迦辽金法在管道不稳定流动分析中的应用

Application of Galerkin Solution in Unsteady Flow of Long Distance Oil Pipeline

针对输油管道系统的组成特点,将系统划分成基本组成单元,建立了油品在单元中不稳定流动方程,并综合考虑它们的边界条件、连接条件和初始条件,通过引入线性化系数,采用迦辽金方法讨论了求解问题。该方法既具有解析解法的特点,又具有数值解法的特点。当所划分的管道单元较大时,可以得到直观的近似解析解;当所划分的管道单元较小时,可以得到更准确的数值解。与常用解析法相比,该方法可适用于各种管道结构,因其可在不同的管道单元和不同时间层上计算线性化系数,从而可以提高求解的准确性。与其它数值解法相比,由于管道单元和时间步长的选取可大可小,各管道单元的大小也可以不一样,这就提高了求解的灵活性。以此为基础,编制了计算机软件,对某输油管道进行了实际模拟分析,获得了满意结果。

In accordance with the constituent properties of oil pipeline system,the system can be divided into fundamental constituent units and an unsteady flow equation of oil in the unit is derived. And in comprehensive consideration of their boundary,connecting and initial conditions, through leading in a linearized coefficient the solving process is discussed by use of the Galerkin method. Such a method is of 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. By contrast with the common analytic method, the method may be suitable for various pipe network structures and owing to the fact that the linearized coefficient may be calculated for various pipeline units and for different time interval,the accuracy of the solution may be enhanced. Because the selected pipeline unit and time step may be larger or smaller and the size of each pipeline unit is different,the flexibility of acquiring solution is raised in comparison to the other numerical solution methods. Based on this,a computer program is made up and the practical simulation analysis is carried out for the local pipe networks in Huatugou-Golmud Oil Pipeline of Qinghai,a satisfactory result is obtained.