摘要
板状柔性体与流体相互作用的现象广泛存在于自然界和人们的日常生产生活中。通过研究这一问题,可以揭示板状柔性体在流体诱导下发生摆动的机理、柔性体与流体间的能量交换过程以及通过流体传递柔性体间相互作用的机制。深入研究这一现象不仅可以帮助人们更好地认识自然界的奥秘,还可以使人们在掌握流体与柔性体相互作用机理的基础上设计、制造或改进一些机械装置,使其能充分利用自然界流场中蕴含的能量。
本文通过在肥皂膜水洞装置中放置柔性细丝研究了二维流场中板状柔性体与流体的相互作用。在本文中具体讨论了以下内容:
1、开展了板状柔性体在均匀来流中摆动的实验,研究了在肥皂膜水洞中开展这类实验的基本实验方法,实验数据处理手段和分析问题的基本理论工具,为本文研究更为复杂的问题打下了基础。
2、建立了研究二维均匀来流中两个并行排列柔性板间耦合的理论模型,使用线性稳定性分析方法首次分析了柔性板间不同耦合模式的作用机理,通过两个具体的例子研究了各种耦合模式在无量纲速度与无量纲密度参数平面内以及在有量纲长度与间距参数平面内的分布,并通过实验定性验证了理论分析的结果。
3、开展了前后排列的柔性体在流场中相互作用的实验研究,发现下游细丝在上游丝线产生的涡街中穿行的现象。通过对梁的振动方程的分析及对实验数据的处理,研究了细丝在相互作用过程中的受力及其能量的变化规律,结果显示了下游丝线能从涡街中获得能量,其增加能量主要用于增加动能,而上游丝线在串行干扰中受影响较小。
4、将细丝置于圆柱尾迹中,研究了周期性流动诱导下柔性体的摆动问题。实验发现了细丝在圆柱尾迹诱导下的三种响应模式:在远离圆柱的卡门涡街中,柔性体以涡街的频率在漩涡中穿行并受到阻力;在圆柱的近尾迹区内,柔性体获得推力;在介于二者之间时,柔性体间歇地前后运动,并从理论上分析了三种模式的机理。
本文通过实验、理论建模和分析,系统地研究了在均匀流和周期性流动中单个板状柔性体的响应以及并行排列和前后串行排列布局下两个板状柔性体之间的相互干扰问题。同时在本文中详细叙述了肥皂膜装置的设计、流场参数和细丝物理性质的测量、流场照明方法、微小力的测量等实验技术。
The interactions between fluid and flexible bodies exist in nature,everyday life and various industry applications.By investigating these phenomena,we can reveal the mechanism of flow induced vibration of flexible bodies,understand the process of energy exchange between flexible bodies and fluid,and learn the way flexible bodies interact with each other in a flowing fluid.The study on the interaction between flexible bodies and fluid not only makes us better understand the nature,but also helps us invent new machines or improve existing devices to harvest more energy from nature.
In this dissertation,the interaction between a two-dimensional flexible plate and a fluid was researched in the soap film tunnels.The main topics discussed are as follows:
1.The experiments of a single flexible filament flapping in a uniform flow were conducted.The basic experimental process,the data handling and the basic theoretical methods with respect to the analysis of the interaction between fluid and flexible body were investigated,making a base for the studies of more complex phenomena.
2.A theoretical model of the interaction between two parallel flexible filaments in a uniform flow was proposed.The mechanism of the coupling modes between two filaments was explored in terms of linear instability analysis.Two special cases were studied and the distributions of the coupling modes in the non-dimensional and dimensional parameter spaces were predicted theoretically.The qualitative accordance with the experimental results was achieved.
3.The experiments of the interaction between two tandem filaments in the soap film were conducted.It was found that the filament downstream slaloms in the vortex street shedding from the upstream filament.The force and energy were calculated in terms of an Euler-Benoulli beam model.The results showed that the downstream filament extracts energy from the flow to increase its kinetic energy,while the upstream filament is influenced little in this process.
4.The flapping of a flexible filament in the wake of a cylinder was investigated experimentally in order to study the behavior of a flexible body in periodic flow. Three response modes that depend on the distance between the cylinder and the filament were observed in the experiments.They are the propulsion mode,swing mode and rock mode.A primary explanation on these modes is given in terms of the waving plate theory.
In this dissertation,the interaction between a flexible body and fluid in a uniform or periodic flow,and the interaction between two flexible bodies in parallel or tandem were investigated experimentally and theoretically.In addition,the soap film tunnel apparatus,flow parameters and filament's properties measurement,flow visualization, and tiny force measurement technique were discussed in detail.
引文
方道腴.1990.钠灯原理和应用[M].上海:上海交通大学出版社.
刘鸿文.1992.材料力学:上下册[M].第三版.北京:高等教育出版社.
倪振华.1989.振动力学[M].西安:西安交通大学出版社.
童秉纲,尹协远,朱克勤.1994.涡运动理论[M].合肥:中国科学技术大学出版社.
张立翔,杨柯.2004.流体结构互动理论[M].北京:科学出版社.
Abrahams MV,Colgan PW.1985.Risk of predation,hydrodynamic efficiency and their influence on school structure[J].Environmental Biology of Fishes,13(3):195-202.
Abrahams MV,Colgan PW.1987.Fish schools and their hydrodynamic function:a reanalysis[J].Environmental Biology of Fishes,20(1):79-80.
Alexander DE.1984.Unusual phase relationships between the forewings and hindwings in flying dragonflies[J].Journal of Experimental Biology,109(I):379-383.
Allen JJ,Smits AJ.2001.Energy harvesting eel[J].Journal of Fluids and Structures,15(3):629-640.
Andersson M,Wallander J.2004.Kin selection and reciprocity in flight formation?[J].Behavioral Ecology,15(1):158-162.
Argentina M,Mahadevan L.2005.Fluid-flow-induced flutter of a flag[J].Proceedings of the National Academy of Sciences,102(6):1829-1834.
Beal DN,Hover FS,Triantafyllou MS,Liao JC,Lauder GV.2006.Passive propulsion in vortex wakes[J].Journal of Fluid Mechanics,549:385-402.
Behdinan K,Stylianou MC,Tabarrok B.1997.Dynamics of flexible sliding beams:Non-linear analysis.Part I:Formulation[J].Journal of Sound and Vibration,208(4):517-539.
Beizaie M,Gharib M.1997.Fundamentals of a liquid(soap) film tunnel[J].Experiments in Fluids,23(2):130-140.
Berg R.2005.Diffraction spectrum of sodium - expendable gratings[EB/OL].University of Maryland,[2009-3-1].http://www.physics.umd.edu/iecdem/services/demos/demosn2/n2-03.htm.
Bernitsas MM,Raghavan K,Ben-Simon Y,Garcia EMH.2008.VIVACE(Vortex Induced Vibration Aquatic Clean Energy):A New Concept in Generation of Clean and Renewable Energy From Fluid Flow[J].Journal of Offshore Mechanics and Arctic Engineering,130(4):041101.
Boys CV.1916.Soap bubbles:their colors and forces which mold them[M].London:Society for promoting Christian knowledge.
Breder CM.1965.Vortices and fish schools[J].Zoologica,50:97-114.
Burmann W.1975.Water hammer in coaxial pipe systems[J].Journal of the Hydraulics Division,101(6):699-715.
Chen JN,Lin SP.2002.Instability of an annular jet surrounded by a viscous gas in a pipe[J].Journal of Fluid Mechanics,450:235-258.
Chen XP,Jia LB,Yin XZ,Cheng JS,Lu J.2005.Spraying modes in coaxial jet electrospray with outer driving liquid[J].Physics of Fluids,17(3):032101.
Cheng JY,Zhuang LX,Tong BG.1991.Analysis of swimming three-dimensional waving plates [J].Journal of Fluid Mechanics,232:341-355.
Chomaz JM.2001.The dynamics of a viscous soap film with soluble surfactant[J].Journal of Fluid Mechanics,442:387-409.
Connell BSH,Yue DKP.2007.Flapping dynamics of a flag in a uniform stream[J].Journal of Fluid Mechanics,581:33-67.
Connell BSH.2006.Numerical investigation of the flow-body interaction of thin flexible foils and ambient flow[D]:[Ph.D.].Massachusetts:Massachusetts Institute of Technology.
Couder Y.1981.The observation of a shear flow instability in a rotating system with a soap membrane[J].Journal de Physique Lettres,42(19):429-431.
Couder Y.1984.Two-dimensional grid turbulence in a thin liquid film[J].Journal de Physique Lettres,45(8):353-360.
Couder Y,Basdevant C.1986.Experimental and numerical study of vortex couples in two-dimensional flows[J].Journal of Fluid Mechanics,173:225-251.
Couder Y,Chomaz JM,Rabaud,M.1989.On the hydrodynamics of soap films[J].Physica D:Nonlinear Phenomena,37:384-405.
Cutts CJ,Speakman JR.1994.Energy savings in formation flight of pink-footed geese[J].Journal of Experimental Biology,189(1):251-261.
du Noüy PL.1919.A new apparatus for measuring surface tension[J].Journal of General Physiology,l(5):521-524.
Du Q,Li X.2005.Effect of gas stream swirls on the instability of viscous annular liquid jets[J].Acta Mechanica,176(1-2):61-81.
Eloy C,Lagrange R,Souilliez C,Schouveiler L.2008.Aeroelastic instability of cantilevered flexible plates in uniform flow[J].Journal of Fluid Mechanics,611:97-106.
Evangelinos C,Karniadakis GEM.1999.Dynamics and flow structures in the turbulent wake of rigid and flexible cylinders subject to vortex-induced vibrations[J].Journal of Fluid Mechanics,400:91-124.
Farnell DJJ,David T,Barton DC.2004a.Numerical simulations of a filament in a flowing soap film[J].International Journal for Numerical Methods in Fluids,44(3):313-330.
Farnell DJJ,David T,Barton DC.2004b.Coupled states of flapping flags[J].Journal of Fluids and Structures,19(1):29-36.
Georgiev D,Vorobieff P.2002.The slowest soap-film tunnel in the Southwest[J].Review of Scientific Instruments,73(3):1177-1184.
Gharib M,Derango P.1989.A liquid film (soap film)tunnel to study two-dimensional laminar and turbulent shear flows[J].Physica D:Nonlinear Phenomena,37:406-416.
Ginzburg VL.1989.Applications of Electrodynamics in Theoretical Physics and Astrophysics[M].New York:Gordon and Breach.
Greco V,Molesini G.1996.Monitoring the thickness of soap films by polarization homodyne interferometry[J].Measurement Science and Technology,7(1):96—101.
Grotberg JB,Jensen OE.2004.Biofluid mechanics in flexible tubes[J].Annual Review of Fluid Mechanics,36:121-147.
Hagerty WW,Shea JF.1955.A study of the stability of plane fluid sheets[J].Journal of Applied Mechanics,22(3):509-514.
Herskin J,Steffensen JF.1998.Reduced tail beat frequency and oxygen consumption due to hydrodynamic interactions of schooling sea bass,Dicentrarchus labrax L.,measured at different swimming speeds[J].Journal of Fish Biology,53:366-376.
Higdon JJL,Corrsin S.1978.Induced drag of a bird flock[J].The American Naturalist,112(986):727-744.
Holmberg K.2002.Handbook of applied surface and colloid chemistry [M].New York:John Wiley & Sons,219.
Hu HH,Patankar N.1995.Non-axisymmetrical instability of core-annular flow[J].Journal of Fluid Mechanics,290:213-224.
Huang L.1995.Flutter of cantilevered plates in axial flow[J].Journal of Fluids and Structures,9(2):127-147.
Ivanov IB.1988.Thin Liquid Films[M].New York:Marcel Dekker.
Jia LB,Li F,Yin XZ,Yin XY.2007.Coupling modes between two flapping filaments[J].Journal of Fluid Mechanics,581:199-220.
Jia LB,Yin XZ.2008.Passive oscillations of two tandem flexible filaments in a flowing soap film[J].Physical Review Letters,100(22):228104.
Kellay H,Wu XL,Goldburg WI.1995.Experiments with turbulent soap films[J].Physical Review Letters,74(20):3975-3978.
Lau YL,So RMC,Leung RCK.2004.Flow-induced vibration of elastic slender structures in a cylinder wake[J].Journal of Fluids and Structures,19(8):1061-1083.
Lauder GV,Anderson EJ,Tangorra J,Madden PGA.2007.Fish biorobotics:kinematics and hydrodynamics of self-propulsion[J].Journal of Experimental Biology,210(16):2767.
Li F,Yin XY,Yin XZ.2006.Instability analysis of a coaxial jet under a radial electric field in the nonequipotential case[J].Physics of Fluids,18(3):037101.
Liao JC,Beal DN,Lauder GV,Triantafyllou MS.2003a.Fish exploiting vortices decrease muscle activity[J].Science,302(5650):1566-1569.
Liao JC,Beal DN,Lauder GV,Triantafyllou MS.2003b.The Karman gait:novel body kinematics of rainbow trout swimming in a vortex street[J].Journal of Experimental Biology,206(6):1059-1073.
Lopez-Herrera JM,Barrero A,Lopez A,Loscertales IG,Marquez M.2003.Coaxial jets generated from electrified Taylor cones.Scaling laws[J].Journal of Aerosol Science,34(5):535-552.
Lord Rayleigh.1878.On the instability of jets[J].Proceedings of the London Mathematical Society,10(1):4-13.
Loscertales IG,Barrero A,Guerrero I,Cortijo R,Marquez M,Ganan-Calvo AM.2002.Mi-cro/nano encapsulation via electrified coaxial liquid jets[J].Science,295(5560):1695-1698.
Lu XY,Yin XZ.2005.Propulsive performance of a fish-like travelling wavy wall[J].Acta Mechanica,175(1):197-215.
Lynch DG,Waters SL,Pedley TJ.1996.Flow in a tube with non-uniform,time-dependent curvature:Governing equations and simple examples[J].Journal of Fluid Mechanics,323:237-265.
Maa YF,Nguyen PAT,Hsu SW.1998.Spray-drying of air-liquid interface sensitive recombinant human growth hormone[J].Journal of Pharmaceutical Sciences,87(2):152-159.
Martin B,Wu XL.1995.Shear flow in a two-dimensional Couette cell:A technique for measuring the viscosity of free-standing liquid films[J].Review of Scientific Instruments,66(12):5603-5608.
Muller UK.2003.Fish'n Flag[J].Science,302:1511-1512.
Parrish JK,Hamner WM.1997.Animal groups in three dimensions[M].New York:Cambridge University Press.
Partridge BL,Johansson J,Kalish J.1983.The structure of schools of giant bluefin tuna in Cape Cod Bay[J].Environmental Biology of Fishes,9(3):253-262.
Partridge BL,Pitcher TJ.1979.Evidence against a hydrodynamic function for fish schools[J].Nature,279(5712):418-419.
Pitcher TJ,Parrish JK.1993.Functions of shoaling behaviour in teleosts[M]//Pitcher TJ.Behaviour of teleost fishes.2~(nd)ed.London:Chapman & Hall,363-439.
Ristroph L,Zhang J.2008.Anomalous hydrodynamic drafting of interacting flapping flags[J].Physical Review Letters,101(19):194502.
Rosen MJ.2004.Surfactants and interfacial phenomena[M].3~(rd)ed.Hoboken:John Wiley & Sons.
Rossiter BW,Baetzold RC.1993.Investigations of surfaces and interfaces—Part A[M].2~(nd)ed.New York:John Wiley & Sons.
Ruppell G.1989.Kinematic analysis of symmetrical flight manoeuvres of Odonata[J].Journal of Experimental Biology,144(1):13-42.
Rutgers MA,Wu XL,Daniel WB.2001.Conducting fluid dynamics experiments with vertically falling soap films[J].Review of Scientific Instruments,72(7):3025-3037.
Schouveiler L,Eloy C.2009.Coupled flutter of parallel plates[J].Under review.
Settles GS.2001.Schlieren and shadowgraph techniques:visualizing phenomena in transparent media[M].Berlin:Springer.
Shelley M,Vandenberghe N,Zhang J.2005.Heavy flags undergo spontaneous oscillations in flowing water[J].Physical Review Letters,94(9):094302.
Shen J,Li X.1996.Instability of an annular viscous liquid jet[J].Acta Mechanica,114(1-4):167-183.
Shen L,Zhang X,Yue DKP,Triantafyllou MS.2003.Turbulent flow over a flexible wall undergoing a streamwise travelling wave motion[J].Journal of Fluid Mechanics,484:197-221.
Smith BW,Chase JG,Nokes RI,Shaw GM,Wake G.2004.Minimal haemodynamic system model including ventricular interaction and valve dynamics[J].Medical Engineering and Physics,26(2):131-139.
Somasundaran P.2006.Encyclopedia of surface and colloid science[M].2~(nd)ed.London:Taylor & Francis.
Squire HB.1953.Investigation of the instability of a moving liquid film[J].British Journal of Applied Physics,4(6):167-169.
Stanley S,Sarkar S.1997.Simulations of spatially developing two-dimensional shear layers and jets[J].Theoretical and Computational Fluid Dynamics,9(2):121-147.
Sugimoto T.2003.A theoretical analysis of formation flight as a nonlinear self-organizing phenomenon[J].IMA Journal of Applied Mathematics,68(5):441-470.
Tabarrok B,Leech CM,Kim YI.1974.On the dynamics of an axially moving beam[J].Journal of the Franklin Institute,297(3):201-220.
Taylor GK,Nudds RL,Thomas ALR.2003.Flying and swimming animals cruise at a Strouhal number tuned for high power efficiency[J].Nature,425(6959):707-711.
Theodorsen T.1935.General theory of aerodynamic instability and the mechanism of flutter [R]. USA:National Advisory Committee for Aeronautics,NACA-TR-496.
Trapeznikov AA.1957.Application of the method of two-dimensional viscosity and shear strength to the investigation of the structure and composition of two-sided films and surface layers in solutions of soaps and saponins[C]//Shulman JH.Proc.2~(nd)Intl Congress on Surface Activity.London:Butterworths,242-258.
Triantafyllou MS,Triantafyllou GS,Gopalkrishnan R.1991.Wake mechanics for thrust generation in oscillating foils[J].Physics of Fluids A:Fluid Dynamics,3(12):2835-2837.
Triantafyllou MS,Triantafyllou GS.1995.An efficient swimming machine[J].Scientific American,272(3):64-71.
Tucker C,Mohler C,Harris K.2008.High Throughput Surfactant Synthesis,Characterization and Formulation[C/OL].Paris:CESIO 2008,[2009-3-1].http://www.kibron.com/user_data/O-A 19_Tucker.pdf.
Videler JJ.1993.Fish swimming[M].London:Chapman and Hall.
Villermaux E,Clanet C.2002.Life of a flapping liquid sheet[J].Journal of Fluid Mechanics,462:341-363.
Watanabe Y,Suzuki S,Sugihara M,Sueoka Y.2002a.An experimental study of paper flutter[J].Journal of Fluids and Structures,16(4):529-542.
Watanabe Y,Isogai K,Suzuki S,Sugihara M.2002b.A theoretical study of paper flutter[J].Journal of Fluids and Structures,16(4):543-560.
Weidman PD,Afenchenko VO,Ezersky AB,Kiyashko SV,Rabinovich MI.1997.The generation of two-dimensional vortices by transverse oscillation of a soap film[J].Physics of Fluids,9(9):S2.
Weihs D.1973.Hydromechanics of fish schooling[J].Nature,241(5387):290-291.
Weihs D.1975.Some hydrodynamical aspects of fish schooling[M]// Wu TYT,Brokaw CJ,Brennen C.Swimming and Flying in Nature:Volumes Ⅰ & Ⅱ.New York:Plenum Press,703-718.
Weimerskirch H,Martin J,Clerquin Y,Alexandre P,Jiraskova S.2001.Energy saving in flight formation[J].Nature,413(6857):697-698.
Wu CJ,Xie YQ,Wu JZ.2003.“Fluid Roller Bearing” effect and flow control[J].Acta Mechenica Sinica,19(5):476-484.
Wu TYT.1960.Swimming of a waving plate[J].Journal of Fluid Mechanics,10(03):321-344.
York JL,Stubbs HE,Tek MR.1953.The mechanism of disintegration of liquid sheets[J].Trans.ASME:1279-1286.
Zhang J,Childress S,Libchaber A,Shelley M.2000.Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind[J].Nature,408(6814):835-838.
Zhu L,Peskin CS.2002.Simulation of a flexible flapping filament in a flowing soap film by the immersed boundary method[J].Journal of Computational Physics,179(2):452-468.
Zhu L,Peskin CS.2003.Interaction of two flapping filaments in a flowing soap film[J].Physics of Fluids,15(7):1954-1960.
Zinkova M.2007.Reflection in a soap bubble[EB/OL].Wikipedia,[2009-3-1].http://en.wikipedia.Org/wiki/File:Reflection_in_a_soap_bubble_edit.jpg.
