基于泛函理论分析输气管道不稳定流动

在天然气输送管网中，枝状管网是的一种常见的形式。针对天然气枝状管道系统的组成特征，采用系统分析的观点，将管道系统划分成一系列基本组成单元，建立单元中不稳定流动方程，并根据单元之间的关系，综合考虑相关的连接条件、边界条件以及初始条件，从而提出了整个系统的联立模型。然后基于泛函分析理论和算子级数法求解联立模型，得到了问题的广义解。该方法具有解析解和数值解的特点，当所划分的基本单元较大时，可以得到直观的近似解析解；当所划分的基本单元较小时，可以得到更准确的数值解。由于管道单元和时间步长的取值可长可短，这就提高了求解的灵活性。以此为基础，编制了计算机程序，并应用于四川某气田管网的实际模拟。通过分析和应用表明，其模型和算法具有计算方便，精度高，省时和适用范围广等优点。

An Unsteady Flow Analysis in Gas Transmission Pipeline Based on Theory of Functional Analysis

Branch -like pipeline is a common structure in gas transmission pipeline. In the light of the constituent properties of natural gas branch - like pipeline system, the system can be divided into fundamental constituent units. This paper presents a realistic unsteady flow model consisting of simple models of pipeline units and connecting conditions, boundary conditions and initial condition associated with units by using system analysis method. The solutions in wide sense are obtained by theory of functional analysis and operator series method, Such a method has the properties of both analytical solution and numerical solution methods. When the divided pipeline unit is larger, an intuitive approximate analytical solution may be obtained; while the one is smaller, a more accurate numerical solution may be acquired. Based on this, a general computer program has been developed for this model and solutions have been used successfully in a local natural gas transmission network in Sichuan. It is proved that the model and algorithm proposed in this paper are of the advantages of convenient calculation, high precision, time saving and wide application range by way of analysis and application.