基于傅里叶级数的渗流管道压力模型研究

Research on the Seepage Pipeline Pressure Model Based on Fourier Series

该文将渗流模型抽象简化成存在n段沙子渗流段的管道物理模型,建立了流体在多孔介质中流动的基本方程。通过建立渗流偏微分方程,结合达西定律、Kozeny-Carman方程,并利用傅里叶变换的方法求解偏微分方程,推导出关于渗流率K的表达式。通过确定管道中的沙子段渗流参数的关系表达式,进而确定了管道中的沙子段压力分布的数学模型。最后,通过分析求得压力分布,建立了管道中的压力分布的数学模型。

This paper simplifies the percolation model into a physical model of the n- stage pipeline presence of sand seepage segment,and establishes the basic equations of fluid flow in porous media. By establishing the seepage partial differential equations,combining with Darcy＇s law,Kozeny- Carman equation,and then using Fourier transform method to solve these partial differential equations,we derive the expression equation of seepage rate K. We then determine the expression of the pipeline segment sand seepage parameters and mathematical model of pressure in the pipeline. Finally,by analyzing obtained pressure distribution,the mathematical model of the pipeline pressure distribution is established