液压技术中复杂流道流场的数值模拟与可视化研究
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摘要
本文在参阅大量国内外有关流体动力技术、计算流体力学、流场的数值计算方
法、流场实验可视化技术、计算机数字图像处理技术等相关资料的基础上，推导确
定了复杂流道和液压阀中流体流动的数学模型，首次用有限元方法对液压技术中各
种异形断面流道、各种复杂流道和液压阀内部流道等的流场进行数值模拟，并将计
算结果以可视化的图形图像形式给出，在此基础上定性分析了流场结构（速度、流
线、流动的分离与再附壁，旋涡的产生与消失等）与噪声、能量损失的关系。同时
对流场进行DPIV（Digital Particle Image Velocimetry）实验可视化研究，验证了数值
计算的正确性。为设计高效率、低能耗、低噪声的液压阀和流体管道系统奠定了基
础，具有重要的理论意义和实际应用价值。
第一章综述了液压技术发展趋势及本科题的意义、来源，介绍了液压技术中液
体在复杂流道中的流动问题，简单叙述了计算流体力学中的各种数值计算方法，较
为详细地介绍了计算流体力学在液压技术中的应用现状，论述了流场数值计算可视
化技术，概述了流场实验可视化技术中的各种方法，阐述了计算机数字图像处理在
流场实验可视化中的应用，确定了本文的主要研究内容。
第二章建立了支配异形断面流道内流体流动的数学模型，并用有限元方法进行
离散。对包括等边三角形断面流道、矩形断面流道、梯形断面流道、半椭园形断面
流道等各种异形断面流道，在不同流动条件下断面上的速度、流量等参数进行数值
计算，并与有关的解析结果相比较，证明了所用方法的正确性。为工程实际中设计
和选择异形断面流道提供依据。
第三章简述了用有限元方法求解流体流动问题时，可以采用的几种不同形式的
数学模型，并简要说明了各种形式的特点。然后从连续性方程和Navier-Stokes方
程出发，推导出无量纲流函数-涡量式。分别介绍了当采用三节点三角形单元和四
节点等参四边形单元时，如何对单元进行有限元分析，以及如何计算各相关系数等。
这是能否用有限元方法正确描述流场的关键。
第四章分析研究了在用有限元方法求解流函数—涡量式时，如何确定进口处、
出口处，上、下壁面处，角点处等流函数和涡量的边界条件，特别是涡量边界条件。
对几种不同的涡量边界条件的确定方法进行了讨论，并以平行平板管道中的流动为
例进行计算，以便确定它们的精度。在此基础上计算方腔驱动流动和后台阶流动，
并讨论进、出流边界条件对后台阶流动的影响。这是进一步研究液压技术中各种复
杂流道流场的前期和基础工作。
第五章针对液压技术中常见的断面突然扩大管道、断面突然缩小管道、液压集
成块内部的复杂流道、各种节流孔口（包括薄壁孔口、偏置细长孔口）等的流场进
行有限元数值模拟，并给出流场的数值计算可视化图形图像，在此基础上定性分析
流体噪声、能量损失与流场结构之间的关系等，并提出相应的改进措施，为分析管
道系统的能量损失和降低噪声奠定理论基础。
第六章用有限元方法对液压传动与控制中最常见的两种结构形式的液压阀—液
压滑阀和液压锥阀流场进行数值预报，给出不同开口度和不同结构尺寸下流场结构
的可视化图像，定性分析涡旋的产生对流体噪声及能量损失可能产生的影响，并对
阀的流道结构进行改进。
第七章建立流场DPIV实验可视化系统，制做突然扩大流道模型，外流式锥阀
燕山大学工学博士学位论文
模型和滑阀模型，并利用粒子图像测速技术对模型的速度场进行测量。利用图像处
理分析软件对实验结果进行计算机数字图像处理，给出模型流场的实验可视化图
像，并与有限元计算结果进行对比分析，对导致数值计算与实验可视化之间出现误
差的各种可能原因进行了分析，便于今后进一步研究中加以注意和改进。
In this article, based on reading and studying a great number of references about
fluid dynamic technique, computational fluid mechanics, numerical computing methods
of flow field, visualization in science computing, experimental visualization in fluid flow
computer digital image processing technique etc, the mathematical models which
governing the flow in complicated conduits and hydraulic valve have been derived, the
finite element method is applied to simulate the flow field of various non-circular cross-
section duct, various complicated channel and hydraulic valve, the computing results are
given in the form of visualized pictures or images, based on these results, the relationship
between the flow field structure and the flow noise, energy loss are analyzed
quantitatively. At the same time, the experimental visualization - DPIV(Digital Particle
Image Velocimetry) is also carried out, and it proves the computing result is correct. It has
important significance for us to design hydraulic valves and pipeline systems which are
high in efficiency, low in energy loss, low in noise.
In chapter 1, hydraulic technique and its developing trends are summarized, the flow
problems in complicated flow channel of hydraulic technique are introduced. Various
numerical methods of computational fluid dynamics are present briefly, the present
situations of application of computational fluid dynamics in hydraulic technique are
described in detail. The computational visualization technique of flow field is outlined,
various flow field experimental visualization methods are surveyed. The application of
computer digital image processing technique in experimental visualization of flow field is
discussed. The main researching contents are determined.
In chapter 2, the mathematical model which governs the flow in non-circular cross-
section channel is established, FEM(Finite Element Method)is used to discrete the
equations. The cross-section parameters such as velocity and flowrate at different flow
conditions for various non-circular duct such as equilateral triangle channel, rectangle
channel, terrace channel, semi-elliptical channel etc are calculated. Parts of the numerical
results are compared with the analytical results, it shows that the numerical method used
here is correct.
In chapter 3, several different kinds of mathematical models and their characteristics
when we solve the flow problems with FEM are presented. From continuity equation and
Navier-Stokes equation, non-dirnensionalized stream function ?vorticity equations is
derived. Ho~v to analyze the elements with FEM and how to calculated the related
coefficients when adopting three nodes triangle elements and four nodes quadrilateral
elements respectively is proposed, which is the key for computing the flow field correctly.
In chapter 4, how to determine the boundary conditions of stream function and
vorticity, especially vorticity boundary conditions at inlet, outlet, up wall, down wall and
the corner are studied when using FEM to solve the stream function-vorticity equation.
Several approaches of determining the vorticity boundary condition are discussed. The
flow in parallel plate channel is computed as an example to verify their accuracy. Based
on above analysis, the flow in square cavity and backward-facing step is investigated, the
influence of inlet and outlet boundary conditions on backward facing step are also
examed.
In chapter 5, the flow field of several different flow channels frequently used in
hydraulic technique such as sudden expansion channel, sudden contraction channel,
法、流场实验可视化技术、计算机数字图像处理技术等相关资料的基础上，推导确
定了复杂流道和液压阀中流体流动的数学模型，首次用有限元方法对液压技术中各
种异形断面流道、各种复杂流道和液压阀内部流道等的流场进行数值模拟，并将计
算结果以可视化的图形图像形式给出，在此基础上定性分析了流场结构（速度、流
线、流动的分离与再附壁，旋涡的产生与消失等）与噪声、能量损失的关系。同时
对流场进行DPIV（Digital Particle Image Velocimetry）实验可视化研究，验证了数值
计算的正确性。为设计高效率、低能耗、低噪声的液压阀和流体管道系统奠定了基
础，具有重要的理论意义和实际应用价值。
第一章综述了液压技术发展趋势及本科题的意义、来源，介绍了液压技术中液
体在复杂流道中的流动问题，简单叙述了计算流体力学中的各种数值计算方法，较
为详细地介绍了计算流体力学在液压技术中的应用现状，论述了流场数值计算可视
化技术，概述了流场实验可视化技术中的各种方法，阐述了计算机数字图像处理在
流场实验可视化中的应用，确定了本文的主要研究内容。
第二章建立了支配异形断面流道内流体流动的数学模型，并用有限元方法进行
离散。对包括等边三角形断面流道、矩形断面流道、梯形断面流道、半椭园形断面
流道等各种异形断面流道，在不同流动条件下断面上的速度、流量等参数进行数值
计算，并与有关的解析结果相比较，证明了所用方法的正确性。为工程实际中设计
和选择异形断面流道提供依据。
第三章简述了用有限元方法求解流体流动问题时，可以采用的几种不同形式的
数学模型，并简要说明了各种形式的特点。然后从连续性方程和Navier-Stokes方
程出发，推导出无量纲流函数-涡量式。分别介绍了当采用三节点三角形单元和四
节点等参四边形单元时，如何对单元进行有限元分析，以及如何计算各相关系数等。
这是能否用有限元方法正确描述流场的关键。
第四章分析研究了在用有限元方法求解流函数—涡量式时，如何确定进口处、
出口处，上、下壁面处，角点处等流函数和涡量的边界条件，特别是涡量边界条件。
对几种不同的涡量边界条件的确定方法进行了讨论，并以平行平板管道中的流动为
例进行计算，以便确定它们的精度。在此基础上计算方腔驱动流动和后台阶流动，
并讨论进、出流边界条件对后台阶流动的影响。这是进一步研究液压技术中各种复
杂流道流场的前期和基础工作。
第五章针对液压技术中常见的断面突然扩大管道、断面突然缩小管道、液压集
成块内部的复杂流道、各种节流孔口（包括薄壁孔口、偏置细长孔口）等的流场进
行有限元数值模拟，并给出流场的数值计算可视化图形图像，在此基础上定性分析
流体噪声、能量损失与流场结构之间的关系等，并提出相应的改进措施，为分析管
道系统的能量损失和降低噪声奠定理论基础。
第六章用有限元方法对液压传动与控制中最常见的两种结构形式的液压阀—液
压滑阀和液压锥阀流场进行数值预报，给出不同开口度和不同结构尺寸下流场结构
的可视化图像，定性分析涡旋的产生对流体噪声及能量损失可能产生的影响，并对
阀的流道结构进行改进。
第七章建立流场DPIV实验可视化系统，制做突然扩大流道模型，外流式锥阀
燕山大学工学博士学位论文
模型和滑阀模型，并利用粒子图像测速技术对模型的速度场进行测量。利用图像处
理分析软件对实验结果进行计算机数字图像处理，给出模型流场的实验可视化图
像，并与有限元计算结果进行对比分析，对导致数值计算与实验可视化之间出现误
差的各种可能原因进行了分析，便于今后进一步研究中加以注意和改进。
In this article, based on reading and studying a great number of references about
fluid dynamic technique, computational fluid mechanics, numerical computing methods
of flow field, visualization in science computing, experimental visualization in fluid flow
computer digital image processing technique etc, the mathematical models which
governing the flow in complicated conduits and hydraulic valve have been derived, the
finite element method is applied to simulate the flow field of various non-circular cross-
section duct, various complicated channel and hydraulic valve, the computing results are
given in the form of visualized pictures or images, based on these results, the relationship
between the flow field structure and the flow noise, energy loss are analyzed
quantitatively. At the same time, the experimental visualization - DPIV(Digital Particle
Image Velocimetry) is also carried out, and it proves the computing result is correct. It has
important significance for us to design hydraulic valves and pipeline systems which are
high in efficiency, low in energy loss, low in noise.
In chapter 1, hydraulic technique and its developing trends are summarized, the flow
problems in complicated flow channel of hydraulic technique are introduced. Various
numerical methods of computational fluid dynamics are present briefly, the present
situations of application of computational fluid dynamics in hydraulic technique are
described in detail. The computational visualization technique of flow field is outlined,
various flow field experimental visualization methods are surveyed. The application of
computer digital image processing technique in experimental visualization of flow field is
discussed. The main researching contents are determined.
In chapter 2, the mathematical model which governs the flow in non-circular cross-
section channel is established, FEM(Finite Element Method)is used to discrete the
equations. The cross-section parameters such as velocity and flowrate at different flow
conditions for various non-circular duct such as equilateral triangle channel, rectangle
channel, terrace channel, semi-elliptical channel etc are calculated. Parts of the numerical
results are compared with the analytical results, it shows that the numerical method used
here is correct.
In chapter 3, several different kinds of mathematical models and their characteristics
when we solve the flow problems with FEM are presented. From continuity equation and
Navier-Stokes equation, non-dirnensionalized stream function ?vorticity equations is
derived. Ho~v to analyze the elements with FEM and how to calculated the related
coefficients when adopting three nodes triangle elements and four nodes quadrilateral
elements respectively is proposed, which is the key for computing the flow field correctly.
In chapter 4, how to determine the boundary conditions of stream function and
vorticity, especially vorticity boundary conditions at inlet, outlet, up wall, down wall and
the corner are studied when using FEM to solve the stream function-vorticity equation.
Several approaches of determining the vorticity boundary condition are discussed. The
flow in parallel plate channel is computed as an example to verify their accuracy. Based
on above analysis, the flow in square cavity and backward-facing step is investigated, the
influence of inlet and outlet boundary conditions on backward facing step are also
examed.
In chapter 5, the flow field of several different flow channels frequently used in
hydraulic technique such as sudden expansion channel, sudden contraction channel,
引文
1 杨尔庄．国际液压、气动工业及市场发展动向．液压气动与密封．2000；(1)：1～9
2 朱帆，张志军．国内外液压机技术现状及发展趋势．机床与液压．2000；(1)：6～7
3 王意．流体技术与电子技术的新成就．液压与气动．1998；(2)：1～2
4 刘世勋，刘少军．国外液压控制技术发展动向．液压与气动．1996；(4)：3～4
5 杨尔庄．我国液压气动技术的现状与展望．液压与气动．1998；(6)：1～6
6 杨尔庄．液压技术现状及发展趋势．液压气动与密封．1998；(2)：3～7
7 李运华，史维祥．流体动力技术的现状与发展．机床与液压．1994；(4)：187～193
8 曹秉刚．液压控制锥阀液动力及其补偿方法的研究．西安交通大学博士学位论文．1991：1～50
9 胡国清．液压阀流道能耗研究．成都科技大学博士学位论文．1993：40～75
10 Kazuo Nakano, Haruo Watanabe and Mao-ying Guo. "Experimental study for the compensation of axial flow force in a spool valve". The Journal of Fluid Control. 1989; Vol.21(2): 7～26
11 Tsukoji Takahashi T and Hori H. A studyon the axial flow force in a spool valve using flow visualization and image processing technique. Proceedings of the 2nd International Conference on Fluid Power Transmission and Control. Hangzhou, 1989. Beijing. Intemationa! Academic Publishes. 1989:177-182
12 刘振北，王成敏．锥面间流体考虑流动惯性的近似解．应用数学和力学．1992；Vol．9(3):74～81
13 刘振北，包刚，王致清．球形静压推力轴承考虑流动惯性和离心惯性的承载能力分析．机械工程学报．1985；Vol．21(3)：64～74
14 廖建勇．高压园缝泄漏数学模型及其计算机仿真．机床和液压．1994；(2)：83～86
15 王致清，刘振北．球面间流体流动考虑惯性的近似解．应用数学和力学，1984；Vol．5(2)：263～276
16 Babu V, and Korpela A. Numerical simulation of the incompressible three dimensional Navier-Stokes Equations. Computer fluids. 1994; Vol.23(5): 675～691
17 Mahesh C and Kwon T H. Accuracy and efficiency of multi-variant finite element for three-Dimensional simulation of viscous incompressible flows. Communication in numerical methods in engineering. 1994; Vol. 10.(2): 135～148
18 熊杰，愈守勤．N-S方程SUPG有限元法．水动力学研究与进展．A辑．1991；Vol．16(1)：120～127
19 忻孝康，刘儒勋，蒋伯诚编著．计算流体力学．长沙：国防科技大学出版社．1989；1～300
20 张廷芳．计算流体力学．大连：大连理工大学出版社．1992．1～230
21 杨志峰，周雪漪，许协庆．对流扩散方程的一种高精度优化差分格式．水动力学研究与进展；A辑．1991．Vol．6(1)：113～119
22 Neunon S P. An Eulerian-Lagrangian Numerical Scheme for the Dispersionconvection Equation Using Conjugate Space-Time Grids. J. compu. phys. 1984; Vol.41: 270～294
23 ZienKiewicz, Loehner O C R etal. Finite Element in Fluid Mechanics-A Decade of rogress. Finite Element in Fluids. 1981; Vol.5:1～26
24 Henrich J C etal. An Upwind Finite Element Scheme for 2D convection Transport Equation. Int. J. Num. Meth. Eng. 1977; Vol. 11(1): 131～144
25 Vries G D and Norrin D H. The Application of the Finite Element Technique to Potential Flow Problems. Transaction of the ASME. 1997; (11): 798～802
26 兰学奎，胡庆康．一种用边界元方法求解二维不可压缩粘性流体的方法．应用力学报．1991；Vol．18(1)：80～87
27 Vaughan N D, Johnston D N and Burnell L R, The use of computational Fluid Dynamics in Hydraulic Valve Design. Circuit. component and System Design. New York:John Wiley and Sons. 1992; 226～244
28 Ito K, Takahashi K and Inoue K. Pressure Distributions and Flow Force on the Body of a Poppet Valve. Fluid Power Systems Modeling and Control. John Wiley and sons. New York: 1991; 123～138
29 Tukiji T, K. Takahashi. Numerical Analysis of an Axisymmetric Jet Using a Streamline Coordinate System, Trans JSME(in Japanese). 1987; Vol.53(487): 843～849
30 Guo M Y and Nakano K. Numical Analysis for the Flow in Spool Valve by a Boundary Element Method(1st report, A BEM Using u-w-p as variables); J. JHPs (The Japan Hydraulics and Pneumatics Society)(in Japanese). 1989; Vol.20. (6):538～545
31 Guo M Y and Nakano K. Numerical Analysisi for the Flow in a Spool Valve by a Boundary Element Method(2nd report, Study on the Flow in a flow fule compensational bucket). J. JHPs (in Japanese). 1989; Vol.20.(6): 546～552
32 曹秉刚，郭卯应，中野和夫，史维祥．锥阀流场的边界元法解析．机床与液压．1991；(2)：2～10
33 Guo Mao Ying and Koji Takahashi et al. Diserete-Vortex Simulation of a Two-Dimensional Flow in Oil Hydraulic Valve. the Journal of Fluid Control. 1991; Vol.21(1): 43～60
34 胡国清，罗任飞．ASM和K-ε模型对比研究液压集成块流道．水动力学研究与进展．A辑．1998；Vol．13(1)：8～13
35 胡国清．代数应力模型在液压集成块流道中的应用．上海交通大学学报．1994；Vol．28(4)：130～137
36 潘地林．Whitefield A. 蜗壳内部流动特性数值分析及改进设计研究．流体机械．1991；(1)：14～18
37 王志刚，王冬声等．电子膨胀内制冷剂两相流动的数值计算与实验验证．流体机械．1999；(8)：51～55
38 姜继海，马文琦，张冬泉．旋转对称密封隙流场的有限元分析．中国机械工程．1999；Vol．10(5)：506～508
39 王林翔，陈鹰，路甬祥．液压阀道内的三维流体流动的数值分析．中国机械工程．1999．Vol．10(2)：127～129
40 Verma A K and Eswaran V. An overlapping Control Volume Method for the Navier-Stokes Equations on Non-staggereal Grids, Int. J. Numer. Meth. Fluids, 1999; Vol.30(3): 279～308
41 刘晓利，明晓．二维突扩管流的有限元分析解．南京航空航天大学学报．1996；Vol．28(3)：427～431
42 张晓元，李炜．用混合有限分析法模拟二维后台阶分离流．武汉水利电力大学学报．1995；Vol．28(5)：470～474
43 苏明德．有压管道双孔板水流流场的数值模拟．水利学报．1995；Vol．27(6)：641～646
44 蒋莉，王小平，沈孟育．应用RNG k-ε湍流模型数值模拟90°弯曲槽道内的湍流流动．水动力学研究与进展．A辑．1998；Vol．13(1)：8～13
45 Alleborn N, Nandakumar K, Raszillier H and Dorst F. Further contributions on the Two-Dimensional Flow in a Sudden Expansion. J. Fluid Meth. 1997; Vol.330:169～188
46 邵金雨，吴望一，卢文强．在低中高三种Re数下圆管入口流的有限元分析．水动力学研究与进展．A辑．1994；Vol．9(5)：531～540
47 刘有军．锯齿型迷宫密封流场的有限元模拟及泄漏特性的数值预报．[博士学位论文]．大连：大连理工大学．1997
48 石教英，蒋文立编著．科学计算可视化算法与系统．北京：北京科学出版社．1996
49 Paul R, Wood ward. Interactive Scientific Visualization of Fluid Flow IEEE Computer. 1993; Vol. 10:13～25
50 Haimes R and Darmofal D. Visualization in Computational Fluid Dynamics: a case study. Proceedings of Visualization '91.San Diego: CA, IEEE Computer Society Press. 1991. 392～397
51 Gallagher R S and Negtegual J C. An Efficient 3-D Visualization Technique for Finite Element Models and Other Coarse Volume. Computer Graphics. 1989;vol.23(3): 185～193
52 Gallagher R S et al. Applying 3D Visualization Techniques to Finite Element Analysis. Proceedings of Visualization '91, San Diego, CA, IEEE computer Society Press, 1991. 330～340
53 Gerald and Edgar W. Visualization for Non-linear Engineering FEM Analysis in Manufacturing. Proceedings of Visualization '90, San Francisco, CA, IEEE Computer Society Press, 1990,422～423
54 林锐，蔡文立．微机科学可视化系统设计．西安：西安电子科技大学出版社，1996，1～100
55 孙启明．流动显示的现状和发展．气动实验与测量控制．1989；Vol．3(3)：9～15
56 崔尔杰等. Experimental Investigation of Wired Environments Around Building, Proc. APSOWE Ⅱ. 1989. 813～820
57 孙仁，魏庆鼎．烟线方法在流动显示中的应用．第二届全国流动显示学术会议论文集．1986．32～36
58 夏雪漪．用烟线技术显示三维分离流．空气动力学学报，1984；Vol．2(1)：71～76．
59 赵栋，王忠岐．氦气泡显示流态技术的研究与应用．哈尔滨空气动力研究所：科技资料，1983
60 连琪祥. The Structures of Starting Vortex Behind True Dimensional Flat Plate. Proc. Int. Conf. On Fluid Mech. 1987.690～695
61 邓学蓥，刘谋佶，吕志泳．油流显示技术原理和流谱分析．第六届全国风洞实验技术交流会论文集．1985
62 夏生杰等. Applications of Two New Kinds of Apparatuses in Fluid Dynamics Measurement. Proc. ICFDMA. 1989. 349～354
63 Adrian Ronald J. Particle-Image Techniques for Experimental Fluid Mechanics. Annu. Rev. Fluid Mech, 1991; Vol.23.261～304
64 许耀铭，韩德才，螺旋阻尼槽型静压支承滑靴的设计理论与实验研究．机床与液压，1983；(3)：34～39
65 贾光政，邹龙庆，张勃立．螺旋阻尼器的分析及应用．机床与液压，1998；(3)：46～47
66 韩德才等．一边滑动下等边三角形断面管的速度分布．东北重型机械学院学报，1988；(1)：49～53
67 高殿荣，赵永凯等．高压液压缓冲装置的设计．机械设计与制造，1999；(2)：23～25
68 Prasuhn Alans L. Fundamentals of Fluid Mechanics. Prentice-Hall, Inc., Englewood Cliffs, N. J.,1980
69 赵学端，廖其奠．粘性流体力学．北京：机械工业出版社．1983．30～150
70 Norrie D H and Vires G De. A Survey of Finite Element Application in Fluid Mechanics, in R.H.Gallagher etal. (eds). Finite Element in Fluids. 1978;Vol. 3: Wiley,Newyork.363～396
71 Zienkiewicz O C and Talor R L. Some Development of the Finite Element Methods for Fluid Mechanics, Pro.of the 3th Inter. Conf. On Finite Element in Flow Problems. Vol.Ⅱ. 1980
72 Hughes T J R. Some Current Trends in Finite Element Research. Applied Mechanics Reviews, 1980; Vol.33(11): 1210～1220
73 Talor C and Hood P. Navier-Stokes Equations Using Mixed Interpolation, Finite Element in Flow Problems, 1974; 121～132
74 章本照编著．流体力学中的有限元方法．北京：机械工业出版社．1986．1～200
75 Baker A J. Finite Element Solution Algorithm for Viscous Incompressible Fluid Dynamics. Int. J. Numer. Meth. Fluids, 1973; Vol.6:89～101
76 Roache P J. Computational Fluid Dynamics. Hermosa Publisher. 1976. 1～200
77 Gosman A D et al. Heat and Mass Transfer in Recirculating Flows. London:Academic Press. 1969. 1～150
78 Tanahashi T and Okanaka H. Finite Element Method for Unsteady Incompressible Navier-tokes Equations at High Reynolds Numbers, Int. J. Numer. Meth. Fluids. 1999; Vol. 11: 479～499
79 戴韧，王宏光，陈康民．不可压缩粘性流动N-S耦合方程的有限元解法—Ⅱ应用．华东工业大学学报，1997；Vol．19(1)：64～70
80 Peeters M F, Ghabashi W and Dveck E G. Finite Element Stream Function-Vorticity Solutions of the Incompressible Navier-Stokes Equations. Int. J. Numer. Meth. Fluids, 1987; Vol.7:17～27
81 Ghia V, Ghin K N and Shin C T. High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrade Method. Journal of computational Physics, 1982; Vol.48:387～411
82 Tezdtar T E, Liou J, Ganjov D K and Behr M. Solution Techniques for the Vorticity-Stream Function Formulation of Two-dimensional Unsteady Incompressible Flow. Int. J. Numer. Meth. Fluids, 1990; Vol.11:515～539
83 Shih-Yu Tuann and Mervyn D OLSON. A Transient Finite Element Solution Method for the Navier-Stokes Equations. Computes and Flows. 1978; Vol.6:141～152
84 Rek Z and Skerget L. Boundary Element Method for Steady 2D High-Reynolds-Number Flow. Int. J. Numer. Mech. Fluids, 1994; Vol. 19:343～361
85 Gartling David K. A Test Problem for Outflow Boundary Conditions -Flow Over a Backwavel-Facing Step. Int. J. Numer. Meth. Fluids, 1990; Vol. 11:953～967
86 Hwang R R and Peng Y F. Computational of Backward-facing Step Flows by a Second-order Reynolds Stress Closure Model. Int. J. Numer. Meth. Fluids. 1995; Vol. 21: 223～235
87 Autret A and Grandotto M. Finite Element Computation of a Turbulent Flow Over a Two-dimensional Backward-facing Step. Int. J. Numer. Meth. Fluids. 1988; Vol.8: 997～1010
88 Manean M and Comini G. Inflow and Outflow Boundary Conditions in the Finite Element Solution of the Stream Function-Vorticity Equations. Communications in Numerical Methods in Engineering, 1995; Vol. 11: 33～40
89 Comini G, Manian M and Nonino C. Finite Element Solutions of the Stream Equations for Incompressible Two-dimensional Flows. Int. J. Functions-Vorticity Equation Numer. Meth. Fluids. 1994; Vol. 19:513～525
90 朱刚，谷传纲，胡庆康．对Taylar-Galerkin有限元法的一点改进和应用．应用数学和力学．1993；Vol．14(12)：1115～1120
91 胡庆康，王琦．用有限元法计算绕后掠的后台阶的不可压层流流动．应用力学学报，1986；Vol．3(3)：43～49
92 朱刚，胡庆康，谷传纲．各向加权异性有限元法在不可压缩粘性流动计算中的应用．水动力学研究与进展，A辑．1994；Vol．9(2)：139～143
93 Williams P T and Baker A J. Numerical Simulations of Laminar Flow Over a 3D Bakeward-facing Step. Int. J.Numer. Meth. Fluids, 1997; Vol 24:1195～1183
94 Barton I E. Laminar Flow Over a Backward-facing Step with a Stream of hot Particles. Int. J. Heat and Fluid Flow, 1997; Vol. 18:400～410
95 朱刚，沈孟育，胡庆康，张力Hermite有限元的构造及在叶轮机械内部准三元流场计算中的应用．水动力学研究与进展，A辑，1994；Vol．9(5)：593～598
96 朱刚，王小平，沈孟育，胡庆康．叶轮机内部流场的修正Taylor-Galerkin (MDTGFE)有限元法．上海力学，1994；Vol．15(4)：58～62
97 Yves Gagnon Andre Giovannini and Patrrick Hebrard. Numberical Simulation and Physical Analysis of High Reynolds Number Recirculation Flow Behind Sudden Expansions. Phys. Fluids, 1993; Vol.5(10): 2378～2389
98 Luo X.-L. Operater-splitting Computation of Turbulence Flow in an Axisymmetric 180°Narrowing Bead Using Several k-ε Models and Wall Functions. Int. J. Numer. Meth. Fluids. 1996; Vol.22:1189～1205
99 胡国清，罗任飞，多路换向阀流道数值模拟的一种新方法——代数应力模型．水动力学研究与进展，A辑．1996；Vol．11(3)：272～275
100 胡国清，多路换向阀流道优化计算方法——代数应力模型．机床与液压，1995，(4)：203～206
101 范洁川等编著．流动显示与测量．北京：机械工业出版社．1997
102 康琦，申功新．全场测速技术进展．力学进展，1997；Vol．27(1)：106～121
103 盛森芝，徐月亭等．九十年代的流动测量技术．北京：北京大学出版社．1933．50～130
104 杜斯特F，梅林A，怀特洛J H，激光多普勒测速技术的原理与实践．北京：科学出版社．1992．1～150
105 Hiller B, Booman R A, Hassa C and Hanson R K. Velocity Visualization in Gas Flows Using Laser-induced Phosphorescene of Boacetyl. Rev., Sci. Instrum, 1984; Vol.55:1964～1967
106 Cattolica R J, etal. Aerodynamic Separation of Gases by Velocity Slip in Freejet Expansions. AIAA Journal, 1979; Vol.7:334～355
107 Clutter D W, Smith A M O. Flow Visualization by Electrolysis of Water. Aerosp. Eng., 1961; Vol.20:24～27
108 Schraub F A, Kline S J, etal. Use of Hydrogen Bubbles for Quantitative Determination of Time-dependent Velocity Field in Low-speed Water Flows. J. of Basic Eng., 1965; 429～444
109 Baker D B. Measuring Fluid Velocities with Speckle Patterns. Opt. Lett., 1977; Vol.1:135～137
110 Grousson R, Mallick S. Study of Flow Pattern in a Fluid by Scattered Flow Light. Appl. Opt., 1977; Vol.16:2334～2336
111 Dudderar T D, Simpkins P G. Laser Speckle Photography in a Fluid Medium. Nature, 1977; Vol.270:45～47
112 段俐，康琪，申功忻．PIV技术的粒子图像处理方法．北京航空航天大学学报，2000；Vol．26：79～82
113 段俐，康琪，丁汉泉，申功忻．HPIV及其初步应用研究．北京航空航天大学学报，2000；Vol．13：350～356
114 Grant I, Owens E and Yan Y Y. Particle Imgae Velocimety Measurements of the Separated Flow Behind a Rearward Facing Step. Experiments in Fluid, 1992; Vol. 12: 238～244
115 Tassin A L, Li C Y, Ceccio S 1 and Bernal L P. Velocity Field Measurements of Cavitaling Flow. Experiment in Fluid, 1995; Vol.20:125～130
116 Hassan Yassin A, Schmidl Willian D et al. Three-dimensional Bubbly Flow Measurement Using PIV. Proceedings of the Second International Workshop on PIV97-FuKui, July 8-11, FuKui, Japan,1-12
117 Willert C E and Gharib M. Digital Particle Image Velocimety. Experiment in Fluids 1991; Vol. 10:181～193
118 Murata Shigeru. Measurement of Near-periodic Cylinder Wake by PIV. Journal of Flow Visualization and Image Processing. 1993; Vol. 1: 297～316
119 Hesselink Lambertus. Digital Image Processing in Flow Visualization. Ann.Rev. Fluid Mech. 1998; Vol.20:421～485
120 Vemura Tomomasa. Digital Image Analysis for the Incoherent Medium Density PIV. Journal of Flow Visualization and Image processing. 1995; Vol.2:83～91
121 Roesgen T, Totaro R. Two-dimensional on-line Particle Imaging Velocimetry. Experiment in Fluids, 1995; Vol. 19:188～193
122 Adrian R J. Multi-point Optical Measurement of Simultaneous Vectors in Unsteady Flow——A Review. Int. J. Heat and Fluid Flow, 1986; Vol.7:127～130
123 许宏庆，吴中权，杨京龙．图象测速的原理和实践．72～78
124 陈辉，吴嘉，许协庆．用PIV技术测量自由射流瞬态流场．气动实验与测量技术，1996；Vol．10(4)：56～60
125 许协庆，Adrian R J．粒子像测速技术(PIV)和激光散斑测速技术(LSU)的实验研究．气动实验与测量技术，1995；Vol．9(2)：9～15
126 许宏庆，俞昌，袁格．一种快速PIV诊断系统．实验力学，1994；Vol．9(3)：241～246
127 康琪，体视3D-PIV技术及其初步应用．北京航空航天大学博士论文．1995
128 颜大椿．实验流体力学．北京：高等教育出版社．1992．1～120
129 李宇红，叶大均，陈佐一．局部狭窄管内振荡流场的流动可视化研究．气动实验与测量控制，1991；Vol．5(4)：34～39
130 朱锡锋．液体比例混合与流动可视化研究．浙江大学博士学位论文．1996
131 崔尔杰，洪金森．流动显示技术及其在流体力学研究中的应用．空气动力学学报，1991；Vol．9(2)：190～197
2 朱帆，张志军．国内外液压机技术现状及发展趋势．机床与液压．2000；(1)：6～7
3 王意．流体技术与电子技术的新成就．液压与气动．1998；(2)：1～2
4 刘世勋，刘少军．国外液压控制技术发展动向．液压与气动．1996；(4)：3～4
5 杨尔庄．我国液压气动技术的现状与展望．液压与气动．1998；(6)：1～6
6 杨尔庄．液压技术现状及发展趋势．液压气动与密封．1998；(2)：3～7
7 李运华，史维祥．流体动力技术的现状与发展．机床与液压．1994；(4)：187～193
8 曹秉刚．液压控制锥阀液动力及其补偿方法的研究．西安交通大学博士学位论文．1991：1～50
9 胡国清．液压阀流道能耗研究．成都科技大学博士学位论文．1993：40～75
10 Kazuo Nakano, Haruo Watanabe and Mao-ying Guo. "Experimental study for the compensation of axial flow force in a spool valve". The Journal of Fluid Control. 1989; Vol.21(2): 7～26
11 Tsukoji Takahashi T and Hori H. A studyon the axial flow force in a spool valve using flow visualization and image processing technique. Proceedings of the 2nd International Conference on Fluid Power Transmission and Control. Hangzhou, 1989. Beijing. Intemationa! Academic Publishes. 1989:177-182
12 刘振北，王成敏．锥面间流体考虑流动惯性的近似解．应用数学和力学．1992；Vol．9(3):74～81
13 刘振北，包刚，王致清．球形静压推力轴承考虑流动惯性和离心惯性的承载能力分析．机械工程学报．1985；Vol．21(3)：64～74
14 廖建勇．高压园缝泄漏数学模型及其计算机仿真．机床和液压．1994；(2)：83～86
15 王致清，刘振北．球面间流体流动考虑惯性的近似解．应用数学和力学，1984；Vol．5(2)：263～276
16 Babu V, and Korpela A. Numerical simulation of the incompressible three dimensional Navier-Stokes Equations. Computer fluids. 1994; Vol.23(5): 675～691
17 Mahesh C and Kwon T H. Accuracy and efficiency of multi-variant finite element for three-Dimensional simulation of viscous incompressible flows. Communication in numerical methods in engineering. 1994; Vol. 10.(2): 135～148
18 熊杰，愈守勤．N-S方程SUPG有限元法．水动力学研究与进展．A辑．1991；Vol．16(1)：120～127
19 忻孝康，刘儒勋，蒋伯诚编著．计算流体力学．长沙：国防科技大学出版社．1989；1～300
20 张廷芳．计算流体力学．大连：大连理工大学出版社．1992．1～230
21 杨志峰，周雪漪，许协庆．对流扩散方程的一种高精度优化差分格式．水动力学研究与进展；A辑．1991．Vol．6(1)：113～119
22 Neunon S P. An Eulerian-Lagrangian Numerical Scheme for the Dispersionconvection Equation Using Conjugate Space-Time Grids. J. compu. phys. 1984; Vol.41: 270～294
23 ZienKiewicz, Loehner O C R etal. Finite Element in Fluid Mechanics-A Decade of rogress. Finite Element in Fluids. 1981; Vol.5:1～26
24 Henrich J C etal. An Upwind Finite Element Scheme for 2D convection Transport Equation. Int. J. Num. Meth. Eng. 1977; Vol. 11(1): 131～144
25 Vries G D and Norrin D H. The Application of the Finite Element Technique to Potential Flow Problems. Transaction of the ASME. 1997; (11): 798～802
26 兰学奎，胡庆康．一种用边界元方法求解二维不可压缩粘性流体的方法．应用力学报．1991；Vol．18(1)：80～87
27 Vaughan N D, Johnston D N and Burnell L R, The use of computational Fluid Dynamics in Hydraulic Valve Design. Circuit. component and System Design. New York:John Wiley and Sons. 1992; 226～244
28 Ito K, Takahashi K and Inoue K. Pressure Distributions and Flow Force on the Body of a Poppet Valve. Fluid Power Systems Modeling and Control. John Wiley and sons. New York: 1991; 123～138
29 Tukiji T, K. Takahashi. Numerical Analysis of an Axisymmetric Jet Using a Streamline Coordinate System, Trans JSME(in Japanese). 1987; Vol.53(487): 843～849
30 Guo M Y and Nakano K. Numical Analysis for the Flow in Spool Valve by a Boundary Element Method(1st report, A BEM Using u-w-p as variables); J. JHPs (The Japan Hydraulics and Pneumatics Society)(in Japanese). 1989; Vol.20. (6):538～545
31 Guo M Y and Nakano K. Numerical Analysisi for the Flow in a Spool Valve by a Boundary Element Method(2nd report, Study on the Flow in a flow fule compensational bucket). J. JHPs (in Japanese). 1989; Vol.20.(6): 546～552
32 曹秉刚，郭卯应，中野和夫，史维祥．锥阀流场的边界元法解析．机床与液压．1991；(2)：2～10
33 Guo Mao Ying and Koji Takahashi et al. Diserete-Vortex Simulation of a Two-Dimensional Flow in Oil Hydraulic Valve. the Journal of Fluid Control. 1991; Vol.21(1): 43～60
34 胡国清，罗任飞．ASM和K-ε模型对比研究液压集成块流道．水动力学研究与进展．A辑．1998；Vol．13(1)：8～13
35 胡国清．代数应力模型在液压集成块流道中的应用．上海交通大学学报．1994；Vol．28(4)：130～137
36 潘地林．Whitefield A. 蜗壳内部流动特性数值分析及改进设计研究．流体机械．1991；(1)：14～18
37 王志刚，王冬声等．电子膨胀内制冷剂两相流动的数值计算与实验验证．流体机械．1999；(8)：51～55
38 姜继海，马文琦，张冬泉．旋转对称密封隙流场的有限元分析．中国机械工程．1999；Vol．10(5)：506～508
39 王林翔，陈鹰，路甬祥．液压阀道内的三维流体流动的数值分析．中国机械工程．1999．Vol．10(2)：127～129
40 Verma A K and Eswaran V. An overlapping Control Volume Method for the Navier-Stokes Equations on Non-staggereal Grids, Int. J. Numer. Meth. Fluids, 1999; Vol.30(3): 279～308
41 刘晓利，明晓．二维突扩管流的有限元分析解．南京航空航天大学学报．1996；Vol．28(3)：427～431
42 张晓元，李炜．用混合有限分析法模拟二维后台阶分离流．武汉水利电力大学学报．1995；Vol．28(5)：470～474
43 苏明德．有压管道双孔板水流流场的数值模拟．水利学报．1995；Vol．27(6)：641～646
44 蒋莉，王小平，沈孟育．应用RNG k-ε湍流模型数值模拟90°弯曲槽道内的湍流流动．水动力学研究与进展．A辑．1998；Vol．13(1)：8～13
45 Alleborn N, Nandakumar K, Raszillier H and Dorst F. Further contributions on the Two-Dimensional Flow in a Sudden Expansion. J. Fluid Meth. 1997; Vol.330:169～188
46 邵金雨，吴望一，卢文强．在低中高三种Re数下圆管入口流的有限元分析．水动力学研究与进展．A辑．1994；Vol．9(5)：531～540
47 刘有军．锯齿型迷宫密封流场的有限元模拟及泄漏特性的数值预报．[博士学位论文]．大连：大连理工大学．1997
48 石教英，蒋文立编著．科学计算可视化算法与系统．北京：北京科学出版社．1996
49 Paul R, Wood ward. Interactive Scientific Visualization of Fluid Flow IEEE Computer. 1993; Vol. 10:13～25
50 Haimes R and Darmofal D. Visualization in Computational Fluid Dynamics: a case study. Proceedings of Visualization '91.San Diego: CA, IEEE Computer Society Press. 1991. 392～397
51 Gallagher R S and Negtegual J C. An Efficient 3-D Visualization Technique for Finite Element Models and Other Coarse Volume. Computer Graphics. 1989;vol.23(3): 185～193
52 Gallagher R S et al. Applying 3D Visualization Techniques to Finite Element Analysis. Proceedings of Visualization '91, San Diego, CA, IEEE computer Society Press, 1991. 330～340
53 Gerald and Edgar W. Visualization for Non-linear Engineering FEM Analysis in Manufacturing. Proceedings of Visualization '90, San Francisco, CA, IEEE Computer Society Press, 1990,422～423
54 林锐，蔡文立．微机科学可视化系统设计．西安：西安电子科技大学出版社，1996，1～100
55 孙启明．流动显示的现状和发展．气动实验与测量控制．1989；Vol．3(3)：9～15
56 崔尔杰等. Experimental Investigation of Wired Environments Around Building, Proc. APSOWE Ⅱ. 1989. 813～820
57 孙仁，魏庆鼎．烟线方法在流动显示中的应用．第二届全国流动显示学术会议论文集．1986．32～36
58 夏雪漪．用烟线技术显示三维分离流．空气动力学学报，1984；Vol．2(1)：71～76．
59 赵栋，王忠岐．氦气泡显示流态技术的研究与应用．哈尔滨空气动力研究所：科技资料，1983
60 连琪祥. The Structures of Starting Vortex Behind True Dimensional Flat Plate. Proc. Int. Conf. On Fluid Mech. 1987.690～695
61 邓学蓥，刘谋佶，吕志泳．油流显示技术原理和流谱分析．第六届全国风洞实验技术交流会论文集．1985
62 夏生杰等. Applications of Two New Kinds of Apparatuses in Fluid Dynamics Measurement. Proc. ICFDMA. 1989. 349～354
63 Adrian Ronald J. Particle-Image Techniques for Experimental Fluid Mechanics. Annu. Rev. Fluid Mech, 1991; Vol.23.261～304
64 许耀铭，韩德才，螺旋阻尼槽型静压支承滑靴的设计理论与实验研究．机床与液压，1983；(3)：34～39
65 贾光政，邹龙庆，张勃立．螺旋阻尼器的分析及应用．机床与液压，1998；(3)：46～47
66 韩德才等．一边滑动下等边三角形断面管的速度分布．东北重型机械学院学报，1988；(1)：49～53
67 高殿荣，赵永凯等．高压液压缓冲装置的设计．机械设计与制造，1999；(2)：23～25
68 Prasuhn Alans L. Fundamentals of Fluid Mechanics. Prentice-Hall, Inc., Englewood Cliffs, N. J.,1980
69 赵学端，廖其奠．粘性流体力学．北京：机械工业出版社．1983．30～150
70 Norrie D H and Vires G De. A Survey of Finite Element Application in Fluid Mechanics, in R.H.Gallagher etal. (eds). Finite Element in Fluids. 1978;Vol. 3: Wiley,Newyork.363～396
71 Zienkiewicz O C and Talor R L. Some Development of the Finite Element Methods for Fluid Mechanics, Pro.of the 3th Inter. Conf. On Finite Element in Flow Problems. Vol.Ⅱ. 1980
72 Hughes T J R. Some Current Trends in Finite Element Research. Applied Mechanics Reviews, 1980; Vol.33(11): 1210～1220
73 Talor C and Hood P. Navier-Stokes Equations Using Mixed Interpolation, Finite Element in Flow Problems, 1974; 121～132
74 章本照编著．流体力学中的有限元方法．北京：机械工业出版社．1986．1～200
75 Baker A J. Finite Element Solution Algorithm for Viscous Incompressible Fluid Dynamics. Int. J. Numer. Meth. Fluids, 1973; Vol.6:89～101
76 Roache P J. Computational Fluid Dynamics. Hermosa Publisher. 1976. 1～200
77 Gosman A D et al. Heat and Mass Transfer in Recirculating Flows. London:Academic Press. 1969. 1～150
78 Tanahashi T and Okanaka H. Finite Element Method for Unsteady Incompressible Navier-tokes Equations at High Reynolds Numbers, Int. J. Numer. Meth. Fluids. 1999; Vol. 11: 479～499
79 戴韧，王宏光，陈康民．不可压缩粘性流动N-S耦合方程的有限元解法—Ⅱ应用．华东工业大学学报，1997；Vol．19(1)：64～70
80 Peeters M F, Ghabashi W and Dveck E G. Finite Element Stream Function-Vorticity Solutions of the Incompressible Navier-Stokes Equations. Int. J. Numer. Meth. Fluids, 1987; Vol.7:17～27
81 Ghia V, Ghin K N and Shin C T. High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrade Method. Journal of computational Physics, 1982; Vol.48:387～411
82 Tezdtar T E, Liou J, Ganjov D K and Behr M. Solution Techniques for the Vorticity-Stream Function Formulation of Two-dimensional Unsteady Incompressible Flow. Int. J. Numer. Meth. Fluids, 1990; Vol.11:515～539
83 Shih-Yu Tuann and Mervyn D OLSON. A Transient Finite Element Solution Method for the Navier-Stokes Equations. Computes and Flows. 1978; Vol.6:141～152
84 Rek Z and Skerget L. Boundary Element Method for Steady 2D High-Reynolds-Number Flow. Int. J. Numer. Mech. Fluids, 1994; Vol. 19:343～361
85 Gartling David K. A Test Problem for Outflow Boundary Conditions -Flow Over a Backwavel-Facing Step. Int. J. Numer. Meth. Fluids, 1990; Vol. 11:953～967
86 Hwang R R and Peng Y F. Computational of Backward-facing Step Flows by a Second-order Reynolds Stress Closure Model. Int. J. Numer. Meth. Fluids. 1995; Vol. 21: 223～235
87 Autret A and Grandotto M. Finite Element Computation of a Turbulent Flow Over a Two-dimensional Backward-facing Step. Int. J. Numer. Meth. Fluids. 1988; Vol.8: 997～1010
88 Manean M and Comini G. Inflow and Outflow Boundary Conditions in the Finite Element Solution of the Stream Function-Vorticity Equations. Communications in Numerical Methods in Engineering, 1995; Vol. 11: 33～40
89 Comini G, Manian M and Nonino C. Finite Element Solutions of the Stream Equations for Incompressible Two-dimensional Flows. Int. J. Functions-Vorticity Equation Numer. Meth. Fluids. 1994; Vol. 19:513～525
90 朱刚，谷传纲，胡庆康．对Taylar-Galerkin有限元法的一点改进和应用．应用数学和力学．1993；Vol．14(12)：1115～1120
91 胡庆康，王琦．用有限元法计算绕后掠的后台阶的不可压层流流动．应用力学学报，1986；Vol．3(3)：43～49
92 朱刚，胡庆康，谷传纲．各向加权异性有限元法在不可压缩粘性流动计算中的应用．水动力学研究与进展，A辑．1994；Vol．9(2)：139～143
93 Williams P T and Baker A J. Numerical Simulations of Laminar Flow Over a 3D Bakeward-facing Step. Int. J.Numer. Meth. Fluids, 1997; Vol 24:1195～1183
94 Barton I E. Laminar Flow Over a Backward-facing Step with a Stream of hot Particles. Int. J. Heat and Fluid Flow, 1997; Vol. 18:400～410
95 朱刚，沈孟育，胡庆康，张力Hermite有限元的构造及在叶轮机械内部准三元流场计算中的应用．水动力学研究与进展，A辑，1994；Vol．9(5)：593～598
96 朱刚，王小平，沈孟育，胡庆康．叶轮机内部流场的修正Taylor-Galerkin (MDTGFE)有限元法．上海力学，1994；Vol．15(4)：58～62
97 Yves Gagnon Andre Giovannini and Patrrick Hebrard. Numberical Simulation and Physical Analysis of High Reynolds Number Recirculation Flow Behind Sudden Expansions. Phys. Fluids, 1993; Vol.5(10): 2378～2389
98 Luo X.-L. Operater-splitting Computation of Turbulence Flow in an Axisymmetric 180°Narrowing Bead Using Several k-ε Models and Wall Functions. Int. J. Numer. Meth. Fluids. 1996; Vol.22:1189～1205
99 胡国清，罗任飞，多路换向阀流道数值模拟的一种新方法——代数应力模型．水动力学研究与进展，A辑．1996；Vol．11(3)：272～275
100 胡国清，多路换向阀流道优化计算方法——代数应力模型．机床与液压，1995，(4)：203～206
101 范洁川等编著．流动显示与测量．北京：机械工业出版社．1997
102 康琦，申功新．全场测速技术进展．力学进展，1997；Vol．27(1)：106～121
103 盛森芝，徐月亭等．九十年代的流动测量技术．北京：北京大学出版社．1933．50～130
104 杜斯特F，梅林A，怀特洛J H，激光多普勒测速技术的原理与实践．北京：科学出版社．1992．1～150
105 Hiller B, Booman R A, Hassa C and Hanson R K. Velocity Visualization in Gas Flows Using Laser-induced Phosphorescene of Boacetyl. Rev., Sci. Instrum, 1984; Vol.55:1964～1967
106 Cattolica R J, etal. Aerodynamic Separation of Gases by Velocity Slip in Freejet Expansions. AIAA Journal, 1979; Vol.7:334～355
107 Clutter D W, Smith A M O. Flow Visualization by Electrolysis of Water. Aerosp. Eng., 1961; Vol.20:24～27
108 Schraub F A, Kline S J, etal. Use of Hydrogen Bubbles for Quantitative Determination of Time-dependent Velocity Field in Low-speed Water Flows. J. of Basic Eng., 1965; 429～444
109 Baker D B. Measuring Fluid Velocities with Speckle Patterns. Opt. Lett., 1977; Vol.1:135～137
110 Grousson R, Mallick S. Study of Flow Pattern in a Fluid by Scattered Flow Light. Appl. Opt., 1977; Vol.16:2334～2336
111 Dudderar T D, Simpkins P G. Laser Speckle Photography in a Fluid Medium. Nature, 1977; Vol.270:45～47
112 段俐，康琪，申功忻．PIV技术的粒子图像处理方法．北京航空航天大学学报，2000；Vol．26：79～82
113 段俐，康琪，丁汉泉，申功忻．HPIV及其初步应用研究．北京航空航天大学学报，2000；Vol．13：350～356
114 Grant I, Owens E and Yan Y Y. Particle Imgae Velocimety Measurements of the Separated Flow Behind a Rearward Facing Step. Experiments in Fluid, 1992; Vol. 12: 238～244
115 Tassin A L, Li C Y, Ceccio S 1 and Bernal L P. Velocity Field Measurements of Cavitaling Flow. Experiment in Fluid, 1995; Vol.20:125～130
116 Hassan Yassin A, Schmidl Willian D et al. Three-dimensional Bubbly Flow Measurement Using PIV. Proceedings of the Second International Workshop on PIV97-FuKui, July 8-11, FuKui, Japan,1-12
117 Willert C E and Gharib M. Digital Particle Image Velocimety. Experiment in Fluids 1991; Vol. 10:181～193
118 Murata Shigeru. Measurement of Near-periodic Cylinder Wake by PIV. Journal of Flow Visualization and Image Processing. 1993; Vol. 1: 297～316
119 Hesselink Lambertus. Digital Image Processing in Flow Visualization. Ann.Rev. Fluid Mech. 1998; Vol.20:421～485
120 Vemura Tomomasa. Digital Image Analysis for the Incoherent Medium Density PIV. Journal of Flow Visualization and Image processing. 1995; Vol.2:83～91
121 Roesgen T, Totaro R. Two-dimensional on-line Particle Imaging Velocimetry. Experiment in Fluids, 1995; Vol. 19:188～193
122 Adrian R J. Multi-point Optical Measurement of Simultaneous Vectors in Unsteady Flow——A Review. Int. J. Heat and Fluid Flow, 1986; Vol.7:127～130
123 许宏庆，吴中权，杨京龙．图象测速的原理和实践．72～78
124 陈辉，吴嘉，许协庆．用PIV技术测量自由射流瞬态流场．气动实验与测量技术，1996；Vol．10(4)：56～60
125 许协庆，Adrian R J．粒子像测速技术(PIV)和激光散斑测速技术(LSU)的实验研究．气动实验与测量技术，1995；Vol．9(2)：9～15
126 许宏庆，俞昌，袁格．一种快速PIV诊断系统．实验力学，1994；Vol．9(3)：241～246
127 康琪，体视3D-PIV技术及其初步应用．北京航空航天大学博士论文．1995
128 颜大椿．实验流体力学．北京：高等教育出版社．1992．1～120
129 李宇红，叶大均，陈佐一．局部狭窄管内振荡流场的流动可视化研究．气动实验与测量控制，1991；Vol．5(4)：34～39
130 朱锡锋．液体比例混合与流动可视化研究．浙江大学博士学位论文．1996
131 崔尔杰，洪金森．流动显示技术及其在流体力学研究中的应用．空气动力学学报，1991；Vol．9(2)：190～197