复杂几何流道内运动变形气泡上升特性的研究
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摘要
气-液两相流中气泡的运动现象在自然界和工程领域中广泛存在。化工、能源、动力和石油等工程行业中均涉及对气泡运动现象的研究。但是,由于受认知程度和实验研究设备的局限性,对液体中气泡在管道壁面的运动特性这一方面的研究还不全面。鉴于此种情况,本文在结合国家自然基金项目的基础上,应用高速摄影技术和计算机图像处理技术,研究了单气泡在上升过程中与圆管壁面的相互作用问题,初步探讨了气泡在复杂几何流道圆管壁面之间的上升、滚动、反弹和贴附等运动变形特性和规律,主要研究内容包括以下几个方面：
1、自行设计并搭建了一个可视化实验装置。选用透光性能优良的有机玻璃材料作为复杂几何流道实验观察段的主体部分；通过对多种光源的分析与比较,采用碘镍丝灯作为光源,得到了清晰度非常高的图像；设置了注气泵和调节阀,实现了单气泡的等时间隔均匀释放。
2、编制了一整套完善的图像处理程序和数据后处理程序。采用编程思想最优的Canny算子作为图像处理中边缘检测的核心算法,并加以专业的图像分析处理软件Image-Pro Plus6.0作为辅助工具；数据后处理程序以Matlab软件为基础编制而成。
3、通过图像处理程序和数据后处理程序获得了不同工况下,气泡在上升过程中运动轨迹和形状的演变过程,以及气泡的旋转角、速度、Re数和阻力系数等参数的变化曲线。
4、实验结果表明：单个气泡在复杂几何流道内中以“S”形路线摆动上升,并伴随着滚动和自旋运动；上升过程中的形状变化和运动轨迹与圆管壁面的构成排列情况有关；气泡的速度、Re数和阻力系数均随Eo数的增加而增加,并且在上升的中间阶段变化程度较大,极小值和极大值交替出现；竖直管间距的增加使单气泡的各个动力学参数的变化程度减弱；不同注气位置发射的气泡在经过连续的圆管壁面后达到相同的运动状态。但在上升过程中的初始和中间阶段,注气位置对气泡的形状、旋转角、速度等参数有影响,并且气泡首先接触的圆管壁面对其上升运动的影响作用较大。
The research on the behavior of bubble movement in the gas-liquid two-phase, which exists in nature and many engineering fields, is involved in chemical, energy, power and petroleum engineering industries. However, due to limitations of knowledge and experimental equipment, the bubbles'behaviors across the pipe wall in the liquid is far from comprehensive. Given above situation, on the basis of the National Natural Science Foundation Project, employing high-speed photography and computer image processing technology, the rising single bubbles interacting with the tube wall was studied. The laws of deformation of the bubbles between the tube bundles, rebounding, rolling and adhesion of the bubble nears the tube bundle were stated preliminarily. This research mainly includes the following aspects:
1. The experimental apparatus was self-designed. The main part of the experimental observation recorded by high-speed camera was made of the Lucite glass; High definition images could be obtained by using the iodine-nickel filament lamp as lighting source through a comparative analysis of multiple light sources. The release of single bubbles would be interval uniform by setting up the pump and micro-regulating valve.
2. Canny edge detection algorithm, the best ladder edge detection algorithm, was selected as the key tool to deal with the images, with the Image-Pro Plus6.0as an auxiliary tools.
3. The law of the trajectory, deformation, rotation angle, velocity, Re number and drag coefficient of the bubbles during the rising course were obtained under different working conditions. The rebound of the bubble in the tube wall, adhesion, rolling and sliding are compared and analyzed during the rising course.
4. The experimental results show that:as for a single bubble in the liquid, it was spiraling up with the rolling and spinning, which was effected by arrangement mode of the tube bundle; the bubble velocity, Re number and drag coefficient increased as the Eo number increased, and in the medial stage, the minimum value and maximum value appeared alternately; the dynamic parameter of the bubble reduced as vertical tube spacing increased; the bubbles sprayed from different injection position achieved the same state. But in the initial and the middle stage, the shape, the rotating angle, velocity et al were also affected by the injection position, and the bubble was mainly affected by the first tube contacted in the rising course.
1、自行设计并搭建了一个可视化实验装置。选用透光性能优良的有机玻璃材料作为复杂几何流道实验观察段的主体部分；通过对多种光源的分析与比较,采用碘镍丝灯作为光源,得到了清晰度非常高的图像；设置了注气泵和调节阀,实现了单气泡的等时间隔均匀释放。
2、编制了一整套完善的图像处理程序和数据后处理程序。采用编程思想最优的Canny算子作为图像处理中边缘检测的核心算法,并加以专业的图像分析处理软件Image-Pro Plus6.0作为辅助工具；数据后处理程序以Matlab软件为基础编制而成。
3、通过图像处理程序和数据后处理程序获得了不同工况下,气泡在上升过程中运动轨迹和形状的演变过程,以及气泡的旋转角、速度、Re数和阻力系数等参数的变化曲线。
4、实验结果表明：单个气泡在复杂几何流道内中以“S”形路线摆动上升,并伴随着滚动和自旋运动；上升过程中的形状变化和运动轨迹与圆管壁面的构成排列情况有关；气泡的速度、Re数和阻力系数均随Eo数的增加而增加,并且在上升的中间阶段变化程度较大,极小值和极大值交替出现；竖直管间距的增加使单气泡的各个动力学参数的变化程度减弱；不同注气位置发射的气泡在经过连续的圆管壁面后达到相同的运动状态。但在上升过程中的初始和中间阶段,注气位置对气泡的形状、旋转角、速度等参数有影响,并且气泡首先接触的圆管壁面对其上升运动的影响作用较大。
The research on the behavior of bubble movement in the gas-liquid two-phase, which exists in nature and many engineering fields, is involved in chemical, energy, power and petroleum engineering industries. However, due to limitations of knowledge and experimental equipment, the bubbles'behaviors across the pipe wall in the liquid is far from comprehensive. Given above situation, on the basis of the National Natural Science Foundation Project, employing high-speed photography and computer image processing technology, the rising single bubbles interacting with the tube wall was studied. The laws of deformation of the bubbles between the tube bundles, rebounding, rolling and adhesion of the bubble nears the tube bundle were stated preliminarily. This research mainly includes the following aspects:
1. The experimental apparatus was self-designed. The main part of the experimental observation recorded by high-speed camera was made of the Lucite glass; High definition images could be obtained by using the iodine-nickel filament lamp as lighting source through a comparative analysis of multiple light sources. The release of single bubbles would be interval uniform by setting up the pump and micro-regulating valve.
2. Canny edge detection algorithm, the best ladder edge detection algorithm, was selected as the key tool to deal with the images, with the Image-Pro Plus6.0as an auxiliary tools.
3. The law of the trajectory, deformation, rotation angle, velocity, Re number and drag coefficient of the bubbles during the rising course were obtained under different working conditions. The rebound of the bubble in the tube wall, adhesion, rolling and sliding are compared and analyzed during the rising course.
4. The experimental results show that:as for a single bubble in the liquid, it was spiraling up with the rolling and spinning, which was effected by arrangement mode of the tube bundle; the bubble velocity, Re number and drag coefficient increased as the Eo number increased, and in the medial stage, the minimum value and maximum value appeared alternately; the dynamic parameter of the bubble reduced as vertical tube spacing increased; the bubbles sprayed from different injection position achieved the same state. But in the initial and the middle stage, the shape, the rotating angle, velocity et al were also affected by the injection position, and the bubble was mainly affected by the first tube contacted in the rising course.
引文
[1]董少敏.单个气泡在静水中近壁区域运动规律的图像测量研究[D].西安：西安理工大学,2008.
[2]Evans J D, King J R. Asymptotic results for the Stefan problems with kinetic under cooling [J]. Quarterly Journal of Mechanics and Applied Mathematics,2000,53 (3):449-473
[3]Rayleigh L. On the pressure developed in a liquid during the collapse of a spherical cavity [J]. Phil Mag,1917,34:94-98.
[4]Plesset M S, Chapman R B. Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary [J]. Journal of Fluid Mechanics,1971,47:283-290.
[5]Kulkarni A A, Joshi J B. Bubble formation and bubble rise velocity in gas-liquid systems: a review [J]. Industrial & engineering chemistry research.2005,44:5873-5931.
[6]张建生.孙传东,卢笛.水中气泡的特性研究[J].西安工业学院学报.2000,20(1)：1-8.
[7]郭容.黏性流体中气泡的运动特性[D].北京：北京化工大学,2009.
[8]Marchandise E, Remacle J-F, Chevaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation [J]. Journal of Computational Physics,2006, 212:338-357.
[9]Chen S, Merriman B, Osher S, et al. A simples Level set method for solving stefan problems [J]. Journal of Computational Physics.1997:135:8-29.
[10]Sussman M, Fatemi E. An efficient interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow [J]. Journal of Scientific Computing,1999,20:1156-1191.
[11]Zhu J, Sethian J. Projection methods coupled to level set interface techniques [J]. Journal of Computational Physics,1992,102:128.
[12]Peng D, Merriman B, Osher S, et al. A PDE-based fast local level set method [J]. Journal of Computational Physics,1999,155(2):410-438.
[13]董毅峰,王雪瑶,刘长春.捕获运动界面的有限元方法[J].辽宁工程技术大学学报(自然科学版),2009,28：234-240.
[14]Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. Journal of Computational Physics,1981,39(1):201-225.
[15]Tomiyama A, Sou A, Minagawa H. Numerical analysis of a single bubble by VOF method [J]. JSME International Journal Series B 1993,36(1):51-56.
[16]Pucktt E G, Almgern A S, Bell J B, et al. A high-order projection method for tracking fluid interface in variable density incompressible flows [J]. Journal of Computational Physics 1997,130:269-282.
[17]Lorstad D, Fuchs L. High-order surface tension VOF-model for 3-D bubble flows with high density ratio [J]. Journal of Computational Physics,2004,200:153-176.
[18]Sussman M. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles [J]. Journal of Computational Physics,2003, 187(1):110-136
[19]Osher S, Setian J A. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton- Jacobi formulations [J]. Journal of Computational Physics,1988, 79:12-49.
[20]Sussman M, Smereka P. Axisymmetric free boundary problems [J]. Journal of Fluid Mechanics,1997,341:269-294.
[21]Sussman M, Almgren A S, Bell J B, et al. An adaptive level set approach for incompressible two-phase flows [J]. Journal of Computational Physics,1999, 148:1165-1191.
[22]Oka H, Ishii K. Numerical analysison the motion of gas bubble using Level-set method [J]. Journal of the Physical Society of Japan,1999,68:823-832.
[23]Tornberg K. Interface tracking methods with application to multiphase flows [D]. Stockholm:Royal Institute of Technology,2000.
[24]Donea J. Arbitrary Lagrangian-Eulerian finite element methods [J]. Computational Methods for Transient Analysis,1983,1:473-516.
[25]Hirt C W, Amsden A A, Cook J L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds [J]. Journal of Computational Physics,1997,135(2):203-216.
[26]Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free-surface [J]. Physics of Fluids,1965,8(12):2182-2189.
[27]Harlow F H, Welch J E. Numerical study of large-amplitude free-surface motions [J]. Physics of Fluids,1966,9:842-851.
[28]Noh W F. CEL:A time-dependent two-space-dimensional coupled Eulerian-lagrangian code, in:B. Alder, S. Fernbach and M. Rotenberg, eds. Methods in Computational Physics [M]. New York:Academic press,1964.
[29]Hirt C W, Amsden A A, Cook J L. An arbitrary Lagrangian-Eulerian computing method for all flow speed [J]. Journal of Computational Physics,1974,14:227-253.
[30]Baker G, Moored W. The rise and distortion of a two dimensional gas bubble in an inviscid liquid [J]. Physics of Fluids A,1989,1(9):1451-1459.
[31]张慧生.气泡和液滴在上升或下降时大变形的数值模拟[J].空气动力学报,1994,12(1)：51-59.
[32]Canot E, Achard J L. An overview of boundary integral formulations for potential flows in fluid-fluid systems [J]. Arch Mech,1991,43:453-498.
[33]Robinson P B, Boulton-stone J M, Blake J R. Application of boundary integral method to the interaction of rising two-dimensional deformable gas bubbles [J]. Journal of Engineering Mathematics,1995,29:393-412.
[34]Gupta S C. Moving boundaries due to distributed sources in a slab [J]. Applied Sei Res,1995,54:137-160.
[35]陈祖茂,郑冲.用于测定多相流动体系内气泡特性的微型电导探针[J].石汕化工1994：23：46-50.
[36]T Brattberg, H Chchanson, L Toombes. Experimental investigations of free-surface areation in the developing flow of two-dimensional water jets[J]. Journal of Fluids Engineering.1998,120(4):738-744.
[37]许会,白静洁,孙静.阵列式电容传感器测量两相流组分含率[J].沈阳工业大学学报,1996,21(3)：21-24.
[38]黄志尧,王保良,李海青.用于两相流流型显示和空隙率测量的电容层析成像技术[J].化工学报,2001,52：52-55.
[39]杨会伟.高帧频CMOS相机图像采集系统研究[D].西安：西安工业大学,2009.
[40]Walters J K, Davidson J F. The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble [J]. Journal of Fluid Mechanics,1962, 12:408-417.
[41]Walters J K, Davidson J F. The initial motion of a gas bubble formed in an inviscid liquid. Part 2. The three-dimensional bubble and the toroidal bubble [J]. Journal of Fluid Mechanics.1963:17:321-336.
[42]鞠花,陈刚,李国栋等.静水中上升气泡沿倾斜壁面的运动特性实验研究[J].水动力学研究与进展,2011,26(3)：327-332.
[43]汪斌,张光升,高宁等.高速摄影技术在水下爆炸气泡脉动研究中的应用[J].含能材料,2010,18(1)：102-106.
[44]俞小伟,董志勇,汉魏等.掺气泡对空泡影响的高速摄影分析[J].浙江工业大学学报,2011,39(3)：268-272.
[45]黄超,汪斌,姚熊亮等.实验室尺度下水下爆炸气泡试验方法[J].传感器与为系统,2011,30(12)：75-81.
[46]杨敏官,高波,顾海飞等.旋流式模型泵内部三维湍流场的测量[J].排灌机械,2008；26(16)：61-64.
[47]刘成文,李兆敏.LDV用于水射流测量的实验技术研究[J].石汕钻探技术,2001,29(5)：23-25.
[48]王树立,张敏卿,范敏英.鼓泡塔内气液两相流速度分布[J].抚顺石油学院学报,1997,17(3)：27-63.
[49]李琳.贫细赤铁矿的管段高紊流矿化与柱式短流程分选研究[D].天津：天津大学,2010.
[50]许联锋.水气两相流动的数字图像测量方法及应用研究(D).西安：西安理工大学,2004.
[51]百度百科.PIV(粒子成像测速).[2012,04,15].http://baike.baidu.com/view/894076.htm
[52]许联锋,陈刚,李建中等.气液两相流中气泡运动速度场的PIV分析与研究[J].实验力学2002,17(4)：458-463.
[53]张帆,葛颖增,窦勇.超长指令字DSP上的数字图像处理算法优化方法[J].微计算机应用,2008,29(10)：1-6.
[54]百度百科.数字图像处理.[2012,04,15].http://baike.baidu.com/view/286846.htm.
[55]宁辉,唐远河,邵建斌.基于PIV技术的水中气泡图像测速法[J].纺织高校基础科学学报.2006,19(4)：385-388.
[56]赵晓飞,何俊华,韦明智等.一种基于图像处理技术获取尾流特性的新方法[J].光子学报.,2006,35(3)：443-446.
[57]施丽莲,蔡晋辉,周泽魁.基于图像处理的气液两相流流型识别[J].浙江大学学报(工学版),2006,39(8)：1128-1131.
[58]张建生,林书玉,苗润才等.基于图像处理的模拟尾流气泡幕研究[J].光子学报,2007,36(12)：2371-2376.
[59]刚立,许唯临,邓军.含气量测量的图像处理方法[J].四川大学学报(工程科学版),2004,36(2)：21-24.
[60]王雪瑶,姜凡,刘长春等.基于Level Set方法的Ghost技术研究[J].武汉理工大学学报,2008,30(4)：153-156
[61]张涛.改性有机玻璃的制备,结构和性能研究(D).杭州：浙江大学,2007.
[62]吴碧金,胡国清.小型钢筋矫直机连续拉直机构的设计问题[J].机械,2003,30(3)：26-28.
[2]Evans J D, King J R. Asymptotic results for the Stefan problems with kinetic under cooling [J]. Quarterly Journal of Mechanics and Applied Mathematics,2000,53 (3):449-473
[3]Rayleigh L. On the pressure developed in a liquid during the collapse of a spherical cavity [J]. Phil Mag,1917,34:94-98.
[4]Plesset M S, Chapman R B. Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary [J]. Journal of Fluid Mechanics,1971,47:283-290.
[5]Kulkarni A A, Joshi J B. Bubble formation and bubble rise velocity in gas-liquid systems: a review [J]. Industrial & engineering chemistry research.2005,44:5873-5931.
[6]张建生.孙传东,卢笛.水中气泡的特性研究[J].西安工业学院学报.2000,20(1)：1-8.
[7]郭容.黏性流体中气泡的运动特性[D].北京：北京化工大学,2009.
[8]Marchandise E, Remacle J-F, Chevaugeon N. A quadrature-free discontinuous Galerkin method for the level set equation [J]. Journal of Computational Physics,2006, 212:338-357.
[9]Chen S, Merriman B, Osher S, et al. A simples Level set method for solving stefan problems [J]. Journal of Computational Physics.1997:135:8-29.
[10]Sussman M, Fatemi E. An efficient interface-preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow [J]. Journal of Scientific Computing,1999,20:1156-1191.
[11]Zhu J, Sethian J. Projection methods coupled to level set interface techniques [J]. Journal of Computational Physics,1992,102:128.
[12]Peng D, Merriman B, Osher S, et al. A PDE-based fast local level set method [J]. Journal of Computational Physics,1999,155(2):410-438.
[13]董毅峰,王雪瑶,刘长春.捕获运动界面的有限元方法[J].辽宁工程技术大学学报(自然科学版),2009,28：234-240.
[14]Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. Journal of Computational Physics,1981,39(1):201-225.
[15]Tomiyama A, Sou A, Minagawa H. Numerical analysis of a single bubble by VOF method [J]. JSME International Journal Series B 1993,36(1):51-56.
[16]Pucktt E G, Almgern A S, Bell J B, et al. A high-order projection method for tracking fluid interface in variable density incompressible flows [J]. Journal of Computational Physics 1997,130:269-282.
[17]Lorstad D, Fuchs L. High-order surface tension VOF-model for 3-D bubble flows with high density ratio [J]. Journal of Computational Physics,2004,200:153-176.
[18]Sussman M. A second order coupled level set and volume-of-fluid method for computing growth and collapse of vapor bubbles [J]. Journal of Computational Physics,2003, 187(1):110-136
[19]Osher S, Setian J A. Fronts propagating with curvature-dependent speed:algorithms based on Hamilton- Jacobi formulations [J]. Journal of Computational Physics,1988, 79:12-49.
[20]Sussman M, Smereka P. Axisymmetric free boundary problems [J]. Journal of Fluid Mechanics,1997,341:269-294.
[21]Sussman M, Almgren A S, Bell J B, et al. An adaptive level set approach for incompressible two-phase flows [J]. Journal of Computational Physics,1999, 148:1165-1191.
[22]Oka H, Ishii K. Numerical analysison the motion of gas bubble using Level-set method [J]. Journal of the Physical Society of Japan,1999,68:823-832.
[23]Tornberg K. Interface tracking methods with application to multiphase flows [D]. Stockholm:Royal Institute of Technology,2000.
[24]Donea J. Arbitrary Lagrangian-Eulerian finite element methods [J]. Computational Methods for Transient Analysis,1983,1:473-516.
[25]Hirt C W, Amsden A A, Cook J L. An arbitrary Lagrangian-Eulerian computing method for all flow speeds [J]. Journal of Computational Physics,1997,135(2):203-216.
[26]Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free-surface [J]. Physics of Fluids,1965,8(12):2182-2189.
[27]Harlow F H, Welch J E. Numerical study of large-amplitude free-surface motions [J]. Physics of Fluids,1966,9:842-851.
[28]Noh W F. CEL:A time-dependent two-space-dimensional coupled Eulerian-lagrangian code, in:B. Alder, S. Fernbach and M. Rotenberg, eds. Methods in Computational Physics [M]. New York:Academic press,1964.
[29]Hirt C W, Amsden A A, Cook J L. An arbitrary Lagrangian-Eulerian computing method for all flow speed [J]. Journal of Computational Physics,1974,14:227-253.
[30]Baker G, Moored W. The rise and distortion of a two dimensional gas bubble in an inviscid liquid [J]. Physics of Fluids A,1989,1(9):1451-1459.
[31]张慧生.气泡和液滴在上升或下降时大变形的数值模拟[J].空气动力学报,1994,12(1)：51-59.
[32]Canot E, Achard J L. An overview of boundary integral formulations for potential flows in fluid-fluid systems [J]. Arch Mech,1991,43:453-498.
[33]Robinson P B, Boulton-stone J M, Blake J R. Application of boundary integral method to the interaction of rising two-dimensional deformable gas bubbles [J]. Journal of Engineering Mathematics,1995,29:393-412.
[34]Gupta S C. Moving boundaries due to distributed sources in a slab [J]. Applied Sei Res,1995,54:137-160.
[35]陈祖茂,郑冲.用于测定多相流动体系内气泡特性的微型电导探针[J].石汕化工1994：23：46-50.
[36]T Brattberg, H Chchanson, L Toombes. Experimental investigations of free-surface areation in the developing flow of two-dimensional water jets[J]. Journal of Fluids Engineering.1998,120(4):738-744.
[37]许会,白静洁,孙静.阵列式电容传感器测量两相流组分含率[J].沈阳工业大学学报,1996,21(3)：21-24.
[38]黄志尧,王保良,李海青.用于两相流流型显示和空隙率测量的电容层析成像技术[J].化工学报,2001,52：52-55.
[39]杨会伟.高帧频CMOS相机图像采集系统研究[D].西安：西安工业大学,2009.
[40]Walters J K, Davidson J F. The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble [J]. Journal of Fluid Mechanics,1962, 12:408-417.
[41]Walters J K, Davidson J F. The initial motion of a gas bubble formed in an inviscid liquid. Part 2. The three-dimensional bubble and the toroidal bubble [J]. Journal of Fluid Mechanics.1963:17:321-336.
[42]鞠花,陈刚,李国栋等.静水中上升气泡沿倾斜壁面的运动特性实验研究[J].水动力学研究与进展,2011,26(3)：327-332.
[43]汪斌,张光升,高宁等.高速摄影技术在水下爆炸气泡脉动研究中的应用[J].含能材料,2010,18(1)：102-106.
[44]俞小伟,董志勇,汉魏等.掺气泡对空泡影响的高速摄影分析[J].浙江工业大学学报,2011,39(3)：268-272.
[45]黄超,汪斌,姚熊亮等.实验室尺度下水下爆炸气泡试验方法[J].传感器与为系统,2011,30(12)：75-81.
[46]杨敏官,高波,顾海飞等.旋流式模型泵内部三维湍流场的测量[J].排灌机械,2008；26(16)：61-64.
[47]刘成文,李兆敏.LDV用于水射流测量的实验技术研究[J].石汕钻探技术,2001,29(5)：23-25.
[48]王树立,张敏卿,范敏英.鼓泡塔内气液两相流速度分布[J].抚顺石油学院学报,1997,17(3)：27-63.
[49]李琳.贫细赤铁矿的管段高紊流矿化与柱式短流程分选研究[D].天津：天津大学,2010.
[50]许联锋.水气两相流动的数字图像测量方法及应用研究(D).西安：西安理工大学,2004.
[51]百度百科.PIV(粒子成像测速).[2012,04,15].http://baike.baidu.com/view/894076.htm
[52]许联锋,陈刚,李建中等.气液两相流中气泡运动速度场的PIV分析与研究[J].实验力学2002,17(4)：458-463.
[53]张帆,葛颖增,窦勇.超长指令字DSP上的数字图像处理算法优化方法[J].微计算机应用,2008,29(10)：1-6.
[54]百度百科.数字图像处理.[2012,04,15].http://baike.baidu.com/view/286846.htm.
[55]宁辉,唐远河,邵建斌.基于PIV技术的水中气泡图像测速法[J].纺织高校基础科学学报.2006,19(4)：385-388.
[56]赵晓飞,何俊华,韦明智等.一种基于图像处理技术获取尾流特性的新方法[J].光子学报.,2006,35(3)：443-446.
[57]施丽莲,蔡晋辉,周泽魁.基于图像处理的气液两相流流型识别[J].浙江大学学报(工学版),2006,39(8)：1128-1131.
[58]张建生,林书玉,苗润才等.基于图像处理的模拟尾流气泡幕研究[J].光子学报,2007,36(12)：2371-2376.
[59]刚立,许唯临,邓军.含气量测量的图像处理方法[J].四川大学学报(工程科学版),2004,36(2)：21-24.
[60]王雪瑶,姜凡,刘长春等.基于Level Set方法的Ghost技术研究[J].武汉理工大学学报,2008,30(4)：153-156
[61]张涛.改性有机玻璃的制备,结构和性能研究(D).杭州：浙江大学,2007.
[62]吴碧金,胡国清.小型钢筋矫直机连续拉直机构的设计问题[J].机械,2003,30(3)：26-28.