网格对高超声速钝头体表面热流数值模拟结果的影响

doi:10.7527/S1000-6893.2022.26710

Abstract

Abstract:

Accurate prediction of aerothermal heating load over hypersonic blunt bodies is of great significance to the design of hypersonic vehicle thermal protection， while grid metric affects the prediction accuracy of aircraft surface heating load. By theoretical analysis and numerical simulation， a grid generation method is proposed according to the cell Reynolds number and freestream Reynolds number， respectively， based on the wall parameters and characteristic length of blunt bodies， and the reference value range of the cell Reynolds number based on wall parameters is also provided. The proposed grid generation method is then applied to the simulation of hypersonic aeroheating computations over semi-cylinders and semi-spheres under different incoming flow conditions. The results show that the proposed grid generation method and the suggested range of the cell Reynolds number based on wall parameters can satisfy the precision requirement of thermal environment simulation over hypersonic blunt bodies， facilitate the rational distribution of grids， and simultaneously improve the efficiency of numerical calculations.

Key words: hypersonic flow, aerothermal heating, blunt body, error analysis, grid metric

CLC Number:

V211.5

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.

Figures/Tables 14

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Table 1

Collections of grid scales for different numerical cases

来流外形	$M a ∞$	$R e$	D/m	$λ w$	$Δ n w, m a x$ /m	$R e c e l l, w, m a x$	$Δ x m a x$ /m	$R e$	$Δ x m a x Δ n w, m a x$
半圆柱	8.0	3.76×10⁵	0.076 00	1.1×10^-7	8.1×10^-6	170	4.9×10^-3	613	605
半圆柱	16.34	2.97×10⁵	0.076 00	2.6×10^-7	2.0×10^-5	171	1.1×10^-2	545	550
球头	8.0	1.70×10⁵	0.015 00	1.1×10^-7	4.3×10^-6	85	1.8×10^-3	410	419
球头^［17］	8.0	1.70×10⁵	0.015 00	1.1×10^-7	1.3×10^-6	26	5.3×10^-4	410	408
球头	13.24	6.26×10⁴	0.350 00	6.2×10^-7	3.9×10^-5	140	1.1×10^-2	250	282
球头^［26］	13.24	6.26×10⁴	0.350 00	6.2×10^-7	3.5×10^-5	125	1.0×10^-2	250	286
钝头锥^［18］	10.6	2.20×10⁵	0.055 88	4.6×10^-7	4.2×10^-6	20	1.4×10^-3	469	333
升力体^［26］	15.0	1.68×10⁵	0.140 00	9.1×10^-8	8.4×10^-6	206	4.1×10^-3	410	488

Table 1

Fig. 12

Table 2

Collections of flow field parameters for different numerical cases

来流外形	$M a ∞$	$T ∞ / K$	$T t / K$	$T w / K$	$T ∞ / T w$	$T t / T w$	$q s / k W ⋅ m - 2$
半圆柱	8.0	125	1 725.0	294	0.425	5.867	406.2
半圆柱	8.0	125	1 725.0	1 200	0.104	1.438	95.1
半圆柱	16.34	52	2 828.6	294.4	0.177	9.609	527.1
半圆柱	16.34	52	2 828.6	1 000	0.052	2.829	350.4
球头	8.0	64.64	892.0	294	0.220	3.034	554.8
球头	8.0	64.64	892.0	500	0.129	1.784	315.3
球头	13.24	265	9 555.8	294.4	0.900	32.458	911.8
球头	13.24	265	9 555.8	2 000	0.133	4.778	696.2
钝头锥^［18］	10.6	47.3	1 110.2	294.4	0.161	3.771	184.9
升力体^［26］	15.0	250.35	11 516.1	300	0.850	39.117	5 000

Table 2

References 28

1	程晓丽，艾邦成，王强. 基于分子平均自由程的热流计算壁面网格准则［J］. 力学学报， 2010， 42（6）： 1083-1089.
	CHENG X L， AI B C， WANG Q. A wall grid scale criterion based on the molecule mean free path for the wall heat flux computations by the Navier-Stokes equations［J］. Chinese Journal of Theoretical and Applied Mechanics， 2010， 42（6）： 1083-1089 （in Chinese）.
2	张智超，高振勋，蒋崇文，等. 高超声速气动热数值计算壁面网格准则［J］. 北京航空航天大学学报， 2015， 41（4）： 594-600.
	ZHANG Z C， GAO Z X， JIANG C W， et al. Grid generation criterions in hypersonic aeroheating computations［J］. Journal of Beijing University of Aeronautics and Astronautics， 2015， 41（4）： 594-600 （in Chinese）.
3	HOFFMANN K， SIDDIQUI M， CHIANG S. Difficulties associated with the heat flux computations of high speed flows by the Navier-Stokes equations［C］∥ 29th Aerospace Sciences Meeting. Reston： AIAA， 1991.
4	MEN'SHOV I S， NAKAMURA Y. Numerical simulations and experimental comparisons for high-speed nonequilibrium air flows［J］. Fluid Dynamics Research， 2000， 27（5）： 305-334.
5	PAPADOPOULOS P， VENKATAPATHY E， PRABHU D， et al. Current grid-generation strategies and future requirements in hypersonic vehicle design， analysis and testing［J］. Applied Mathematical Modelling， 1999， 23（9）： 705-735.
6	KLOPFER G， YEE H. Viscous hypersonic shock-on-shock interaction on blunt cowl lips［C］∥ 26th Aerospace Sciences Meeting. Reston： AIAA， 1988.
7	潘沙，冯定华，丁国昊，等. 气动热数值模拟中的网格相关性及收敛［J］. 航空学报， 2010， 31（3）： 493-499.
	PAN S， FENG D H， DING G H， et al. Grid dependency and convergence of hypersonic aerothermal simulation［J］. Acta Aeronautica et Astronautica Sinica， 2010， 31（3）： 493-499 （in Chinese）.
8	张翔，阎超，杨威，等. 高超声速飞行器气动热网格依赖性研究［J］. 战术导弹技术， 2016（3）： 21-27.
	ZHANG X， YAN C， YANG W， et al. Investigation of the grid-dependency in heat transfer simulation for hypersonic vehicle［J］. Tactical Missile Technology， 2016（3）： 21-27 （in Chinese）.
9	闫文辉，任立磊. 计算网格对气动力气动热数值模拟影响的研究［J］. 航空计算技术， 2017， 47（2）： 1-4.
	YAN W H， REN L L. Grid study on numerical simulation of aerodynamic flowfield［J］. Aeronautical Computing Technique， 2017， 47（2）： 1-4 （in Chinese）.
10	QU F. A study of upwind schemes on the laminar hypersonic heating predictions for the reusable space vehicle［J］. Acta Astronautica， 2018， 147： 412-420.
11	ZHAO Y P， HU Y M， HUANG H M. Numerical analysis of convergence property of heat flux next to the wall［J］. Acta Astronautica， 2019， 155： 230-237.
12	QU F. A grid strategy for predicting the space plane's hypersonic aerodynamic heating loads［J］. Aerospace Science and Technology， 2019， 86： 659-670.
13	YANG J L， LIU M. A wall grid scale criterion for hypersonic aerodynamic heating calculation［J］. Acta Astronautica， 2017， 136： 137-143.
14	REN X， YUAN J Y， HE B J， et al. Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime［J］. Journal of Fluid Mechanics， 2019， 881： 585-601.
15	HUANG H M， HU Y M. New criterion for first grid spacing off wall surface in hypersonic flow［J］. Journal of Spacecraft and Rockets， 2019， 56（1）： 171-178.
16	张亮，程晓丽，艾邦成. 高超声速气动热数值模拟法向网格准则［J］. 力学与实践， 2014， 36（6）： 722-727， 741.
	ZHANG L， CHENG X L， AI B C. Normal grid rule for hypersonic heat flux numerical simulation［J］. Mechanics in Engineering， 2014， 36（6）： 722-727， 741 （in Chinese）.
17	王浩. 高超音速流动数值模拟与热流数值计算［D］. 北京：北京航空航天大学， 2002： 77-82.
	WANG H. Numerical simulation of hypersonic flow and numerical calculation of heat flux［D］. Beijing： Beihang University， 2002： 77-82 （in Chinese）.
18	谢锦睿，吴颂平，王浩. 高超音速热流数值计算中的误差匹配原则［J］. 北京航空航天大学学报， 2005， 31（3）： 274-277.
	XIE J R， WU S P， WANG H. Error matching principle for heat transfer calculations in hypersonic flow simulations［J］. Journal of Beijing University of Aeronautics and Astronautics， 2005， 31（3）： 274-277 （in Chinese）.
19	方芳，鲍麟，童秉纲. 基于斜驻点模型的剪切层撞击壁面流动及传热特性［J］. 物理学报， 2020， 69（21）： 214401.
	FANG F， BAO L， TONG B G. Heat transfer characteristics of shear layer impinging on wall based on oblique stagnation-point model［J］. Acta Physica Sinica， 2020， 69（21）： 214401 （in Chinese）.
20	WHITE F M. Viscous fluid flow［M］. 3rd ed. New York： McGraw-Hill， 2006： 26， 225-228， 505-506.
21	TSIEN H S. Superaerodynamics， mechanics of rarefied gases［J］. Journal of the Aeronautical Sciences， 1946， 13（12）： 653-664.
22	张涵信. 关于CFD高精度保真的数值模拟研究［J］. 空气动力学学报， 2016， 34（1）： 1-4.
	ZHANG H X. Investigations on fidelity of high order accurate numerical simulation for computational fluid dynamics［J］. Acta Aerodynamica Sinica， 2016， 34（1）： 1-4 （in Chinese）.
23	GNOFFO P A. An upwind-biased， point-implicit relaxation algorithm for viscous， compressible perfect-gas flows： NASA TP-2953［R］. Washington， D.C.： NASA， 1990.
24	HOLDEN M， MOSELLE J， WIETING A， et al. Studies of aerothermal loads generated in regions of shock/shock interaction in hypersonic flow［C］∥ 26th Aerospace Sciences Meeting. Reston： AIAA， 1988.
25	MUYLAERT J， WALPOT L， HAEUSER J， et al. Standard model testing in the European High Enthalpy Facility F4 and extrapolation to flight［C］∥ 28th Joint Propulsion Conference and Exhibit. Reston： AIAA， 1992.
26	王勇达. 典型外形高超声速气动热数值模拟的网格无关性研究［D］. 绵阳：西南科技大学， 2020： 16-63.
	WANG Y D. Study on grid independence in numerical simulation of hypersonic aerodynamic heat for typical configuration［D］. Mianyang： Southwest University of Science and Technology， 2020： 16-63 （in Chinese）.
27	黎作武. 近似黎曼解对高超声速气动热计算的影响研究［J］. 力学学报， 2008， 40（1）： 19-25.
	LI Z W. Study on the dissipative effect of approximate Riemann solver on hypersonic heat flux simulation［J］. Chinese Journal of Theoretical and Applied Mechanics， 2008， 40（1）： 19-25 （in Chinese）.
28	周伟江，姜贵庆. 迎风TVD格式在粘性流计算中的应用研究与改进［J］. 计算物理， 1999， 16（4）： 401-408.
	ZHOU W J， JIANG G Q. The study and modification of upwind TVD scheme for computing viscous flows［J］. Chinese Journal of Computation Physics， 1999， 16（4）： 401-408 （in Chinese）.

[1]	You WU, Bing CHEN, Qingchun YANG, Xu XU. Effects of thermal nonequilibrium on hydrocarbon⁃fueled scramjets [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(11): 529399-529399.
[2]	Weimin WANG, Dongfang HU. Review on non⁃contact dynamic stress measurement methods of rotating blades [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(22): 28516-028516.
[3]	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.
[4]	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.
[5]	LIAO Wenhe, TIAN Wei, LI Bo, LI Pengcheng, ZHANG Wei, LI Yufei. Error compensation technology and its application progress of an industrial robot [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(5): 627142-627142.
[6]	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.
[7]	LIN Chuang, ZHENG Yu, GUANG Chenhan, WANG Yan, YANG Yang. Design implementation and error analysis of mass and centroid measurement of aircraft with wingspan [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(1): 224893-224893.
[8]	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.
[9]	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.
[10]	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.
[11]	JIA Hongyin, ZHANG Peihong, ZHAO Wei, ZHOU Guiyu, WU Xiaojun. Aerodynamic characteristics of vertical recovery of rocket sub-stage and influence of engine nozzle [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(2): 623995-623995.
[12]	GULJAINA Kazezkhan, XIANG Binbin, WANG Na, AILI Yusup, CHEN Maozheng, LI Ning, XUE Fei. Errors analysis of a subreflector adjustment mechanism for NSRT [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2020, 41(4): 423271-423271.
[13]	LI Jin, GENG Xiangren, CHEN Jianqiang, JIANG Dingwu, LI Hongzhe. Numerical simulation on DSMC quantum kinetic chemical reaction model [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(4): 122176-122176.
[14]	QI Zhongyang, WANG Yankui, WANG Lei, SHA Yongxiang. Effects of nose and afterbody of blunt body on side force [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(9): 121117-121117.
[15]	PENG Jun, ZHANG Zijian, ZHOU Kai, HU Zongmin, JIANG Zonglin. Effects of vibration excitation on shock reflections [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(8): 121055-121055.

Effect of grid strategy on numerical simulation results of aerothermal heating loads over hypersonic blunt bodies

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 14

References 28

Related Articles 15

Recommended Articles

Metrics

Comments