树状分形分叉网络的输运特性
|
摘要
不管是在生命系统还是非生命系统中都大量存在着一种非常普遍而又很特殊的几何结构——树状分叉结构。其中最明显和典型的例子是植物躯干网络和叶片的脉络网络。生物组织中也大量存在这种结构,比如哺乳动物的血液循环系统、支气管、肺动脉以及神经网络等等,和植物的分叉网络不同的是,这些生理分叉网络一般隐藏于生理组织的内部而且具有更为复杂的结构。另外这种树状分叉网络的存在范围非常广泛,诸如河流盆地、三角洲、闪电、地下油藏、裂缝、材料科学等都存在典型的树状分叉结构。近年来随着多学科的交叉以及微电子冷却的需求,这种树状分叉网络又引发了全球范围内的多个领域的研究热潮,并且在很多新兴的工程领域得到广泛应用。其中比较典型的是树状分叉网络在电子器件微通道冷却技术、燃料电池流道设计、微流体流动控制以及城市水电气供给、通讯和信息网络等领域的应用。这类树状分叉网络,尤其是自然分叉结构,往往具有自相似的特征,并在一定尺度范围内具有分形结构,分形几何理论为研究这类复杂的结构提供了一个很好的理论工具。本文的研究目的是系统研究这类具有分形特征的树状分叉网络输运特性,本研究对于理解和揭示自然分叉结构的输运机理的科学理论以及工程应用都有非常重要的意义。
本文共分六章,第一章介绍树状分叉网络的研究背景、最新研究进展以及分形和输运过程的基本理论,并且给出树状分形分叉网络的一般描述方法;第二章介绍了Murray定律及其推广形式,根据阻力最小化原理在不同输运过程中优化单分叉结构;第三章研究了树状分形分叉网络的传热特性,推导了分叉网络的有效热导率,计算了嵌入H型分叉网络的复合材料的导热特性,还通过计算流体力学的方法(CFD)数值计算了圆形分叉网络的对流换热特性;第四章研究了两种特殊分叉网络的层流流动和渗流特性,并且提出了由母体多孔介质和分形分叉网络模型组成双重多孔介质的理论模型、并计算了各向异性多孔介质的径向有效渗透率;第五章研究和总结树状分形分叉网络的输运特性,并较系统地给出了这类网络的传导性标度律;第六章总结了本文的主要内容并且对于树状分形分叉网络理论研究和应用提出了一些展望。
The tree-like branching network structures abound in both living and non-living systems, such as tree, leaves, mammalian circulatory and respiratory systems, neural dendrites, river basins, deltas, lightning, oil/water reservior, streets, rapid solidification etc. The efficient transport characteristics of natural branching systems can provide useful hints for optimal solutions of many engineering problems, which have fascinated researchers in physics, chemistry, biology, physiology, engineering and geology for ages and been applied in microelectronic cooling, flow-field designs in fuel cell, microfluidic manifolds in lab-on-a-chip systems etc. The tree-like branching network has been shown to be a conventional self-similar fractal network and the ideas of fractal geometry can be implemented to study the network. The objective of the current research is to investigate the transport properties of tree-like branching network with fractal characteristics and the effect of microstructures on the transport properties of network, which will shed light on mechanism of natural network and application in engineering.
This thesis is organized as six Chapters. In Chapter 1, the progress of tree-like branching network, fractal and transport theory, and general description of fractal tree-like branching network are introduced and reviewed. In Chapter 2, Murray's law, which is the fundamental in this field, and its generalized forms are addressed, and the single branching structure is optimized by minimizing resistance under fixed volume for different transport processes. Chapter 3 focuses on the thermal properties of fractal tree-like branching network. In this chapter, the effective heat conductivity is derived, the heat conduction of composite material embedded with H shaped branching network is studied, and the disc-shaped branching network with/without loops is simulated with CFD for heat convection. In Chapter 4, the laminar flow and seepage flow in two kinds of fractal tree-like branching network are investigated, the radial effective permeability of heterogeneous porous media is calculated with the proposed dual-domain model of fractal tree-like branching network and homogeneous porous medium model. In Chapter 5, the scaling laws between various transport parameters and volume or surface area are derived. Finally, a summary of the present work is given in Chapter 6, and some potential research interests are commented for future study of tree-like branching network and its applications.
本文共分六章,第一章介绍树状分叉网络的研究背景、最新研究进展以及分形和输运过程的基本理论,并且给出树状分形分叉网络的一般描述方法;第二章介绍了Murray定律及其推广形式,根据阻力最小化原理在不同输运过程中优化单分叉结构;第三章研究了树状分形分叉网络的传热特性,推导了分叉网络的有效热导率,计算了嵌入H型分叉网络的复合材料的导热特性,还通过计算流体力学的方法(CFD)数值计算了圆形分叉网络的对流换热特性;第四章研究了两种特殊分叉网络的层流流动和渗流特性,并且提出了由母体多孔介质和分形分叉网络模型组成双重多孔介质的理论模型、并计算了各向异性多孔介质的径向有效渗透率;第五章研究和总结树状分形分叉网络的输运特性,并较系统地给出了这类网络的传导性标度律;第六章总结了本文的主要内容并且对于树状分形分叉网络理论研究和应用提出了一些展望。
The tree-like branching network structures abound in both living and non-living systems, such as tree, leaves, mammalian circulatory and respiratory systems, neural dendrites, river basins, deltas, lightning, oil/water reservior, streets, rapid solidification etc. The efficient transport characteristics of natural branching systems can provide useful hints for optimal solutions of many engineering problems, which have fascinated researchers in physics, chemistry, biology, physiology, engineering and geology for ages and been applied in microelectronic cooling, flow-field designs in fuel cell, microfluidic manifolds in lab-on-a-chip systems etc. The tree-like branching network has been shown to be a conventional self-similar fractal network and the ideas of fractal geometry can be implemented to study the network. The objective of the current research is to investigate the transport properties of tree-like branching network with fractal characteristics and the effect of microstructures on the transport properties of network, which will shed light on mechanism of natural network and application in engineering.
This thesis is organized as six Chapters. In Chapter 1, the progress of tree-like branching network, fractal and transport theory, and general description of fractal tree-like branching network are introduced and reviewed. In Chapter 2, Murray's law, which is the fundamental in this field, and its generalized forms are addressed, and the single branching structure is optimized by minimizing resistance under fixed volume for different transport processes. Chapter 3 focuses on the thermal properties of fractal tree-like branching network. In this chapter, the effective heat conductivity is derived, the heat conduction of composite material embedded with H shaped branching network is studied, and the disc-shaped branching network with/without loops is simulated with CFD for heat convection. In Chapter 4, the laminar flow and seepage flow in two kinds of fractal tree-like branching network are investigated, the radial effective permeability of heterogeneous porous media is calculated with the proposed dual-domain model of fractal tree-like branching network and homogeneous porous medium model. In Chapter 5, the scaling laws between various transport parameters and volume or surface area are derived. Finally, a summary of the present work is given in Chapter 6, and some potential research interests are commented for future study of tree-like branching network and its applications.
引文
[1] Mandelbrot B. B. The Fractal Geometry of Nature. New York: Freeman, 1982.
[2] West B. J. Fractal Physiology and Chaos in Medicine. Singapore: World Scientific, 1990.
[3] Bassingthwaighte, J.B., Liebovitch L.S., West B.J. Fractal Physiology. New York: Oxford University Press, 1994.
[4] Antonets V.A., Atonets M.A., Shereshevsky LA. The statistical cluster dynamics in the dendroid transfer systems. in: Fractal in the Fundamental and Applied Sciences. North-Holland: Elsevier, 1991. 59-71.
[5] Bejan A., Lorente S. Constructal theory of generation of configuration in nature and engineering. Journal of Applied Physics, 2006,100: 041301.
[6] Hess W.R. Uber die periphere Regulierung der Blutzirkulation. Pflugers Archiv Gesamte Physiol. Menschen Tiere. 1917,168: 439-490.
[7] Thompson D.W. On Growth and Form. 2~(nd) ed. Cambridge: Cambridge University Press, 1917.948-957.
[8] Murray C.D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. U. S. A., 1926,12: 207-214.
[9] Murray C.D. The physiological principle of minimum work applied to the angle of branching of arteries. J. Gen. Physiol., 1926, 9: 835-841.
[10] Murray C.D. A relationship between circumference and weight in trees and its bearing on branching angles. J. Gen. Physiol., 1927,10: 725-729.
[11] Sherman T.F. On connecting large vessels to small—The Meaning of Murray's Law. J. Gen. Physiol., 1981, 78: 431-453.
[12] Weibel E.R. Morphometry of the Human Lung. New York: Academic Press Inc., 1963.
[13]Hooper G.Diameters of bronchi and asymmetrical divisions.Respir.Physiol.,1977,31:291-294.
[14]West J.B.Respiratory Physiology—The Essentials.2~(nd) ed.Baltimore:Williams and Wilkins,1979.
[15]Horsfield K.,Cumming G.Morphology of the bronchial tree in man.J.Appl.Physiol.,1968,24:373-383.
[16]Gabrys E.,Rybaczuk M..Kedzia A.Fractal models of circulatory system.Symmetrical and asymmetrical approach comparison.Chaos,Solitons and Fractals,2005,24:707-715.
[17]Dokoumetzidis A.,Macheras P.A model for transport and dispersion int he circulatory system based on the vascular fractal tree.Annals of Biomedical Engineering,2003,31:284-293.
[18]Zhong J.,Nilsson G.An M-ary fractal tree based modeling of microcirculation.Proc Annu ConfEng Med Biol,IEEE.Piscataway:1993,15:553-554.
[19]Masters B.R.Fractal analysis of the vascular tree in the human retina.Annu.Rev.Biomed.Eng.,2004,6:427-452.
[20]Buijs Jorn Op Den,Bajzer Zeljko,Ritman Erik L.Branching morphology of the rat hepatic portal vein tree.Annals of Biomedical Engineering,2006,34:14201428.
[21]Taber L.A.,Ng S.,Quesnel A.M.et al.Investigating Murray's Law in the chick embryo.Journal of Biomechanics,2001,34:121-124.
[22]Mauroy B.Filoche M.,Weibel E.R.et al.An optimal bronchial tree may be dangerous.Nature,2004,427:633-636.
[23]Singhal S.,Henderson R.,Horsfield K.et al.Morphometry of the human pulmonary arterial tree.Cir.Res.,1973,33:190-197.
[24]Horsfield K.Morphometry of the small pulmonary arteries in man.Circ.Res.,1978,42:593-597.
[25]Huang W.,Yen R.T.,McLaurine M.et al.Morphometry of the human pulmonary vasculature. J. Appl. Physiol., 1996, 81: 2123-2133.
[26] Bennett S.H. Modeling methodology for vascular input impedance determination and interpretation. J. Appl. Physiol., 1994,76:455-484.
[27] Bennett S.H., Goetzman B.W., Milstein J.M. et al. Role of arterial design on pulse wave reflection in.a fractal pulmonary network. J. Appl. Physiol., 1996, 80: 1033-1056.
[28] Haworth S.T., Linehan J.H., Bronikowski T.A. et al., A hemodynamic model representation of the dog lung. J. Appl. Physiol., 1991, 70: 15-26.
[29] Krenz G.S., Lin J., Dawson C.A. et al. Impact of parallel heterogeneity on a continuum model of the pulmonary arterial tree. J. Appl. Physiol., 1994, 77: 660-670.
[30] Dawson C.A., Krenz GS., Karau K.L. et al. Structure-function relationships in the pulmonary arterial tree. J. Appl. Physiol., 1999, 86: 569-583.
[31] Frey U., Hislop A., Silverman M. Branching properties of the pulmonary arterial tree during pre- and postnatal development. Respiratory Physiology & Neurobiology, 2004,139: 179-189.
[32] McCulloh K.A., Sperry J.S., Adler F.R. Water transport in plants obeys Murray's law. Nature, 2003,421: 939-942.
[33] West G.B., Brown J.H., Enquist B.J. A general model for the origin of allometric scaling laws in biology. Science, 1997,276: 122-126.
[34] West G.B., Brown J.H., Enquist B.J. A general model for the structure and allometry of plant vascular systems. Nature, 1999,400: 664-667.
[35] Brown J.H., West GB., Enquist B.J. Scaling in Biology. UK: Oxford University, 2000.
[36] West G.B., Brown J.H., Enquist B.J. The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 1999, 284: 1677-1679.
[37] Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Int. J. Heat Mass Transfer, 1997,40: 799-816.
[38] Bejan A. Constructal theory: from thermodynamic and geometric optimization to predicting shape in nature. Energy Conv. Manag., 1998,39: 1705-1718.
[39] Bejan A. Shape and Structure, from Engineering to Nature. Cambridge (UK): Cambridge University Press, 2000.
[40] Bejan A., Lorente S. The Constructal Law. Paris: L'Harmattan, 2005.
[41] Durand M. Architecture of optimal transport networks. Phys. Rev. E. 2006, 73: 016116.
[42] Durand M. Optimizing transport in a homogeneous network. Phys. Rev. E, 2004, 70: 046125.
[43] Lasance C., Simons R.E. Advances in high-performance cooling for electronics. ElectronicsCooling, 2005,11.
[44] Tuckerman D.B., Pease R.F.W. Higher-performance heat sinking for VLSI. IEEE Electron Device Letters, 1981, 2: 126-129.
[45] Bejan A., Errera M.R. Deterministic tree networks for fluid flow: geometry for minimal flow resistance between a volume and one point. Fractals, 1997, 5: 685-695.
[46] Bejan A. Constructal tree network for fluid flow between a finite-size volume and one source or sink. Rev. Gen. Therm., 1997,36: 592-604.
[47] Bejan A. The tree of convective heat stream: its thermal insulation function and the predicted 3/4-power relation between body heat loss and body size. International Journal of Heat and Mass Transfer, 2001,44: 699-704.
[48] Pence D.V. Improved thermal efficiency and temperature uniformity using fractal-like branching channel networks. in: Proceedings of the International Conference on Heat Transfer and Transport Phenomena in Microscale. New York: Banff, Canada and Begell House, 2000. 142-148.
[49] Pence D.V. Reduced pumping power and wall temperature in microchannel heat sinks with fractal-like branching channel networks.Microscale Thermophysical Engineering,2002,6:319-330.
[50]Chen Y.P.,Cheng P.Heat transfer and pressure drop in fractal tree-like microchannel nets.Int.J.Heat Mass Transfer,2002,45:2643-2648.
[51]Chen Y.P.,Cheng P.An experimental investigation on the thermal efficiency of fractal tree-like microchannel nets.International Communications in Heat and Mass Transfer,2005,32:931-938.
[52]Alharbi A.Y.,Pence D.V.,Cullion R..N.Fluid flow through microscale fractal-like branching channel networks.Journal of Fluids Engineering,2003,125:1051-1057.
[53]Alharbi A.Y.,Pence D.V.,Cullion R.N.Thermal characteristics of microscale fractal-like branching channels.Journal of Heat Transfer,2004,126:744-752.
[54]Wang X.Q.,Mujumdar A.S.,Yap C.Thermal characteristics of tree-shaped microchannel nets for cooling of a rectangular heat sink.International Journal of Thermal Sciences,2006,45:1103-1112.
[55]Wang X.Q.,Mujumdar A.S.,Yap C.Numerical analysis of blockage and optimization of heat transfer performance of fractal-like microchannel nets.Journal of Electronic Packaging,2006,128:38-45.
[56]Wang X.Q.,Yap C.,Mujumdar A.S.Laminar heat transfer in constructal microchannel networks with loops.Journal of Electronic Packaging,2006,128:273-280.
[57]Ghodoossi L.Thermal and hydrodynamic analysis of a fractal microchannel network.Energy Conversion and Management,2005,46:771-788.
[58]Mathieu-Potvin F.,Gosselin L.Optimal conduction pathways for cooling a heat-generating body:A comparison exercise.International Journal of Heat and Mass Transfer,2007,50:2996-3006.
[59]Kearney M.M.Engineering fractals enhance process applications.Chemical Engineering Progress,2000,96:61-68.
[60]Tondeur D.,Luo L.Design and scaling laws of ramified fluid distributors by constructal approach.Chemical Engineering Science,2004,59:1799-1813.
[61]Emerson D.R.,Cieslicki K.,Gu X.et al.Biomimetic design of microfluidic manifolds based on a generalized Murray's law.Lab Chip,2006,6:447-454.
[62]Barber R.W.,Emerson D.R.Optimal design of microfluidic networks using biologically inspired principles.Microfluid Nanofluid,2007,DOI:10.1007/s10404-007-0163-6.
[63]T(u|¨)ber K.,Oegegaard A.,Hermann M.et al.Investigation of fractal flow-fields in portable proton exchange membrane and direct methanol fuel cells.Journal of Power Sources,2004,131:175-181.
[64]Senn S.M.,Poulikakos D.Tree network channels as fluid distributors constructing double-staircase polymer electrolyte fuel cells.Journal of Applied Physics,2004,96:842-852.
[65]Senn S.M.,Poulikakos D.Laminar mixing,heat transfer and pressure drop in tree-like microchannel nets and their application for thermal management in polymer electrolyte fuel cells.Journal of Power Sources,2004,130:178-191.
[66]Senn S.M.,Poulikakos D.Pyramidal direct methanol fuel cells.International Journal of Heat and Mass Transfer,2006,49:1516-1528.
[67]Vandewalle N.,Ausloos M.Construction and properties of fractal trees with tunable dimension:The interplay of geometry and physics.Physical Review E,1997,55:94-98.
[68]Wang Ruichun,Guo Jingdong,Zhou Benlian.Preparation of Nickel Materials with Fractal Structure.J.Mater.Sci.Technol.,2003,19:229-231.
[69]Xu Peng,Yu Boming,Yuan Meijuan et al.Heat conduction in fractal tree-like branched networks.International Journal of Heat and Mass Transfer,2006,49:3746-3751.
[70]Yu Boming,Li Bowen.Fractal-like tree networks reducing the thermal conductivity.Physical Review E,2006,73:066302.
[71]Xu Peng,Yu Boming,Feng Yongjin et al.Analysis of permeability for the fractal-like tree network by parallel and series models.Physica A,2006,369:884-894.
[72]Xu Peng,Yu Boming,Feng Yongjin et al.Permeability of the fractal disk-shaped branched network with tortuosity effect.Physics of Fluids,2006,18:078103.
[73]Chen Jun,Yu Boming,Xu Peng et al.Fractal-like tree networks increasing the permeability.Physical Review E,2007,75:056301.
[74]Xu Peng,Yu Boming,Qiu Shuxia et al.An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks.Physica A,2008,387:6471-6483.
[75]Xu Peng,Yu Boming.The scaling laws of transport properties for fractal-like tree networks.Journal of Applied Physics,2006,100:104906.
[76]Feder J.Fractals.New York:Plenum Press,1988.
[77]张济忠.分形[M.].北京:清华大学出版社,1995.
[78]Majumdar A.Role of fractal geometry in the study of thermal phenomena,in:Tien C.L.Annual Review of Heat Transfer.Paris:Hemisphere Publishing Co.,Vol.Ⅳ,1992.
[79]Zamir M.On fractal properties of arterial trees.J.theor.Biol.,1999,197:517-526.
[80]Grasman J.,Brascamp J.W.,Van Leeuwen J.L.et al.The multifractal structure of arterial trees.J.theor.Biol.,2003,220:75-82.
[81]Shlesinger M.F.,West B.J.Complex fractal dimension of the brionchial tree.Phys.Rev.Lett.,1991,67:2106.
[82]Kalda J.On the fractality of the biological tree-like structures.Discrete Dynamics in Nature and Society,1999,3:297-306.
[83]Neagu M.,Bejan A.Constructal-theory tree networks of "constant" thermal resistance.Journal of Applied Physics,1999,86:1136-1144.
[84]戴锅生.传热学[M.].北京:高等教育出版社,1991.
[85]杨世铭,陶文铨(第三版).传热学.北京:高等教育出版社,1998.
[86]张也影.流体力学(第二版).北京:高等教育出版社,2002.
[87]Fox R.W.,McDonald A.T.,Pritehard P.J.Introduction to Fluid Mechanics(6~(th)Edition).USA:John Wiley & Sons,2004.
[88]Bejan A.,Rocha L.A.O.,Lorente S.Thermodynamic optimization of geometry:T-and Y-shaped constructs of fluid streams.Int.J.Therm.Sci.,2000,39:949-960.
[89]Bear J.Dynamics of Fluids in Porous Media.New York:Elsevier,1972.
[90]Scherdegger A.E.The Physics of Flow in Porous Media.New York:Elsevier,1972.
[91]孔祥言.高等渗流力学.安徽:中国科学技术大学出版社,1999.
[92]Cussler E.L.Diffusion,Mass Transfer in Fluid Systems.New York:Cambridge University Press,1984
[93]Cieslicki K.Resistance to the blood flow of a vascular tree-a model study.Polish J Med Eng,1999,5:161-172.
[94]R.W.Barber,K.Cieslicki and D.R.Emerson,Using Murray's law to design artificial vascular microfluidic networks.In:Design and Nature Ⅲ:Comparing design in nature with science and engineering.WIT Press,Southampton,2006,pp 245-254.
[95]Zamir M.Nonsymmetrieal bifurcations in arterial branching.J.Gen.Physiol.,1978,72:837-845.
[96]Zamir M.Arterial branching within the confines of fractal L-System formalism.J.Gen.Physiol.,2001,118:267-275.
[97]Uylings H.B.M.Optimization of diameters and bifurcation angles in lung and vascular tree structures Bull.Math.Biol.,1977,39:509-519.
[98]Bejan A.Advanced Engineeering Thermodynamics(2nd ed.).New York:Wiley,1997.
[99]Neagu M.,Bejan A.Three-dimensional tree constructs of "constant" thermal resistance.Journal of Applied Physics,1999,86:7170-7115.
[100]Gosselin L.,Bejan A.Constructal heat trees at micro and nanoscales.Journal of Applied Physics,2004,96:5852-5859.
[101]Muralidhar K.Equivalent conductivity of a heterogeneous medium.Int.J.Heat Mass Transfer,1990,33:1759-1766.
[102]Hus C.T.,Cheng P.,Wong K.W.A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media.J.Heat Transfer,1995,117:264-269.
[103]Yu Boming,Cheng Ping.Fractal models for the effective thermal conductivity of bi-dispersed porous media.J.Thermophysics and Heat Transfer,2002,16:22-29.
[104]Reis A.H.,Miguel A.F.,Aydin M.Constructal theory of flow architectures of the lungs.Medical Physics,2004,31:1135-1140.
[105]Yu Boming,Yao K.L.Numerical evidence of the critical percolation probability Pc=1 for site problems on Sierpinski gaskets.Journal of Physics A,1988,21:3269-3274.
[106]Yu B.M.,Yao K.L.Computation of heat conduction in self-similar porous structures.Physical Review A,1991,44:3664-3668.
[107]Pence D.V.,Ertfield K.E.Inherent benefits in microscale fractal-like devices for enhanced transport phenomena,in:Collins M.,Brebbia C.A.Design and Nature.Rhodes,Greece:WIT Press,2004.317-328.
[108]Wechsatol W.,Lorente S.,Bejan A.Optimal tree-shaped networks for fluid flow in a disc-shaped body.Int.J.Heat Mass Transfer,2002,45:4911-4924.
[109]Lorente S.,Wechsatol W.,Bejan A.Tree-shaped flow structures designed by minimizing path lengths.International Journal of Heat and Mass Transfer,2002,45:3299-3312.
[110]Tien C.L.,Vafai K.Statistical bounds for the effective thermal conductivity of microsphere and fibrous insulation.AIAA Progress Series,1979,65:135-148.
[111]Dullien F. A. L. Porous Media, Fluid Transport and Pore Structure (2nd ed.). San Diego: Academic Press, 1992.
[112] Wechsatol W., Lorente S., Bejan A. Tree-shaped networks with loops. Int. J. Heat Mass Transfer, 2005,48: 573-583.
[113] Lorente S., Bejan A. Heterogeneous porous media as multiscale structures for maximum flow access. J. Appl. Phys., 2006,100:114909.
[114] Aziz K., Settari A. Petroleum Reservoir Simulation. London: Elsevier, 1985.
[115] Naff R.L. Radial flow in heterogeneous porous media: An analysis of specific discharge. Water Resour. Res., 1991,27: 307-316.
[116] Riva M., Guadagnini A., Neuman S.P. et al. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media, 2001,45: 139-193.
[117] Selley R.C. Elements of petroleum geology (2nd ed.). San Diego: Academic Press, 1998.256-281.
[118] Boggs J.M., Adams E.E. Field study of dispersion in a heterogeneous aquifer, 4. Investigation of adsorption and sampling bias. Water Resour. Res., 1992, 28: 3325-3336.
[119] Harvey C.F., Gorelick S.M. Rate-limited mass transfer of macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site? Water Resour. Res., 2000, 36: 637-650.
[120] Zheng C., Gorelick S.M. Analysis of solute transport in flow fields influenced by preferential flowpaths at the decimeter scale. Ground Water, 2003,41: 142-155.
[121]Ronayne M.J., Gorelick S.M. Effective permeability of porous media containing branching channel networks. Phys. Rev. E, 2006, 73: 026305.
[122] Acuna J.A., Yortsos Y.C. Application of fractal geometry to the study of networks of fractures and their pressure transient. Water Resour. Res., 1995, 31: 527-540.
[123] Fomin S., Chugunov V., Hashida T. Assessment of stimulated area growth during high-pressure hydraulic stimulation of fractured subsurface reservoir. Trans. Porous Media,2006,63:99-125.
[124]Chang J.,Yortsos Y.C.Pressure-transient analysis of fractal reservoirs.SPE Formation Evaluation,1990,March:31-38.
[125]Sahimi M.Flow and Transport in Porous Media and Fractured Rocks.Weinheim,Germany:VCH,1995.
[126]Yu B.M.,Li J.H.Some fractal characters of porous media.Fractals,2001,9:365-372.
[127]Yu B.M.,Cheng P.A fractal permeability model for bi-dispersed porous media.Int.J.Heat Mass Transfer,2002,45:2983-2993.
[128]郁伯铭.多孔介质输运性质的分形分析研究进展.力学进展,2003,33(3):333-346.
[129]郁伯铭.分形介质的传热与传质分析(综述).工程热物理学报,2003,24(3):481-483.
[130]Wheatcraft S.W.,Tyler S.W.Explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry.Water Resour.Res.,1988,24:566-578.
[131]Journel A.G.,Deutsch C.V.,Desbarats A.J.Power averaging for block effective permeability,in:Society of Petroleum Engineers.56th Califomia Regional Meeting.California:1986,329-334.
[132]Dagan G.Flow and transport in porous formations.New York:Springer-Verlag,1989.
[133]Perina T.,Lee T.-C.Transient Soil Vapor Extraction from a Pressure-Controlled Well.Ground Water Monit.Remediat.,2007,27:47-55.
[134]Neuman S.P.Generalized scaling of permeabilities:Validation and effect of support scale.Geophys.Res.Lett.,1994,21:349-352.
[135]Winter C.L.,Tartakovsky Daniel M.Theoretical foundation for conductivity scaling.Geophys.Res.Lett.,2001,22:4367-4369.
[2] West B. J. Fractal Physiology and Chaos in Medicine. Singapore: World Scientific, 1990.
[3] Bassingthwaighte, J.B., Liebovitch L.S., West B.J. Fractal Physiology. New York: Oxford University Press, 1994.
[4] Antonets V.A., Atonets M.A., Shereshevsky LA. The statistical cluster dynamics in the dendroid transfer systems. in: Fractal in the Fundamental and Applied Sciences. North-Holland: Elsevier, 1991. 59-71.
[5] Bejan A., Lorente S. Constructal theory of generation of configuration in nature and engineering. Journal of Applied Physics, 2006,100: 041301.
[6] Hess W.R. Uber die periphere Regulierung der Blutzirkulation. Pflugers Archiv Gesamte Physiol. Menschen Tiere. 1917,168: 439-490.
[7] Thompson D.W. On Growth and Form. 2~(nd) ed. Cambridge: Cambridge University Press, 1917.948-957.
[8] Murray C.D. The physiological principle of minimum work. I. The vascular system and the cost of blood volume. Proc. Natl. Acad. Sci. U. S. A., 1926,12: 207-214.
[9] Murray C.D. The physiological principle of minimum work applied to the angle of branching of arteries. J. Gen. Physiol., 1926, 9: 835-841.
[10] Murray C.D. A relationship between circumference and weight in trees and its bearing on branching angles. J. Gen. Physiol., 1927,10: 725-729.
[11] Sherman T.F. On connecting large vessels to small—The Meaning of Murray's Law. J. Gen. Physiol., 1981, 78: 431-453.
[12] Weibel E.R. Morphometry of the Human Lung. New York: Academic Press Inc., 1963.
[13]Hooper G.Diameters of bronchi and asymmetrical divisions.Respir.Physiol.,1977,31:291-294.
[14]West J.B.Respiratory Physiology—The Essentials.2~(nd) ed.Baltimore:Williams and Wilkins,1979.
[15]Horsfield K.,Cumming G.Morphology of the bronchial tree in man.J.Appl.Physiol.,1968,24:373-383.
[16]Gabrys E.,Rybaczuk M..Kedzia A.Fractal models of circulatory system.Symmetrical and asymmetrical approach comparison.Chaos,Solitons and Fractals,2005,24:707-715.
[17]Dokoumetzidis A.,Macheras P.A model for transport and dispersion int he circulatory system based on the vascular fractal tree.Annals of Biomedical Engineering,2003,31:284-293.
[18]Zhong J.,Nilsson G.An M-ary fractal tree based modeling of microcirculation.Proc Annu ConfEng Med Biol,IEEE.Piscataway:1993,15:553-554.
[19]Masters B.R.Fractal analysis of the vascular tree in the human retina.Annu.Rev.Biomed.Eng.,2004,6:427-452.
[20]Buijs Jorn Op Den,Bajzer Zeljko,Ritman Erik L.Branching morphology of the rat hepatic portal vein tree.Annals of Biomedical Engineering,2006,34:14201428.
[21]Taber L.A.,Ng S.,Quesnel A.M.et al.Investigating Murray's Law in the chick embryo.Journal of Biomechanics,2001,34:121-124.
[22]Mauroy B.Filoche M.,Weibel E.R.et al.An optimal bronchial tree may be dangerous.Nature,2004,427:633-636.
[23]Singhal S.,Henderson R.,Horsfield K.et al.Morphometry of the human pulmonary arterial tree.Cir.Res.,1973,33:190-197.
[24]Horsfield K.Morphometry of the small pulmonary arteries in man.Circ.Res.,1978,42:593-597.
[25]Huang W.,Yen R.T.,McLaurine M.et al.Morphometry of the human pulmonary vasculature. J. Appl. Physiol., 1996, 81: 2123-2133.
[26] Bennett S.H. Modeling methodology for vascular input impedance determination and interpretation. J. Appl. Physiol., 1994,76:455-484.
[27] Bennett S.H., Goetzman B.W., Milstein J.M. et al. Role of arterial design on pulse wave reflection in.a fractal pulmonary network. J. Appl. Physiol., 1996, 80: 1033-1056.
[28] Haworth S.T., Linehan J.H., Bronikowski T.A. et al., A hemodynamic model representation of the dog lung. J. Appl. Physiol., 1991, 70: 15-26.
[29] Krenz G.S., Lin J., Dawson C.A. et al. Impact of parallel heterogeneity on a continuum model of the pulmonary arterial tree. J. Appl. Physiol., 1994, 77: 660-670.
[30] Dawson C.A., Krenz GS., Karau K.L. et al. Structure-function relationships in the pulmonary arterial tree. J. Appl. Physiol., 1999, 86: 569-583.
[31] Frey U., Hislop A., Silverman M. Branching properties of the pulmonary arterial tree during pre- and postnatal development. Respiratory Physiology & Neurobiology, 2004,139: 179-189.
[32] McCulloh K.A., Sperry J.S., Adler F.R. Water transport in plants obeys Murray's law. Nature, 2003,421: 939-942.
[33] West G.B., Brown J.H., Enquist B.J. A general model for the origin of allometric scaling laws in biology. Science, 1997,276: 122-126.
[34] West G.B., Brown J.H., Enquist B.J. A general model for the structure and allometry of plant vascular systems. Nature, 1999,400: 664-667.
[35] Brown J.H., West GB., Enquist B.J. Scaling in Biology. UK: Oxford University, 2000.
[36] West G.B., Brown J.H., Enquist B.J. The fourth dimension of life: Fractal geometry and allometric scaling of organisms. Science, 1999, 284: 1677-1679.
[37] Bejan A. Constructal-theory network of conducting paths for cooling a heat generating volume. Int. J. Heat Mass Transfer, 1997,40: 799-816.
[38] Bejan A. Constructal theory: from thermodynamic and geometric optimization to predicting shape in nature. Energy Conv. Manag., 1998,39: 1705-1718.
[39] Bejan A. Shape and Structure, from Engineering to Nature. Cambridge (UK): Cambridge University Press, 2000.
[40] Bejan A., Lorente S. The Constructal Law. Paris: L'Harmattan, 2005.
[41] Durand M. Architecture of optimal transport networks. Phys. Rev. E. 2006, 73: 016116.
[42] Durand M. Optimizing transport in a homogeneous network. Phys. Rev. E, 2004, 70: 046125.
[43] Lasance C., Simons R.E. Advances in high-performance cooling for electronics. ElectronicsCooling, 2005,11.
[44] Tuckerman D.B., Pease R.F.W. Higher-performance heat sinking for VLSI. IEEE Electron Device Letters, 1981, 2: 126-129.
[45] Bejan A., Errera M.R. Deterministic tree networks for fluid flow: geometry for minimal flow resistance between a volume and one point. Fractals, 1997, 5: 685-695.
[46] Bejan A. Constructal tree network for fluid flow between a finite-size volume and one source or sink. Rev. Gen. Therm., 1997,36: 592-604.
[47] Bejan A. The tree of convective heat stream: its thermal insulation function and the predicted 3/4-power relation between body heat loss and body size. International Journal of Heat and Mass Transfer, 2001,44: 699-704.
[48] Pence D.V. Improved thermal efficiency and temperature uniformity using fractal-like branching channel networks. in: Proceedings of the International Conference on Heat Transfer and Transport Phenomena in Microscale. New York: Banff, Canada and Begell House, 2000. 142-148.
[49] Pence D.V. Reduced pumping power and wall temperature in microchannel heat sinks with fractal-like branching channel networks.Microscale Thermophysical Engineering,2002,6:319-330.
[50]Chen Y.P.,Cheng P.Heat transfer and pressure drop in fractal tree-like microchannel nets.Int.J.Heat Mass Transfer,2002,45:2643-2648.
[51]Chen Y.P.,Cheng P.An experimental investigation on the thermal efficiency of fractal tree-like microchannel nets.International Communications in Heat and Mass Transfer,2005,32:931-938.
[52]Alharbi A.Y.,Pence D.V.,Cullion R..N.Fluid flow through microscale fractal-like branching channel networks.Journal of Fluids Engineering,2003,125:1051-1057.
[53]Alharbi A.Y.,Pence D.V.,Cullion R.N.Thermal characteristics of microscale fractal-like branching channels.Journal of Heat Transfer,2004,126:744-752.
[54]Wang X.Q.,Mujumdar A.S.,Yap C.Thermal characteristics of tree-shaped microchannel nets for cooling of a rectangular heat sink.International Journal of Thermal Sciences,2006,45:1103-1112.
[55]Wang X.Q.,Mujumdar A.S.,Yap C.Numerical analysis of blockage and optimization of heat transfer performance of fractal-like microchannel nets.Journal of Electronic Packaging,2006,128:38-45.
[56]Wang X.Q.,Yap C.,Mujumdar A.S.Laminar heat transfer in constructal microchannel networks with loops.Journal of Electronic Packaging,2006,128:273-280.
[57]Ghodoossi L.Thermal and hydrodynamic analysis of a fractal microchannel network.Energy Conversion and Management,2005,46:771-788.
[58]Mathieu-Potvin F.,Gosselin L.Optimal conduction pathways for cooling a heat-generating body:A comparison exercise.International Journal of Heat and Mass Transfer,2007,50:2996-3006.
[59]Kearney M.M.Engineering fractals enhance process applications.Chemical Engineering Progress,2000,96:61-68.
[60]Tondeur D.,Luo L.Design and scaling laws of ramified fluid distributors by constructal approach.Chemical Engineering Science,2004,59:1799-1813.
[61]Emerson D.R.,Cieslicki K.,Gu X.et al.Biomimetic design of microfluidic manifolds based on a generalized Murray's law.Lab Chip,2006,6:447-454.
[62]Barber R.W.,Emerson D.R.Optimal design of microfluidic networks using biologically inspired principles.Microfluid Nanofluid,2007,DOI:10.1007/s10404-007-0163-6.
[63]T(u|¨)ber K.,Oegegaard A.,Hermann M.et al.Investigation of fractal flow-fields in portable proton exchange membrane and direct methanol fuel cells.Journal of Power Sources,2004,131:175-181.
[64]Senn S.M.,Poulikakos D.Tree network channels as fluid distributors constructing double-staircase polymer electrolyte fuel cells.Journal of Applied Physics,2004,96:842-852.
[65]Senn S.M.,Poulikakos D.Laminar mixing,heat transfer and pressure drop in tree-like microchannel nets and their application for thermal management in polymer electrolyte fuel cells.Journal of Power Sources,2004,130:178-191.
[66]Senn S.M.,Poulikakos D.Pyramidal direct methanol fuel cells.International Journal of Heat and Mass Transfer,2006,49:1516-1528.
[67]Vandewalle N.,Ausloos M.Construction and properties of fractal trees with tunable dimension:The interplay of geometry and physics.Physical Review E,1997,55:94-98.
[68]Wang Ruichun,Guo Jingdong,Zhou Benlian.Preparation of Nickel Materials with Fractal Structure.J.Mater.Sci.Technol.,2003,19:229-231.
[69]Xu Peng,Yu Boming,Yuan Meijuan et al.Heat conduction in fractal tree-like branched networks.International Journal of Heat and Mass Transfer,2006,49:3746-3751.
[70]Yu Boming,Li Bowen.Fractal-like tree networks reducing the thermal conductivity.Physical Review E,2006,73:066302.
[71]Xu Peng,Yu Boming,Feng Yongjin et al.Analysis of permeability for the fractal-like tree network by parallel and series models.Physica A,2006,369:884-894.
[72]Xu Peng,Yu Boming,Feng Yongjin et al.Permeability of the fractal disk-shaped branched network with tortuosity effect.Physics of Fluids,2006,18:078103.
[73]Chen Jun,Yu Boming,Xu Peng et al.Fractal-like tree networks increasing the permeability.Physical Review E,2007,75:056301.
[74]Xu Peng,Yu Boming,Qiu Shuxia et al.An analysis of the radial flow in the heterogeneous porous media based on fractal and constructal tree networks.Physica A,2008,387:6471-6483.
[75]Xu Peng,Yu Boming.The scaling laws of transport properties for fractal-like tree networks.Journal of Applied Physics,2006,100:104906.
[76]Feder J.Fractals.New York:Plenum Press,1988.
[77]张济忠.分形[M.].北京:清华大学出版社,1995.
[78]Majumdar A.Role of fractal geometry in the study of thermal phenomena,in:Tien C.L.Annual Review of Heat Transfer.Paris:Hemisphere Publishing Co.,Vol.Ⅳ,1992.
[79]Zamir M.On fractal properties of arterial trees.J.theor.Biol.,1999,197:517-526.
[80]Grasman J.,Brascamp J.W.,Van Leeuwen J.L.et al.The multifractal structure of arterial trees.J.theor.Biol.,2003,220:75-82.
[81]Shlesinger M.F.,West B.J.Complex fractal dimension of the brionchial tree.Phys.Rev.Lett.,1991,67:2106.
[82]Kalda J.On the fractality of the biological tree-like structures.Discrete Dynamics in Nature and Society,1999,3:297-306.
[83]Neagu M.,Bejan A.Constructal-theory tree networks of "constant" thermal resistance.Journal of Applied Physics,1999,86:1136-1144.
[84]戴锅生.传热学[M.].北京:高等教育出版社,1991.
[85]杨世铭,陶文铨(第三版).传热学.北京:高等教育出版社,1998.
[86]张也影.流体力学(第二版).北京:高等教育出版社,2002.
[87]Fox R.W.,McDonald A.T.,Pritehard P.J.Introduction to Fluid Mechanics(6~(th)Edition).USA:John Wiley & Sons,2004.
[88]Bejan A.,Rocha L.A.O.,Lorente S.Thermodynamic optimization of geometry:T-and Y-shaped constructs of fluid streams.Int.J.Therm.Sci.,2000,39:949-960.
[89]Bear J.Dynamics of Fluids in Porous Media.New York:Elsevier,1972.
[90]Scherdegger A.E.The Physics of Flow in Porous Media.New York:Elsevier,1972.
[91]孔祥言.高等渗流力学.安徽:中国科学技术大学出版社,1999.
[92]Cussler E.L.Diffusion,Mass Transfer in Fluid Systems.New York:Cambridge University Press,1984
[93]Cieslicki K.Resistance to the blood flow of a vascular tree-a model study.Polish J Med Eng,1999,5:161-172.
[94]R.W.Barber,K.Cieslicki and D.R.Emerson,Using Murray's law to design artificial vascular microfluidic networks.In:Design and Nature Ⅲ:Comparing design in nature with science and engineering.WIT Press,Southampton,2006,pp 245-254.
[95]Zamir M.Nonsymmetrieal bifurcations in arterial branching.J.Gen.Physiol.,1978,72:837-845.
[96]Zamir M.Arterial branching within the confines of fractal L-System formalism.J.Gen.Physiol.,2001,118:267-275.
[97]Uylings H.B.M.Optimization of diameters and bifurcation angles in lung and vascular tree structures Bull.Math.Biol.,1977,39:509-519.
[98]Bejan A.Advanced Engineeering Thermodynamics(2nd ed.).New York:Wiley,1997.
[99]Neagu M.,Bejan A.Three-dimensional tree constructs of "constant" thermal resistance.Journal of Applied Physics,1999,86:7170-7115.
[100]Gosselin L.,Bejan A.Constructal heat trees at micro and nanoscales.Journal of Applied Physics,2004,96:5852-5859.
[101]Muralidhar K.Equivalent conductivity of a heterogeneous medium.Int.J.Heat Mass Transfer,1990,33:1759-1766.
[102]Hus C.T.,Cheng P.,Wong K.W.A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media.J.Heat Transfer,1995,117:264-269.
[103]Yu Boming,Cheng Ping.Fractal models for the effective thermal conductivity of bi-dispersed porous media.J.Thermophysics and Heat Transfer,2002,16:22-29.
[104]Reis A.H.,Miguel A.F.,Aydin M.Constructal theory of flow architectures of the lungs.Medical Physics,2004,31:1135-1140.
[105]Yu Boming,Yao K.L.Numerical evidence of the critical percolation probability Pc=1 for site problems on Sierpinski gaskets.Journal of Physics A,1988,21:3269-3274.
[106]Yu B.M.,Yao K.L.Computation of heat conduction in self-similar porous structures.Physical Review A,1991,44:3664-3668.
[107]Pence D.V.,Ertfield K.E.Inherent benefits in microscale fractal-like devices for enhanced transport phenomena,in:Collins M.,Brebbia C.A.Design and Nature.Rhodes,Greece:WIT Press,2004.317-328.
[108]Wechsatol W.,Lorente S.,Bejan A.Optimal tree-shaped networks for fluid flow in a disc-shaped body.Int.J.Heat Mass Transfer,2002,45:4911-4924.
[109]Lorente S.,Wechsatol W.,Bejan A.Tree-shaped flow structures designed by minimizing path lengths.International Journal of Heat and Mass Transfer,2002,45:3299-3312.
[110]Tien C.L.,Vafai K.Statistical bounds for the effective thermal conductivity of microsphere and fibrous insulation.AIAA Progress Series,1979,65:135-148.
[111]Dullien F. A. L. Porous Media, Fluid Transport and Pore Structure (2nd ed.). San Diego: Academic Press, 1992.
[112] Wechsatol W., Lorente S., Bejan A. Tree-shaped networks with loops. Int. J. Heat Mass Transfer, 2005,48: 573-583.
[113] Lorente S., Bejan A. Heterogeneous porous media as multiscale structures for maximum flow access. J. Appl. Phys., 2006,100:114909.
[114] Aziz K., Settari A. Petroleum Reservoir Simulation. London: Elsevier, 1985.
[115] Naff R.L. Radial flow in heterogeneous porous media: An analysis of specific discharge. Water Resour. Res., 1991,27: 307-316.
[116] Riva M., Guadagnini A., Neuman S.P. et al. Radial flow in a bounded randomly heterogeneous aquifer. Transport in Porous Media, 2001,45: 139-193.
[117] Selley R.C. Elements of petroleum geology (2nd ed.). San Diego: Academic Press, 1998.256-281.
[118] Boggs J.M., Adams E.E. Field study of dispersion in a heterogeneous aquifer, 4. Investigation of adsorption and sampling bias. Water Resour. Res., 1992, 28: 3325-3336.
[119] Harvey C.F., Gorelick S.M. Rate-limited mass transfer of macrodispersion: Which dominates plume evolution at the Macrodispersion Experiment (MADE) site? Water Resour. Res., 2000, 36: 637-650.
[120] Zheng C., Gorelick S.M. Analysis of solute transport in flow fields influenced by preferential flowpaths at the decimeter scale. Ground Water, 2003,41: 142-155.
[121]Ronayne M.J., Gorelick S.M. Effective permeability of porous media containing branching channel networks. Phys. Rev. E, 2006, 73: 026305.
[122] Acuna J.A., Yortsos Y.C. Application of fractal geometry to the study of networks of fractures and their pressure transient. Water Resour. Res., 1995, 31: 527-540.
[123] Fomin S., Chugunov V., Hashida T. Assessment of stimulated area growth during high-pressure hydraulic stimulation of fractured subsurface reservoir. Trans. Porous Media,2006,63:99-125.
[124]Chang J.,Yortsos Y.C.Pressure-transient analysis of fractal reservoirs.SPE Formation Evaluation,1990,March:31-38.
[125]Sahimi M.Flow and Transport in Porous Media and Fractured Rocks.Weinheim,Germany:VCH,1995.
[126]Yu B.M.,Li J.H.Some fractal characters of porous media.Fractals,2001,9:365-372.
[127]Yu B.M.,Cheng P.A fractal permeability model for bi-dispersed porous media.Int.J.Heat Mass Transfer,2002,45:2983-2993.
[128]郁伯铭.多孔介质输运性质的分形分析研究进展.力学进展,2003,33(3):333-346.
[129]郁伯铭.分形介质的传热与传质分析(综述).工程热物理学报,2003,24(3):481-483.
[130]Wheatcraft S.W.,Tyler S.W.Explanation of scale-dependent dispersivity in heterogeneous aquifers using concepts of fractal geometry.Water Resour.Res.,1988,24:566-578.
[131]Journel A.G.,Deutsch C.V.,Desbarats A.J.Power averaging for block effective permeability,in:Society of Petroleum Engineers.56th Califomia Regional Meeting.California:1986,329-334.
[132]Dagan G.Flow and transport in porous formations.New York:Springer-Verlag,1989.
[133]Perina T.,Lee T.-C.Transient Soil Vapor Extraction from a Pressure-Controlled Well.Ground Water Monit.Remediat.,2007,27:47-55.
[134]Neuman S.P.Generalized scaling of permeabilities:Validation and effect of support scale.Geophys.Res.Lett.,1994,21:349-352.
[135]Winter C.L.,Tartakovsky Daniel M.Theoretical foundation for conductivity scaling.Geophys.Res.Lett.,2001,22:4367-4369.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |