Progess of discrete Boltzmann modeling and simulation of combustion system

Xu Ai-Guo; Zhang Guang-Cai; Ying Yang-Jun

doi:10.7498/aps.64.184701

Abstract

Detonation is a kind of self-propagating supersonic combustion where the chemical reaction is rapid and violent under an extreme condition. The leading part of a detonation front is pre-shocked by a strong shock wave propagating into the explosive and triggering chemical reaction. The combustion system can be regarded as a kind of chemical reactive flow system. Therefore, the fluid modeling plays an important role in the studies on combustion and detonation phenomena. The discrete Boltzmann method (DBM) is a kind of new fluid modeling having quickly developed in recent thirty years. In this paper we review the progress of discrete Boltzmann modeling and simulation of combustion phenomena. Roughly speaking, the discrete Boltzmann models can be further classified into two categories. In the first category the DBM is regarded as a kind of new scheme to numerically solve partial differential equations, such as the Navier-Stokes equations, etc. In the second category the DBM works as a kind of novel mesoscopic and coarse-grained kinetic model for complex fluids. The second kind of DBM aims to probe the trans- and supercritical fluid behaviors or to study simultaneously the hydrodynamic non-equilibrium (HNE) and thermodynamic non-equilibrium (TNE) behaviors. It has brought significant new physical insights into the systems and promoted the development of new methods in the fields. For example, new observations on fine structures of shock and detonation waves have been obtained; The intensity of TNE has been used as a physical criterion to discriminate the two stages, spinodal decomposition and domain growth, in phase separation; Based on the feature of TNE, some new front-tracking schemes have been designed. Since the goals are different, the criteria used to formulate the two kinds of models are significantly different, even though there may be considerable overlaps between them. Correspondingly, works in discrete Boltzmann modeling and simulation of combustion systems can also be classified into two categories in terms of the two kinds of models. Up to now, most of existing works belong to the first category where the DBM is used as a kind of alternative numerical scheme. The first DBM for detonation [Yan, et al. 2013 Front. Phys. 8 94] appeared in 2013. It is also the first work aiming to investigate both the HNE and TNE in the combustion system via DBM. In this review we focus mainly on the development of the second kind of DBM for combustion, especially for detonation. A DBM for combustion in polar-coordinates [Lin, et al. 2014 Commun. Theor. Phys. 62 737] was designed in 2014. It aims to investigate the nonequilibrium behaviors in implosion and explosion processes. Recently, the multiple-relaxation-time version of DBM for combustion [Xu, et al. 2015 Phys. Rev. E 91 043306] was developed. As an initial application, various non-equilibrium behaviors around the detonation wave in one-dimensional detonation process were preliminarily probed. The following TNE behaviors, exchanges of internal kinetic energy between different displacement degrees of freedom and between displacement and internal degrees of freedom of molecules, have been observed. It was found that the system viscosity (or heat conductivity) decreases the local TNE, but increases the global TNE around the detonation wave. Even locally, the system viscosity (or heat conductivity) results in two competing trends, i.e. to increase and decrease the TNE effects. The physical reason is that the viscosity (or heat conductivity) takes part in both the thermodynamic and hydrodynamic responses to the corresponding driving forces. The ideas to formulate DBM with the smallest number of discrete velocities and DBM with flexible discrete velocity model are presented. As a kind of new modeling of combustion system, mathematically, the second kind of DBM is composed of the discrete Boltzmann equation(s) and a phenomenological reactive function; physically, it is equivalent to a hydrodynamic model supplemented by a coarse-grained model of the TNE behaviors. Being able to capture various non-equilibrium effects and being easy to parallelize are two features of the second kind of DBM. Some more realistic DBMs for combustion are in progress. Combustion process has an intrinsic multi-scale nature. Typical time scales cover a wide range from 10-13 to 10-3 second, and typical spatial scales cover a range from 10-10 to 1 meter. The hydrodynamic modeling and microscopic molecular dynamics have seen great achievements in combustion simulations. But for problems relevant to the mesoscopic scales, where the hydrodynamic modeling is not enough to capture the nonequilibrium behaviors and the molecular dynamics simulation is not affordable, the modeling and simulation are still keeping challenging. Roughly speaking, there are two research directions in accessing the mesoscopic behaviors. One direction is to start from the macroscopic scale to smaller ones, the other direction is to start from the microscopic scale to larger ones. The idea of second kind of DBM belongs to that of the first direction. It will contribute more to the studies on the nonequilibrium behaviors in combustion phenomena.

Keywords:

Authors and contacts

1.
National Laboratory for Science and Technology on Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2.
Center for Applied Physics and Technology, MOE Key Center for High Energy Density Physics Simulations, College of Engineering, Peking University, Beijing 100871, China;
3.
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China;
4.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Xu Ai-Guo, Xu_Aiguo@iapcm.ac.cn

Funds: Project supported by the Science Foundations of National Laboratory for Science and Technology on Computational Physics, the National Natural Science Foundation of China (Grant Nos. 11475028, 11202003), the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Grant No. Y4KF151CJ1), and the Opening Project of State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology) (Grant No. KFJJ14-1M).

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Cited By

[1]	Ju Y 2014 Adv. Mech. 44 201402
[2]	Chu S, Majumdar A 2012 Nature 488 294
[3]	Jangsawang W, Fungtammasan B, Kerdsuwan S 2005 Energ. Convers. Manage. 46 3137
[4]	Schott G L 1965 Phys. Fluids 8 850
[5]	Bykovskii F A, Zhdan S A, Vedernikov E F 2006 Journal of Propulsion and Power 22 1204
[6]	Ju Y, Maruta K 2011 Progress in Energy and Combustion Science 37 669
[7]	Fernandez-Pello A C 2002 Proceedings of the Combustion Institute 29 883
[8]	Sabourin J L, Dabbs D M, Yetter R A, Dryer F L, Aksay I A 2009 ACS Nano 3 3945
[9]	Ohkura Y, Rao P M, Zheng X 2011 Combust. Flame 158 2544
[10]	Dec J E 2009 Proc. Combust. Inst. 32 2727
[11]	Starikovskiy A, Aleksandrov N 2012 Progress in Energy and Combustion Science 39 61
[12]	Uddi M, Jiang N, Mintusov E, Adamovich I V, Lempert W R 2009 Proceedings of the Combustion Institute 32 929
[13]	Sun W, Chen Z, Gou X, Ju Y 2010 Combust. Flame 157 1298
[14]	Won S H, Windom B, Jiang B, Ju Y 2014 Combust. Flame 161 475
[15]	Ombrello T, Qin X, Ju Y, Gutsol A, Fridman A, Carter C 2006 AIAA Journal 44 142
[16]	Sun W, Uddi M, Won S H, Ombrello T, Carter C, Ju Y 2012 Combust. Flame 159 221
[17]	Sun W, Ju Y 2013 J Plasma Fusion Res. 89 208
[18]	Chapman D L 1899 Philos. Mag. 47 90
[19]	Jouguet E J 1905 J. Math. Pures Appl. 1 347
[20]	Zeldovich Ya B 1940 J. Exp. Theor. Phys. 10 542
[21]	von Neumann J 1942 Theory of Detonation Waves (New York: Macmillan)
[22]	Doering W 1943 Ann. Phys. 43 421
[23]	Fickett W, Davis W C 2000 Detonation: Theory and Experiment (Mineola, New York: Dover Publications, INC.)
[24]	Chen Z 2009 Ph. D Dissertation (Princeton: Princeton University)
[25]	Dai P, Chen Z, Chen S, Ju Y 2015 Proc. Combust. Inst. 35 3045
[26]	Yu H, Han W, Santner J, Gou X, Sohn C H, Ju Y, Chen Z 2014 Combust. Flame 161 2815
[27]	Bai B, Chen Z, Zhang H, Chen S 2013 Combust. Flame 160 2810
[28]	Ren Z Y, Lu Z, Hou L Y, Lu L 2014 Sci. China: Phys. Mech. Astron. 57 1495
[29]	Huang X F, Li S J, Zhou D H, Zhao G J, Wang G Q, Xu J R 2014 Acta Phys. Sin. 63 178802(in Chinese) [黄雪峰, 李盛姬, 周东辉, 赵冠军, 王关晴, 徐江荣 2014 63 178802]
[30]	Yang J C, Xia Z X, Hu J X 2013 Acta Phys. Sin. 62 074701(in Chinese) [杨晋朝, 夏智勋, 胡建新 2013 62 074701]
[31]	Shi Y B, Ying Y J, Li J H 2007 Acta Phys. Sin. 56 6911(in Chinese) [施研博, 应阳君, 李金虹 2007 56 6911]
[32]	Benzi R, Succi S, Vergassola M 1992 Phys. Reports 222 145
[33]	Succi S 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (New York: Oxford University Press)
[34]	Succi S, Karlin I V, Chen H 2002 Rev. Mod. Phys. 74 1203
[35]	Chen H, Kandasamy S, Orszag S, Shock R, Succi S, Yakhot V 2003 Science 301 633
[36]	Xu A, Zhang G, Gan Y, Chen F, Yu X 2012 Front. Phys. 7 582
[37]	Xu A G, Zhang G C, Li Y J, Li H 2014 Prog. Phys. 34 136(in Chinese) [许爱国, 张广财, 李英骏, 李华 2014 物理学进展 34 136]
[38]	Guo Z, Shu C 2013 Lattice Boltzmann Method and Its Applications in Engineering (advances in computational fluid dynamics) (Sigapore: World Scientific Publishing Company)
[39]	Chen S 2010 Non-equilibrium Statistical Mechanics (Beijing: Scientific Press) (in Chinese) [陈式刚编著 2010 非平衡统计力学(北京: 科学出版社)]
[40]	Shokhov E M 1968 Fluid Dyn. 3 95
[41]	Bhatnagar L, Gross E P, Krook M 1954 Phys. Rev. 94 511
[42]	Holway Jr L H 1966 Phys. Fluids (1958-1988) 9 1658
[43]	Rykov V A 1975 Fluid Dyn. 10 959
[44]	Liu G 1990 Phys. Fluids A: Fluid Dyn. (1989-1993) 2 277
[45]	Frisch U, Hasslacher B, Pomeau Y 1986 Phys. Rev. Lett. 56 1505
[46]	Koelman J 1991 EPL 15 603
[47]	Chen S, Chen H, Martinez D, Matthaeus W 1991 Phys. Rev. Lett. 67 3776
[48]	Qian Y, d’Humieres D, Lallemand P 1992 EPL 17 479
[49]	He X Y, Luo L S 1997 Phys. Rev. E 55 R6333
[50]	Nie X B 1988 M.S. Dissertation (Beijing: Graduate School, China Academy of Engineering Physics) (in Chinese) [聂小波 1988 硕士学位论文(北京: 中国工程物理研究院研究生部)]
[51]	MeNamara G R, Zanetti G 1988 Phys. Rev. Lett. 61 2332
[52]	Higuera F L, Jimenez J 1989 EPL 9 663
[53]	He Y L, Wang Y, Li Q 2009 Lattice Boltzmann Method: Theory and Applications (Beijing: Scientific Press) (in Chinese) [何雅玲, 王勇, 李庆 2009 格子Boltzmann 方法的理论及应用 (北京: 科学出版社)]
[54]	Yan B 2013 Ph. D. Dissertation (Changchun: Jilin University) (in Chinese) [闫铂 2013 博士学位论文(长春: 吉林大学)]
[55]	Gonnella G, Orlandini E, Yeomans J M 1997 Phys. Rev. Lett. 78 1695
[56]	Denniston C, Yeomans J M 2001 Phys. Rev. Lett. 87 275505
[57]	Toth G, Denniston C, Yeomans Y M 2002 Phys. Rev. Lett. 88 105504
[58]	Shan X, Chen H 1993 Phys. Rev. E 47 1815
[59]	Chen S, Doolen G D 1998 Annu. Rev. Fluid Mech. 30 329
[60]	Kang Q, Zhang D, Chen S, He X 2002 Phys. Rev. E 65 036318
[61]	Fang H, Wang Z, Lin Z, Liu M 2002 Phys. Rev. E 65 051925
[62]	Dawson S, Chen S, Doolen G D 1993 J. Chem. Phys. 98 1514
[63]	Weimar J R, Boon J P 1996 Physica A 224 207
[64]	Zhang R, Xu Y, Wen B, Sheng N, Fang H 2014 Sci. Reports 4 5738
[65]	Chen S, Martinez D, Mei R 1996 Phys. Fluids 8 2527
[66]	Lai H, Ma C 2011 Phys. Rev. E 84 046708
[67]	Xu A, Gonnella G, Lamura A 2006 Phys. Rev. E 74 011505
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[72]	Xu A, Gonnella G, Lamura A 2003 Phys. Rev. E 67 056105
[73]	Gan Y, Xu A, Zhang G, Li Y 2012 Front. Phys. 7 481
[74]	Gan Y, Xu A, Zhang G, Li Y 2012 Commun. Theore. Phys. 57 681
[75]	Gan Y, Xu A, Zhang G, Wang J, Yu X, Yang Y 2014 Int. J. Mod. Phys. C 25 1441002
[76]	Gan Y, Xu A, Zhang G, Li Y 2011 Phys. Rev. E 83 056704
[77]	Gan Y, Xu A, Zhang G, Zhang P, Li Y 2012 EPL 97 44002
[78]	Gan Y, Xu A, Zhang G, Li Y, Li Y 2011 Phys. Rev. E 84 046715
[79]	Chen F, Xu A, Zhang G, Li Y 2011 Phys. Lett. A 375 2129
[80]	Pan X F, Xu A, Zhang G, Jiang S 2007 Int. J. Mod. Phys. C 18 1747
[81]	Yan B, Xu A, Zhang G, Ying Y, Li H 2013 Front. Phys. 8 94
[82]	Lin C, Xu A, Zhang G, Li Y 2014 Commun. Theor. Phys. 62 737
[83]	Xu A, Lin C, Zhang G, Li Y 2015 Phys. Rev. E 91 043306
[84]	Xu A, Zhang G, Gan Y 2014 arXiv:1403.3744
[85]	Gan Y, Xu A, Zhang G, Succi S 2015 Soft Matter 11 5336
[86]	Chen F, Xu A, Zhang G, Wang Y 2014 Front Phys. 9 246
[87]	Lin C, Xu A, Zhang G, Li Y, Succi S 2014 Phys. Rev. E 89 013307
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Vol. 64, Issue 18 - 2015-09-20

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