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一种新的玻尔兹曼方程可计算模型构造与分析

彭傲平 李志辉 吴俊林 皮兴才 蒋新宇

彭傲平, 李志辉, 吴俊林, 皮兴才, 蒋新宇. 一种新的玻尔兹曼方程可计算模型构造与分析. 力学学报, 2021, 53(9): 2583-2595 doi: 10.6052/0459-1879-21-104
引用本文: 彭傲平, 李志辉, 吴俊林, 皮兴才, 蒋新宇. 一种新的玻尔兹曼方程可计算模型构造与分析. 力学学报, 2021, 53(9): 2583-2595 doi: 10.6052/0459-1879-21-104
Peng Aoping, Li Zhihui, Wu Junlin, Pi Xingcai, Jiang Xinyu. Construcrion and analysis of a new computable model for Boltzmann equation. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2583-2595 doi: 10.6052/0459-1879-21-104
Citation: Peng Aoping, Li Zhihui, Wu Junlin, Pi Xingcai, Jiang Xinyu. Construcrion and analysis of a new computable model for Boltzmann equation. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2583-2595 doi: 10.6052/0459-1879-21-104

一种新的玻尔兹曼方程可计算模型构造与分析

doi: 10.6052/0459-1879-21-104
基金项目: 国家自然科学基金(11902339)和国家数值风洞工程(NNW2018-ZT5B10)资助项目
详细信息
    作者简介:

    李志辉, 研究员, 主要研究方向: 航天再入跨流域空气动力学与结构响应失效解体数值预报. E-mail: zhli0097@x263.net

  • 中图分类号: V211.3

CONSTRUCRION AND ANALYSIS OF A NEW COMPUTABLE MODEL FOR BOLTZMANN EQUATION

  • 摘要: 临近空间飞行器因各部件尺寸差异较大, 在高空高马赫数条件下飞行会出现多流区共存的多尺度复杂非平衡流动现象, 流场中的气体分子速度分布函数与当地位置、流场分子速度、气体密度、流动速度、温度、热流矢量、应力张量等相关. 通过分析玻尔兹曼方程的一阶查普曼−恩斯科近似解, 构造了一种同时考虑热流矢量和应力张量影响、满足玻尔兹曼方程高阶碰撞矩的跨流域统一可计算模型方程, 并在数学上分析了其守恒性、H定理等基本属性, 证明了新模型方程与玻尔兹曼方程的相容性, 给出了新模型与现有模型如沙克霍夫(Shakhov)模型等的递进关系, 基于碰撞动力学确定了各流域统一气体分子碰撞松弛参数表达式. 在气体动理论统一算法中采用新建模型及现有模型模拟了一维激波结构、二维近空间飞行环境平板和多体圆柱干扰流动, 并与直接模拟蒙特卡洛方法对比分析, 结果表明在流场中粘性效应显著的区域新建模型能更好地捕捉激波位置, 尤其是在激波内部新模型模拟的宏观参数分布与直接模拟蒙特卡洛方法结果符合更好, 验证了新模型的有效性和可靠性, 同时说明在非平衡显著的流动区域碰撞松弛模型受多参数共同作用的影响.

     

  • 图  1  不同模型模拟的激波轮廓与直接模拟蒙特卡洛方法对比

    Figure  1.  Comparison of shock profiles simulated by GKUA with different models and DSMC

    图  2  不同模型模拟的无量纲热流和切应力对比

    Figure  2.  Comparison of non-dimensional heat fluxes and shear stresses simulated by GKUA with different models

    图  3  本文模拟的温度云图与直接模拟蒙特卡洛方法结果对比

    Figure  3.  Comparison of temperature contours simulated by GKUA with new model and DSMC

    图  4  $x $ = 0.1 m截面上压力和温度沿y方向不同碰撞模型的统一算法计算值与直接模拟蒙特卡洛方法模拟结果的对比

    Figure  4.  Comparison of pressure and temperature simulated by GKUA with different collision models and DSMC along the direction of y on the section of $x $ = 0.1 m

    图  5  $x $ = 0.5 m截面上压力和温度沿y方向不同碰撞模型统一算法计算结果与直接模拟蒙特卡洛方法模拟值比较

    Figure  5.  Comparison of pressure and temperature simulated by GKUA with different collision models and DSMC along the direction of y on the section of $x $ = 0.5 m

    图  6  $x $ = 0.8 m截面上压力和温度沿y方向不同碰撞模型统一算法模拟结果与直接模拟蒙特卡洛方法的对比

    Figure  6.  Comparison of pressure and temperature simulated by GKUA with different collision models and DSMC along the direction of y on the section of $x $ = 0.8 m

    图  7  驻点线上不同碰撞模型统一算法计算的温度分布与直接模拟蒙特卡洛方法模拟值比较

    Figure  7.  Comparison of temperature simulated by GKUA with different collision models and DSMC along the stagnation line

    图  8  3种模型方程计算得到的温度分布云图与直接模拟蒙特卡洛方法结果的对比

    Figure  8.  Comparison of temperature contours simulated by GKUA with three collision models and DSMC

    图  9  $y $ = 0 m截面上压力、温度和速度沿$ x $方向不同碰撞模型模拟结果与直接模拟蒙特卡洛方法的对比

    Figure  9.  Comparison of pressure, temperature and velocity simulated by GKUA with different collision models and DSMC along the direction of x on the section of $y $ = 0 m

    表  1  不同模型/方法所得轴向力系数及其偏差与法向力系数

    Table  1.   The axial and normal force coefficients by different models and DSMC method and errors between axial force coefficients

    Model/MethodCaError/%Cn
    DSMC1.287 03.82 × 10−4
    New model1.34584.575.76 × 10−3
    Shakhov model1.37606.928.25 × 10−3
    Belyi model1.32613.043.90 × 10−3
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-03-17
  • 录用日期:  2021-07-23
  • 网络出版日期:  2021-07-24
  • 刊出日期:  2021-09-18

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