铁饼飞行轨迹的CFD/RBD耦合仿真与投掷策略分析

CFD/RBD flight simulation and throwing strategy analysis of discus

摘要

研究铁饼投掷过程的空气动力学和飞行力学问题、精确预测铁饼的飞行轨迹，可以指导运动员运用更优的投掷策略来提高比赛成绩。本研究采用数值虚拟飞行仿真技术，耦合求解非定常雷诺平均N-S方程和刚体动力学方程，充分考虑铁饼飞行过程中显著的气动/运动非定常耦合效应，对不同铁饼投掷参数情况下的飞行轨迹和运动姿态进行了仿真预测，分析了自转角速度、抛投姿态角等投掷参数对铁饼飞行距离的影响，并筛选出使铁饼的飞行距离最远的投掷参数组合。数值仿真结果表明：铁饼在大迎角失速飞行段存在显著的气动迟滞现象，失速和气动回滞能够减小铁饼在自旋飞行中的进动速度，进而对铁饼的飞行轨迹产生显著的影响。因此，精确计入铁饼气动力的迟滞效应对于准确预测铁饼飞行轨迹和姿态非常关键。通过增加自旋角速度，并配置适当的初始滚转角和初始俯仰角，能够合理控制铁饼飞行的进动速度，利用气动力延长铁饼飞行滞空时间，进而有效提升铁饼的飞行距离。

Abstract

Studying the aerodynamics and flight mechanics of discus throwing and accurately predicting trajectory of the discus can help athletes improve their performance in competition by using optimal throwing strategies. In this study, numerical virtual flight simulation is adopted to solve unsteady Reynolds average Navier-Stokes equations combined with rigid body dynamics equations, taking into full consideration of unsteady effects caused by coupling aerodynamics and motion. By predicting the trajectories and motion attitude of discus under different throwing parameters, such as spin rate and initial attitude angles, the influence on discus flight distance is investigated, and the optimal combination of throwing parameters that maximizes the flight distance is determined. The results reveal that significant aerodynamic hysteresis exists in discus stall under a high angle of attack. However, the stall and aerodynamic hysteresis can reduce the precession speed of the discus and significantly influence discus trajectory. Therefore, accurately simulating the aerodynamic hysteresis is crucial for predicting trajectory and motion attitude of discus. By increasing spin rate and specifying appropriate initial roll and pitch angles, the precession speed of the discus can be reasonably controlled, and the aerodynamic force can extend the hang time of discus. Thus discus flight distance can be effectively improved.

关键词

虚拟飞行仿真 / 动态气动力 / 迟滞效应 / 大迎角 / 进动 / 铁饼

Key words

virtual flight / dynamic aerodynamics / hysteresis / high angles of attack / precession / discus

参考文献

[1] GANSLEN R V. Aerodynamic and mechanical forces in discus flight[J]. The athletic journal, 1964: 44-50.

[2] FROHLICH C. Aerodynamic effects on discus flight[J]. American journal of physics, 1981, 49(12): 1125-1132.

[3] SOONG T C. The dynamics of discus throw[J]. Journal of applied mechanics, 1976, 43(4): 531-536.

[4] HUBBARD M, CHENG K B. Optimal discus trajectories[J]. Journal of biomechanics, 2007, 40(16): 3650-3659.

[5] 饶秋磊, 韩意新. 大迎角气动力建模与失速/尾旋模态仿真[J]. 应用力学学报, 2018, 35(3): 472-478.

[6] RAO Qiulei, HAN Yixin. High angle of attack aerodynamic modeling and simulation and analysis of stall/spin mode[J]. Chinese journal of applied mechanics, 2018, 35(3): 472-478(in Chinese).

[7] 饶秋磊, 张奇. 基于最优化理论的稳态尾旋求解方法[J]. 应用力学学报, 2019, 36(4): 759-764.

[8] RAO Qiulei, ZHANG Qi. Solving method of steady state spin based on optimization theory[J]. Chinese journal of applied mechanics, 2019, 36(4): 759-764(in Chinese).

[9] 齐贤德, 程昭武, 白存儒. 一种圆翼飞行器风洞实验与随动机制[J]. 南京航空航天大学学报, 2015, 47(4): 613-618.

[10] QI Xiande, CHENG Zhaowu, BAI Cunru. Wind tunnel experiment and passive rotation of round wing aircraft[J]. Journal of Nanjing University of Aeronautics & Astronautics, 2015, 47(4): 613-618(in Chinese).

[11] SERAJ S, MARTINS J R R A. Predicting the high-angle-of-attack characteristics of a delta wing at low speed[J]. Journal of aircraft, 2022, 59(4): 1071-1081.

[12] 薛臣, 周洲, 李旭, 等. 小振幅振动翼型升力迟滞环变向的成因分析[J]. 航空学报, 2019, 40(5): 129-143.

[13] XUE Chen, ZHOU Zhou, LI Xu, et al. Factors analysis of lift hysteresis loop direction changing for small amplitude oscillating airfoils[J]. Acta aeronautica et astronautica Sinica, 2019, 40(5): 129-143(in Chinese).

[14] 王皓田, 朱杨柱, 车学科, 等. S1223翼型低雷诺数下分离泡及气动特性[J]. 空气动力学学报, 2021, 39(3): 90-98.

[15] WANG Haotian, ZHU Yangzhu, CHE Xueke, et al. Separation bubble and aerodynamic characteristics of S1223 airfoil at low Reynolds numbers[J]. Acta aerodynamica Sinica, 2021, 39(3): 90-98(in Chinese).

[16] 赵炜, 祝小平, 周洲, 等. 时变风场中低雷诺数翼型气动特性研究[J]. 西北工业大学学报, 2019, 37(1): 177-185.

[17] ZHAO Wei, ZHU Xiaoping, ZHOU Zhou, et al. Exploring on aerodynamic characteristics of low Reynolds number airfoil in time-varying wind field[J]. Journal of Northwestern Polytechnical University, 2019, 37(1): 177-185(in Chinese).

[18] POTTS J R, MASTERS D. Validation of the aerodynamic loading on basic flying disc geometries derived from CFD simulations[J]. Procedia engineering, 2015, 112: 400-405.

[19] SEO K, OHTA K, OHGI Y, et al. Aerodynamic hysteresis of a discus[J]. Procedia engineering, 2013, 60: 294-299.

[20] 杨可, 蒋卫民, 熊健, 等. 飞翼模型高速风洞PIV试验研究[J]. 空气动力学学报, 2015, 33(3): 313-318.

[21] YANG Ke, JIANG Weimin, XIONG Jian, et al. Experimental research on flying-wing by PIV in high speed wind tunnel[J]. Acta aerodynamica Sinica, 2015, 33(3): 313-318(in Chinese).

[22] ZHANG L P, CHANG X H, MA R, et al. A CFD-based numerical virtual flight simulator and its application in control law design of a maneuverable missile model[J]. Chinese journal of aeronautics, 2019, 32(12): 2577-2591.

[23] ZHANG L P, ZHAO Z L, MA R, et al. Validation of numerical virtual flight system with wind-tunnel virtual flight testing[J]. AIAA journal, 2020, 58(4): 1566-1579.

[24] WANG N H, MA R, CHANG X H, et al. Numerical virtual flight simulation of quasi-cobra maneuver of a fighter aircraft[J]. Journal of aircraft, 2021, 58(1): 138-152.

[25] 周东辉, 贾会霞, 施红辉, 等. 高速航行体齐射出水过程的空化与运动特性研究[J]. 空气动力学学报, 2023, 41(2): 64-74.

[26] ZHOU Donghui, JIA Huixia, SHI Honghui, et al. Research on cavitation and motion characteristics of high-speed vehicles exiting water in underwater salvo[J]. Acta aerodynamica Sinica, 2023, 41(2): 64-74(in Chinese).

[27] 施红辉, 周东辉, 周栋, 等. 两连发射弹出入水的轴对称超空泡流动特性[J]. 空气动力学学报, 2020, 38(6): 1064-1074.

[28] SHI Honghui, ZHOU Donghui, ZHOU Dong, et al. Flow characteristics of axisymmetric supercavitation induced by two successively fired projectiles in water entry and exit[J]. Acta aerodynamica Sinica, 2020, 38(6): 1064-1074(in Chinese).

[29] 陈晓, 曹勇, 黄桥高, 等. 非正弦升沉运动对扑翼自主推进的影响[J]. 西北工业大学学报, 2022, 40(2): 281-287.

[30] CHEN Xiao, CAO Yong, HUANG Qiaogao, et al. Nonsinusoidal motion effect on a self-propelled heaving foil[J]. Journal of Northwestern Polytechnical University, 2022, 40(2): 281-287(in Chinese).

[31] 吴翰, 王正平, 周洲, 等. 无人机伞降回收十二自由度模型建立与仿真[J]. 西北工业大学学报, 2020, 38(1): 68-74.

[32] WU Han, WANG Zhengping, ZHOU Zhou, et al. Establishment and simulation of twelve-degree-of-freedom model for UAV parachute recovery system[J]. Journal of Northwestern Polytechnical University, 2020, 38(1): 68-74(in Chinese).

[33] 黄宇, 阎超, 席柯, 等. 基于数值虚拟飞行技术的飞行器动态特性分析[J]. 航空学报, 2016, 37(8): 2525-2538.

[34] HUANG Yu, YAN Chao, XI Ke, et al. Analysis of flying vehicle's dynamic characteristics based on numerical virtual flight technology[J]. Acta aeronautica et astronautica Sinica, 2016, 37(8): 2525-2538(in Chinese).

[35] LIU Y, WANG G, YE Z Y. Dynamic mode extrapolation to improve the efficiency of dual time stepping method[J]. Journal of computational physics, 2018, 352: 190-212.

[36] JAMESON A. Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings[C]// 10th Computational Fluid Dynamics Conference. Reston, VA, USA: AIAA, 1991:AIAA 1991-1596.

[37] 刘世前. 现代飞机飞行动力学与控制[M]. 2版. 上海: 上海交通大学出版社, 2018.

[38] 韩子鹏. 弹箭外弹道学[M]. 北京: 北京理工大学出版社, 2014.

[39] WANG G, ZENG Z, SUO Q. Trajectory simulation of a spinning projectile based on variable step size CFD/RBD method[C]// AIAA Atmospheric Flight Mechanics Conference. Reston, VA, USA: AIAA, 2015: AIAA 2015-0522.

[40] WANG G, CHEN X, XING Y, et al. Multi-body separation simulation with an improved general mesh deformation method[J]. Aerospace science and technology, 2017, 71: 763-771.

[41] 王刚, 邢宇, 朱亚楠. 旋转弹气动力建模与飞行轨迹仿真[J]. 航空学报, 2017, 38(1): 103-112.

[42] WANG Gang, XING Yu, ZHU Yanan. Aerodynamic modeling and flight trajectory simulation of spinning projectile[J]. Acta aeronautica et astronautica Sinica, 2017, 38(1): 103-112(in Chinese).

[43] 中华人民共和国国家质量监督检验检疫总局, 中国国家标准化管理委员会. 铁饼:GB/T 23123-2008[S]. 北京: 中国标准出版社, 2008.

[44] BARTLETT R M. The biomechanics of the discus throw:a review[J]. Journal of sports sciences, 1992, 10(5): 467-510.

基金资助

国家自然科学基金资助项目(U2141254)