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

DOI: 10.12677/CMP.2015.43012, PP. 102-111

Keywords: 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

Full-Text   Cite this paper   Add to My Lib

Abstract:

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.

References

[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]	D？ering, 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 H？nel, 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

Full-Text