EI、Scopus 收录
中文核心期刊

转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用

李志辉, 蒋新宇, 吴俊林, 彭傲平

李志辉, 蒋新宇, 吴俊林, 彭傲平. 转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J]. 力学学报, 2014, 46(3): 336-351. DOI: 10.6052/0459-1879-13-246
引用本文: 李志辉, 蒋新宇, 吴俊林, 彭傲平. 转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J]. 力学学报, 2014, 46(3): 336-351. DOI: 10.6052/0459-1879-13-246
Li Zhihui, Jiang Xinyu, Wu Junlin, Peng Aoping. GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 336-351. DOI: 10.6052/0459-1879-13-246
Citation: Li Zhihui, Jiang Xinyu, Wu Junlin, Peng Aoping. GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 336-351. DOI: 10.6052/0459-1879-13-246
李志辉, 蒋新宇, 吴俊林, 彭傲平. 转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J]. 力学学报, 2014, 46(3): 336-351. CSTR: 32045.14.0459-1879-13-246
引用本文: 李志辉, 蒋新宇, 吴俊林, 彭傲平. 转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用[J]. 力学学报, 2014, 46(3): 336-351. CSTR: 32045.14.0459-1879-13-246
Li Zhihui, Jiang Xinyu, Wu Junlin, Peng Aoping. GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 336-351. CSTR: 32045.14.0459-1879-13-246
Citation: Li Zhihui, Jiang Xinyu, Wu Junlin, Peng Aoping. GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(3): 336-351. CSTR: 32045.14.0459-1879-13-246

转动非平衡玻尔兹曼模型方程统一算法与全流域绕流计算应用

基金项目: 973计划(2014CB744100),国家自然科学基金(91016027,11325212)和空气动力学国家重点实验室研究基金资助项目.
详细信息
    作者简介:

    李志辉,研究员,主要研究方向:稀薄气体动力学与计算流体力学.E-mail:zhli0097@x263.net

  • 中图分类号: V211.25

GAS-KINETIC UNIFIED ALGORITHM FOR BOLTZMANN MODEL EQUATION IN ROTATIONAL NONEQUILIBRIUM AND ITS APPLICATION TO THE WHOLE RANGE FLOW REGIMES

Funds: The project was supported by the 973 Program (2014CB744100), the National Natural Science Foundation of China (91016027, 11325212) and the Researching Fund of State Key Laboratory of Aerodynamics.
  • 摘要: 基于过去开展稀薄自由分子流到连续流气体运动论统一算法框架,采用转动惯量描述气体分子自旋运动,确立含转动非平衡效应各流域统一玻尔兹曼模型方程.基于转动能量对分布函数守恒积分,得到计及转动非平衡效应气体分子速度分布函数方程组,使用离散速度坐标法对分布函数方程所依赖速度空间离散降维;应用拓展计算流体力学有限差分方法,构造直接求解分子速度分布函数的气体动理论数值格式;基于物面质量流量通量守恒与能量平衡关系,发展计及转动非平衡气体动理论边界条件数学模型及数值处理方法,提出模拟各流域转动非平衡效应玻尔兹曼模型方程统一算法.通过高、低不同马赫数1:5~25氮气激波结构与自由分子流到连续流全飞行流域不同克努森数(9×10-4~10)Ramp制动器、圆球、尖双锥飞行器、飞船返回舱外形体再入跨流域绕流模拟研究,将计算结果与有关实验数据、稀薄流DSMC模拟值等结果对比分析,验证统一算法模拟自由分子流到连续流再入过程高超声速绕流问题的可靠性与精度.
    Abstract: Based on the gas-kinetic unified algorithm (GKUA) for flows from rarefied transition to continuum, the effect of rotational non-equilibrium is investigated involving the kinetic Rykov model with relaxation property of rotational degrees of freedom. The spin movement of diatomic molecule is described by moment of inertia, and the conservation of total angle momentum is taken as a new Boltzmann collision invariant, then the unified Boltzmann model equation involving rotational non-equilibrium effect is presented for various flow regimes. The molecular velocity distribution function is integrated by the weight factor on the energy of rotational motion, and the closed system of two kinetic controlling equations is obtained with inelastic and elastic collisions. The discrete velocity ordinate technique and numerical quadrature methods are applied to discretize the velocity space, and the gas-kinetic finite-difference numerical scheme is constructed to capture the time evolution of the discretized velocity distribution functions. The gas-kinetic boundary conditions in rotational non-equilibrium and numerical procedures are studied and implemented by directly acting on the velocity distribution function, and then the unified algorithm of the Boltzmann kinetic model equation involving rotational non-equilibrium effect is presented for the whole range of flow regimes. As the applications of the GKUA, the hypersonic flows of diatomic gas involving rotational non-equilibrium effect are numerically simulated including the inner flows of shock wave structures in nitrogen with different Mach numbers of 1.5-25, the two-dimensional planar Ramp flow with the whole range of Knudsen numbers of 9×10-4-10 and the three-dimensional re-entering hypersonic flows around sphere, tine double-cone and spacecraft body. The computed results match the relevant experimental data, DSMC results, and the solutions of the generalized Boltzmann equation (GBE) and ellipsoidal statistical (ES) model equation well. It is tested and validated from this study that the GKUA solving the Boltzmann model equation in rotational nonequilibrium can simulate the complex hypersonic flow problems and flow mechanisms from high rarefied free-molecule flow to continuum flow regimes with good reliability and precision.
  • Tsien HS. Superaerodynamics, mechanics of rarefied gases. Journal of Aeronautics Science, 1946, 13(12): 653-664
    Koppenwallner G, Legge H. Drag of bodies in rarefied hypersonic flow. AIAA Paper 85-0998, Progress in Astronautics and Aeronautics: Thermophysical Aspects of Reentry Flows, New York, 1985, 103: 44-59
    李志辉,吴振宇.阿波罗指令舱稀薄气体动力学特征的蒙特卡罗数值模拟. 空气动力学学报,1996, 14(2): 230-233 (Li Zhihui, Wu Zhenyu, DSMC simulation on rarefied aerodynamics of Apollo-CM. Acta Aerodynamica Sinica, 1996, 14(2): 230-233 (in Chinese))
    Yoon S, Gnoffo PA, White JA, et al. Computational challenges in hypersonic flow simulations. AIAA 2007-4265, 2007
    庄逢甘,崔尔杰,张涵信. 未来空间飞行器的某些发展和空气动力学的任务. 中国第一届近代空气动力学与气动热力学会议论文集,2006. 1-12 (Zhuang Fenggan, Cui Erjie, Zhang Hanxin. Some development of future spacecrafts and aerodynamics tasks. In: Proc. of First Aerodynamics and Aerothermodynamics, 2006. 1-12 (in Chinese))
    Chapmann S,Cowling TG.The Mathematical Theory of Non-uniform Gases.3rd edn.Cambridge,1990
    Bhatnagar PL,Gross EP,Krook M. A model collision processes in gases.Phys Rev,1954, 94:511-525
    Holway Jr LH. New statistical models for kinetic theory. Methods of Construction, Phys Fluids, 1966, 9: 1658-1673
    Shakhov EM.Kinetic model equations and numerical results.In:Oguchi H ed.Proceedings of 14th International Symposium on Rarefied Gas Dynamics, Tokyo: University of Tokyo Press, 1984. 137-148
    Li ZH, Fang M, Jiang XY, et al. Convergence proof of the DSMC method and the gas-kinetic unified algorithm for the Boltzmann equation. Sci China-Phys Mech Astron, 2013, 56(2): 404-417, doi: 10.1007/s11433-013-4999-3  
    Chu CK. Kinetic-theoretic description of the formation of a shock wave. Physics of Fluids, 1965, 8(1): 12-22
    Morinishi K, Oguchi H. A computational method and its application to analyses of rarefied gas flows.In:Oguchi H ed. Proc. of 14th International Symposium on Rarefied Gas Dynamics, Tokyo: University of Tokyo Press, 1984. 149-158
    Yang JY, Huang JC. Rarefied flow computations using nonlinear model boltzmann equations. J of Comput Phys, 1995, 120: 323-339
    Huang AB, Giddens DP. The discrete ordinate method for the linearized boundary value problems in kinetic theory of gases. In: Proc. of 5th International Symposium on Rarefied Gas Dynamics, Brundin CL, ed. New York, 1967. 481-486
    李志辉,张涵信. 稀薄流到连续流的气体运动论统一数值算法初步研究. 空气动力学学报,2000, 18(3): 251-259 (Li Zhihui, Zhang Hanxin. Pilot study on gas-kinetic unified numerical algorithm for flows from rarefied transition to continuum. Acta Aerodynamica Sinica, 2000, 18(3): 251-259 (in Chinese))
    李志辉, 张涵信. 稀薄流到连续流的气体运动论模型方程算法研究. 力学学报, 2002, 34(2): 145-155 (Li Zhihui, Zhang Hanxin. Study on gas kinetic algorithm for flows from rarefied transition to continuum using Boltzmann model equation. Acta Mechanica Sinica, 2002, 34(2): 145-155 (in Chinese))
    李志辉,张涵信. 稀薄流到连续流的气体运动论统一算法研究. 空气动力学学报,2003, 21(3): 255-266 (Li Zhihui, Zhang Hanxin. Study on gas kinetic unified algorithm for flows from rarefied to continuum. Acta Aerodynamica Sinica, 2003, 21(3): 255-266 (in Chinese))
    Li ZH, Zhang HX. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. J of Comput Phys, 2004, 193: 708-738
    Li ZH, Zhang HX. Gas-kinetic numerical method solving mesoscopic velocity distribution function equation. Acta Mechanica Sinica, 2007, 23(3): 121-132
    Li ZH. Gas-kinetic unified algorithm for re-entering complex problems covering various flow regimes by solving Boltzmann model equation. In: Advances in Spacecraft Technologies, InTech Publisher, 2011: 273-332
    Li ZH, Zhang HX, Fu S, et al. A gas kinetic algorithm for flows in Microchannel. International Journal of Nonlinear Sciences and Numerical Simulation, 2005, 6(3): 261-270
    Li ZH, Zhang HX, Fu S. Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation. Sci China-Phys Mech & Astron, 2005, 48(4): 496-512
    Li ZH, Zhang HX. Gas-kinetic numerical studies of three-dimensional complex flows on spacecraft re-entry. J Comput Phys, 2009, 228: 1116-1138
    Li ZH, Bi L, Zhang HX, et al. Gas-kinetic numerical study of complex flow problems covering various flow regimes. Computers and Mathematics with Application, 2011, 61(12): 3653-3667
    Xu K.Gas-kinetic schemes for unsteady compressible flow simulations.Von Karman Institute for Fluid Dynamics Lecture Series,Feb.23-27, 1998.
    Xu K. A gas-kinetic bgk scheme for the Navier-Stokes equations and its connection with artificial dissipation and godunov method. J Comput Phys, 2001, 171(1): 289-335
    Li QB, Xu K, Fu S. A high-order gas-kinetic Navier-Stokes flow solver. J Comput Phys, 2010, 229: 6715-6731
    Xiong SW, Zhong CW, Zhou CS. Numerical simulation of compressible turbulent flow via improved gas-kinetic BGK scheme. Int J Numer Meth Fluids, 2011, 67(12): 1833-1847
    Guo ZL, Zhao TS. Lattice Boltzmann model for incompressible flows through porous media. Phys Rev E, 2002, 66(3): 036304(1-9)
    Lee T, Lin CL. A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio. J of Comput Phys, 2005, 206: 16-47
    卓丛山,钟诚文,李凯等. 高雷诺数下的翼型绕流LBM数值模拟. 航空学报,2010, 31(2): 238-243 (Zhuo Congshan, Zhong Chengwen, Li Kai, et al. Numerical simulation of flow around an airfoil with LBM method. Acta Aeronautica et Astronautica Sinica, 2010, 31(2): 238-243 (in Chinese))
    张海军,祝长生,杨琴. 基于稀薄效应的微气体径向轴承稳态性能. 力学学报,2009, 41(6): 941-946 (Zhang Haijun, Zhu Changsheng, Yang Qin. Steady characteristics of micro gas journal bearings based on rarefaction effect. Chinese Journal of Theoretical and Applied Mechanics, 2009, 41(6): 941-946 (in Chinese))
    Gu XJ, Emerson DR. Modeling oscillatory flows in the transition regime using a high-order moment method. Microfluids and Nanofluidics, 2011, 10(2): 389-401
    Xu K, Huang JC. A unified gas-kinetic scheme for continuum and rarefied flows. J Comput Phys, 2010, 229: 7747-7764
    Chen SZ, Xu K, Lee CB, et al. A unified gas kinetic scheme with moving mesh and velocity space adaptation. J Comput Phys, 2012, 231: 6643-6664
    Huang JC, Xu K, Yu PB. A unified gas-kinetic scheme forcontinuum and rarefied flows II: Multi-dimensional cases. Commun Comput Phys, 2012, 12(3): 662-690
    Agrwal RK, Chen R, Cheremisin FG. Computation of hypersonic shock wave flows of a diatomic using generalized Boltzmann equation. AIAA 2007-4541,39th AIAA Thermophysics Conference,Miami, 25-28 June, 2007
    Rykov VA. Model kinetic equation of a gas with rotational degrees of Freedom. Fluid Dynamics, 1975, 10: 959-966
    Rykov VA, Titarev VA, Shakhov EM. Shock wave structure in a diatomic gas based on a kinetic model. Fluid Dynamics, 2008, 43(2): 316-326
    李志辉,吴俊林,彭傲平等. 考虑转动非平衡效应Boltzmann模型方程统一算法与跨流域绕流问题模拟研究. 见: 第七届全国流体力学学术会议论文集,CSTAM 2012-B03-0195,11月12-14日,桂林,2012 (Li Zhihui, Wu Junlin, Peng Aoping, et al. Study of the unified algorithm for various flow regimes solving Boltzmann model equation with the effect of rotational non-equilibrium. In: Proc. of the 7th National Conference on Fluid Dynamics, CSTAM2012-B03-0195, Nov. 12-14, Guilin, 2012 (in Chinese))
    Larina IN, Rykov VA. Diatomic gas flow past a sphere based on kinetic Equations. Dokl Akad Nauk SSSR, 1976, 227: 60-62
    李志辉. 从稀薄流到连续流的气体运动论统一数值算法研究. [博士论文]. 绵阳:中国空气动力研究与发展中心研究生部, 2001 (Li Zhihui. Study on the unified algorithm from rarefied flow to continuum. [PhD Thesis]. Mianyang: China Aerodynamics Researchment and Development Center, 2001 (in Chinese))
    李志辉. 稀薄流到连续流气体流动问题统一算法应用研究. [博士后研究报告]. 北京:清华大学,2003 (Li Zhihui. Applications of gas kinetic unified algorithm for flows from rarefied transition to continuum. [Post-doctor Dissertation]. Beijing: Tsinghua University, 2003 (in Chinese))
    Alsmeyer H. Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J Fluid Mech,1976, 74: 497-513
    Robben F, Talbot L. Experimental study of the rotational distribution function of nitrogen in a shock wave. Physics of Fluids, 1966, 9: 653-662
    Andries P. Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases. INRIA,No.3872. Jan. 31. 2000
    Kinslow M, Potter JL. The drag of sphere in rarefied hypervelocity flow. AEDC-TDR-62-205, 1962
    Wilson CD, Agarwal RK, Tcheremissine FG. Computation of hyersonic flow of a diatomic gas in rotational nonequilibrium past 3D blunt bodies using the generalized Boltzmann equation. AIAA 2009-3836, 2009
计量
  • 文章访问数:  1776
  • HTML全文浏览量:  107
  • PDF下载量:  3486
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-07-29
  • 修回日期:  2014-02-12
  • 刊出日期:  2014-05-17

目录

    /

    返回文章
    返回