燃烧系统的离散Boltzmann建模与模拟研究进展

许爱国; 张广财; 应阳君

doi:10.7498/aps.64.184701

摘要

燃烧系统的诸多模拟依托于流体建模, 离散Boltzmann方法(discrete Boltzmann method, DBM) 是近年来发展起来的一种新的流体介观建模方法. 本文简要评述DBM发展的两个方向Navier-Stokes等偏微分方程的数值逼近解法和复杂系统的微介观动理学建模. 主要介绍在燃烧系统模拟方面DBM已有的工作、新近的思路、与传统流体建模的异同以及近期的研究成果. 本文重点传递的信息为: 作为复杂系统微介观动理学建模出现的DBM在模拟过程中同时给出流动及其相伴随的、关系最密切的那部分热动非平衡效应; 它为燃烧等复杂系统中各类非平衡行为的描述、非平衡信息的提取、非平衡程度的度量提供了一种简洁、有效的方法; 它所提供的热动非平衡测量量有两类: 一类是直接比较分布函数和平衡态分布函数的动理学矩关系得到的, 一类是来自于Chapman-Enskog多尺度分析给出的热传导和黏性项. 基于第二类DBM, 可以实现(燃烧等)一大类复杂流体系统的多尺度物理建模.

关键词:

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:

作者及机构信息

1.
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 100088;

2.
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 100871;

3.
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 100190;

4.
爆炸科学与技术国家重点实验室(北京理工大学), 北京 100081

通信作者: 许爱国, Xu_Aiguo@iapcm.ac.cn

基金项目: 计算物理重点实验室基金、国家自然科学基金(批准号: 11475028, 11202003)、理论物理国家重点实验室(中国科学院理论物理研究所)开放课题(批准号: Y4KF151CJ1)和爆炸科学与技术国家重点实验室(北京理工大学)开放课题(批准号: KFJJ14-1M)资助的课题.

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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施引文献

[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
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[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
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[45]	Frisch U, Hasslacher B, Pomeau Y 1986 Phys. Rev. Lett. 56 1505
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