以及近连续流、稀薄过渡流特有的分子输运现象,揭示不同马赫数、不同分子模型的激波内流动与传热变化规律,证实基于Bo-ltzmann模型方程的气体运动论数值计算方法用于激波结构内流动研究的准确可靠性。Based on the mesoscopic theory of the Bohzmann-type velocity distribution function, the Boltzmann model equation describing the one-dimensional gas flows from various flow regimes can be presented with developing the molecular models involving in the viscosity cross-section and the diffusion cross-section. The gas-kinetic numerical method for directly solving the velocity distribution function is studied by introducing the reduced velocity distribution functions and the discrete velocity ordinate method, in which the unsteady time-splitting method and the NND scheme from computational fluid dynamics are applied. To study the inner flows of shock wave structures, the one-dimensional unsteady shock-tube problems with various Knudsen numbers and the steady normal shock wave problems with different Mach numbers are numerically simulated. The varying process of the shock wave disturbances from various flow regimes is studied, the molecular transport phe-nomena from near-continuum and rarefied transition flows are analyzed specially. The varying laws of gas flow and heat flux of the shock wave structures are revealed with different Mach numbers and molecular models. The computing practice has confirmed the good precision and reliability of the gas-kinetic numerical algorithm in solving the inner flow problems of shock wave structures.

关 键 词：激波结构 BOLTZMANN模型方程 速度分布函数 离散速度坐标法 有限差分计算 

分 类 号：V211.3[航空宇航科学与技术—航空宇航推进理论与工程]