Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows

LIN Chuandong

doi:10.7638/kqdlxxb-2021.0285

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Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows

更新时间：2026-05-28

- Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows
- Vol. 40, Issue 3, Pages: 98-108(2022)
- 作者机构：
  
  中山大学中法核工程与技术学院,珠海,519082
- 作者简介：
- 基金信息：
- DOI：10.7638/kqdlxxb-2021.0285
  CLC： O354
- Published：2022
- 稿件说明：
移动端阅览
林传栋. 高速可压反应流的二维简化离散玻尔兹曼模型[J]. 空气动力学学报, 2022, 40(3): 98−108.

LIN Chuandong. Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows[J]. 2022, 40(3): 98-108.
林传栋. 高速可压反应流的二维简化离散玻尔兹曼模型[J]. 空气动力学学报, 2022, 40(3): 98−108. DOI： 10.7638/kqdlxxb-2021.0285

LIN Chuandong. Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows[J]. 2022, 40(3): 98-108. DOI： 10.7638/kqdlxxb-2021.0285.

摘要

如何有效模拟高速反应流现象是当前航空航天、能源与动力工程等领域的难点和热点。为此，本文提出了适用于超声速可压缩反应流的简化离散玻尔兹曼模型（DBM）。该模型基于动理学方法，使用形式统一的离散玻尔兹曼方程描述化学反应流的演化过程。在方程右侧，通过化学反应项将化学反应与多物理场自然耦合。该DBM使用二维九速模型，其离散速度分为三组，每组大小独立可调。为了描述分子转动和振动对应的额外自由度，引入了三组独立可调的参数用于描述额外自由度部分的内能。由此，该DBM具备了模拟比热比可调的反应流系统的功能。另外，平衡态离散速度分布函数与化学反应项各自满足九个独立的矩关系，其表达式都可以通过矩阵求逆的方式获得。通过Chapman-Enskog多尺度分析可以证明，该DBM除了能够在连续性极限条件下恢复描述化学反应流的Euler方程组之外，还具有描述一定热力学非平衡行为的功能。最后，通过数值算例表明，该DBM的数值结果与理论解吻合。

Abstract

How to investigate high-speed reactive flows effectively is an important open issue in the fields of aerospace

energy

and power engineering

etc. For this purpose

a simplified discrete Boltzmann model (DBM) is proposed for supersonic compressible reactive flows. Based on the kinetic method

this model uses a unified discrete Boltzmann equation to describe the evolution of reactive flows. The chemical reaction is naturally coupled with multi-physics fields through the reaction term on the right-hand side of the discrete Boltzmann equation. A two-dimensional nine-velocity model is proposed with the velocities divided into three groups

and the speed of each group is independently adjustable. To describe extra degrees of freedom corresponding to molecular rotation and/or oscillation

three groups of independently adjustable parameters are employed to describe the internal energies in extra degrees of freedom. Therefore

DBM is suitable for reactive flows with adjustable specific heat ratios. In addition

both the equilibrium discrete distribution functions and reaction terms satisfy nine independent moment relations

and their expressions can be obtained by the matrix inversion method. Through Chapman-Enskog multiscale analysis

it is proved that DBM not only can recover the reactive Euler equations in the continuum limit

but also has the capability of describing some thermodynamic nonequilibrium behaviors. Finally

three benchmarks

including the homogeneous reaction

Sod tube

and detonation wave

are employed to verify and validate DBM. It turns out that results of DBM agree well with theoretical solutions.

关键词

Keywords

references

LAW C K. Combustion physics[M]. Cambridge: Cambridge University Press, 2010.

陈坚强, 张益荣, 郭勇, 等. 高超声速流动数值模拟方法及应用[M]. 北京: 科学出版社, 2019.

艾邦成. 临近空间高超声速飞行器计算空气动力学[M]. 北京: 科学出版社, 2020.

MAO M L, CHEN L Z, WAN Z, et al. Review on influence of the multi-physical effects in hypersonic flow on aerodynamic characteristics of the United States space shuttle[J]. Acta Aerodynamica Sinica, 2017, 35(1): 1-12. (in Chinese)

沈青. 稀薄气体动力学[M]. 北京: 国防工业出版社, 2003.

FAN J. Rarefied gas dynamics: Advances and applications[J]. Advances in Mechanics, 2013, 43(2): 185-201. (in Chinese)

WOLF-GLADROW D A. Lattice-gas cellular automata and lattice Boltzmann models: An introduction[M ] . Springer, 2004. https://epic.awi.de/id/eprint/3739/1/Wol2000c.pdf

HARDY J, POMEAU Y, DE PAZZIS O. Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions[J]. Journal of Mathematical Physics, 1973, 14(12): 1746-1759. DOI:10.1063/1.1666248

FRISCH U, HASSLACHER B, POMEAU Y. Lattice-gas automata for the Navier-Stokes equation[J]. Physical Review Letters, 1986, 56(14): 1505-1508. DOI:10.1103/physrevlett.56.1505

SUCCI S. The lattice Boltzmann equation for fluid dynamics and beyond[M]. Oxford : Clarendon Press ; New York : Oxford University Press, 2001.

何雅玲, 王勇, 李庆. 格子Boltzmann方法的理论及应用[M]. 北京: 科学出版社, 2009.

郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京: 科学出版社, 2009.

SUCCI S, BELLA G, PAPETTI F. Lattice kinetic theory for numerical combustion[J]. Journal of Scientific Computing, 1997, 12(4): 395-408. DOI:10.1023/A:1025676913034

YAMAMOTO K, TAKADA N, MISAWA M. Combustion simulation with Lattice Boltzmann method in a three-dimensional porous structure[J]. Proceedings of the Combustion Institute, 2005, 30(1): 1509-1515. DOI:10.1016/j.proci.2004.08.030

HOSSEINI S A, DARABIHA N, THÉVENIN D. Mass-conserving advection-diffusion Lattice Boltzmann model for multi-species reacting flows[J]. Physica A: Statistical Mechanics and Its Applications, 2018, 499: 40-57. DOI:10.1016/j.physa.2018.01.034

CHEN S, LIU Z H, ZHANG C, et al. A novel coupled lattice Boltzmann model for low Mach number combustion simulation[J]. Applied Mathematics and Computation, 2007, 193(1): 266-284. DOI:10.1016/j.amc.2007.03.087

CHEN L, HE Y L, TAO W Q, et al. Pore-scale study of multiphase reactive transport in fibrous electrodes of vanadium redox flow batteries[J]. Electrochimica Acta, 2017, 248: 425-439. DOI:10.1016/j.electacta.2017.07.086

CHEN L, WANG M Y, KANG Q J, et al. Pore scale study of multiphase multicomponent reactive transport during CO 2 dissolution trapping[J ] . Advances in Water Resources, 2018, 116: 208-218. DOI:10.1016/j.advwatres.2018.02.018

ZHANG L, WANG M R. Modeling of electrokinetic reactive transport in micropore using a coupled lattice Boltzmann method[J]. Journal of Geophysical Research: Solid Earth, 2015, 120(5): 2877-2890. DOI:10.1002/2014JB011812

YAN Z F, YANG X F, LI S L, et al. Two-relaxation-time lattice Boltzmann method and its application to advective-diffusive-reactive transport[J]. Advances in Water Resources, 2017, 109: 333-342. DOI:10.1016/j.advwatres.2017.09.003

ASADOLLAHI A, RASHIDI S, ESFAHANI J A. Simulation of liquid reaction and droplet formation on a moving micro-object by lattice Boltzmann method[J]. Meccanica, 2018, 53(4-5): 803-815. DOI:10.1007/s11012-017-0780-4

YAN B, XU A G, ZHANG G C, et al. Lattice Boltzmann model for combustion and detonation[J]. Frontiers of Physics, 2013, 8(1): 94-110. DOI:10.1007/s11467-013-0286-z

LIN C D, XU A G, ZHANG G C, et al. Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena[J]. Communications in Theoretical Physics, 2014, 62(5): 737-748. DOI:10.1088/0253-6102/62/5/18

XU A G, LIN C D, ZHANG G C, et al. Multiple-relaxation-time lattice Boltzmann kinetic model for combustion[J]. Physical Review E, 2015, 91(4): 043306. DOI:10.1103/physreve.91.043306

LIN C D, XU A G, ZHANG G C, et al. Double-distribution-function discrete Boltzmann model for combustion[J]. Combustion and Flame, 2016, 164: 137-151. DOI:10.1016/j.combustflame.2015.11.010

ZHANG Y D, XU A G, ZHANG G C, et al. Kinetic modeling of detonation and effects of negative temperature coefficient[J]. Combustion and Flame, 2016, 173: 483-492. DOI:10.1016/j.combustflame.2016.04.003

LIN C D, LUO K H, FEI L L, et al. A multi-component discrete Boltzmann model for nonequilibrium reactive flows[J]. Scientific Reports, 2017, 7: 14580. DOI:10.1038/s41598-017-14824-9

LIN C D, LUO K H. Mesoscopic simulation of nonequilibrium detonation with discrete Boltzmann method[J]. Combustion and Flame, 2018, 198: 356-362. DOI:10.1016/j.combustflame.2018.09.027

LIN C D, LUO K H. MRT discrete Boltzmann method for compressible exothermic reactive flows[J]. Computers Fluids, 2018, 166: 176-183. DOI:10.1016/j.compfluid.2018.02.012

LIN C D, LUO K H. Discrete Boltzmann modeling of unsteady reactive flows with nonequilibrium effects[J]. Physical Review E, 2019, 99: 012142. DOI:10.1103/physreve.99.012142

ZHANG Y D, XU A G, ZHANG G C, et al. Discrete Boltzmann method with Maxwell-type boundary condition for slip flow[J]. Communications in Theoretical Physics, 2018, 69(1): 77. DOI:10.1088/0253-6102/69/1/77

ZHANG Y D, XU A G, ZHANG G C, et al. Entropy production in thermal phase separation: a kinetic-theory approach[J]. Soft Matter, 2019, 15(10): 2245-2259. DOI:10.1039/c8sm02637h

GAN Y B, XU A G, ZHANG G C, et al. Lattice Boltzmann study on Kelvin-Helmholtz instability: Roles of velocity and density gradients[J]. Physical Review E, 2011, 83(5): 056704. DOI:10.1103/physreve.83.056704

YE H Y, LAI H L, LI D M, et al. Knudsen number effects on two-dimensional Rayleigh–Taylor instability in compressible fluid: based on a discrete Boltzmann method[J]. Entropy, 2020, 22(5): 500. DOI:10.3390/e22050500

LIN C, LUO K H, XU A, et al. Multiple-relaxation-time discrete Boltzmann modeling of multicomponent mixture with nonequilibrium effects[J]. Physical Review E, 2021, 103(1): 013305. DOI:10.1103/physreve.103.013305

GAN Y, XU A, ZHANG G, et al. Discrete Boltzmann trans-scale modeling of high-speed compressible flows[J]. Physical Review E, 2018, 97(5): 053312. DOI:10.1103/physreve.97.053312

NG H D, RADULESCU M I, HIGGINS A J, et al. Numerical investigation of the instability for one-dimensional Chapman-Jouguet detonations with chain-branching kinetics[J]. Combustion Theory and Modelling, 2005, 9(3): 385-401. DOI:10.1080/13647830500307758

ZHANG H X, ZHUANG F G. NND schemes and their applications to numerical simulation of two- and three-dimensional flows[J]. Advances in Applied Mechanics, 1991, 29: 193-256. DOI:10.1016/S0065-2156(08)70165-0

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