Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

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理论物理通讯 ›› 2014, Vol. 62 ›› Issue (05) : 737-748.

林传栋¹, 许爱国^2,3,4, 张广财^2,4,5, 李英骏¹

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Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena

LIN Chuan-Dong¹, XU Ai-Guo^2,3,4, ZHANG Guang-Cai^2,4,5, LI Ying-Jun¹

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摘要

A novel polar coordinate lattice Boltzmann kinetic model for detonation phenomena is presented and applied to investigate typical implosion and explosion processes. In this model, the change of discrete distribution function due to local chemical reaction is dynamically coupled into the modified lattice Boltzmann equation which could recover the Navier-Stokes equations, including contribution of chemical reaction, via the Chapman-Enskog expansion. For the numerical investigations, the main focuses are the nonequilibrium behaviors in these processes. The system at the disc center is always in its thermodynamic equilibrium in the highly symmetric case. The internal kinetic energies in different degrees of freedom around the detonation front do not coincide. The dependence of the reaction rate on the pressure, influences of the shock strength and reaction rate on the departure amplitude of the system from its local thermodynamic equilibrium are probed.

Abstract

导出引用

林传栋, 许爱国, 张广财, 李英骏. Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena[J]. 理论物理通讯, 2014, 62(05): 737-748

LIN Chuan-Dong, XU Ai-Guo, ZHANG Guang-Cai, LI Ying-Jun. Polar Coordinate Lattice Boltzmann Kinetic Modeling of Detonation Phenomena[J]. Communications in Theoretical Physics, 2014, 62(05): 737-748

中图分类号： 47.40.Rs 47.11.-j 47.70.-n

参考文献

[1] W. Fickett and W.C. Davis, Detonation, University of California Press, Berkeley (1979).

[2] W.Y. Cheng, X.Y. Liu, and K.J. Wang, et al, Journal of China Coal Society 29 (2004) 57 (in Chinese).

[3] X.J. Li and B.Q. Lin, Coal Geology & Exploration 38 (2010) 7 (in Chinese).

[4] D.L. Chapman, Philos. Mag. 47 (1899) 90.

[5] E.J. Jouguet, J. Math. Pures Appl. 1 (1905) 347.

[6] Ya. B. Zeldovich, J. Exp. Theor. Phys. 10 (1940) 542.

[7] J. Von Neumann, Theory of Detonation Waves, Macmillan, New York (1942).

[8] W. Doering, Ann. Phys. 43 (1943) 421.

[9] D. Bjerketvedt, J.R. Bakke, and K. Van Wingerden, J. Hazard. Mater. 52 (1997) 1.

[10] Y. Lian and K. Xu, J. Comput. Phys. 163 (2000) 349.

[11] C. Wang, X. Zhang, C.W. Shu, and J. Ning, J. Comput. Phys., 231 (2012) 653.

[12] J. Sun and J. Zhu, Theory of Detonation Physics, Beijing: National Defense Industry Press (1995) (in Chinese).

[13] S.G. Cochran and J. Chan, Shock Initiation and Detonation in One and Two Dimensions, Lawrence Livermore National Laboratory Report UCID-18024 (1979).

[14] E.L. Lee and C.M. Tarver, Phys. Fluids 23 (1980) 2362.

[15] J. Cao, Explosion and Shock Waves 6 (1986) 137 (in Chinese).

[16] F. Zhao, C. Sun, Y. Wei, and J. Chi, Explosion and Shock Waves 9 (1989) 338 (in Chinese).

[17] S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, New York (2001).

[18] S. Succi, I.V. Karlin, and H. Chen, Rev. Mod. Phys. 74 (2002) 1203.

[19] H. Chen, S. Kandasamy, S. Orszag, R. Shock, S. Succi, and V. Yakhot, Science 301 (2003) 633.

[20] A. Lamura and S. Succi, Phys. Rev. Lett. 95 (2005) 224502.

[21] M. Sbragaglia, R. Benzi, L. Biferale, S. Succi, and F. Toschi, Phys. Rev. Lett. 97 (2006) 204503.

[22] J. Horbach, S. Succi, Phys. Rev. Lett. 96 (2006) 224503.

[23] R. Benzi, S. Chibbaro, and S. Succi, Phys. Rev. Lett. 102 (2009) 026002.

[24] G. Gonnella, E. Orlandini, and J.M. Yeomans, Phys. Rev. Lett. 78 (1997) 1695.

[25] C. Denniston and J.M. Yeomans, Phys. Rev. Lett. 87 (2001) 275505.

[26] G. Toth, C. Denniston, and J.M. Yeomans, Phys. Rev. Lett. 88 (2002) 105504.

[27] D. Marenduzzo, E. Orlandini, and J.M. Yeomans, Phys. Rev. Lett. 92 (2004) 188301.

[28] R. Verberg, C.M. Pooley, J.M. Yeomans, and A.C. Balazs, Phys. Rev. Lett. 93 (2004) 184501.

[29] C.M. Pooley and J.M. Yeomans, Phys. Rev. Lett. 93 (2004) 118001.

[30] D. Marenduzzo, E. Orlandini, and J.M. Yeomans, Phys. Rev. Lett. 98 (2007) 118102.

[31] A. Sengupta, U. Tkalec, M. Ravnik, J.M. Yeomans, C. Bahr, and S. Herminghaus, Phys. Rev. Lett. 110 (2013) 048303.

[32] X.W. Shan and H.D. Chen, Phys. Rev. E 47 (1993) 1815; Phys. Rev. E 49 (1994) 2941.

[33] S. Chen, G.D. Doolen, Annu. Rev. Fluid Mech. 30 (1998) 329.

[34] Q. Kang, D. Zhang, S. Chen, and X. He, Phys. Rev. E 65 (2002) 036318.

[35] H. Fang, Z. Wang, Z. Lin, and M. Liu, Phys. Rev. E 65 (2002) 051925.

[36] Z. Guo and C. Shu, Lattice Boltzmann Method and Its Applications in Engineering (advances in computational fluid dynamics), World Scientific Publishing Company, Singapore (2013).

[37] A. Xu, G. Zhang, Y. Li, and H. Li, Prog. Phys. 34 (2014) 136 (in Chinese).

[38] S. Ponce Dawson, S. Chen, and G.D. Doolen. J. Chem. Phys. 98 (1993) 1514.

[39] J.R. Weimar and J.P. Boon. Physica A 224 (1996) 207.

[40] R. Zhang, Y. Xu, and B. Wen, et al., Scientific Reports 4 (2014) 5738.

[41] S. Chen, D. Martinez, and R. Mei, Phys. Fluids 8 (1996) 2527.

[42] S. Succi, G. Bella, and F. Papetti, J. Sci. Comput. 12 (1997) 395.

[43] O. Filippova and D. Hänel, Int. J. Mod. Phys. C 9 (1998) 1439.

[44] O. Filippova and D. Hänel, J. Comput. Phys. 158 (2000) 139.

[45] O. Filippova and D. Hänel, Comput. Phys. Commun. 129 (2000) 267.

[46] H. Yu, L. S. Luo, and S.S. Girimaji, Int. J. Comput. Eng. Sci. 3 (2002) 73.

[47] K. Yamamoto, X. He, and G.D. Doolen, J. Stat. Phys. 107 (2002) 367.

[48] K. Yamamoto, Int. J. Mod. Phys. B 17 (2003) 197.

[49] K. Yamamoto, N. Takada, and M. Misawa, Proc. Comb. Inst. 30 (2005) 1509.

[50] T. Lee, C. Lin, and L.D. Chen, J. Comput. Phys. 215 (2006) 133.

[51] E. Chiavazzo, I.V. Karlin, and A.N. Gorban, et al., Combust. Flame 157 (2010) 1833.

[52] S. Chen, Z. Liu, C. Zhang, et al., Appl. Math. Comput. 193 (2007) 266.

[53] S. Chen, Z. Liu, Z. Tian, et al., Comput. Math. Appl. 55 (2008) 1424.

[54] S. Chen and M. Krafczyk, Int. J. Therm. Sci. 48 (2009) 1978.

[55] S. Chen, Int. J. Hydrogen Energ. 35 (2010) 1401.

[56] S. Chen, J. Li, H. Han, et al., Int. J. Hydrogen Energ. 35 (2010) 3891.

[57] S. Chen, H. Han, Z. Liu, et al., Int. J. Hydrogen Energ. 35 (2010) 4736.

[58] S. Chen and C. Zheng, Int. J. Hydrogen Energ. 36 (2011) 15403.

[59] S. Chen, J. Mi, H. Liu, et al., Int. J. Hydrogen Energ. 37 (2012) 5234.

[60] F.J. Alexander, H. Chen, S. Chen, et al., Phys. Rev. A 46 (1992) 1967.

[61] F.J. Alexander, S. Chen, and J.D. Sterling. Phys. Rev. E 47 (1993) R2249.

[62] Y. Chen, H. Ohashi, and M. Akiyama, Phys. Rev. E 50 (1994) 2776.

[63] G.R. McNamara, A.L. Garcia, and B.J. Alder, J. Stat. Phys. 87 (1997) 1111.

[64] X. Pan, A. Xu, G. Zhang, and S. Jiang, Int. J. Mod. Phys. C 18 (2007) 1747.

[65] Y. Gan, A. Xu, G. Zhang, and Y. Li, Physica A 387 (2008) 1721; Phys. Rev. E 83 (2011) 056704.

[66] F. Chen, A. Xu, G. Zhang, Y. Li, and S. Succi, Europhys. Lett. 90 (2010) 54003.

[67] A. Xu, G. Zhang, Y. Gan, F. Chen, and X. Yu, Front. Phys. 7 (2012) 582.

[68] B. Yan, A. Xu, G. Zhang, Y. Ying, and H. Li, Frontiers of Physics 8 (2013) 94.

[69] I. Halliday, L.A. Hammond, C.M. Care, et al., Phys. Rev. E 64 (2001) 011208.

[70] X.D. Niu, C. Shu, and Y.T. Chen, Int. J. Mod. Phys. C 14 (2003) 785.

[71] K.N. Premnath and J. Abraham, Phys. Rev. E 71 (2005) 056706.

[72] T. Reis and T.N. Phillips. Phys. Rev. E 75 (2007) 056703.

[73] Z. Guo, H. Han, B. Shi, et al., Phys. Rev. E 79 (2009) 046708.

[74] M. Watari, Commun. Comput. Phys. 9 (2011) 1293.

[75] C. Lin, A. Xu, G. Zhang, Y. Li, and S. Succi, Phys. Rev. E 89 (2014) 013307.

[76] Y. Gan, A. Xu, G. Zhang, and Y. Yang, Europhys. Lett. 103 (2013) 24003.

[77] F. Chen, A. Xu, G. Zhang, and Y. Wang, Front. Phys. 9 (2014) 246.

[78] M. Watari and M. Tsutahara, Phys. Rev. E 67 (2003) 036306.

[79] C. Lin, A. Xu, G. Zhang, and Y. Li, e-print arXiv:1405.5500.

基金

AX and GZ acknowledge support of the Science Foundations of National Key Laboratory of Computational Physics, National Natural Science Foundation of China under Grant No.11202003 and the opening project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) under Grant No.KFJJ14-1M. YL and CL acknowledge support of National Natural Science Foundation of China under Grant Nos. 11074300 and 41472130, National Basic Research Program of China under Grant No.2013CBA01504