Influence of Initial Angle on the Freely Falling Plates
-
摘要: 平板的自由下落是一个经典的流体力学-动力学耦合问题，且具有明显的非线性特性.针对二维平板自由下落的非线性特性，文章通过耦合求解N-S方程和运动方程，以期认识其非线性特征.从不同初始角度对平板自由下落状态和轨迹的影响出发，分析了运动状态的相轨线和频谱特性，以及其中的非线性系统特征.研究发现，在平板自由下落初期，不同初始角度下平板呈现不同的运动状态和轨迹，常为非周期性摆动或小幅翻滚运动.在自由下落后期，平板自由下落最终呈现周期性摆动或翻滚运动，运动模态归为一致，初始角度对该模态没有影响.Abstract: The free fall of plates is a classic problem of fluid mechanics-dynamics coupling, which has obvious nonlinear characteristics. According to the nonlinear characteristics of 2D freely falling plates, the equations of motion coupled with the Navier-Stokes equations were numerically solved in this paper. The motion states and trajectories of freely falling plates at different initial angles were compared, and characteristics of the nonlinear system were studied with phase trajectories and spectrum analysis method. The research results indicate that there are differences on motion states and trajectories with different initial angles in initial stage of free fall, and these motions are non-regular fluttering and small-amplitude tumbling. However, the motions finally turn into periodic fluttering or tumbling in later stage of free fall. The initial angle has little effect on the motion mode.
-
Key words:
- freely falling plates /
- initial angle /
- nonlinear system /
- fluttering /
- tumbling
-
图 1 坐标系和状态变量示意图
Figure 1. Definition of the state variables and sketchof the reference frame
图 6 无量纲速度和气动力变化曲线(I+=0.03, θ0=20°)
Figure 6. Dimensionless velocities and aerodynamic force components (I+=0.03, θ0=20°)
图 7 θ-ω+相轨迹和u+-v+曲线(I+=0.03, θ0=0°, θ0=90°)
Figure 7. θ versus ω+ and u+ versus v+(I+=0.03, θ0=0°, θ0=90°)
图 14 无量纲速度和气动力变化曲线(I+=1.0, θ0=20°)
Figure 14. Dimensionless velocities and aerodynamic force components (I+=1.0, θ0=20°)
-
[1] Maxwell J C. On a particular case of the descent of a heavy body in a resisting medium[J]. Cambridge and Dublin Mathematics Journal, 1853, 9: 115-118. [2] Andersen A, Pesavento U, Wang Z J. Unsteady aerodynamics of fluttering and tumbling plates[J]. Journal of Fluid Mechanics, 2005, 541: 65-90. doi: 10.1017/S002211200500594X [3] Pesavento U, Wang Z J. Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation[J]. Physical Review Letters, 2004, 93(14): 144501. doi: 10.1103/PhysRevLett.93.144501 [4] Belmonte A, Eisenberg H, Moses E. From flutter to tumble: inertial drag and Froude similarity in falling paper[J]. Physical Review Letters, 1998, 81(2): 345-348. doi: 10.1103/PhysRevLett.81.345 [5] Assemat P, Fabre D, Magnaudet J. The onset of unsteadiness of two-dimensional bodies falling or rising freely in a viscous fluid: a linear study[J]. Journal of Fluid Mechanics, 2012, 690: 173-202. doi: 10.1017/jfm.2011.419 [6] Wan H, Dong H B, Liang Z X. Vortex formation of freely falling plates[R]. AIAA 2012-1079, 2012. [7] Tian R J, Shu F J. Experimental study of the fluid and structure interaction for gravity driven falling plates[C]. Proceedings of the 67th Annual Meeting of the APS Division of Fluid Dynamics, San Francisco: APS, 2014. [8] Tian R J. Experimental and theoretical study of fluid-structure interactions in plunging hydrofoils and gravity-driven falling plates[D]. Las Cruces: New Mexico State University, 2015: 77-85. [9] Kubota Y, Mochizuki O. Numerical investigation of aerodynamic characteristics by a rotating thin plate[J]. World Journal of Mechanics, 2015, 5(3): 42-47. doi: 10.4236/wjm.2015.53005 [10] 周琪. 自由下落平板非定常致力机理研究[D]. 上海: 上海交通大学, 2012.Zhou Q. The study of unsteady aerodynamics of freely falling plates[D]. Shanghai: Shanghai Jiao Tong University, 2012(in Chinese). [11] 蔡琛芳, 梁彬. 平板自由下落的数值模拟[J]. 空气动力学学报, 2019, 37(3): 400-405, 411. doi: 10.7638/kqdlxxb-2016.0129Cai C F, Liang B. Numerical simulation of freely falling plates[J]. Acta Aerodynamica Sinica, 2019, 37(3): 400-405, 411(in Chinese). doi: 10.7638/kqdlxxb-2016.0129 [12] Lentink D, Dickson W B, van Leeuwen J L, et al. Leading-edge vortices elevate lift of autorotating plant seeds[J]. Science, 2009, 324(5933): 1438-1440. doi: 10.1126/science.1174196 [13] Lee E J, Lee S J. Effect of initial attitude on autorotation flight of maple Samaras (Acer palmatum)[J]. Journal of Mechanical Science and Technology, 2016, 30(2): 741-747. doi: 10.1007/s12206-016-0129-2 [14] Kim Y, Peskin C S. A penalty immersed boundary method for a rigid body in fluid[J]. Physics of Fluids, 2016, 28(3): 033603. doi: 10.1063/1.4944565 [15] Magnaudet J, Eames I. The motion of high-Reynolds-number bubbles in inhomogeneous flows[J]. Annual Review of Fluid Mechanics, 2000, 32: 659-708. doi: 10.1146/annurev.fluid.32.1.659 [16] 孙茂. 动物飞行的空气动力学[J]. 空气动力学学报, 2018, 36(1): 122-128. doi: 10.7638/kqdlxxb-2017.0195Sun M. Aerodynamics of animal flight[J]. Acta Aerodynamica Sinica, 2018, 36(1): 122-128(in Chinese). doi: 10.7638/kqdlxxb-2017.0195 [17] 鲍锋, 邹赫, 曾华轮, 等. 扑翼尾流脱落涡特性的PIV实验研究[J]. 气体物理, 2017, 2(1): 48-56. doi: 10.19527/j.cnki.2096-1642.2017.01.006Bao F, Zou H, Zeng H L, et al. Experimental investigation with PIV on characteristics of shedding vortices in wake of flapping wings[J]. Physics of Gases, 2017, 2(1): 48-56(in Chinese). doi: 10.19527/j.cnki.2096-1642.2017.01.006 [18] 贾博博, 宫武旗. 串列扑翼间前缘涡在不同间距下对平均推力的影响[J]. 气体物理, 2017, 2(3): 44-53. doi: 10.19527/j.cnki.2096-1642.2017.03.006Jia B B, Gong W Q. Influence of leading-edge vortex on mean thrust of two plunging wings in tandem under different spacing distances[J]. Physics of Gases, 2017, 2(3): 44-53(in Chinese). doi: 10.19527/j.cnki.2096-1642.2017.03.006 [19] 黄安基. 非线性振动[M]. 成都: 西南交通大学出版社, 1993: 12-53.Huang A J. Nonlinear oscillations[M]. Chengdu: Southwest Jiaotong University Press, 1993: 12-53(in Chinese). [20] 关发明. 超声速平面混合层非线性失稳[D]. 北京: 中国航天空气动力技术研究院, 2008.Guan F M. Nonlinear instability of supersonic planar mixing layer[D]. Beijing: China Academy of Aerospace Aerodynamics, 2008(in Chinese). -
下载:
点击查看大图
图(15)
计量
- 文章访问数: 181
- HTML全文浏览量: 28
- PDF下载量: 22
- 被引次数: 0
邮件订阅
RSS