考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

计算物理 ›› 2013, Vol. 30 ›› Issue (3): 326-336.

考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法

吴俊林¹, 李志辉^1,2, 蒋新宇²

1. 中国空气动力研究与发展中心超高速研究所, 绵阳 621000;
2. 国家计算流体力学实验室, 北京 100191

收稿日期:2012-07-17 修回日期:2012-10-26 出版日期:2013-05-25 发布日期:2013-05-25
作者简介:吴俊林(1985-),男,硕士,助理工程师,从事稀薄气体动力学研究,E-mail:wujunlinggexinghua@yahoo.oom.cn
基金资助:
国家自然科学基金(91016027)资助项目

One-dimensional Shock-tube and Two-dimensional Plate Flows in Boltzmann-Rykov Model Involving Rotational Energy

WU Junlin¹, LI Zhihui^1,2, JIANG Xinyu²

1. China Aerodynamics Research and Development Center, Hypervelocity Aerodynamics Institute, Mianyang 621000, China;
2. National Laboratory for Computational Fluid Dynamics, Beijing 100191, China

Received:2012-07-17 Revised:2012-10-26 Online:2013-05-25 Published:2013-05-25

摘要/Abstract

摘要： 研究考虑转动能的Boltzmann-Rykov模型方程,基于转动自由度对气体分子速度分布函数矩积分,引入约化速度分布函数,应用离散速度坐标法与数值积分技术,将气体运动论模型方程化为在离散速度坐标点处关于三个约化速度分布函数的联立方程组.应用拓展计算流体力学有限差分方法,数值计算考虑转动自由度的双原子气体一维、二维Boltzmann模型方程,得到高、低Knudsen数一维激波管内流动和二维竖直平板绕流问题的流场,分析验证考虑转动能的Boltzmann-Rykov模型方程全流域统一算法求解一维/二维气体流动问题的可靠性.结果表明,气体稀薄程度与分子内自由度对流场具有较大影响,且Knudsen数较高的稀薄气体流动呈现严重的非平衡流动特点.

关键词: 转动自由度, Boltzmann-Rykov模型方程, 激波管, 竖直平板绕流, 统一算法

Abstract: To investigate effect of rotational degree of freedom on gas flows covering various flow regimes,Boltzmann-Rykov model is studied and reduced velocity distribution functions are introduced with quadrature to rotational degree of freedom of molecular velocity distribution function.A single gas-kinetic model equation is translated into simultaneous equations of three reduced velocity distribution functions at discrete velocity ordinate points with discrete velocity ordinate method and numerical integration technique.One-and two-dimensional Boltzmann-Rykov model equations for diatomic gases are computed with finite-difference method of computational fluid dynamics.One-dimensional shock-tube and the two-dimensional flow past erect plate are analyzed in the whole range of Knudsen numbers.Reliability of gas-kinetic unified algorithm(GKUA) is validated in solving one-and two-dimensional flows from free molecular flow to continuum regimes.It is indicated that the gas rarefaction degree and molecular inner degree of freedom affect flow field greatly.And rarefied gas flows with high Knudsen numbers take serious non-equilibrium effect.

Key words: rotational degree of freedom, Boltzmann-Rykov model equation, shock-tube problem, erect plate flow, gas-kinetic unified algorithm

中图分类号:

O246
O355

吴俊林, 李志辉, 蒋新宇. 考虑转动能的一维/二维Boltzmann-Rykov模型方程数值算法[J]. 计算物理, 2013, 30(3): 326-336.

WU Junlin, LI Zhihui, JIANG Xinyu. One-dimensional Shock-tube and Two-dimensional Plate Flows in Boltzmann-Rykov Model Involving Rotational Energy[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 30(3): 326-336.

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