模擬非穩態流體餘氣相管線系統之研究

本研究主要是利用電路來模擬及計算非穩態之氣體網路管路。傳統之求解方法牽涉複雜的數值分析原理用以解偏微分方程式；如牛頓拉弗生配合有限元素分析法，Von Neumann 穩態分析法及迭代法等。為了增快求解速度、增進便利性且不同於傳統的管路分析方法，本研究應用基本電學電路原理並且透過轉置理論來模擬分析非穩態的管路系統。轉置張量的設定主要是基於網路的構型及柯希何夫定理之應用。而本研究之電路模型的主要特色在於利用阻抗及電容搭配，進而引導出一組積分方程式用來取代傳統以質量、動量及能量方程式主導之複雜的偏微分方程式，以期有效且快速的進行求解。本研究所推導之數學模式曾與相關文獻之案例相比對並且獲得理想的結果。

關鍵字

電路模擬；氣體管路；電阻；電容；張量分析

並列摘要

In this study, the electrical analogy method was applied to investigate the unsteady flow in the pipeline network. The conventional governing equations involve two partial differential equations which are always solved by complicated numerical method; therefore, several methods considered faster and easier to apply have been developed. For example, Newton-Raphson calculated by finite-difference, Von Neumann stability analysis, Iterative convergence etc. Unlike the conventional methods for pipe network analysis, in which the Kirchhoff’s laws are applied to each node and mesh respectively and either one of the two equations is only used to verify the solution in most cases; in this study a mathematical model based on electrical analogy and transformation theory was applied to analyse unsteady pipe network. The transformation methods with transformation tensor are based on structure of network and the application of Kirchhoff’s laws. The feature of this new modeling method is that the system equations are extended by combining resistance and capacitance, which leads to a set of integral equations instead of the conventional partial differential equations describing conservation of mass, momentum and energy. It is found that the results obtained are comparable to those obtained from traditional methods published in the literature. The proposed method is computationally efficient and is readily applicable as a method for control of networks.

並列關鍵字

Electrical analogy ； Gas pipeline ； Resistance and capacitance ； Tensor analysis

參考文獻

2. Gay, B. and P. Middleton. The Solution of Pipe Network Problems, Chem. Engrg. Sci., 26, pp. 109-123. 1971.

4. Gay, B. and P. E. Preece. Matrix Methods for The Solution of Fluid Network Problems: PartⅠ- Mesh Methods, Ttans. Inst. Of Chem. Engrs, 53, pp. 12-15. 1975.

5. Gay, B. and P. E. Preece. Matrix Methods for The Solution of Fluid Network Problems: PartⅡ- Diakoptic Methods, Ttans. Inst. Of Chem. Engrs, 55, pp. 38-45. 1977.

6. Ti, H. C., The Use of Network Analysis for The Simulation of Flows in Pipe Network Systems, Ph.D. Thesis, University of Leeds, U.K., 1981

7. S.L. Ke., Transient Analysis of Isothermal Gas Flow in Pipeline Network, Mister Thesis, National University of Singapore, 1998.

國際替代計量

模擬非穩態流體餘氣相管線系統之研究

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