THE DEFORMATION AND VIBRATION OF TULIP LEAVES IN WIND
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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.
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Key words:
- tree leaves /
- reconfiguration /
- vibration /
- critical wind speed
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图 2 所测试树叶叶片面积的概率分布
Figure 2. Probability density of lamina area of the tested tulip leaves
图 3 (a) 叶片悬挂于风洞中, (b) 集中力作用于叶柄悬臂梁模型
Figure 3. Sketch of (a) the leaf in wind tunnel, and (b) concentrated aerodynamic load on cantilevered beam model of the petiole
图 4 叶片反面迎风时其状态随风速的变化
Figure 4. The back surface facing the wind: status changes with wind speed
图 6 叶片正面迎风时各临界风速的概率密度
Figure 6. Probability densities of the critical wind speeds, with the front leaf surface facing wind
图 7 反面迎风时树叶的形状、方位及尾流变化侧图
Figure 7. Side view of the shape, orientation and wake of the leaf with its back surface fcaing wind
图 8 在叶柄固定棒下游0.4 m处测量的树叶尾流的横向流动图案
Figure 8. Upstream view of the transverse flow 0.4 m downstream of the leaf
图 9 正面迎风时各叶片阻力系数随雷诺数的变化
Figure 9. Drag coefficients of leaves vs Reynolds number, with the front surface facing wind
图 10 不同树叶的叶片角随风速的变化, 其中叶柄弹性模量E=600 MPa, 叶柄长度和直径因叶柄的不同而变化
Figure 10. Change of leaf angle with wind speed, where the petiole elastic modulus E=600 MPa, the petiole length and diameter vary with the difference of petiole
图 11 叶柄弯曲程度随风速的变化, 其中叶柄弹性模量 $E=600$ MPa, 叶柄长 $\ell=0.12$ m, 叶柄平均直径 $d=1.8$ mm
Figure 11. Change of a petiole bending with wind speeds, where the petiole elastic modulus $E=600$ MPa, the petiole length $\ell=0.12$ m, and the averaged petiole diameter $d=1.8$ mm
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
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