爆轰问题的一个高效二维离散玻尔兹曼模型
An Efficient Two-Dimensional Discrete Boltzmann Model of Detonation

作者: 林传栋 , 李英骏 :中国矿业大学(北京)深部岩土力学与地下工程国家重点实验室,北京; 许爱国 :北京应用物理与计算数学研究所计算物理重点实验室,北京;北京大学应用物理与技术研究中心和高能量密度物理数值模拟教育部重点实验室,北京;理论物理国家重点实验室(中国科学院理论物理研究所),北京; 张广财 :北京应用物理与计算数学研究所计算物理重点实验室,北京;理论物理国家重点实验室(中国科学院理论物理研究所),北京;爆炸科学与技术国家重点实验室(北京理工大学),北京;

关键词: 离散玻尔兹曼模型爆轰波Richtmyer-Meshkov不稳定性非平衡效应Discrete Boltzmann Model Detonation Richtmyer-Meshkov Instability Non-Equilibrium Effect

摘要:
本文构建了多松弛时间离散玻尔兹曼模型,并使用该模型模拟爆轰现象。相对于我们之前的一个模型[Xu A., Lin C., Zhang G., Li Y., Phys. Rev. E 91 (2015) 043306],本模型在模拟有化学反应或无化学反应流体系统时的计算效率更高。这是因为前者使用了24个离散速度,而本模型只使用16个。在模拟部分高马赫物理系统时,本模型表现出更高的数值稳定性。使用该模型,本文分四种情况模拟了爆轰波激发的Richtmyer-Meshkov不稳定性问题。当爆轰波由反应物传向另一种较轻的不反应的物质时,由于突然失去能量补充,温度急剧下降,在物质界附近将会出现一层高密区域。

Abstract: A modified multiple-relaxation-time discrete Boltzmann model is proposed to simulate detona-tion. Compared with our previous model [A. Xu, C. Lin, G. Zhang, Y. Li, Phys. Rev. E 91 (2015) 043306] adopting 24 discrete velocities, this model employs only 16 ones and consequently has smaller computational cost of simulating reactive or nonreactive fluid flows. Additionally, this model has a better stability than the previous one in our numerical tests. Using this model, we simulate the Richtmyer-Meshkov instability induced by detonation wave in four cases. It is in-teresting to find that, when a detonation wave travels from the chemical reactant to a lighter nonreactive medium, since the chemical energy does not release any more, the temperature re-duces suddenly, and consequently a region with higher density exists around the material in-terface.

文章引用: 林传栋 , 许爱国 , 张广财 , 李英骏 (2015) 爆轰问题的一个高效二维离散玻尔兹曼模型。 凝聚态物理学进展, 4, 102-111. doi: 10.12677/CMP.2015.43012

参考文献

[1] Fickett, W. and Davis, W.C. (2000) Detonation: theory and experiment. Dover publications, Inc., New York.

[2] Chapman, D.L. (1899) On the rate of explosion in gases. Philosophical Magazine, 47, 90-104.
http://dx.doi.org/10.1080/14786449908621243

[3] Jouguet, E. (1905) On the propagation of chemical reactions in gases. Journal de Mathématiques Pures et Appliquées, 1, 347-425.

[4] Zeldovich, Y.B. (1940) On the theory of the propagation of detonation in gaseous systems. Journal of Experimental and Theoretical Physics, 10, 542-568.

[5] von Neumann, J. (1942) Theory of detonation waves. Macmillan, New York.

[6] Döering, W. (1943) On detonation processes in gases. Annals of Physics, 435, 421-436.

[7] Succi, S. (2001) The lattice Boltzmann equation for fluid dynamics and beyond. Oxford University Press, New York.

[8] Succi, S., Bella, G. and Papetti, F. (1997) Lattice kinetic theory for numerical combustion. Journal of Scientific Computing, 12, 395-408.
http://dx.doi.org/10.1023/A:1025676913034

[9] Filippova, O. and Hänel, D. (2000) A novel numerical scheme for reactive flows at low mach numbers. Computer Physics Communications, 129, 267-274.
http://dx.doi.org/10.1016/S0010-4655(00)00113-2

[10] Yu, H., Luo, L.S. and Girimaji, S.S. (2002) Scalar mixing and chemical reaction simulations using lattice Boltzmann method. International Journal of Computational Engineering Science, 3, 73-87.
http://dx.doi.org/10.1142/S1465876302000551

[11] Yamamoto, K., Takada, N. and Misawa, M. (2005) Combustion simulation with lattice Boltzmann method in a three-dimensional porous structure. Proceedings of the Combustion Institute, 30, 1509-1515.
http://dx.doi.org/10.1016/j.proci.2004.08.030

[12] Lee, T., Lin, C. and Chen, L.D. (2006) A lattice Boltzmann algorithm for calculation of the laminar jet diffusion flame. Journal of Computational Physics, 215, 133-152.
http://dx.doi.org/10.1016/j.jcp.2005.10.021

[13] Chiavazzo, E., Karlin, I.V., Gorban, A.N. and Boulouchos, K. (2011) Efficient simulations of detailed combustion fields via the lattice Boltzmann method. International Journal of Numerical Methods for Heat & Fluid Flow, 21, 494- 517.
http://dx.doi.org/10.1108/09615531111135792

[14] Chen, S., Mi, J., Liu, H. and Zheng, C. (2012) First and second thermodynamic-law analyses of hydrogen-air counter- flow diffusion combustion in various combustion modes. International Journal of Hydrogen Energy, 37, 5234-5245.
http://dx.doi.org/10.1016/j.ijhydene.2011.12.039

[15] Yan, B., Xu, A., Zhang, G., Ying, Y. and Li, H. (2013) Lattice Boltzmann model for combustion and detonation. Frontiers of Physics, 8, 94-110.
http://dx.doi.org/10.1007/s11467-013-0286-z

[16] Lin, C., Xu, A., Zhang, G. and Li, Y. (2014) Polar coordinate lattice Boltzmann kinetic modeling of detonation phenomena. Communications in Theoretical Physics, 62, 737-748.
http://dx.doi.org/10.1088/0253-6102/62/5/18

[17] Xu, A., Lin, C., Zhang, G. and Li, Y. (2015) Multiple-relaxation-time lattice Boltzmann kinetic model for combustion. Physical Review E, 91, Article ID: 043306.
http://dx.doi.org/10.1103/PhysRevE.91.043306

[18] 许爱国, 张广财, 应阳君 (2015) 燃烧系统的离散Boltzmann建模与模拟研究进展. 物理学报, 64, 184701.

[19] Richtmyer, R.D. (1960) Taylor instability in shock acceleration of compressible fluids. Communications on Pure and Applied Mathematics, 13, 297-319.
http://dx.doi.org/10.1002/cpa.3160130207

[20] Meshkov, E.E. (1969) Instability of the interface of two gases accelerated by a shock wave. Fluid Dynamics, 4, 101-104.
http://dx.doi.org/10.1007/BF01015969

分享
Top