紫藤萝复叶气动特性的风洞实验研究
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摘要
树叶的形状重构和减阻能力在太阳能帆板、机翼结构、仿生天线设计和新型发电技术等方面具有应用价值.紫藤萝羽状复叶垂直悬挂于风洞中,在风速0～25 m/s范围内进行正面和反面迎风测试.发现存在前期稳定、中间过渡和后期稳定3个阶段以及5个临界风速.在前期阶段叶轴随风速弯曲变化剧烈,出现小叶分层飞翼和分层多形状稳定.过渡阶段出现叶轴大幅低频振动和部分小叶小幅高频振动两种不稳定形式.后期出现两层或单一整体稳定,横截面形状分为锥形、楔形和U形.随着风速增大,复叶宽度减小,小叶层数逐步减少,直至出现流线形单一整体.随着雷诺数增大,复叶阻力系数先是快速下降,后又缓慢地趋于常数.复叶Vogel负指数绝对值|α|随小叶数目的增大而增大.反面迎风时|α|比正面迎风时大,但随着小叶数目增加两者趋于一致.当复叶旋涡脱落频率与叶轴固有频率接近时,叶轴出现大幅振动.理论分析得到叶轴振动的第二临界风速V_2/(E/ρ)~(1/2)是b/l和d/l的函数,其中E,ρ, d和l分别为叶轴弹性模量、密度、直径和长度,b为变形后的复叶宽度,并由实验数据得到了其变化图.
The capability of reconfiguration of tree leaves is of significance in the designs of solar panel, aerofoil, bionic antenna, and wind power generation tree. The leaf was clamped at the base end of the rachis and vertically suspended in the center of wind tunnel test section, and tested with its front and back surface facing on-coming stream respectively at step-by-step increasing wind speed from 0 to 25 m/s. Results show that the changing process of the leaf can be divided into three stages: earlier steady, intermediate transition, and later steady, and critical wind speeds are observed. In earlier stage, the downstream bending curvature of the rachis increases rapidly with wind speed, and multi-layer wing steady and multi-layer multi-shape steady states exist. In intermediate stage, large amplitude low frequency rachis vibration,and small amplitude high frequency lobules vibration are observed. In later steady stage, two-layer structure or single streamlined body of conic, or wedge or U-shape cross section can be found. As wind speed increasing, the number of lobule layers and the width of the compound leaf b decrease, until the single streamlined body formed. As Re increasing,the drag coefficient of the leaf decreases rapidly at first, then slowly approaching to a constant. The absolute value ofthe negative Vogel component |α| decreases with the increase of lobule number of the leaf. |α| of the leaf with its back surface is larger than that with its front surface facing wind, but they tend to converge with the increase of lobule number.Rachis vibration occurs if the frequency of vortex shedding from the leaf is close to the natural frequency of the rachis.The second critical wind speed V2/E/ρ, at which the rachis vibration begins, is shown to be the function of b/l and d/l, where E, ρ, d,and l are respectively elastic module, mass density, diameter and length of the rachis, b is width of the deformed leaf, and a figure about this function is drawn using experimental data.
The capability of reconfiguration of tree leaves is of significance in the designs of solar panel, aerofoil, bionic antenna, and wind power generation tree. The leaf was clamped at the base end of the rachis and vertically suspended in the center of wind tunnel test section, and tested with its front and back surface facing on-coming stream respectively at step-by-step increasing wind speed from 0 to 25 m/s. Results show that the changing process of the leaf can be divided into three stages: earlier steady, intermediate transition, and later steady, and critical wind speeds are observed. In earlier stage, the downstream bending curvature of the rachis increases rapidly with wind speed, and multi-layer wing steady and multi-layer multi-shape steady states exist. In intermediate stage, large amplitude low frequency rachis vibration,and small amplitude high frequency lobules vibration are observed. In later steady stage, two-layer structure or single streamlined body of conic, or wedge or U-shape cross section can be found. As wind speed increasing, the number of lobule layers and the width of the compound leaf b decrease, until the single streamlined body formed. As Re increasing,the drag coefficient of the leaf decreases rapidly at first, then slowly approaching to a constant. The absolute value ofthe negative Vogel component |α| decreases with the increase of lobule number of the leaf. |α| of the leaf with its back surface is larger than that with its front surface facing wind, but they tend to converge with the increase of lobule number.Rachis vibration occurs if the frequency of vortex shedding from the leaf is close to the natural frequency of the rachis.The second critical wind speed V2/E/ρ, at which the rachis vibration begins, is shown to be the function of b/l and d/l, where E, ρ, d,and l are respectively elastic module, mass density, diameter and length of the rachis, b is width of the deformed leaf, and a figure about this function is drawn using experimental data.
引文
1 Bohdan K,Peter Z,J′an K.Wind-an important ecological factor and destructive agent in forests.Forestry Journal,2016,62(2):123-130
2 Moore GM.Wind-thrown trees:Storms or management.Arboriculture&Urban Forestry,2014,40(2):53-69
3 Cleugh HA,Miller JM,Bohm M.Direct mechanical effects of wind on crops.Agroforestry Systems,1998,41:85-112
4 Wu T,Zhang P,Zhang L,et al.Morphological response of eight quercus species to simulated wind load.Plos One,2016,11(9):e0163613
5 Speck HO,Hurd CL,Speck T.Reconfiguration as a prerequisite for survival in highly unstable flow-dominated habitats.Journal of Plant Growth Regulation,2004,23(2):98-107
6 Steinberg V.Hydrodynamics:Bend and survive.Nature,2002,420(6915):473
7 Hadhazy A.Power plants:Artificial trees that harvest sun and wind to generate electricity.Scientific American,2009,306(5):31-32
8 Sharif S,Gentry TR,Yen J,Goodman JN.Transformative solar panels:A multidisciplinary approach.International Journal of Architectural Computing,2013,11(2):227-245
9陈志超,詹家礼,周斌等.基于仿生学理论的机翼结构布局设计.机电产品开发与创新,2014,27(3):12-14(Chen Zhichao,Zhan Jiali,Zhou Bin,et al.Wing structural layout design based on bionics theory.Development&Innovation of Machinery&Electrical Products,2014,27(3):12-14(in Chinese))
10张昊明.银杏叶状仿生天线的构想与设计.新疆师范大学学报,2012,31(1):33-40(Zhang Haoming.The Design of a Bionic Antenna.Journal of Xinjiang Normal University(Natural Sciences Edition),2012,31(1):33-40(in Chinese))
11 Vogel S.Drag and reconfiguration of broad leaves in high winds.Journal of Experimental Botany,1989,40(217):941-948
12 Albayrak I,Nikora V,Miler O,et al.Flow-plant interactions at leaf,stem and shoot scales:Drag,turbulence,and biomechanics.Aquatic Sciences,2014,76(2):269-294
13 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
14 King M,Vincent JV,Warwick H.Curling and folding of leaves of monocotyledons-a strategy for structural stiffness.New Zealand Journal of Botany,1996,34(3):411-416
15 Albayrak I,Nikora V,Miller O,et al.Effects of plant leaf shape on drag forces imposed by water flow.Sbe.hw.ac.uk,2010
16 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(Pt 15):2716
17 Schouveiler L,Boudaoud A.The rolling up of sheets in a steady flow.Journal of Fluid Mechanics,2006,563(563):71-80
18邵传平,朱园园.鹅掌楸树叶在风中的变形与振动.力学学报,2017,49(2):431-440(Shao Chuanping,Zhu Yuanyuan.The deformation and vibration of tulip leaves in wind.Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):431-440(in Chinese))
19 Shao CP,Chen YJ,Lin JZ.Wind induced deformation and vibration of a Platanus acerifolia leaf.Acta Mechnica Sinica,2012,28(3):583-594
20 Tadrist L,Julio K,Saudreau M,et al.Leaf flutter by torsional galloping:Experiments and model.Journal of Fluids&Structures,2015,56:1-10
21 Vogel S.Twist-to-bend ratios and cross-sectional shapes of petioles and stems.Journal of Experimental Botany,1992,43:1527-1532
22 Etnier SA.Twisting and bending of biological beams:Distribution of biological beams in a stiffness mechanospace.The Biological Bulletin,2003,205:36-46
23 Zhao Z,Huang W,Li B,et al.Synergistic effects of chiral morphology and reconfiguration in cattop leaves.Journal of Bionic Engineering,2015,12(4):634-642
24 Niklas KJ.A mechanical perspective on foliage leaf form and function.New Phytologist,1999,143(1):19-31
25 Grant RH.The scaling of flow in vegetative structures.BoundaryLayer Meteorology,1983,27(2):171-184
26 Guan DX,Zhu TY,Han SJ.Wind tunnel experiment of drag of isolated tree models in surface boundary layer.Journal of Forestry Research,2000,11(3):156-160
27 O’Hare MT,Hutchinson KA,Clarke RT.The drag and reconfiguration experienced by five macrophytes from a lowland river.Aquatic Botany,2007,86(3):253-259
28 Holland MR,Grace J,Hedley CL.Momentum absorption by driedpea crops.I.Field measurements over and within varieties of differing leaf structure.Agricultural&Forest Meteorology,1991,54(1):67-79
29 Holland MR,Grace J,Hedley CL.Momentum absorption by driedpea crops.II.Wind tunnel measurements of drag on isolated leaves and pods.Agricultural&Forest Meteorology,1991,54(1):81-93
30 Ristroph L,Zhang J.Anomalous hydrodynamic drafting of interacting flapping flags.Physical Review Letters,2008,101(19):194502
31 Sang JL,Kim JJ,Yeom E.Vortex-induced reconfiguration of a tandem arrangement of flexible cylinders.Wind&Structures An International Journal,2015,21(1):25-40
32 Roshko A.On the wake and drag of bluff bodies.Journal of Aeronautical Science,1955,22(2):124-132.
33 Alben S.The flapping-flag instability as a nonlinear eigenvalue problem,Physics of Fluids,2008,20:104106
34 Alben S,Shelley MJ.Flapping states of a flag in an inviscid fluid:bistability and the transition to chaos.Physical Review Letters,2008,100:074301
35 Chen M,Jia LB,Wu YF,et al.Bifurcation and chaos of a flag in an inviscid flow.Journal of Fluids and Structures,2014,45:124-137
36 Eloy C,Souilliez C,Schouveiler L.Flutter of a rectangular plate.Journal of Fluids and Structures,2007,23(6):904-919
37 Eloy C,Kofman N,Schouveiler L.The origin of hysteresis in the flag instability.Journal of Fluid Mechanics,2012,691(1):583-593
38 Watanabe Y,Suzuki S,Sugihara M.An experimental study of paper flutter.Journal of Fluids and Structures,2002,16(4):529-542
39 Watanabe Y,Isogai K,Suzuki S,et al.A theoretical study of paper flutter.Journal of Fluids and Structures,2002,16(4):543-560
40 Tian FB,Lu XY,Luo HX.Onset of instability of a flag in uniform flow.Thoeretical&Applied Mechanics Letters,2012,2:022005
41 Yu ZS,Wang Y,Shao XM.Numerical simulations of the flapping of a three-dimensional flexible plate in uniform flow.Journal of Sound and Vibration,2012,331:4448-4463
42 Tian FB.Role of mass on the stability of flag/flags in uniform flow.Applied Physics Letters,2013,103(3):034101
2 Moore GM.Wind-thrown trees:Storms or management.Arboriculture&Urban Forestry,2014,40(2):53-69
3 Cleugh HA,Miller JM,Bohm M.Direct mechanical effects of wind on crops.Agroforestry Systems,1998,41:85-112
4 Wu T,Zhang P,Zhang L,et al.Morphological response of eight quercus species to simulated wind load.Plos One,2016,11(9):e0163613
5 Speck HO,Hurd CL,Speck T.Reconfiguration as a prerequisite for survival in highly unstable flow-dominated habitats.Journal of Plant Growth Regulation,2004,23(2):98-107
6 Steinberg V.Hydrodynamics:Bend and survive.Nature,2002,420(6915):473
7 Hadhazy A.Power plants:Artificial trees that harvest sun and wind to generate electricity.Scientific American,2009,306(5):31-32
8 Sharif S,Gentry TR,Yen J,Goodman JN.Transformative solar panels:A multidisciplinary approach.International Journal of Architectural Computing,2013,11(2):227-245
9陈志超,詹家礼,周斌等.基于仿生学理论的机翼结构布局设计.机电产品开发与创新,2014,27(3):12-14(Chen Zhichao,Zhan Jiali,Zhou Bin,et al.Wing structural layout design based on bionics theory.Development&Innovation of Machinery&Electrical Products,2014,27(3):12-14(in Chinese))
10张昊明.银杏叶状仿生天线的构想与设计.新疆师范大学学报,2012,31(1):33-40(Zhang Haoming.The Design of a Bionic Antenna.Journal of Xinjiang Normal University(Natural Sciences Edition),2012,31(1):33-40(in Chinese))
11 Vogel S.Drag and reconfiguration of broad leaves in high winds.Journal of Experimental Botany,1989,40(217):941-948
12 Albayrak I,Nikora V,Miler O,et al.Flow-plant interactions at leaf,stem and shoot scales:Drag,turbulence,and biomechanics.Aquatic Sciences,2014,76(2):269-294
13 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
14 King M,Vincent JV,Warwick H.Curling and folding of leaves of monocotyledons-a strategy for structural stiffness.New Zealand Journal of Botany,1996,34(3):411-416
15 Albayrak I,Nikora V,Miller O,et al.Effects of plant leaf shape on drag forces imposed by water flow.Sbe.hw.ac.uk,2010
16 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(Pt 15):2716
17 Schouveiler L,Boudaoud A.The rolling up of sheets in a steady flow.Journal of Fluid Mechanics,2006,563(563):71-80
18邵传平,朱园园.鹅掌楸树叶在风中的变形与振动.力学学报,2017,49(2):431-440(Shao Chuanping,Zhu Yuanyuan.The deformation and vibration of tulip leaves in wind.Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):431-440(in Chinese))
19 Shao CP,Chen YJ,Lin JZ.Wind induced deformation and vibration of a Platanus acerifolia leaf.Acta Mechnica Sinica,2012,28(3):583-594
20 Tadrist L,Julio K,Saudreau M,et al.Leaf flutter by torsional galloping:Experiments and model.Journal of Fluids&Structures,2015,56:1-10
21 Vogel S.Twist-to-bend ratios and cross-sectional shapes of petioles and stems.Journal of Experimental Botany,1992,43:1527-1532
22 Etnier SA.Twisting and bending of biological beams:Distribution of biological beams in a stiffness mechanospace.The Biological Bulletin,2003,205:36-46
23 Zhao Z,Huang W,Li B,et al.Synergistic effects of chiral morphology and reconfiguration in cattop leaves.Journal of Bionic Engineering,2015,12(4):634-642
24 Niklas KJ.A mechanical perspective on foliage leaf form and function.New Phytologist,1999,143(1):19-31
25 Grant RH.The scaling of flow in vegetative structures.BoundaryLayer Meteorology,1983,27(2):171-184
26 Guan DX,Zhu TY,Han SJ.Wind tunnel experiment of drag of isolated tree models in surface boundary layer.Journal of Forestry Research,2000,11(3):156-160
27 O’Hare MT,Hutchinson KA,Clarke RT.The drag and reconfiguration experienced by five macrophytes from a lowland river.Aquatic Botany,2007,86(3):253-259
28 Holland MR,Grace J,Hedley CL.Momentum absorption by driedpea crops.I.Field measurements over and within varieties of differing leaf structure.Agricultural&Forest Meteorology,1991,54(1):67-79
29 Holland MR,Grace J,Hedley CL.Momentum absorption by driedpea crops.II.Wind tunnel measurements of drag on isolated leaves and pods.Agricultural&Forest Meteorology,1991,54(1):81-93
30 Ristroph L,Zhang J.Anomalous hydrodynamic drafting of interacting flapping flags.Physical Review Letters,2008,101(19):194502
31 Sang JL,Kim JJ,Yeom E.Vortex-induced reconfiguration of a tandem arrangement of flexible cylinders.Wind&Structures An International Journal,2015,21(1):25-40
32 Roshko A.On the wake and drag of bluff bodies.Journal of Aeronautical Science,1955,22(2):124-132.
33 Alben S.The flapping-flag instability as a nonlinear eigenvalue problem,Physics of Fluids,2008,20:104106
34 Alben S,Shelley MJ.Flapping states of a flag in an inviscid fluid:bistability and the transition to chaos.Physical Review Letters,2008,100:074301
35 Chen M,Jia LB,Wu YF,et al.Bifurcation and chaos of a flag in an inviscid flow.Journal of Fluids and Structures,2014,45:124-137
36 Eloy C,Souilliez C,Schouveiler L.Flutter of a rectangular plate.Journal of Fluids and Structures,2007,23(6):904-919
37 Eloy C,Kofman N,Schouveiler L.The origin of hysteresis in the flag instability.Journal of Fluid Mechanics,2012,691(1):583-593
38 Watanabe Y,Suzuki S,Sugihara M.An experimental study of paper flutter.Journal of Fluids and Structures,2002,16(4):529-542
39 Watanabe Y,Isogai K,Suzuki S,et al.A theoretical study of paper flutter.Journal of Fluids and Structures,2002,16(4):543-560
40 Tian FB,Lu XY,Luo HX.Onset of instability of a flag in uniform flow.Thoeretical&Applied Mechanics Letters,2012,2:022005
41 Yu ZS,Wang Y,Shao XM.Numerical simulations of the flapping of a three-dimensional flexible plate in uniform flow.Journal of Sound and Vibration,2012,331:4448-4463
42 Tian FB.Role of mass on the stability of flag/flags in uniform flow.Applied Physics Letters,2013,103(3):034101