Development of an Electrical Computer Tomography Method using Capacitance for Analysis of Two-phase Flow in the Rectangular Pipe : 사각관에서의 이상유동 해석을 위한 캐패시턴스를 이용한 전기적 컴퓨터 토모그라피 방법의 개발

국문 초록 (Abstract)

이상유동의 해석을 위한 전기적 캐패시턴스 토모그라피 시스템이 개발되었다. 순방향 전사에서는 전극판 사이에 축적되는 캐패시턴스의 유전율 분포와의 비선형성이 선형화 되었다. 전기장은 포이손 방정식의 유한차분화를 통해 계산되었으며, 캐패시턴스의 선형화는 민감도 행렬, S를 통해 이루어졌다. 본 연구에서는 역전사를 위해 LBP, TR, ITR, PLI의 등의 알고리즘이 채택 되었으며, 더 나아가 ITR 방법에서의 항등 행렬을 S^(T)S의 대각 행렬로 대체하여 MITR 알고리즘을 새롭게 개발하였다. 직관에서의 이상 유동 해석을 위해, 제시된 방법을 코드화 하였다.
제안된 다양한 알고리즘의 성능 및 유효성을 평가하기 위해 유전율의 변화 효과와 노이즈의 간섭효과 등의 두 가지 경우가 선택되었다. 유전율 변화 효과에 대해서는 PLI와 새롭게 개발된 방법이 좋은 성능을 가졌다. 노이즈의 저항성에 대한 평가를 위해 오프셋 노이즈와 랜덤 노이즈가 이용되었다. 채택된 알고리즘들 중 MITR 방법이 가장 좋은 성능을 보여줬다.
이상의 연구를 통해 사각관에서의 이상유동해석을 위해 본 연구에서 개발된 전기적 캐패시턴스 토모그라피 코드가 사용 가능함을 알 수 있었다.

다국어 초록 (Multilingual Abstract)

An Electric Capacitance Tomography system for the analysis of two-phase flow was developed. The forward projection was linearized from the nonlinear relation between the fields of the capacitance accumulated onto the electrode pairs. The electric field was calculated by the finite difference formulation of the Poisson Equation. The linear relation between the capacitance and the distribution of the dielectric constant of medium produced the sensitivity matrix S as the linear forward projection. For the backward projection procedures, in the present study, we furnished almost all the algorithms known LBP, TR, ITR and PLI. Furthermore, we developed a new method by changing the identity matrix of the Tikhonov method with the diagonalized S^(T)S. The developed methods were actualized in a computer code for the analysis of the two-phase flow in the rectangular pipe.
In order to evaluate the validity and performance of the various suggested algorithms, two cases were selected: the effect of the variation of the dielectric constant and the effect of noise interference. For the variation of the dielectric constant according to the pressure and temperature, the PLI method and the present new method showed a good performance. For the noise resistance, the offset noises were introduced to the reference capacitance values. Among the algorithms the new method developed in this work had the strong noise immunity.
Through the study, it was found that the developed code for the electrical capacitance tomography can be used for the analysis of two-phase flow in the rectangular pipe.

목차 (Table of Contents)

• Abstract = ⅰ
• 국문초록 = ⅱ
• Contents = ⅲ
• List of Figures = ⅴ
• List of Tables = ⅷ
• Ⅰ. Introduction = 1
• 1. Background and motivation = 1
• 2. Research objectives = 11
• Ⅱ. Mathematical and Physical Basis = 12
• 1. Inverse problem and regularization = 12
• 1.1 Least squares estimation = 13
• 1.2 Regularization techniques = 17
• 2. Finite Difference Formulation of Electric field in the ECT = 22
• 2.1 Governing Equation for Electric field = 22
• 2.2 Discrete equation for ECT = 27
• 2.3 Evaluation of the FDM code for the electric field = 31
• Ⅲ. Electric Capacitance Tomography = 41
• 1. General = 41
• 2. Construction of Linear Forward Projection using sensitivity matrix = 43
• 3. Backward Projection = 46
• 4. Various Backward Projection Algorithms = 47
• 4.1 Linear back-projection, LBP = 47
• 4.2 Tikhonov regularization, TR = 47
• 4.3 Multiple linear regression and regularization = 49
• 4.4 Iterative Tikhonov method, ITR = 49
• 4.5 Projected Landweber iteration, PLI = 51
• 4.6 Algebraic reconstruction technique = 53
• 4.7 Simultaneous iterative reconstruction technique = 53
• 4.8 The present method = 55
• Ⅳ. Results and Discussion = 57
• 1. Two-phase flow reconstruction = 57
• 2. Effect of dielectric constant variation = 66
• 3. Noise sensitivity = 72
• Ⅴ. Conclusions = 80
• Ⅵ. References = 81
• Ⅶ. Appendix = 83
• 감사의 글 (Acknowledgement) = 97