方形电容敏感场建模与仿真研究
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摘要
电容层析成像技术(ECT)是一种用于解决多相流检测难题的新兴技术,在许多工业应用中,如工业锅炉和循环流化床等,需要将ECT系统设计成方型结构或矩形结构。
对电容传感器而言,获得均匀的电容场灵敏度分布是传感器优化设计的主要目标;对电容层析成像系统而言,设计传感器阵列结构时需依据电容场灵敏度分布确定最优参数;并且图像重建时又以电容场灵敏度分布为先验知识,因此电容传感器敏感场的确定是极为重要的。
目前电容场灵敏度获取方法有实验法和有限元法仿真法。前者实验工作量巨大而且测量准确度难以得到保证,后者可由计算机较精确地获得在特定介质分布下的响应值,并且数据处理等都大为简化。因此,本文采用有限元法获得电容敏感场的分布。
通过对电容层析成像系统的工作原理进行详尽的理论分析,建立了电容测量值与多相流含相率之间的数学模型,依据变分原理将此二重积分的数学模型转换为对微元的近似求和运算,进而建立系统的有限元模型;在系统有限元模型的基础上,建立了敏感场的数学模型;在电容敏感场的有限元求解过程中,采用电荷法计算各极板上电荷和极板间的电容,该方法具有运算简单速度快的优点,能显著提高电容层析成像系统的实时性;编制出电容敏感场的有限元仿真软件,并从不同角度对有限元仿真电容数值解和实测电容值进行比较,结果表明两者之间的平均相对误差小于0.9%,从而证明电容层析成像系统有限元模型的正确性;利用有限元模型,定性地分析电容传感器各结构参数对其性能的影响,并对传感器结构参数进行优化设计,使其性能得到明显的改善。
电容测量值与多相流含相率之间的数学模型表明,可以应用电容层析成像技术对多相流截面进行图像重建;根据电容敏感场有限元数学模型,编制的电容敏感场的有限元仿真软件,能够得到电容敏感场的数值解,最后将电容敏感场分布结果应用于电容层析成像系统样机之中,经实验证明本文建立的电容敏感场分布符合实际,在实际应用中获得良好效果。
Electrical Capacitance Tomography (ECT) is a new technology, but it needs to be designed as the square or the rectangular in many industrial applications, such as industrial boiler and circular fluid bed, i.e..The main object of the optimal capacitance sensor is to obtain the symmetrical capacitance field sensitivity. The ECT must base on the capacitance field sensitivity to design the array structure of the capacitance sensor. The ECT system must base on the prior knowledge of capacitance field sensitivity distribution of capacitance sensor when reconstructing image. So it is vital to get the capacitance field sensitivity distribution of capacitance sensor.At present, capacitance field sensitivity distribution can be obtained in two ways, i.e., experiment and finite element simulation. The former has many difficulties ensuring the degree of accuracy of measurement and simultaneously needs to do a lot of experiments, but, by using a computer, the latter not only makes the process of data simplified also gets more accurate response values in the distribution of given medium, which is the reason why this paper adopts the latter.The author analyses the operating principle of ECT and builds up the mathematical model of the capacitance and the component factor of multi-component. According to variation principle, it establishes the Finite Element Model (FEM) of the system by changing the finite boundary value problem of ECT into equivalence variation problem. On the basis of the FEM of the system, the paper builds the finite element model of the capacitance field sensitivity distribution. Electric charge method adopted in the course of evaluation has several advantages such as simplicity and quickness in calculating quantity of electric charge on an electrode and capacitance between two electrodes and
enhances the real-time ability of ECT system obviously. The author programs the finite element software of capacitance field sensitivity, the compare of the simulated result with the static experimental result shows that the error of them is less than 0.9%, and then it proves the validity of the FEM of the ECT from different aspects. With FEM and qualitative analysis of effect of each structural parameter of the capacitance sensor on its capability, this paper optimizes the structural parameters of the capacitance sensor, and obviously improves its capability.The mathematical model of the capacitance and the component factor of multi-component flow shows we can build up the image of the multi-component flow section. The author programs the finite element software of capacitance field sensitivity according to its finite element mathematic model, then the numerical value can be got. The ultimate results are applied to the prototype of ECT system, ant it proves that the field sensitivity proposed in this paper is in accordance with the practice and obtains good results in the application.
对电容传感器而言,获得均匀的电容场灵敏度分布是传感器优化设计的主要目标;对电容层析成像系统而言,设计传感器阵列结构时需依据电容场灵敏度分布确定最优参数;并且图像重建时又以电容场灵敏度分布为先验知识,因此电容传感器敏感场的确定是极为重要的。
目前电容场灵敏度获取方法有实验法和有限元法仿真法。前者实验工作量巨大而且测量准确度难以得到保证,后者可由计算机较精确地获得在特定介质分布下的响应值,并且数据处理等都大为简化。因此,本文采用有限元法获得电容敏感场的分布。
通过对电容层析成像系统的工作原理进行详尽的理论分析,建立了电容测量值与多相流含相率之间的数学模型,依据变分原理将此二重积分的数学模型转换为对微元的近似求和运算,进而建立系统的有限元模型;在系统有限元模型的基础上,建立了敏感场的数学模型;在电容敏感场的有限元求解过程中,采用电荷法计算各极板上电荷和极板间的电容,该方法具有运算简单速度快的优点,能显著提高电容层析成像系统的实时性;编制出电容敏感场的有限元仿真软件,并从不同角度对有限元仿真电容数值解和实测电容值进行比较,结果表明两者之间的平均相对误差小于0.9%,从而证明电容层析成像系统有限元模型的正确性;利用有限元模型,定性地分析电容传感器各结构参数对其性能的影响,并对传感器结构参数进行优化设计,使其性能得到明显的改善。
电容测量值与多相流含相率之间的数学模型表明,可以应用电容层析成像技术对多相流截面进行图像重建;根据电容敏感场有限元数学模型,编制的电容敏感场的有限元仿真软件,能够得到电容敏感场的数值解,最后将电容敏感场分布结果应用于电容层析成像系统样机之中,经实验证明本文建立的电容敏感场分布符合实际,在实际应用中获得良好效果。
Electrical Capacitance Tomography (ECT) is a new technology, but it needs to be designed as the square or the rectangular in many industrial applications, such as industrial boiler and circular fluid bed, i.e..The main object of the optimal capacitance sensor is to obtain the symmetrical capacitance field sensitivity. The ECT must base on the capacitance field sensitivity to design the array structure of the capacitance sensor. The ECT system must base on the prior knowledge of capacitance field sensitivity distribution of capacitance sensor when reconstructing image. So it is vital to get the capacitance field sensitivity distribution of capacitance sensor.At present, capacitance field sensitivity distribution can be obtained in two ways, i.e., experiment and finite element simulation. The former has many difficulties ensuring the degree of accuracy of measurement and simultaneously needs to do a lot of experiments, but, by using a computer, the latter not only makes the process of data simplified also gets more accurate response values in the distribution of given medium, which is the reason why this paper adopts the latter.The author analyses the operating principle of ECT and builds up the mathematical model of the capacitance and the component factor of multi-component. According to variation principle, it establishes the Finite Element Model (FEM) of the system by changing the finite boundary value problem of ECT into equivalence variation problem. On the basis of the FEM of the system, the paper builds the finite element model of the capacitance field sensitivity distribution. Electric charge method adopted in the course of evaluation has several advantages such as simplicity and quickness in calculating quantity of electric charge on an electrode and capacitance between two electrodes and
enhances the real-time ability of ECT system obviously. The author programs the finite element software of capacitance field sensitivity, the compare of the simulated result with the static experimental result shows that the error of them is less than 0.9%, and then it proves the validity of the FEM of the ECT from different aspects. With FEM and qualitative analysis of effect of each structural parameter of the capacitance sensor on its capability, this paper optimizes the structural parameters of the capacitance sensor, and obviously improves its capability.The mathematical model of the capacitance and the component factor of multi-component flow shows we can build up the image of the multi-component flow section. The author programs the finite element software of capacitance field sensitivity according to its finite element mathematic model, then the numerical value can be got. The ultimate results are applied to the prototype of ECT system, ant it proves that the field sensitivity proposed in this paper is in accordance with the practice and obtains good results in the application.
引文
1 徐苓安.多相流流量测量技术.天津大学出版社,1988:20～58
2 邓之初.多相流研究和多相流检测技术.第二届全国多相流检测技术学术讨论会论文集.南京,1988:1～8
3 陈苷棠.化工中若干多相流检测问题.第三届全国多相流检测技术学术讨论会论文集.上海,1990:1～7
4 冯文锁,徐苓安.气液两相流反射式超声层析成像系统的仿真研究.第四届全国多相流检测技术学术讨论会论文集.天津,1992:191～192
5 徐苓安.超声波层析成像技术在气液两相流检测中的应用.第三届全国多相流检测技术学术讨论会论文集.上海,1990:90～99
6 Artur J. Jaworski, Tomasz Dyakowski. Investigation of Flow Instabilities within the Dense Pneumatic. Powder Technology, 2002, 125: 279～291
7 Lahey R. T. A high-intensity X-ray System for Stochatic Measurements of Two-Phase Flows. ANS Trans, Vol. 30, 1979: 497～499
8 Pike R. W. Measurement of the Void Fraction in Two-Phaseflow by X-ray Attenuation. AIChE Journal, Vol. 11, No. 5, 1965: 794～800
9 蒙建波,朱林章.检测理论的现状及展望.第四届全国多相流检测技术学术讨论会论文集.天津,1992:89～91
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13 Bemrose C. R. Application of Positron Emission Tomography to Particulate Flow Measurement in Chemical Engineering Processes. Nuclear Instruments and Methods in Physics Research, 1998, 73: 874～880
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18 K. L. Ostrowski, S. P. Luke. Application of Capacitance Electrical Tomography for on-Line and off-Line Analysis of Flow Pattern in Horizontal Pipeline of Pnenumatic Conveyer. Chemical Engineering Journal, 2000, 77: 43～50
19 王海刚,刘石.内—外置电极ECT传感器两相流成像仿真研究.仪器仪表学报,2001,22(2):21～25
20 MacCuaiy N. Application of Gamma-ray Tomography Tp Gas Fluidized beds. Applied Optics, Vol. 24, No. 23, 1985: 4083～4085
21 赵创进,王师.电容层析成像用新型电容/电压转换电路的研制.仪器仪表学报,2001,22(1):18～21
22 Hussein E. M. A and Menekeu D. A. Single-exposure Neutron Tomography of Two-phase Flow, Int. J. Multiphase Flow, Vol. 12, No. 1, 1986: 1～34
23 蒋泉.电容层析成像技术在两相流浓度测量中的应用.浙江大学本科毕业设计学位论文.1994:28～42
24 Banerjee S. Simulation of a Nertron Scatterint Method for Measuring Void Fraction in Two-Phase Flow. Nuclear Engineering and Design, 1979, (53): 393～405
25 黄松明.层析成像技术在过程检测中的应用.清华大学学报(自然科学版),1989,29(4):98～105
26 黄志尧,王保良.电容层析成像两相流流型可视化系统.仪器仪表学报,2001,22(5):25～29
27 M. A. Bennet, R. M. West. The Investigation of Bubble Column and Foam Process Using Electrical Capacitance Tomography . Minerals Engineering, 2002, 15: 225～234
28 王保良,黄志尧.新型电容层析成像数据采集系统的研制.仪器仪表学报,2001,22(3):31～33
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30 W. Warsito, L. S. Fan. Measurement of Real-Time Flow Structures in Gas- Liquid and Gas-Liquid-Solid Flow Systems Using Electrical Capacitance Tomography. Chemical EngineeringScience, 2001, 56: 6455～6462
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2 邓之初.多相流研究和多相流检测技术.第二届全国多相流检测技术学术讨论会论文集.南京,1988:1～8
3 陈苷棠.化工中若干多相流检测问题.第三届全国多相流检测技术学术讨论会论文集.上海,1990:1～7
4 冯文锁,徐苓安.气液两相流反射式超声层析成像系统的仿真研究.第四届全国多相流检测技术学术讨论会论文集.天津,1992:191～192
5 徐苓安.超声波层析成像技术在气液两相流检测中的应用.第三届全国多相流检测技术学术讨论会论文集.上海,1990:90～99
6 Artur J. Jaworski, Tomasz Dyakowski. Investigation of Flow Instabilities within the Dense Pneumatic. Powder Technology, 2002, 125: 279～291
7 Lahey R. T. A high-intensity X-ray System for Stochatic Measurements of Two-Phase Flows. ANS Trans, Vol. 30, 1979: 497～499
8 Pike R. W. Measurement of the Void Fraction in Two-Phaseflow by X-ray Attenuation. AIChE Journal, Vol. 11, No. 5, 1965: 794～800
9 蒙建波,朱林章.检测理论的现状及展望.第四届全国多相流检测技术学术讨论会论文集.天津,1992:89～91
10 李海青.两相流参数检测及应用.浙江大学出社,1991:25～36
11 黄松明,徐苓安.两相流测量的现状和发展趋势.第二届全国多相流检测技术学术讨论会论文集.南京,1988:9～26
12 黄志尧.层析成像技术在多相流检测中的应用.浙江大学博士学位论文,1995:8～25
13 Bemrose C. R. Application of Positron Emission Tomography to Particulate Flow Measurement in Chemical Engineering Processes. Nuclear Instruments and Methods in Physics Research, 1998, 73: 874～880
14 金锋,许会,颜华,王师.气/固两相流相浓度传感器.东北大学学报,1999,20(5):457～460
15 W. Q. Yang. Role of Tomography in Gas/Solids Flow Measurement. Flow Measurement and Instrumentation, 2003, 11: 237～244
16 傅文利,赵进创.电容层析成像技术在气力输运粉体两相流流型可视化识 别中的应用.自动化与仪器仪表,2001,5:42～44
17 许华,颜华.气液两相流液相体积含量的精确测量.仪器仪表学报,1999,20(6):641～643
18 K. L. Ostrowski, S. P. Luke. Application of Capacitance Electrical Tomography for on-Line and off-Line Analysis of Flow Pattern in Horizontal Pipeline of Pnenumatic Conveyer. Chemical Engineering Journal, 2000, 77: 43～50
19 王海刚,刘石.内—外置电极ECT传感器两相流成像仿真研究.仪器仪表学报,2001,22(2):21～25
20 MacCuaiy N. Application of Gamma-ray Tomography Tp Gas Fluidized beds. Applied Optics, Vol. 24, No. 23, 1985: 4083～4085
21 赵创进,王师.电容层析成像用新型电容/电压转换电路的研制.仪器仪表学报,2001,22(1):18～21
22 Hussein E. M. A and Menekeu D. A. Single-exposure Neutron Tomography of Two-phase Flow, Int. J. Multiphase Flow, Vol. 12, No. 1, 1986: 1～34
23 蒋泉.电容层析成像技术在两相流浓度测量中的应用.浙江大学本科毕业设计学位论文.1994:28～42
24 Banerjee S. Simulation of a Nertron Scatterint Method for Measuring Void Fraction in Two-Phase Flow. Nuclear Engineering and Design, 1979, (53): 393～405
25 黄松明.层析成像技术在过程检测中的应用.清华大学学报(自然科学版),1989,29(4):98～105
26 黄志尧,王保良.电容层析成像两相流流型可视化系统.仪器仪表学报,2001,22(5):25～29
27 M. A. Bennet, R. M. West. The Investigation of Bubble Column and Foam Process Using Electrical Capacitance Tomography . Minerals Engineering, 2002, 15: 225～234
28 王保良,黄志尧.新型电容层析成像数据采集系统的研制.仪器仪表学报,2001,22(3):31～33
29 颜华,王师,邵富群.电容层析成像系统中微小电容测量法.仪表技术与传感器,1998,18(4):16～19
30 W. Warsito, L. S. Fan. Measurement of Real-Time Flow Structures in Gas- Liquid and Gas-Liquid-Solid Flow Systems Using Electrical Capacitance Tomography. Chemical EngineeringScience, 2001, 56: 6455～6462
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