三维空间下非均匀泥沙絮团分形维数计算方法比较  

Calculation of fractal dimension for non-uniform sediment flocs in three-dimensional spaces

作　　者：刘林双[1,2] 陈萌[1,2] 杨国录[1,2] 余明辉[2] 

机构地区：[1]武汉大学水资源与水电工程科学国家重点实验室,武汉430072 [2]武汉大学污淤泥研究中心,武汉430072

出　　处：《应用力学学报》2012年第6期661-665,772,共5页Chinese Journal of Applied Mechanics

基　　金：国家重点基础研究发展计划(973)项目(2011CB403300)

摘　　要：运用有限扩散凝聚模型对絮凝体的成长过程进行了三维模拟。在三维空间下，分别运用密度函数法、球体的回转半径法、沉降法推导了均匀沙、非均匀沙絮凝体分形维数的计算方法，建立模型计算并比较了各分形维数方法的计算值。结果表明：三种方法计算得出的分形维数均为1．75-2．19，回转半径法得到的分形维数略大于密度函数法和沉降法；均匀沙、非均匀沙维数均随颗粒数的增加而降低；非均匀沙絮团的分形维数略大于均匀沙絮团维数值。研究结果对黄河等高浊度细颗粒含沙水流的治理与处理具有一定的理论和实际应用价值。A simulation for floc growth in three-dimensional space is presented with diffusion-limited aggregation model.In three-dimensional space,calculation methods of fractal dimension for non-uniform sediment flocs are deduced from density function method,radius of gyration method and sedimenation method,respectively.Fractal dimensions are calculated using diffusion-limited aggregation model.Results obtained show that the fractal dimensions calculated by three methods are all at the range of 1.75 to 2.19.However,the fractal dimensions calculated by radius of gyration method are little greater than those by density function method and sedimenation method.The fractal dimensions calculated from non-uniform sediment flocs are greater than those of uniform sediment flocs,and they are both decreased with the increase of floc size.Researches presented have some theoretical and practical meanings on the control and treatment of the Yellow River high turbidity flow.

关 键 词：有限扩散凝聚模型 非均匀沙 絮凝体 分形维数 粘滞力 

分 类 号：TV142.1[水利工程—水力学及河流动力学]