非线性耦合本构在高空侧向喷流中的数值研究

doi:10.7527/S1000-6893.2022.27700

Abstract

Abstract:

As the altitude climbs， the aircraft control efficiency by the pneumatic rudder drops sharply with the increase of the Kn number， when the lateral jet， as the most commonly used type of a Reaction Control System （RCS）， plays a key role in the aircraft maneuvering process. Despite the good performance of the Navier-Stokes（NS） equations in low-altitude continuous flow problems， they fail to predict the slip flows （0.01<Kn<0.1） and even the transitional flows （0.1<Kn<10） due to the breakdown of continuity assumptions. To accurately capture the flow interference characteristics of the lateral jet and free stream in the rarefied transitional flow regime， this paper simulated typical lateral jet flow problems at different altitudes using the Nonlinear Coupled Constitutive Relations （NCCR） model and the NS model. The results of Direct Simulation of Monte Carlo （DSMC） were compared to further illustrate the reliability of the NCCR model in these cases. The research showed that the simulation results of the NCCR model and NS model have a high consistency in the continuous flow regime， and the NCCR model can more accurately predict the separation zone size and surface flow characteristics near the nozzle in the slip flow and transitional flow regimes. Moreover， compared with the NS equations， the NCCR model agrees better with the DSMC prediction in describing the complex flow mechanism of shock-shock interaction caused by the lateral jet.

Key words: lateral jet, multi-scale, high-altitude rarefaction, constitutive equations, hypersonic flow, generalized hydrodynamics

CLC Number:

V211.3

Yifeng HUANG, Shuhua ZENG, Zhongzheng JIANG, Weifang CHEN. Numerical study on high-altitude lateral jet based on nonlinear coupled constitutive relation[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(S2): 8-22.

Figures/Tables 20

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig.12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Fig. 18

Fig. 19

References 40

1	TARTABINI P, WILMOTH R, RAULT D. A systems approach to a DSMC calculation of a control jet interaction experiment[C]∥ 28th Thermophysics Conference. Reston: AIAA, 1993: 2798.
2	GLASS C E. Numerically simulating an expanding continuum jet into a surrounding non-continuum region[M].Washington, D.C.: NASA, 2018.
3	陈伟芳, 吴明巧, 任兵. DSMC/EPSM混合算法研究[J]. 计算力学学报, 2003, 20(3): 274-278.
	CHEN W F, WU M Q, REN B. On study of hybrid DSMC/EPSM method[J]. Chinese Journal of Computational Mechanics, 2003, 20(3): 274-278 (in Chinese).
4	BIRD G A. Molecular gas dynamics and the direct simulation of gas flows[M]. Oxford: Clarendon Press, 1994
5	EU B C. Relativistic kinetic theory for matter[M]∥Kinetic theory of nonequilibrium ensembles, irreversible thermodynamics, and generalized hydrodynamics. Cham: Springer International Publishing, 2016: 1-95.
6	EU B C. Kinetic theory and irreversible thermodynamics[M]. New York: J. Wiley, 1992
7	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 H, SHANG Y H, WU D, 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).
8	JIANG Z Z, ZHAO W W, CHEN W F, 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.
9	JIANG Z Z, ZHAO W W, YUAN Z Y, et al. Computation of hypersonic flows over flying configurations using a nonlinear constitutive model[J]. AIAA Journal, 2019, 57(12): 5252-5268.
10	JIANG Z, ZHAO W, CHEN W, et al. Computation of shock wave structure using a simpler set of generalized hydrodynamic equations based on nonlinear coupled constitutive relations[J]. Shock Waves, 2019, 29(8): 1227-1239.
11	江中正, 赵文文, 袁震宇, 等. 基于非线性耦合本构关系的改进边界条件[J]. 航空学报, 2018, 39(10): 122057.
	JIANG Z Z, ZHAO W W, YUAN Z Y, et al. An enhanced wall-boundary condition based on nonlinear coupled constitutive relations[J]. Acta Aeronautica et Astronautica Sinica, 2018, 39(10): 122057 (in Chinese).
12	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 Z Z. Theoretical and numerical investigations of nonlinear coupled constitutive relation model in rarefied gas flows[D]. Hangzhou: Zhejiang University, 2019 (in Chinese).
13	JIANG Z Z, CHEN W F, ZHAO W W. Numerical analysis of the micro-Couette flow using a non-Newton-Fourier model with enhanced wall boundary conditions[J]. Microfluidics and Nanofluidics, 2018, 22(1): 10.
14	YUAN Z Y, ZHAO W W, JIANG Z Z, et al. Numerical simulation of hypersonic reaction flows with nonlinear coupled constitutive relations[J]. Aerospace Science and Technology, 2021, 112: 106591.
15	HE Z Q, JIANG Z Z, ZHANG H W, et al. Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows[J]. Chinese Journal of Aeronautics, 2021, 34(2): 136-153.
16	王振. 非线性耦合本构方程的计算方法与验证[D]. 杭州: 浙江大学, 2020.
	WANG Z. Calculation method and verification of nonlinear coupled constitutive equations[D]. Hangzhou: Zhejiang University, 2020 (in Chinese).
17	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(S1): 726359.
	WU Y, XU X, CHEN B, et al. Numerical study on transverse/opposing jet interaction flowfield under high Mach number[J]. Acta Aeronautica et Astronautica Sinica, 2021, 42(S1): 726359 (in Chinese).
18	王泽江, 李杰, 曾学军, 等. 逆向喷流对双锥导弹外形减阻特性的影响[J]. 航空学报, 2020, 41(12): 124116.
	WANG Z J, LI J, ZENG X J, et al. Effect of opposing jet on drag reduction characteristics of double-cone missile shape[J]. Acta Aeronautica et Astronautica Sinica, 2020, 41(12): 124116 (in Chinese).
19	CURTISS C F. The classical Boltzmann equation of a gas of diatomic molecules[J]. Journal of Chemical Physics, 1981, 75: 376-378.
20	BHATNAGAR P L, GROSS E P, KROOK M. A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems[J]. Physical Review, 1954, 94(3): 511-525.
21	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.
22	GRAD H. Asymptotic theory of the boltzmann equation[J]. The Physics of Fluids, 1963, 6(2): 147-181.
23	LEVERMORE C D. Moment closure hierarchies for kinetic theories[J]. Journal of Statistical Physics, 1996, 83: 5-6.
24	TORRILHON M, STRUCHTRUP H. Regularized 13-moment equations: Shock structure calculations and comparison to Burnett models[J]. Journal of Fluid Mechanics, 2004, 513: 171-198.
25	AL-GHOUL M, EU B. Generalized hydrodynamics and shock waves[J]. Physical Review E, 1997, 56(3): 2981-2992.
26	EU B C. The modified moment method, irreversible thermodynamics, and the nonlinear viscosity of a dense fluid[J]. Journal of Chemical Physics, 1981, 74: 6362-6372.
27	MYONG R S. Thermodynamically consistent hydrodynamic computational models for high-Knudsen-number gas flows[J]. Physics of Fluids, 1999, 11(9): 2788-2802.
28	MYONG R S. A computational method for Eu's generalized hydrodynamic equations of rarefied and microscale gasdynamics[J]. Journal of Computational Physics, 2001, 168(1): 47-72.
29	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.
30	MAXWELL J C. On stresses in rarified gases arising from inequalities of temperature[J]. Philosophical Transactions of the Royal Society of London, 1879, 170: 231-256.
31	陈坚强, 张益荣, 郭勇颜. 高超声速流动数值模拟方法及应用[M]. 北京: 科学出版社, 2019: 153-154.
	CHEN J Q, ZHANG Y R, GUO Y Y. Numerical simulation method of hypersonic flow and its application[M]. Beijing: Science Press, 2019: 153-154 (in Chinese).
32	OSHER S. Convergence of generalized MUSCL schemes[J]. SIAM Journal on Numerical Analysis, 1985, 22(5): 947-961.
33	KIM K H, KIM C, RHO O H. Methods for the accurate computations of hypersonic flows[J]. Journal of Computational Physics, 2001, 174(1): 38-80.
34	YOON S, JAMESON A. Lower-upper Symmetric-Gauss-Seidel method for the Euler and Navier-Stokes equations[J]. AIAA Journal, 1988, 26(9): 1025-1026.
35	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): 012002.
36	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.
37	JIANG Z Z. An undecomposed hybrid algorithm for nonlinear coupled constitutive relations of rarefied gas dynamics[J]. Communications in Computational Physics, 2019, 26(3): 880-912.
38	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): 017103.
39	张庆虎. 超声速流动分离及其控制的试验研究[D]. 长沙: 国防科学技术大学, 2013.
	ZHANG Q H. Experimental investigation of supersonic flow separation and its micro-ramp control[D]. Changsha: National University of Defense Technology, 2013 (in Chinese).
40	李季. 高温非平衡效应下的激波干扰与激波反射[D]. 合肥: 中国科学技术大学, 2015.
	LI J. On shock interactions and reflections with high temperature non-equilibrium effects[D]. Hefei: University of Science and Technology of China, 2015 (in Chinese).

高度/km	速度/（m·s^-1）	温度/K	压力/Pa	来流气体自由程/m	努森数Kn
60	3 150.9	247.02	21.959	0.000 26	0.002 6
70	2 970.9	219.59	5.221	0.001（0.000 98）	0.01
85	2 755	188.84	0.446	0.01（0.009 9）	0.1

[1]	Weihong ZHANG, Han ZHOU, Shaoying LI, Jihong ZHU, Lu ZHOU. Material⁃structure integrated design for high⁃performance aerospace thin⁃walled component [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(9): 627428-627428.
[2]	Chongli MA, Jingyuan LIU. Effect of grid strategy on numerical simulation results of aerothermal heating loads over hypersonic blunt bodies [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 126710-126710.
[3]	Bin LIU, Jing XU, Meiling HUO, Xueying CUI, Xiufeng XIE, Donghui YANG, Jia WANG. Remaining useful life prediction based on multi-scale adaptive attention network [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(5): 226918-226918.
[4]	Xiaoqian CHEN, Yong ZHAO, Senlin HUO, Zeyu ZHANG, Bingxiao DU. A review of topology optimization design methods for multi-scale structures [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(15): 528863-528863.
[5]	Bo DING, Zhenli CHEN, Zihan JIAO, Jincheng WANG, Zheng LI, Guanghui BAI. Unsteady control mechanisms of hypersonic compression corner using pulsed surface arc discharge [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(12): 127744-127744.
[6]	Yuanliang XUE, Guodong JIN, Lining TAN, Jiankun XU. Adaptive UAV target tracking algorithm based on multi-scale fusion [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2023, 44(1): 326107-326107.
[7]	HAN Songyu, SHAO Haidong, JIANG Hongkai, ZHANG Xiaoyang. Intelligent fault diagnosis of aero-engine high-speed bearings using enhanced CNN [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 625479-625479.
[8]	TIAN Jing, ZHANG Yuwei, ZHANG Fengling, AI Xinping, GAO Chong. Inter-shaft bearing fault diagnosis method based on multi-scale quantum entropy [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 625485-625485.
[9]	LIU Fang, HAN Xiao. Adaptive aerial object detection based on multi-scale deep learning [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 325270-325270.
[10]	LIU Pengxin, YUAN Xianxu, SUN Dong, FU Yalu, LI Chen. Direct numerical simulation of high-temperature turbulent boundary layer with chemical nonequilibrium [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(1): 124877-124877.
[11]	REN Weijie, XIE Wenjia, TIAN Zhengyu, ZHANG Ye, YU Hang. Grid dependence of hypersonic numerical shock instability [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(S1): 726376-726376.
[12]	XIANG Xinghao, ZHANG Yifeng, YUAN Xianxu, TU Guohua, WAN Bingbing, CHEN Jianqiang. C-γ-Re_θ model for hypersonic three-dimensional boundary layer transition prediction [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(9): 625711-625711.
[13]	WU Han, WANG Jianhong, HUANG Wei, DU Zhaobo, YAN Li. Research progress on shock wave/boundary layer interactions and flow controls induced by micro vortex generators [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(6): 25371-025371.
[14]	ZHAO Chenwei, MAO Junkui, TU Zecan, QIU Penglin. Thermal analysis methods for high-temperature ceramic matrix composite components: Review and prospect [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(6): 24126-024126.
[15]	NI Weiyu, ZHANG Heng, YAO Shengwei. Concurrent topology optimization of composite structures for considering structural damping [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(3): 224807-224807.

Numerical study on high-altitude lateral jet based on nonlinear coupled constitutive relation

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 20

References 40

Related Articles 15

Recommended Articles

Metrics

Comments