化学非平衡流动解耦算法的回顾与新进展

doi:10.7527/S1000-6893.2017.021090

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化学非平衡流动解耦算法的回顾与新进展

刘君¹, 董海波¹, 刘瑜²

1. 大连理工大学航空航天学院, 大连 116024;
2. 航天工程大学航天装备系, 北京 101416

收稿日期:2016-12-30 修回日期:2017-03-23 出版日期:2018-01-15 发布日期:2018-01-15
通讯作者: 刘君,E-mail:liujun65@dlut.edu.cn E-mail:liujun65@dlut.edu.cn
基金资助:
国家自然科学基金（91541117，11532016）

Review and recent advances in uncoupled algorithms for chemical non-equilibrium flows

LIU Jun¹, DONG Haibo¹, LIU Yu²

1. School of Aeronautics and Astronautics, Dalian University of Technology, Dalian 116024, China;
2. Department of Space Equipment, Aerospace Engineering University, Beijing 101416, China

Received:2016-12-30 Revised:2017-03-23 Online:2018-01-15 Published:2018-01-15
Supported by:
National Natural Science Foundation of China (91541117, 11532016)

摘要/Abstract

摘要： 超声速化学非平衡流动的数值模拟一直是计算流体力学领域的难点，主要体现在如下几个方面：物理过程非常复杂，存在着激波、燃烧波等各种复杂波系的相互作用；超声速化学非平衡流动属于典型的时空多尺度物理问题，其控制方程存在严重的刚性，给数值求解带来了很大困难。对国内外的解耦算法研究现状简单综述后，主要介绍1993年刘君提出的解耦算法的理论基础，流动方程采用冻结流模型，源项方程模拟流体微团在当地绝热、定容的热力学系统内发生的化学反应过程。通过引入两个中间变量，即等效内能和等效比热比，将与温度无关的生成焓从流动方程组能量项中分离出去，源项方程组中包含等效内能，使用不同算子对流动方程和源项方程解耦求解。与传统解耦算法相比，源项方程的求解过程中包含状态参数和组元同时变化。结合刘君解耦算法机理和有限体积法空间平均特性，介绍近期在提高算法计算效率方面的研究进展，包括流动方程优化算法和耦合过程优化。采用优化算法对经典的激波诱导燃烧算例进行数值模拟，与不同文献结果进行对比，验证了优化算法的时空精度。通过总结经验发现化学非平衡反应仅发生在流场局部区域，提出质量生成率判据，结合相应模拟结果验证了方法的可行性，可以进一步提高化学反应算子的计算效率。

关键词: 非平衡流, 解耦算法, 有限体积法, 结构网格, 数值模拟

Abstract: Numerical simulation of supersonic chemical non-equilibrium flow is a challenge in computational fluid dynamics because of two main reasons. First, the physical process is very complex because many interactions occur between shock waves and other intricate phenomena. Second, the supersonic chemical non-equilibrium flow is a typical space-time multi-scale physical problem, and its governing equations can result in serious rigidity to significantly affect numerical simulation. This paper concentrates on an introduction of Liu's uncoupled methods for simulating chemical non-equilibrium flow, following a brief review of the development home and abroad. In Liu's method, the flow equations use frozen flow model, and the reaction source equations simulate chemical reaction process in the local adiabatic and constant volume thermodynamic system. The temperature-independent enthalpy is separated from the energy term by introducing the equivalent internal energy and equivalent specific heat ratio. The flow and source equations are solved using different operators. Different from classical uncoupled methods, the solution for source term equation includes simultaneous change of state parameters and components. Considering Liu's uncoupled method and the space mean characteristic of the finite volume method, this paper also introduces recent advances in improving computational efficiency, including the flow equation optimization method and the optimization of the coupling process. Numerical simulation of shock-induced combustion is conducted using the optimization method, and the accuracy of the method is verified by comparing the results with those in literature. The chemical non-equilibrium reaction is found to occur only locally. According to the mass production rate criterion, the feasibility of the method is verified using the corresponding simulation results, and the computational efficiency of the chemical reaction operator can be improved.

Key words: non-equilibrium flow, uncoupled algorithm, finite volume method, structured mesh, numerical

中图分类号:

V211.3

刘君, 董海波, 刘瑜. 化学非平衡流动解耦算法的回顾与新进展[J]. 航空学报, 2018, 39(1): 21090-021090.

LIU Jun, DONG Haibo, LIU Yu. Review and recent advances in uncoupled algorithms for chemical non-equilibrium flows[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2018, 39(1): 21090-021090.

参考文献

[1] 常亚超. 基于解耦法的柴油和生物柴油表征燃料骨架反应机理研究[D]. 大连:大连理工大学, 2016:1-13. CHANG Y C. Investigation of skeletal chemical mechanisms for diesel and biodiesel surrogate fuel based on decoupling methodology[D]. Dalian:Dalian University of Technology, 2016:1-13(in Chinese).[2] 梁剑寒, 王承尧. 超燃冲压发动机燃烧室三维化学反应流场的数值模拟[J]. 推进技术, 1997, 18(4):1-4. LIANG J H, WANG C Y. 3D numerical simulation of supersonic reacting flows in scramjet combustion[J]. Journal of Propulsion Technology, 1997, 18(4):1-4(in Chinese).[3] ROGERS R C, CHINITZ W. Using a global hydrogen-air combustion model in turbulent reacting flow calculations[J]. AIAA Journal, 1983, 21(4):586-592.[4] 黄生洪, 徐胜利, 刘小勇. 煤油超燃冲压发动机两相流场数值模拟(I)数值校验及总体流场特征[J].推进技术, 2004, 25(6):484-490. HUANG S H, XU S L, LIU X Y. Numerical investigation on two phase flow of akerosene-fueled scramjet with 3D cavity (I) Numerical calibration and characteristics of general flow[J]. Journal of Propulsion Technology, 2004, 25(6):484-490(in Chinese).[5] 杨顺华, 乐嘉陵, 赵慧勇, 等. 煤油超燃冲压发动机三维大规模并行数值模拟[J]. 计算物理, 2009, 26(4):534-540. YANG S H, LE J L, ZHAO H Y, et al. Three-dimensional massively parallel numerical simulation of kerosene-fueled scramjet[J]. Chinese Journal of Computational Physics, 2009, 26(4):534-540(in Chinese).[6] YANENKO N N. The method of fractional steps[M]. Heidelberg:Springer-verlag, 1971:42-50.[7] DESCOMBES S, DUMONT T. Numerical simulation of a stroke:Computational problems and methodology[J]. Progress in Biophysics & Molecular Biology, 2008, 97(1):40-53.[8] DUMONT T, DUARTE M, DESCOMBES S, et al. Simulation of human ischemic stroke in realistic 3D geometry[J]. Communications in Nonlinear Science & Numerical Simulation, 2013, 18(6):1539-1557.[9] CUI S, KURGANOV A, MEDOVIKOV A. Particle methods for PDEs arising in financial modeling[J]. Applied Numerical Mathematics, 2015, 93:123-139.[10] DESCOMBES S, THALHAMMER M. The Lie-Trotter splitting for nonlinear evolutionary problems with critical parameters:A compact local error representation and application to nonlinear schrödinger equations in the semiclassical regime[J]. IMA Journal of Numerical Analysis, 2013, 33(2):722-745.[11] KULIKOV I, VOROBYOV E. Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows[J]. Journal of Computational Physics, 2016, 317:318-346.[12] CAMBIER J, ADELMAN H, MENEES G P. Numerical simulations of an oblique detonation wave engine[J]. Journal of Propulsion and Power, 1990, 6(3):315-323.[13] 刘君. 超音速完全气体和H₂/O₂燃烧非平衡气体的复杂喷流流场数值模拟[D]. 绵阳:中国空气动力研究与发展中心, 1993:56-65. LIU J. Numerical simulation of the complex jet flow field of supersonic gas and H₂/O₂ combustion[D]. Mianyang:China Aerodynamics Research and Development Center, 1993:56-65(in Chinese).[14] 刘君, 张涵信, 高树椿. 一种新型的计算化学非平衡流动的解耦方法[J]. 国防科技大学学报, 2000, 22(5):19-22. LIU J, ZHANG H X, GAO S C. A new uncoupled method for numerical simulation of non-equilibrium flow[J]. Journal of National University of Defense Technology, 2000, 22(5):19-22(in Chinese).[15] 刘君. 冲压加速器非平衡流动数值模拟[J]. 弹道学报, 2002, 14(4):31-35. LIU J. Numerical study on the non-equilibrium flow of ram accelerator in the combustive mixture gas[J]. Journal of Ballistics, 2002, 14(4):31-35(in Chinese).[16] 刘君. 非平衡流计算方法及其模拟激波诱导振荡燃烧[J]. 空气动力学学报, 2003, 21(1):53-58. LIU J. A new non-equilibrium numerical method and simulation of oscillating shock-induced combustion[J]. Acta Aerodynamica Sinica, 2003, 21(1):53-58(in Chinese).[17] 刘君. 化学动力学模型对H₂/Air超燃模拟的影响[J]. 推进技术, 2003, 24(1):67-70. LIU J. Numerical study on chemical mechanism in supersonic H₂/Air mixture gas flow[J]. Journal of Propulsion Technology, 2003, 24(1):67-70(in Chinese).[18] 刘君. 甲烷/空气超声速燃烧流动数值模拟[J]. 推进技术, 2003, 24(4):296-299. LIU J. Numerical study for CH₄/air supersonic combustion[J]. Journal of Propulsion Technology, 2003, 24(4):296-299(in Chinese).[19] 刘君, 刘瑜, 周松柏. 基于新型解耦算法的激波诱导燃烧过程数值模拟[J]. 力学学报, 2010, 42(3):572-578. LIU J, LIU Y, ZHOU S B. Simulation of shock induced combustion based on a novel uncoupled method[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(3):572-578(in Chinese).[20] 刘瑜. 化学非平衡流的计算方法研究及其在激波诱导燃烧现象模拟中的应用[D].长沙:国防科学技术大学, 2008:20-24. LIU Y. Investigations into numerical methods of chemical nonequilibrium flow and its application to simulation of shock-induced combustion phenomena[D]. Changsha:National University of Defense Technology, 2008:20-24(in Chinese).[21] 刘瑜, 刘君, 白晓征. 基于新型非结构有限体积解耦算法的激波诱导燃烧数值模拟[J]. 国防科技大学学报, 2011, 33(6):139-144. LIU Y, LIU J, BAI X Z. Numerical simulation of shock-induced combustion with a new uncoupled algorithm in university finite volume method[J]. Journal of National University of Defense Technology, 2011, 33(6):139-144(in Chinese).[22] 刘瑜, 刘君, 唐玲艳, 等. 一种求解化学非平衡流动的新型解耦算法[J]. 力学学报, 2015, 47(1):82-94. LIU Y, LIU J, TANG L Y, et al. A novel uncoupled algorithm for solving chemical nonequilibrium flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(1):82-94(in Chinese).[23] 汪洪波, 孙明波, 梁剑寒, 等. 含双时间步法的化学非平衡流解耦算法[J]. 计算物理, 2010, 27(5):685-691. WANG H B, SUN M B, LIANG J H, et al. An uncoupled method with dual time-step for chemical nonequilibrium flows[J]. Chinese Journal of Computational Physics, 2010, 27(5):685-691(in Chinese).[24] 周松柏. 超声速内外流干扰的数值方法研究及其实验验证与应用[D]. 长沙:国防科学技术大学, 2009:76-92. ZHOU S B. Research on numerical method, experimental verification and application in simulation jet interaction in supersonic external flow[D]. Changsha:National University of Defense Technology, 2009:76-92(in Chinese).[25] 孙明波, 梁剑寒, 王振国. 非平衡流解耦方法及其计算激波诱导燃烧的应用验证[J]. 航空动力学报, 2008, 23(11):2055-2061. SUN M B, LIANG J H, WANG Z G. Validation of an uncoupled solver of non-equilibrium flow for shock-induced combustion[J]. Journal of Aerospace Power, 2008, 23(11):2055-2061(in Chinese).[26] 刘世杰, 孙明波, 林志勇, 等. 钝头体激波诱导振荡燃烧现象的数值模拟[J]. 力学学报, 2010, 42(4):597-606. LIU S J, SUN M B, LIN Z Y, et al. Numerical research on blunt body shock-induced oscillating combustion phenomena[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(4):597-606(in Chinese).[27] 韩旭, 周进, 林志勇, 等. 突跃型与平滑型斜爆震波起爆机制数值模拟[J]. 航空动力学报, 2012, 27(12):2674-2680. HAN X, ZHOU J, LIN Z Y, et al. Initiation mechanism investigation of saltation and smoothness oblique detonation waves[J]. Journal of Aerospace Power, 2012, 27(12):2674-2680(in Chinese).[28] 刘君, 杨彦广. 带有横喷控制的导弹流场数值模拟[J]. 空气动力学学报, 2004, 22(3):309-312. LIU J, YANG Y G. Numerical simulation of lateral jet control of a hypersonic missile[J]. Acta Aerodynamica Sinica, 2004, 22(3):309-312(in Chinese).[29] 杨彦广, 刘君, 唐志共. 横向喷流干扰中的真实气体效应研究[J]. 空气动力学学报, 2006, 24(1):28-33. YANG Y G, LIU J, TANG Z G. A study of real gas effects on lateral jet interaction[J]. Acta Aerodynamica Sinica, 2006, 24(1):28-33(in Chinese).[30] 刘世杰, 林志勇, 孙明波, 等. 旋转爆震波发动机二维数值模拟[J]. 推进技术, 2010, 31(5):634-640. LIU S J, LIN Z Y, SUN M B, et al. Two-dimensional numerical simulation of rotating detonation wave engine[J]. Journal of Propulsion Technology, 2010, 31(5):634-640(in Chinese).[31] 余文杰, 余永刚. 底排装置尾部化学非平衡流的数值模拟[J]. 推进技术, 2015, 36(11):1610-1615. YU W J, YU Y G. Numerical simulation of base flow with chemical non-equilibrium for base bleed equipment[J]. Journal of Propulsion Technology, 2015, 36(11):1610-1615(in Chinese).[32] DEITERDING R. Parallel adaptive simulation of multidimensional detonation structures[D]. Cottbus:Brandenburg University of Technology, 2003:18-27.[33] ZIEGLER J L, DEITERDING R, SHEPHERD J E, et al. An adaptive high-order hybrid scheme for compressive, viscous flows with detailed chemistry[J]. Journal of Computational Physics, 2011, 230(20):7598-7630.[34] BILLET G, RYAN J. A runge kutta discontinuous Galerkin approach to solve reactive flows:The hyperbolic operator[J]. Journal of Computational Physics, 2011, 230(4):1064-1083.[35] BILLET G, RYAN J, BORREL M. A Runge Kutta discontinuous Galerkin approach to solve reactive flows on conforming hybrid grids:The parabolic and source operators[J]. Computers and Fluids, 2014, 95:98-115.[36] LV Y, IHME M. Discontinuous Galerkin method for multicomponent chemically reacting flows and combustion[J]. Journal of Computational Physics, 2014, 270:105-137.[37] GLOWINSKI R, OSHER S J, YIN W. Splitting methods in communication, imaging, science, and engineering[M]. Heidelberg:Springer-Verlag, 2016:627-641.[38] TROTTER H F. On the product of semi-groups of operators[J]. Proceedings of the American Mathematical Society, 1959, 10(4):545-551.[39] STRANG G. On the construction and comparison of difference schemes[J]. SIAM Journal on Numerical Analysis, 1968, 5(3):506-517.[40] LU P. A consistent-splitting approach to computing stiff steady-state reacting flows with adaptive chemistry[J]. Combustion Theory and Modelling, 2003, 7(2):383-399.[41] REN Z, XU C, LU T, et al. Dynamic adaptive chemistry with operator splitting schemes for reactive flow simulations[J]. Journal of Computational Physics, 2014, 263:19-36.[42] DUARTE M. Adaptive numerical methods in time and space for the simulation of multi-scale reaction fronts[D]. Paris:Ecole Centrale Paris, 2011:104-128.[43] DUARTE M, DESCOMBES S, TENAUD C, et al. Time-space adaptive numerical methods for the simulation of combustion fronts[J]. Combustion and Flame, 2013, 160(6):1083-1101.[44] HELLANDER A, LAWSON M J, DRAWERT B, et al. Local error estimates for adaptive simulation of the reaction-diffusion equation via operator splitting[J]. Journal of Computational Physics, 2014, 266:89-100.[45] SPORTISSE B. An analysis of operator splitting techniques in the stiff case[J]. Journal of Computational Physics, 2000, 161(1):140-168.[46] SANTILLANA M, ZHANG L, YANTOSCA R. Estimating numerical errors due to operator splitting in global atmospheric chemistry models:Transport and chemistry[J]. Journal of Computational Physics, 2015, 305:909-917.[47] GOU X, SUN W, CHEN Z, et al. A dynamic multi-timescale method for combustion modeling with detailed and reduced chemical kinetic mechanisms[J]. Combustion and Flame, 2010, 157(6):1111-1121.[48] SUN W, GOU X, ELASRAG H A, et al. Multi-timescale and correlated dynamic adaptive chemistry modeling of ignition and flame propagation using a real jet fuel surrogate model[J]. Combustion and Flame, 2015, 162(4):1530-1539.[49] YANG G, LIU Y, REN Z, et al. A dynamic adaptive method for hybrid integration of stiff chemistry[J]. Combustion and Flame, 2015, 162(2):287-295.[50] XU C, GAO Y, REN Z, et al. A sparse stiff chemistry solver based on dynamic adaptive integration for efficient combustion simulations[J]. Combustion and Flame, 2016, 172:183-193.[51] 刘君, 周松柏, 徐春光. 超声速流动中燃烧现象的数值模拟方法及应用[M]. 长沙:国防科学技术大学出版社, 2008:61-63. LIU J, ZHOU S B, XU C G. The numerical simulation method of supersonic flow and its application[M]. Changsha:National University of Defense Technology Press, 2008:61-63(in Chinese).[52] GUPTA R N, YOS J M, THOMPSON R A. A review of reaction rates and thermodynamic and transport properties for the 11-species air model for chemical and thermal non-equilibrium calculations to 30000 K[J]. Philosophy, 1990, 92(6):32-34.[53] CHOI J Y, JEUNG I S, YOON Y, et al. Computational fluid dynamics algorithms for unsteady shock-induced combustion, Part 1:Validation[J]. AIAA Journal, 2000, 38(7):1179-1187.[54] CHOI J Y, JEUNG I S, YOON Y. Computational fluid dynamics algorithms for unsteady shock-induced combustion, Part 2:Comparison[J]. AIAA Journal, 2000, 38(7):1188-1195.[55] LEHR H F. Experiments on shock-induced combustion[J]. Acta Astronautica, 1972(1):589-597.[56] 杨彦广, 刘君. 高超声速主流中横向喷流干扰非定常特性研究[J]. 空气动力学学报, 2004, 22(3):295-302. YANG Y G, LIU J. Unsteady characteristic research of lateral jet in hypersonic external flow[J]. Acta Aerodynamica Sinica, 2004, 22(3):295-302(in Chinese).[57] 徐春光, 刘君. 某型导弹尾喷流形状的数值模拟[J]. 推进技术, 2003, 24(2):141-143. XU C G, LIU J. Numerical simulation on the plume flow structures for a missile[J]. Journal of Propulsion Technology, 2003, 24(2):141-143(in Chinese).[58] 周松柏, 刘君, 郭正, 等. 激波诱导异质气体界面失稳的数值模拟[J]. 国防科技大学学报, 2009, 31(1):1-4. ZHOU S B, LIU J, GUO Z, et al. Numerical simulation for shock induced interfacial instabilities of heterogeneous gases[J]. Journal of National University of Defense Technology, 2009, 31(1):1-4(in Chinese).[59] 崔小强, 白晓征, 周伟, 等. 点火冲击波与药柱裂纹流固耦合作用机理数值模拟研究[J]. 固体火箭技术, 2010, 33(1):9-12. CUI X Q, BAI X Z, ZHOU W, et al. Numerical simulation of the fluid-structure interaction mechanism between ignition shock wave and elastic cracks of grain[J]. Journal of Solid Rocket Technology, 2010, 33(1):9-12(in Chinese).[60] 刘瑜. 量热完全气体/化学非平衡气体流动ALE有限体积计算方法研究[D]. 长沙:国防科学技术大学, 2014:128-134. LIU Y. Numerical research of ALE finite volume method for calorically perfect gas chemical nonequilibrium gas flow[D]. Changsha:National University of Defense Technology, 2014:128-134(in Chinese).[61] VANLEER B. Towards the ultimate conservative difference scheme:V. A second-order sequel to Godunov's method[J]. Journal of Computational Physics, 1979, 32(1):101-136.[62] ZHANG F, LIU J, CHEN B, et al. Evaluation of rotated upwind schemes for contact discontinuity and strong shock[J]. Computers and Fluids, 2016, 134(1):11-22.[63] WILSON G J, MACCORMACK R W. Modeling supersonic combustion using a fully implicit numerical method[J]. AIAA Journal, 1992, 30(4):1008-1015.[64] ZELDOVICH Y B. On the theory of the propagation of detonation in gaseous systems[J]. Journal of Experimental and Theoretical Physics, 1940, 10(5):542-568.

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