多孔介质热弥散系数的分形模型  

A Fractal Model for Thermal Dispersion Coefficients of Porous Media

作　　者：张杰[1] 张赛[1] 高伟业 胡世旺 汪振毅 ZHANG Jie;ZHANG Sai;GAO Weiye;HU Shiwang;WANG Zhenyi(Faculty of Mechanical and Electrical Engineering,Kunming University of Science and Technology,Kunming 650500,P.R.China)

机构地区：[1]昆明理工大学机电工程学院,昆明650500

出　　处：《应用数学和力学》2022年第5期553-560,共8页Applied Mathematics and Mechanics

基　　金：昆明理工大学省级项目(人培)(KKSY201601011);云南省科学技术厅青年基金(KKSQ201701008)。

摘　　要：热弥散系数是与流体的物性和多孔介质结构有关的,表征多孔介质传热传质强弱的重要参数.该文建立了分形多孔介质的孔喉结构模型,研究了在孔喉结构处流体由湍流状态变为层流状态的局部水头损失和速度弥散效应,在考虑微观孔喉结构和速度弥散效应的影响下,推导了热弥散系数关系式.研究表明,热弥散系数与孔喉比、孔喉结构个数和迂曲分形维数成正比,与孔隙率和面积分形维数成反比.进一步研究发现,孔喉比在1~150范围内对速度弥散效应有显著影响,流体在孔喉结构处存在局部水头损失,导致速度弥散效应增强,热弥散系数增大.The thermal dispersion coefficient is an important parameter to characterize heat and mass transfer in porous media,which is related to the physical properties of fluid and the structure of porous media.The pore-throat structure model for fractal porous media was established,and the local head loss and the velocity dispersion effect were studied for the fluid changing from the turbulent state to the laminar state around the pore-throat structure.The thermal dispersion coefficient formula was derived under the influences of the micropore-throat structure and the velocity dispersion effect.The results show that,the thermal dispersion coefficient is directly proportional to the pore-throat ratio,the number of pore-throat structures and the tortuous fractal dimension,and is inversely proportional to the porosity and the area fractal dimension.Furthermore,in the range of 1~150,the pore-throat ratio has a significant influence on the velocity dispersion effect,and the fluid has a local head loss around the pore-throat structure,which leads to an enhancement of the velocity dispersion effect and an increase of the thermal dispersion coefficient.

关 键 词：多孔介质 孔喉比 局部水头损失 分形 热弥散 

分 类 号：O357.5[理学—流体力学]