基于非线性耦合本构化学反应模型的高空逆向喷流数值模拟

黄依峰; 江中正; 曾舒华; 陈伟芳

doi:10.13224/j.cnki.jasp.20220662

基于非线性耦合本构化学反应模型的高空逆向喷流数值模拟

doi: 10.13224/j.cnki.jasp.20220662

浙江大学航空航天学院，杭州 310027

基金项目: 国家自然科学基金（12002306，U20B2007）

详细信息

作者简介:
黄依峰（1997-），男，硕士生，主要从事喷流与稀薄气体研究。E-mail：1085072426@qq.com

通讯作者:
江中正（1992-），男，副研究员，博士，主要从事稀薄气体动力学研究。E-mail：jzhongzh@zju.edu.cn

中图分类号: V211.3
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出版历程
- 收稿日期: 2022-09-06
- 网络出版日期: 2024-10-12

Numerical simulation of high altitude reverse jet based on nonlinear coupled constitutive chemical-reaction model

School of Aeronautics and Astronautics，Zhejiang University，Hangzhou 310027，China

摘要

摘要:
考虑到NS（Navier-Stokes）方程由于连续性假设失效在高空逆向喷流多尺度流动预示中存在的局限性，同时为了准确捕捉逆向喷流与高速来流相互作用后的高温化学反应流场特征以及压力系数变化，运用非线性耦合本构关系（nonlinear coupled constitutive relations, NCCR）理论结合高温化学反应模型对不同稀薄来流高度下的逆向喷流问题进行数值计算，并与NS方程和蒙特卡洛直接模拟（direct simulation of Monte Carlo, DSMC）方法的结果进行对比。模拟的流场结果表明：逆向喷流能够通过形成马赫盘将头部的脱体激波推离物面，并且在其与喷口附近的环形回流低压区的共同作用下达到较为显著的减阻降热效果。此外，通过部分算例与DSMC结果的对比可以看到，在考虑化学反应的滑移/过渡流域逆向喷流计算中NCCR模型预测结果较NS方程的高温结果更为准确，检验了NCCR高温化学反应模型在高空复杂流动情况下的准确性和适用性。
- 逆向喷流 /
- TCE化学反应模型 /
- NCCR模型 /
- 高超声速流动 /
- 直接模拟蒙特卡洛方法
Abstract:
Considering the limitation of NS (Navier-Stokes) equation in predicting the multi-scale flow of high-altitude reverse jet due to the failure of continuity assumption, in order to accurately capture the characteristics of high temperature chemical reaction flow field of interaction between reverse jet and high-speed free stream as well as the variation of pressure coefficient, the nonlinear coupled Constitutive relations (NCCR) theory combined with the high temperature chemical reaction model was adopted to numerically calculate the reverse jet flow at different rarefied heights. The results were compared with those obtained by NS equation and direct simulation of Monte Carlo (DSMC). The simulation results showed that the reverse jet can push the detached shock wave away from the object surface by forming a Mach disk, and achieve a significant drag and heat reduction effect under the joint action of the detached shock wave and the annular reflux low-pressure area around the nozzle. In addition, by comparing with part of DSMC results, it can be seen that the prediction results of NCCR model were more accurate than the high temperature results of NS equation in calculating the chemical reverse jet flow in slip/transition regimes, which verified the accuracy and applicability of NCCR high temperature chemical reaction model in complex flow conditions at high altitude.
- reverse jet /
- TCE chemical reaction model /
- NCCR model /
- hypersonic flow /
- DSMC

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图 1 氮氧离解程度随温度变化

Figure 1. Degree of nitrogen and oxygen dissociation varies with temperature

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图 2 不同分子模型对比

Figure 2. Comparison of different molecular models

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图 3 Kn=0.052时NS/NCCR/DSMC无量纲压力曲线

Figure 3. Dimensionless pressure curve of NS/NCCR/DSMC at Kn=0.052

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图 4 Kn=0.052时NS/NCCR/DSMC驻点在线组分分布

Figure 4. Composition distribution on the stagnation line of NS/NCCR/DSMC at Kn=0.052

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图 5 圆柱表面压力/摩阻系数分布

Figure 5. Distribution of pressure/friction coefficient on cylindrical surface

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图 6 RAM-C几何外形与网格划分

Figure 6. Geometry and meshing of RAM-C

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图 7 带喷流RAM-C驻在线无量纲速度曲线

Figure 7. Dimensionless velocity of RAM-C stationary line with reverse jet

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图 8 带喷流RAM-C驻在线无量纲压力曲线

Figure 8. Dimensionless pressure of RAM-C stationary line with reverse jet

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图 9 相同压比不同高度下的逆向喷流

Figure 9. Reverse jet flow at the same pressure ratio and different altitudes

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图 10 喷流扩张的角度

Figure 10. Jet expands angle

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图 11 88 km高度RAM-C侧面气动参数

Figure 11. RAM-C side aerodynamic parameters at 88 km

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图 12 88 km时逆向喷流的流线图

Figure 12. Streamtraces in reverse jet at 88 km

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图 13 RAM-C侧面上的滑移速度/速度梯度分布

Figure 13. Slip velocity/velocity gradient distribution on the side of RAM-C

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图 14 DSMC所得80 km物面压力系数分布（有喷/无喷）

Figure 14. Distribution of pressure coefficients on the 80 km surface obtained by DSMC （jet/No jet）

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图 15 头部附近的压力系数对比

Figure 15. Comparison of pressure coefficients near the head

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图 16 头部附近的摩阻系数对比

Figure 16. Comparison of friction coefficients near the head

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图 17 80 km高度RAM-C逆向喷流中轴在线流场数据对比

Figure 17. Comparison of field data on axis of RAM-C reverse jet at 80 km altitude

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表 1 不同高度下的工况设置

Table 1. Case setting at different altitude

参数	高度/km
参数	80	88	96
来流马赫数	25	25	25
来流温度/K	198.639	186.867	189.305
来流压力/Pa	1.0525	0.2617	0.0638
喷口压力/Pa	105.25	26.17	6.38
喷口马赫数	12.5	12.5	12.5
（喷口/壁面温度）/K	1500	1500	1500

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表 2 RAM-C头部X=0.01 m处喷流引起的压力系数变化

Table 2. Changes of surface coefficient caused by jet flow at X=0.01 m of RAM-C head

工况		C_p	C_f	C_h
88 km	喷流	0.235	0.088	0.108
88 km	无喷	0.52	0.186	0.188
	降低/%	54.8	52.7	42.6
96 km	喷流	0.262	0.14	0.139
96 km	无喷	0.553	0.202	0.223
	降低/%	52.6	30.7	37.7

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参考文献(43)

[1]	吴忧,徐旭,陈兵,等. 高马赫数下横/逆向喷流干扰流场数值研究[J]. 航空学报,2021,42(增刊1): 726359. WU You,XU Xu,CHEN Bing,et al. Numerical study on transverse/opposing jet interaction flowfield under high Mach number[J]. Acta Aeronautica et Astronautica Sinica,2021,42(Suppl.1): 726359. (in Chinese WU You, XU Xu, CHEN Bing, et al. Numerical study on transverse/opposing jet interaction flowfield under high Mach number[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(Suppl.1): 726359. (in Chinese)
[2]	GOLDSWORTHY M J,MACROSSAN M N,ABDEL-JAWAD M M. Nonequilibrium reaction rates in the macroscopic chemistry method for direct simulation Monte Carlo calculations[J]. Physics of Fluids,2007,19(6): 066101. doi: 10.1063/1.2742747
[3]	BIRD G A,GALLIS M A,TORCZYNSKI J R,et al. Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows[J]. Physics of Fluids,2009,21(1): 17103.1-17103.12. doi: 10.1063/1.3067865
[4]	AL-GHOUL M,EU B. Generalized hydrodynamics and shock waves[J]. Physical Review E,1997,56(3): 2981-2992. doi: 10.1103/PhysRevE.56.2981
[5]	AL-GHOUL M,EU B C. Generalized hydrodynamic theory of shock waves in rigid diatomic gases[J]. Physical Review E,2001,64(4): 046303. doi: 10.1103/PhysRevE.64.046303
[6]	AL-GHOUL M,EU B C. Generalized hydrodynamic theory of shock waves: Mach-number dependence of inverse shock width for nitrogen gas[J]. Physical Review Letters,2001,86(19): 4294-4297. doi: 10.1103/PhysRevLett.86.4294
[7]	MYONG R S. Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows[J]. Physics of Fluids,1999,11(9): 2788-2802. doi: 10.1063/1.870137
[8]	MYONG R S. A generalized hydrodynamic computational model for rarefied and microscale diatomic gas flows[J]. Journal of Computational Physics,2004,195(2): 655-676. doi: 10.1016/j.jcp.2003.10.015
[9]	MYONG R S. Coupled nonlinear constitutive models for rarefied and microscale gas flows: subtle interplay of kinematics and dissipation effects[J]. Continuum Mechanics and Thermodynamics,2009,21(5): 389-399. doi: 10.1007/s00161-009-0112-6
[10]	AHN J W,KIM C. An axisymmetric computational model of generalized hydrodynamic theory for rarefied multi-species gas flows[J]. Journal of Computational Physics,2009,228(11): 4088-4117. doi: 10.1016/j.jcp.2009.02.026
[11]	YUAN Zhenyu,JIANG Zhongzheng,ZHAO Wenwen,et al. Multiple temperature model of nonlinear coupled constitutive relations for hypersonic diatomic gas flows[J]. AIP Advances,2020,10(5): 055023. doi: 10.1063/5.0010232
[12]	YUAN Zhenyu,ZHAO Wenwen,JIANG Zhongzheng,et al. Numerical simulation of hypersonic reaction flows with nonlinear coupled constitutive relations[J]. Aerospace Science and Technology,2021,112: 106591. doi: 10.1016/j.ast.2021.106591
[13]	JIANG Zhongzheng. An undecomposed hybrid algorithm for nonlinear coupled constitutive relations of rarefied gas dynamics[J]. Communications in Computational Physics,2019,26(3): 880-912. doi: 10.4208/cicp.OA-2018-0056
[14]	HE Zhiqiang,FAN Guochao,JIANG Zhongzheng. Numerical application of the nonlinear coupled constitutive relations under three-dimensional hybrid unstructured finite-volume framework[J]. International Journal of Modern Physics B,2020,34(14/15/16): 2040071. doi: 10.1142/S0217979220400718
[15]	JIANG Zhongzheng,ZHAO Wenwen,CHEN Weifang,et al. Eu’s generalized hydrodynamics with its derived constitutive model: comparison to Grad’s method and linear stability analysis[J]. Physics of Fluids,2021,33(12): 127116. doi: 10.1063/5.0071715
[16]	JIANG Zhongzheng,ZHAO Wenwen,YUAN Zhenyu,et al. Computation of hypersonic flows over flying configurations using a nonlinear constitutive model[J]. AIAA Journal,2019,57(12): 5252-5268. doi: 10.2514/1.J057688
[17]	江中正. 稀薄气体流动非线性耦合本构关系模型理论与数值研究[D]. 杭州: 浙江大学,2019. JIANG Zhongzheng. Theoretical and numerical study on nonlinear coupled constitutive relation model of rarefied gas flow[D]. Hangzhou: Zhejiang University,2019. (in Chinese JIANG Zhongzheng. Theoretical and numerical study on nonlinear coupled constitutive relation model of rarefied gas flow[D]. Hangzhou: Zhejiang University, 2019. (in Chinese)
[18]	MYONG R S. A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation[J]. Physics of Fluids,2011,23(1): 12002. doi: 10.1063/1.3540671
[19]	EU B C,OHR Y G. Generalized hydrodynamics,bulk viscosity,and sound wave absorption and dispersion in dilute rigid molecular gases[J]. Physics of Fluids,2001,13(3): 744-753. doi: 10.1063/1.1343908
[20]	MACCORMACK R. The computation of hypersonic ionized flows in chemical and thermal nonequlibrium: AIAA 1988-511 [R]. Reston,Virigina: AIAA,1988.
[21]	WILKE C R. A viscosity equation for gas mixtures[J]. The Journal of Chemical Physics,1950,18(4): 517-519. doi: 10.1063/1.1747673
[22]	BIRD G A. Molecular gas dynamics and the direct simulation of gas flows[M]. Oxford: Clarendon Press,1994.
[23]	GNOFFO P A. Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium[M]. Washington,DC: NASA,1989.
[24]	BIRD G A. The Q-K model for gas-phase chemical reaction rates[J]. Physics of Fluids,2011,23(10): 106101.1-106101.13.
[25]	陈浩,李林颖,张斌,等. Q-K模型在氮氧离解复合反应中的评估[J]. 空气动力学报,2018,36(1): 17-21. CHEN Hao,LI Linying,ZHANG Bin,et al. Assessment of Q-K model for nitrogen and oxygen dissociation recombination[J]. Acta Aerodynamica Sinica,2018,36(1): 17-21. (in Chinese CHEN Hao, LI Linying, ZHANG Bin, et al. Assessment of Q-K model for nitrogen and oxygen dissociation recombination[J]. Acta Aerodynamica Sinica, 2018, 36(1): 17-21. (in Chinese)
[26]	杨浩森,张斌,刘洪,等. DSMC 热化学仿真分子数对氮氧离解反应计算影响的分析[J]. 空气动力学学报,2014,32(4): 511-517. YANG Haosen,ZHANG Bin,LIU Hong,et al. Influence of the molecule number on nitrogen-oxygen dissociation reacting flows in DSMC simulations[J]. Acta Aerodynamica Sinica,2014,32(4): 511-517. (in Chinese doi: 10.7638/kqdlxxb-2012.0164 YANG Haosen, ZHANG Bin, LIU Hong, et al. Influence of the molecule number on nitrogen-oxygen dissociation reacting flows in DSMC simulations[J]. Acta Aerodynamica Sinica, 2014, 32(4): 511-517. (in Chinese) doi: 10.7638/kqdlxxb-2012.0164
[27]	OSHER S. Convergence of generalized MUSCL schemes[J]. SIAM Journal on Numerical Analysis,1985,22(5): 947-961. doi: 10.1137/0722057
[28]	KIM K H,KIM C,RHO O H. Methods for the accurate computations of hypersonic flows: Ⅰ AUSMPW+Scheme[J]. Journal of Computational Physics,2001,174(1): 38-80. doi: 10.1006/jcph.2001.6873
[29]	黄华. 耦合辐射的非平衡流场数值研究[D]. 湖南: 国防科学技术大学,2008. HUANG Hua. Numerical study of non-equilibrium flow field of coupled radiation[D]. Hunan: National University of Defense Technology,2008. (in Chinese HUANG Hua. Numerical study of non-equilibrium flow field of coupled radiation[D]. Hunan: National University of Defense Technology, 2008. (in Chinese)
[30]	柳军. 热化学非平衡流及其辐射现象的实验和数值计算研究[D]. 长沙: 国防科学技术大学,2004. LIU Jun. Experimental and numerical study on thermochemical non-equilibrium flow and its radiation phenomenon[D]. Changsha: National University of Defense Technology,2004. (in Chinese LIU Jun. Experimental and numerical study on thermochemical non-equilibrium flow and its radiation phenomenon[D]. Changsha: National University of Defense Technology, 2004. (in Chinese)
[31]	YOON S,JAMESON A. Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations[J]. AIAA Journal,1988,26(14): 1025.
[32]	LE N T P,XIAO H,MYONG R S. A triangular discontinuous Galerkin method for non-Newtonian implicit constitutive models of rarefied and microscale gases[J]. Journal of Computational Physics,2014,273: 160-184. doi: 10.1016/j.jcp.2014.05.013
[33]	肖洪,商雨禾,吴迪,等. 稀薄气体动力学的非线性耦合本构方程理论及验证[J]. 航空学报,2015,36(7): 2091-2104. XIAO Hong,SHANG Yuhe,WU Di,et al. Nonlinear coupled constitutive relations and its validation for rarefied gas flows[J]. Acta Aeronautica et Astronautica Sinica,2015,36(7): 2091-2104. (in Chinese XIAO Hong, SHANG Yuhe, WU Di, et al. Nonlinear coupled constitutive relations and its validation for rarefied gas flows[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(7): 2091-2104. (in Chinese)
[34]	CLERK MAXWELL J. On stresses in rarified gases arising from inequalities of temperature[J]. Philosophical Transactions of the Royal Society of London Series I,1879,170: 231-256. doi: 10.1098/rstl.1879.0067
[35]	陈坚强. 高超声速流动数值模拟方法及应用[M]. 北京: 科学出版社,2019. CHEN Jianqiang.Numerical simulation method and application of hypersonic flow [M]. Beijing: Science Press,2019. (in Chinese CHEN Jianqiang.Numerical simulation method and application of hypersonic flow [M]. Beijing: Science Press, 2019. (in Chinese)
[36]	沈青. 稀薄气体动力学[M]. 北京: 国防工业出版社,2003. SHEN Qing. Rarefied gas dynamics[M]. Beijing: National Defense Industry Press,2003. (in Chinese SHEN Qing. Rarefied gas dynamics[M]. Beijing: National Defense Industry Press, 2003. (in Chinese)
[37]	KOURA K,MATSUMOTO H. Variable soft sphere molecular model for air species[J]. Physics of Fluids A: Fluid Dynamics,1992,4(5): 1083-1085. doi: 10.1063/1.858262
[38]	FISCKO K A. Study of continuum higher order closure models evaluated by a statistical theory of shock structure[M]. California,US: Stanford University,1988.
[39]	XU K. Direct modeling for computational fluid dynamics: construction and application of unified gas-kinetic schemes[M]. Singapore: World Scientific,2014.
[40]	ANDERSON J D. 高超声速和高温气体动力学[M]. 杨永,李栋,译. 第二版. 北京: 航空工业出版社,2013. ANDERSON J D. Hypersonic and High-Temperature gas dynamics[M]. Yang Yong,LI Dong,Trans. Second Ed. Beijing: Aviation Industry Press,2013. (in Chinese ANDERSON J D. Hypersonic and High-Temperature gas dynamics[M]. Yang Yong, LI Dong, Trans. Second Ed. Beijing: Aviation Industry Press, 2013. (in Chinese)
[41]	KANIPE D B. Plume/flowfield jet interaction effects on the Space Shuttle Orbiterduring entry[J]. Journal of Spacecraft and Rockets,1983,20(4): 351-355. doi: 10.2514/3.25605
[42]	FINLEY P J. The flow of a jet from a body opposing a supersonic free stream[J]. Journal of Fluid Mechanics,1966,26: 337-368. doi: 10.1017/S0022112066001277
[43]	董昊,张旭东,刘是成,等. 高超声速逆向喷流数值模拟和风洞试验[J]. 空气动力学学报,2022,40(4): 101-109. DONG Hao,ZHANG Xudong,LIU Shicheng,et al. Numerical and experimental study on opposing jet in hypersonic flow[J]. Acta Aerodynamica Sinica,2022,40(4): 101-109. (in Chinese doi: 10.7638/kqdlxxb-2021.0240 DONG Hao, ZHANG Xudong, LIU Shicheng, et al. Numerical and experimental study on opposing jet in hypersonic flow[J]. Acta Aerodynamica Sinica, 2022, 40(4): 101-109. (in Chinese) doi: 10.7638/kqdlxxb-2021.0240