随机分布树状分叉网络渗流特性的分形研究  

Analysis on seepage of the randomly distributed fractal-like tree network

作　　者：王世芳[1] 吴涛[2] 邓永菊[1] 戴伟[1] 

机构地区：[1]湖北第二师范学院物理与电子信息学院,武汉430205 [2]武汉工程大学理学院,武汉430074

出　　处：《华中师范大学学报（自然科学版）》2012年第4期406-409,共4页Journal of Central China Normal University：Natural Sciences

基　　金：湖北省教育厅科学技术项目(B20113002)

摘　　要：基于Darcy定律和Hagen-Poiseuille方程,应用分形理论研究了母管直径分布具有分形分布的树状分叉网络的渗流特性,得到了具有随机分布的树状分叉网络渗透率的解析表达式.研究结果表明:通过具有随机分布的树状分叉网络的流量与压力梯度之间呈线性变化关系;其渗透率随分形维数Df和孔隙率的增加而增加,随长度比的增加而减小.Based on Darcy＇s law and Hagen-Poiseuille equation, the flow characteristics of the randomly distributed fractal-like tree network with the diameter do of the 0th branching level are investigated by use of fraetal theory, which follows the fractal scaling law. An analytical expression for permeability of the randomly distributed fractal-like tree network is presented. The results show that the flow rate for the randomly distributed fractal-like tree network scales linearly with pressure gradient. The dimensionless permeability for the randomly distributed fractal-like tree network increases with the increase of fractal dimension and porosity and decreases with the increase of the length ratio.

关 键 词：树状分叉网络 渗透率 Darcy定律 压力梯度 

分 类 号：O357[理学—流体力学]