A COMPARATIVE STUDY OF TWO TURBULENCE MODELS FOR MAGNUS EFFECT IN SPINNING PROJECTILE

doi:10.6052/0459-1879-16-151

Abstract

Abstract:

Magnus force and moment must be predicted precisely during calculating trajectories and designing rotating projectiles.Domestic studies have focused on adult spin projectile, and foreign studies have not compared turbulence model utility in spinning wind-body combination either.This paper simulated the flow field around a spinning wind-body combination by solving unsteady compressible three dimensional Navier-Stokes equations with dual time step method.At the same time the discrepancy between Splalrt-Allmaras (SA) and k-!shear stress transport (SST) turbulence models are studied.For both turbulence models, dynamic coefficients have a good agreement with the Arnold Engineering Development Center (AEDC) experimental data and Army Research Laboratory (ARL) computational data.Flow field parameters such as velocity gradient, pressure magnitude, show significant change in the latter half profile due to spin.Distortion of boundary layer in middle and rear part is conspicuous.Asymmetric distortion of circumferential surface pressure and shear stress is the fundamental reasons for the Magnus effect.Flow field parameters on the left side of body show larger variance between SA and SST turbulence models than the right side, indicating that speed pulse and pressure fluctuation are stronger on the left.The turbulent viscosity coefficient near the wall computed by SA is larger than SST.According to the slice of y=0 m, surface pressure shows SA is smaller than SST, reaching a maximum difference of 6%, and shear stress of SA is larger than SST, up to a maximum difference of 35%.The inhibition strength for flow separation indicates that SA is stronger than SST.

Key words:

turbulence model|wing-body combination|spinning projectile|Magnus effect|numerical simulation

CLC Number:

V211.3

Shi Lei, Yang Yunjun, Zhou Weijiang. A COMPARATIVE STUDY OF TWO TURBULENCE MODELS FOR MAGNUS EFFECT IN SPINNING PROJECTILE[J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(1): 84-92.

References

1 臧国才, 李树常. 弹箭空气动力学. 北京:兵器工业出版社, 1984:260-262(Zang Guocai, Li Shuchang. Aerodynamics of Projectiles and Missiles. Beijing:The Publishing House of Ordnance Industry, 1984:260-262(in Chinese))

2 苗瑞生, 吴甲生. 旋转空气动力学. 力学进展, 1987, 17(4):479-488(Miao Ruisheng, Wu Jiasheng. Aerodynamics of spinning projectiles. Advances in Mechanics, 1987, 17(4):479-488(in Chinese))

3 Walter BS, Harry AD, Lyle DK, et al. Computations of magnus effects for a yawed spinning body of revolution. AIAA Journal, 1978, 16(7):687-692

4 Sturek WB, Schiff LB. Computations of the magnus effect for slender bodies in supersonic flow. AIAA-80-1586, 1980

5 Nietubicz CJ, Sturek WB, Heavey KR. Computations of projectile magnus effect at transonic velocities. AIAA Journal, 1985, 23(7):998-1004

6 Pechier M, Guillen P, Cayzac R. A combined theoretical-experimental investigation of magnus effects. AIAA-98-2797, 1998

7 DeSpirito J. CFD prediction of Magnus effect in subsonic to supersonic flight. AIAA-2008-427, 2008

8 Vishal AB. Numerical prediction of roll damping and Magnus dynamic derivatives for finned projectiles at angle of attack. AIAA-2012-2905, 2012

9 吴甲生, 雷娟棉. 制导兵器气动布局与气动特性. 北京:国防工业出版, 2008:79-80(Wu Jiasheng, Lei Juanmian. Aerodynamic Configuration and Characteristics of Guided Weapons. Beijing:National Defense Industry Press, 2008:79-80(in Chinese))

10 王智杰, 陈伟芳, 李浩. 旋转弹丸空气动力特性数值解法. 国防科技大学学报, 2003, 25(4):15-19(Wang Zhijie, Chen Weifang, Li Hao. Numerical solution ofthe aerodynamic projectiles of the rotating projectiles. Journalof National University of Defense Technology, 2003, 25(4):15-19(in Chinese))

11 高旭东, 武晓松, 王晓鸣. 高速旋转侧喷流场数值分析. 弹道学报, 2005, 17(2):8-12(Gao Xudong, Wu Xiaosong, Wang Xiaoming. A numerical study on high-speed spinning and lateral jet flow field. Journal of Ballistics, 2005, 17(2):8-12(in Chinese))

12 宋琦, 杨树兴, 徐勇等. 滚转状态下卷弧翼火箭弹气动特性的数值模拟. 固体火箭技术, 2008, 31(6):552-560(Song Qi, Yang Shuxing, Xu Yong, et al. Numerical simulation on aerodynamic characteristicsof rolling rocketwith wraparound fins. Journal of Solid Rocket Technology, 2008, 31(6):552-560(in Chinese))

13 郁伟, 张小兵. 旋转弹丸在复杂激波影响下气动特性数值模拟与分析. 南京理工大学学报, 2012, 36(4):624-628(Yu Wei, Zhang Xiaobing. Numerical simulation and analysis of aerodynamic characteristics of spinning projectile while flying over complex shock flow fields. Journal of Nanjing University of Science and Technology, 2012, 36(4):624-628(in Chinese))

14 邓帆, 陈少松, 陶钢. 带栅格翼导弹超声速阶段滚转阻尼导数的数值研究. 空气动力学学报, 2012, 30(2):151-156(Deng Fan, Chen Shaosong, Tao Gang. CFD analysis of roll damping derivatives for missile with grid fins at supersonic speeds. Acta Aerodynamica Sinica, 2012, 30(2):151-156(in Chinese))

15 陈东阳, Laith KA, 芮筱亭. 旋转弹箭气动导数与气动热仿真计算. 计算机仿真, 2014, 31(5):26-30(Chen Dongyang,Laith KA,Rui Xaoting. Aerodynamic derivative and aerodynamic heatingsimulation and computation of spinning vehicle. Computer Emulation, 2014, 31(5):26-30(in Chinese))

16 闫超. 计算流体力学方法及应用. 北京:北京航空航天大学出版社, 2006:19-25(Yan Chao. Theory and Application of Computational Fluid Dynamics. Beijing:BUAA Press, 2006:19-25(in Chinese))

17 Spalart PR, Allmaras SR. A one-equation turbulence model for aerodynamics flows. AIAA-92-0439, 1992

18 Menter FR. Two equation eddy viscosity turbulence models for engineering applications. AIAA Journal, 1994, 32:598-1605

19 Roe PL. Approximate riemann solvers, parameter vector and difference scheme. Journal of Computational Physics, 1981, 43:357-372

20 Venkatafrishnan V, Jameson A. Computation of unsteady transonic flows by the solution of euler equations. AIAA Journal, 1988, 26(8):974-981

21 Eleuterio FT. Riemann Solvers and Numerical Methods for Fluid Dynamics. Berlin:Springer-Verlag, 1999:341-350

22 杨云军. 飞行器非稳定运动的流动物理与动力学机制. 北京:中国航天空气动力技术研究院, 2009:35-42(Yang Yunjun. Flow Physics and Dynamic Mechanism on Unsteady Motions of the Vehicles. Beijing:China Academy of Aerospace Aerodynamics, 2009:35-42(in Chinese))

23 Jameson A. Time dependent calculations using multigrid with application to unsteady flows past airfoil and wings. AIAA-91-1596, 1991

24 Evelyn O, Peter E. Parameter investigation with line-implicit lower-upper symmetric gauss-seidel on 3D stretched grids. AIAA-2014-2094, 2014

25 Leroy MJ. Experimental roll-damping, magnus, and static stability characteristics of two slender missile configurations at high angles of attack (0° to 90°) and Mach number 0.2 through 2.5. AEDC-TR-76-58, 1976

26 Li Z, Chen HX, Zhang YF, et al. Grid-convergence studyof two-dimensionaleuler solutions. Journal of Aircraft, 2016, 53(1):294-298

[1]	Kong Lingfa, Dong Yidao, Liu Wei. THE INFLUENCE OF GLOBAL-DIRECTION STENCIL ON GRADIENT AND HIGH-ORDER DERIVATIVES RECONSTRUCTION OF UNSTRUCTURED FINITE VOLUME METHODS ¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(5): 1334-1349.
[2]	. The Influence of Global-Direction Stencil on Gradient and High-Order Derivatives of Unstructured Finite Volume Methods [J]. Chinese Journal of Theoretical and Applied Mechanics, 0, 0(0): 0-0.
[3]	Luo Xin, Wu Songping. AN IMPROVED FIFTH-ORDER WENO-Z+ SCHEME ¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(6): 1927-1939.
[4]	Nianhua Wang, Xinghua Chang, Rong Ma, Laiping Zhang. VERIFICATION AND VALIDATION OF HYPERFLOW SOLVER FOR SUBSONIC AND TRANSONIC TURBULENT FLOW SIMULATIONS ON UNSTRUCTURED/HYBRID GRIDS¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 813-825.
[5]	Qiao Chenliang, Xu Heyong, Ye Zhengyin. CIRCULATION CONTROL ON WIND TURBINE AIRFOIL WITH BLUNT TRAILING EDGE [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 135-145.
[6]	Liu Huixiang, He Guoyi, Wang Qi. NUMERICAL STUDY ON THE AERODYNAMIC PERFORMANCE OF THEFLEXIBLE AND CORRUGATED FOREWING OF DRAGONFLY IN GILDINGFLIGHT [J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 94-102.
[7]	Shao Shuai, Li Ming, Wang Nianhua, Zhang Laiping. HIGH-ORDER DDG/FV HYBRID METHOD FOR VISCOUS FLOW SIMULATION ON UNSTRUCTURED/HYBRID GRIDS¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1470-1482.
[8]	Ye Youda, Zhang Hanxin, Jiang Qinxue, Zhang Xianfeng. SOME KEY PROBLEMS IN THE STUDY OF AERODYNAMIC CHARACTERISTICS OF NEAR-SPACE HYPERSONIC VEHICLES¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(6): 1292-1310.
[9]	Wan Yunbo, Ma Rong, Wang Nianhua, Zhang Laiping, Gui Yewei. ACCURATE AERO-HEATING PREDICTIONS BASED ON MUL-TI-DIMENSIONAL GRADIENT RECONSTRUCTION ON HYBRID UNSTRUCTURED GRIDS¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1003-1012.
[10]	Zhang Yang, Zou Jianfeng, Zheng Yao. AN IMPROVED GHOST-CELL IMMERSED BOUNDARY METHOD FOR SOLVING SUPERSONIC FLOW PROBLEMS [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 538-552.
[11]	Wang Nianhua, Li Ming, Zhang Laiping. ACCURACY ANALYSIS AND IMPROVEMENT OF VISCOUS FLUX SCHEMES IN UNSTRUCTURED SECOND-ORDER FINITE-VOLUME DISCRETIZATION [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 527-537.
[12]	Tong Fulin, Li Xin, Yu Changping, Li Xinliang. DIRECT NUMERICAL SIMULATION OF HYPERSONIC SHOCK WAVE AND TURBULENT BOUNDARY LAYER INTERACTIONS ¹⁾ [J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(2): 197-208.
[13]	Wang Nianhua, Zhang Laiping, Zhao Zhong, He Xin. ACCURACY VERIFICATION OF UNSTRUCTURED SECOND-ORDER FINITE VOLUME DISCRETIZATION SCHEMES BASED ON THE METHOD OF MANUFACTURED SOLUTIONS [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(3): 627-637.
[14]	Deng Kaiwen, Chen Haixin. HYBRID OPTIMIZATION ALGORITHM BASED ON DIFFERENTIAL EVOLUTION AND RBF RESPONSE SURFACE [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(2): 441-455.
[15]	Tong Fulin, Li Xinliangy, Tang Zhigong. NUMERICAL ANALYSIS OF UNSTEADY MOTION IN SHOCK WAVE/TRANSITIONAL BOUNDARY LAYER INTERACTION [J]. Chinese Journal of Theoretical and Applied Mechani, 2017, 49(1): 93-104.