Numerical Study On Fractal Growth Mechanism Of DLA/DLCA Virtual Flocs By Using Orthogonal-test Method

As the core of water treatment process,flocculation is widely used in various water treatment processes.The performance of flocs formed in this process?including particle size and structure,etc.?directly influences the operation status of subsequent processes and final effluent quality.In order to improve flocc ulation performance and optimize flocculation process effectively,most of previous studies used flocculation test as the main means to investigate the influence of physic o-chemical condition,hydrodynamic environment and other factors,however,due to the complexity of the actual flocculation process,no satisfactory results have been achieved.With the development of computer technology and fractal theory,computer simulation provides a new way to study particle aggregation process,while fractal theory provides a new theoretical framework.In fractal dynamics model,Diffusion-Limited Aggregation?DLA?model and Diffusion-Limited Cluster Aggregation?DLCA?model are widely used in different disciplines and fields,many scholars at home and abroad have also attempted to use these two models to simulate the fractal growth process of flocs in order to re-understand the flocculation process essentially.However,previous studies simply analyzed the changes of various morphological characteristics of flocs under the action of single factor combined with the flocculation process,resulting in a great discrepancy between the simulated results and the actual process.Orthogonal test method is one of the most commonly used optimization test design methods based on mathematical statistics and orthogonality principle to explore the parameter changes under the action of multiple factors.This study intends to use this method to carry out computer simulation of virtual floc growth-breakage-regrowth process of DLA and DLCA model on MATLAB.Visual analysis method and variance analysis method are used to investigate the variation rule of floc morphological characteristics under the action of multiple factors,and significant factors affecting floc growth are obtained.Meanwhile,matrix analysis method,efficacy coefficient method and comprehensive balance method were used to explore the main factors influencing the flocs morphological characteristics and the corresponding optimal test combinations were explored.In addition,the breakage-regrowth process of virtual flocs obtained from DLA model and DLCA model under the optimal combination scheme was simulated,in order to provide theoretical guidance for further understanding the fractal growth mechanism of flocs and optimizing the control conditions of flocculation process.Through orthogonal experiment design of DLA model,combining with actual flocculation process,total number of coagulated particles,moving area of particles,bonding mode and bonding probability were investigated.The statistical characteristics of DLA virtual floc adhesion rate,fractal dimension,void fraction and radius of rotation as well as characteristic length obtained under different test numbers were analyzed by single index and multi-index analysis,the following conclusions are drawn:total number of coagulated particles in DLA model is the main factor affecting radius of rotation and characteristic length;moving area of particles is the main factor affecting the flocs adhesion rate;and the bond ing mode is the main factor affecting the void fraction and fractal dimension of flocs.Meanwhile,the significance of moving area of particles on flocs adhesion rate was highly significant.Total number of coagulated particles has a significant influence on the radius of rotation.Bonding mode has a certain influence on the significance analysis of void fraction and fractal dimension.In addition,in the process of multi-index analysis of virtual floc morphological characteristics obtained by DLA model,mo ving area of particles is the main influencing factor of floc morphological indexes,and total number of coagulated particles is the main influencing factor of floc characteristic length in all directions.Through various multi-index analysis methods,comprehensiving floc morphological indexes and characteristic length indexes,and eventually obtain the DLA model of optimal combination scheme for test:A₃B₃C₃D₃?Corresponding to the conditions that total number of coagulated particles is20000,moving area of particles is 100,bonding mode is NNN and bonding probability is 1?.By orthogonal experiment design,DLCA model combined with the actual flocculation process,total number of coagulated particles,particle moving boundary,bonding probability and particle movement step were investigated.Fractal dimension,void fraction and radius of rotation as well as characteristic length of DLCA virtual flocs obtained under different test numbers were analyzed by single index and multi-index.The main conclusions are as follows:total number of coagulated particles in DLCA model is the main factor affecting radius of rotation,fractal dimension and characteristic length;particle moving boundary is the main factor affecting void fraction and fractal dimension.In addi tion,in the process of multi-index analysis of virtual floc morphological characteristics obtained by DLCA model,the number of coagulated particles and particle moving boundary are the main influencing factors of floc morphological indexes,and total num ber of coagulated particles is also the main influencing factor of floc characteristic length.Through many multi-index analysis methods,the optimal experimental combination scheme of DLCA model is finally obtained as follows:A₃B₃C₂D₁?Corresponding to the conditions that total number of coagulated particles is 20000,particle moving boundary is 700,bonding probability is 2/3 and particle movement step is 1?.On the basis of the optimal combination scheme obtained by orthogonal experiment of DLA and DLCA models,simulation studies on the breakage-regrowth process of virtual flocs formed by the two models were carried out respectively,in order to investigate the effect of breaking behavior on the morphological characteristics of flocs.It is found that the density of DLA and DLCA virtual flocs is greatly improved after breaking,and the more breaking strength,the denser structure of flocs achieved;the breaking scale of flocs under medium breaking strength is more reasonable,which provides more growth for the formation of particles and clusters,therefore,the structure of re-formed flocs under moderate breaking strength is improved most prominently.At the same breaking strength,the compactness of DLA virtual flocs after breakage and regrowth is higher than that of corresponding flocs in DLCA model.In order to further explore the fractal growth mechanism of flocs,the flocs formed by DLA and DLCA models were compared and analyzed.It is found that the structure and properties of flocs formed by DLA and DLCA models under different crushing intensities are better than those of flocculation,especially under medium crushing intensities.Therefore,it is necessary to control the physicochemical conditions of flocs in actual flocculation,not make them over-crushed,nor make the scale of flocs too small.It has fractal characteristics,floc growth is completed under the combined process of growth-breakage-regrowth,and finally achieves dynamic equilibrium.In this process,appropriate degree of floc fragmentat ion is conducive to the improvement of its final structure,thus significantly enhancing its shear resistance.