THE DEFORMATION AND VIBRATION OF TULIP LEAVES IN WIND
-
摘要: 树叶的空气动力与流固耦合特性研究在树木保护、新发电技术开发、太阳能帆板设计等方面具有重要意义.Vogel首次发现树叶在较高风速下具有形状重构以避免受损害的能力.Vogel实验时叶柄端部是简支的,与叶柄与树枝的自然连接方式不同.在本文的研究中,叶柄端部是固支的,叶片垂直悬挂,正面或反面迎风.在风速0~27 m/s范围内,存在两种叶片静止状态,即飞翼形稳定和锥形稳定;还有3种叶片振动状态,即低频摆动、第1和第2高频振动.这5种状态由5个临界风速决定.通过70余片树叶测试结果的统计,得到了树叶每个状态存在的概率,及每个临界风速的期望值.流动显示发现树叶变形后其尾流中存在旋涡脱落现象.天平测量发现叶片阻力系数随叶片雷诺数的增大而减小并逐渐接近于0.1.引入悬臂梁模型,采用测量的叶片气动力,对叶柄静态弯曲形状进行计算,结果表明当风速由0逐渐增至5 m/s时,叶柄向下游弯曲迅速;但风速由5 m/s进一步增大时,向下游的弯曲则变慢.Abstract: The study of aerodynamic and solid-fluid coupling characteristics of tree leaves is of significance in tree protection, new power generation technology and solar panel design. Vogel first observed that a tree leaf could reconfigure itself at high winds to avoid damage. Vogel's leaf was freely supported at its petiole end, which is quite different from the natural way of petiole-branch connection. In our study, the leaf was clamped at the end of its petiole. The lamina was vertically hanging, with its front or back surface facing wind. Two types of lamina steady status, i.e, wing steady and conic steady, three types of lamina vibration, i.e, low frequency sway, 1st and 2nd high frequency vibration, and 5 critical wind speeds were observed in the range of wind speed 0~27 m/s. The probability of existance of every status and the expected value of each critical wind speed were obtained by statistics of the results of more than 70 leaves. The phenomenon of vortex shedding from a deformed leaf was found by flow visualization. Wind tunnel balance measurement revealed that the leaf drag coefficient decreased with the increase of lamina Re, and finally reached 0.1. A cantilevered beam model was introduced, and the measured aerodynamic force on the lamina was used to simulate the static bending curve of a petiole. Results showed that, the downstream bending increased rapidly with the increase of wind speed from 0 to 5 m/s, but it slowed down from 5 m/s to higher ones.
-
Key words:
- tree leaves /
- reconfiguration /
- vibration /
- critical wind speed
-
表 1 正面F和反面B迎风时各临界风速存在的概率
Table 1. Probability of existence of each critical wind speed, F-front surface facing wind, B-back surface facing wind
表 2 正面F和反面B迎风时各状态存在的概率
Table 2. Probability of existence of each status, F-front surface facing wind, B-back surface facing wind
表 3 正面F和反面B迎风时各临界风速期望值
Table 3. Expected values of each critical wind speed F-front surface facing wind, B-back surface facing wind
-
[1] Ennos AR. Compliance in plants//Jenkins CHM ed. Compliant Structures in Nature and Engineering, 21-40. Montana:WIT Press, 2005 [2] Vogel S. The Life of A Leaf, 204-225. Chicago:The University of Chicago Press, 2012 [3] Hadhazy A. Power plants:Artificial trees that harvest sun and wind to generate electricity. Scientific American, 2009, 306(5):31-32 https://www.scientificamerican.com/article/artificial-trees-harvest-sun-and-wind-energy/ [4] Sharif S, Gentry TR, Yen J, et al. Transformative solar panels:a multidisciplinary approach. International Journal of Architectural Computing, 2013, 11(2):227-245 doi: 10.1260/1478-0771.11.2.227 [5] Schindler D, Bauhus J, Mayer H. Wind effects on trees. European Journal of Forest Research, 2012, 131:159-163 doi: 10.1007/s10342-011-0582-5 [6] Vogel S. Drag and reconfiguration of broad leaves in high winds. Journal of Experimental Botany, 1989, 40(217):941-948 https://www.researchgate.net/profile/Steven_Vogel3/publication/245974119_Drag_and_Reconfiguration_of_Broad_Leaves_in_High_Winds/links/55a4fdde08aef604aa041490.pdf [7] Miller LA, Santhanakrishnan A, Jones S, et al. Reconfiguration and the reduction of vortex-induced vibrations in broad leaves. Journal of Experimental Biology, 2012, 215:2716-2727 doi: 10.1242/jeb.064501 [8] Speck O. Field measurements of wind speed and reconfiguration in Arundo Donax (Poaceae) with estimates of drag forces. American Journal of Botany, 2003, 90(8):1253-1256 doi: 10.3732/ajb.90.8.1253 [9] Schouveiler L, Boudaoud A. The rolling up of sheets in a steady flow. Journal of Fluid Mechanics, 2006, 563:71-80 doi: 10.1017/S0022112006000851 [10] Alben S, Shelley M, Zhang J. Drag reduction through self-similar bending of a flexible body. Nature, 2002, 420:479-481 doi: 10.1038/nature01232 [11] Gosselin FP, de Langre E. Drag reduction by reconfiguration of a poroelastic system. Journal of Fluids and Structures, 2011, 27(7): 1111-1123 doi: 10.1016/j.jfluidstructs.2011.05.007 [12] Shelley MJ, Zhang J. Flapping and bending bodies interacting with fluid flows. Annual Review of Fluid Mechanics, 2011, 43:449-465 doi: 10.1146/annurev-fluid-121108-145456 [13] Albayrak I, Nikora V, Miler O, et al. Flow-plant interactions at leaf, stem and shoot scales:drag, turbulence, and biomechanics. Aquatic Science, 2014, 76:269-294 doi: 10.1007/s00027-013-0335-2 [14] Taneda S. Waving motions of flags. Journal of the Physical Society of Japan, 1968, 24:392-401 doi: 10.1143/JPSJ.24.392 [15] Posada JM, Lechowicz MZ, Kaoru Kitajima K. Optimal photosynthetic use of light by tropical tree rows achieved by adjustment of individual leaf angles and nitrogen content. Annals of Botany, 2009, 103:795-805 https://www.researchgate.net/publication/23798136_Optimal_photosynthetic_use_of_light_by_tropical_tree_crowns_achieved_by_adjustment_of_individual_leaf_angles_and_nitrogen_content [16] Pisek J, Ryu Y, Alikas K. Estimating leaf inclination and G-function from leveled digital camera photography in broadleaf canopies. Trees, 2011, 25:919-924 doi: 10.1007/s00468-011-0566-6 [17] McNeil BE, Pisek J, Lepisk H, et al. Measuring leaf angle distribution in broadleaf canopies using UAVs. Agricultural and Forest Meteorology, 2016, 218-219:204-208 doi: 10.1016/j.agrformet.2015.12.058 [18] Hernandez LF. Leaf angle and light interception in sunflower (Helianthus annuus L.). Role of the petiole's mechanical and anatomical properties. Phyton-International Journal of Experimental Botany, 2010, 79:109-115 http://www.oalib.com/paper/985374 [19] 张富云, 赵燕.鹅掌楸属植物研究进展.云南农业大学学报, 2005, 20(5):697-701 http://www.cnki.com.cn/Article/CJFDTOTAL-YNDX200505021.htm [20] 王沁峰, 张晓平, 王乐林等.二球悬铃木展叶期叶片生长及3个生理指数的动态变化.植物资源与环境学报, 2009, 18(2):94-96 http://www.cnki.com.cn/Article/CJFDTOTAL-ZWZY200902016.htmWang Qinfeng, Zhang Xiaoping, Wang Lelin, et al. Dynamic changes of leaf growth and three physiological indexes of Platanus acerifolia during leaf expansion stage. Journal of Plant Resources and Environment, 2009, 18(2):94-96(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-ZWZY200902016.htm [21] 曹利祥, 袁方, 石喜乐等.悬铃木早期萌芽及叶片生长的动态变化.北方园艺, 2011, 24:95-96 http://www.cnki.com.cn/Article/CJFDTOTAL-BFYY201124034.htm [22] Niinemets U, Fleck S. Petiole mechanics, leaf inclination, morphology, and investment in support in relation to light availability in the canopy of liriodendron tulipifera. Oecologia, 2012, 132(1):21-33 doi: 10.1007/s00442-002-0902-z [23] Niklas KJ. A mechanical perspective on foliage leaf form and function. New Phytologist, 1999, 143:19-31 doi: 10.1046/j.1469-8137.1999.00441.x [24] Scholes RJ, Prost PGH, Tian Y. Canopy structure in savannas along a moisture gradienton Kalahari sands. Global Change Biology, 2004, 10:292-302 doi: 10.1046/j.1365-2486.2003.00703.x [25] Shao CP, Chen YJ, Lin JZ. Wind induced deformation and vibration of a Platanus acerifolia leaf. Acta Mechnica Sinica, 2012, 28(3): 583-594 doi: 10.1007/s10409-012-0074-y [26] Tadrist L, Julio K, Saudreau M, et al. Leaf flutter by torsional galloping:Experiments and model. Journal of Fluids and Structures, 2015, 56:1-10 doi: 10.1016/j.jfluidstructs.2015.04.001 [27] Roshko A. On the wake and drag of bluff bodies. Journal of Aeronautical Science, 1955, 22:124-132 doi: 10.2514/8.3286 [28] Williamson CHK, Govardhan R. Vortex-induced vibrations. Annual Review of Fluid Mechanics, 2004, 36(1):413-455 doi: 10.1146/annurev.fluid.36.050802.122128 [29] Williamson CHK, Govardhan R. A brief review of recent results in vortex-induced vibrations. Journal of Wind Engineering and Industrial Aerodynamics, 2008, 96(6):713-735 https://www.researchgate.net/publication/222951736_A_brief_review_of_recent_results_in_vortex-induced_vibrations [30] Niklas KJ. The elastic moduli and mechanics of Populas tremuloides (Salicaceae) petioles in bending and torsion. American Journal of Botany, 1991, 78(7):989-996 doi: 10.2307/2445178 -