CMP  >> Vol. 4 No. 3 (August 2015)

    An Efficient Two-Dimensional Discrete Boltzmann Model of Detonation

  • 全文下载: PDF(1704KB) HTML   XML   PP.102-111   DOI: 10.12677/CMP.2015.43012  
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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


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。

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.

林传栋, 许爱国, 张广财, 李英骏. 爆轰问题的一个高效二维离散玻尔兹曼模型[J]. 凝聚态物理学进展, 2015, 4(3): 102-111.


[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.
[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.
[9] Filippova, O. and Hänel, D. (2000) A novel numerical scheme for reactive flows at low mach numbers. Computer Physics Communications, 129, 267-274.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[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.
[20] Meshkov, E.E. (1969) Instability of the interface of two gases accelerated by a shock wave. Fluid Dynamics, 4, 101-104.