Research On Evaluation Methods And Applications Of Stirring And Mixing Effects In Multiphase Systems

Mixing is often the most essential process in the industrial production, which is applied in the metallurgy, paper making, food processing, pharmaceutical, biotechnology and other fields, in which, Isa furnace, Ausmelt furnace, Hismelt furnace and so on are all related to the mixing,85%of the polymerization reactors are mixing equipments, and also almost all of the pharmaceutical fermentation process include the mixing process. The purpose of mixing is to lower the nonhomogeneity of the inside of the materials system, and to achieve the mixing homogeneity as soon as possible, and then to promote the reaction. How to get the effective quantitative of multiphase mixture homogeneity and nonhomogeneity of the mixture and further to improve the mixing efficiency is significant for the design optimization of agitation reactor and energy saving.The more systematic study of evaluation methods and applications of multi-phase mixing effects in agitating tank has been done in this paper by algebraic topology, digital image processing technology, chaotic dynamics and statistical theory focus on the evaluation of multi-phase mixing effects in agitating tank, the contents mainly include the design of the hydrodynamic experiment for multiphase mixing, the Betti numbers evaluation method of multiphase mixing, statistical and chaotic characteristics analysis of multiphase mixing effects, and the application research of our evaluation method in Zn-SiO2composite electrodeposition.The basic theories of the evaluation of stirring and mixing is reviewed, the purpose of definiting the design proposal of multiphase mixing hydrodynamic experiments, and seting up the platform including high-speed cameras, transparent stirred tank, rotameter, spray gun and the nitrogen bottle, for hydraulics experiments by top-blown gas stirring and mixing based on the three phase reaction model of CH4and ZnO in molten salt is to expound and propose a novel and simple Betti numbers evaluation method of multiphase mixing effects, this method can achieve the effective quantitative of homogeneity and nonhomogeneity of the mixture at the same time. The effects of different top-blown gun flow Q and different immersion depth of the gun H on the mixing effects in experiments are investigated, the result shows that the trends of zeroth Betti number is increasing firstly and then has a smooth change over time, the mixing time which correspond to the point of inflection is definited as the minimum mixing time, the minimum mixing time trends are decreasing with the increasing of Q, when the flow rate Q is1000L/h, the minimum mixing time has small fluctuations, but the change is small, the average value of the zeroth Betti numbers namely the degree of the homogeneity of the mixture has a big fluctuation with the increasing of H and Q, however, the first Betti numbers average is relatively stable, but it will also deviate the mean value rapidly in some conditions of abnormal mixed, which shows that such nonhomogeneity of the mixture will also affect the mixing effects in the whole mixing process, and at the same time, the evaluation model of multiphase flow mixing effects is proposed, the objective function requires that the average value of the zeroth Betti number should be as big as possible, the average value of the first Betti number, the minimum mixing time, the size of the flow and the amplitude of the zeroth Betti number should be as small as possible, the calculated results of our optimization model show that the best mixing condition is related to the model including size, shape, etc.Secondly, the statistical laws of mixing effects by caculated the histograms of the Betti number time series in different mixing conditions are further investigated, and the result shows that the zeroth Betti number time series in all experiments and the first Betti number time series in part of the experiments approximately fit the Normal distribution, in order to describe the accuracy of Normal distribution fitting, plots of cumulative distribution function and probability distribution are calculated. The mixing effects could be determined by the extent for fitting the normal curves. It is proved that the better mixing effect is, the better cumulative distribution and probability distribution fit; by calculating the histograms, cumulative distribution and probability distribution of the first Betti numbers time series, the normal or abnormal mixing effects could also be differentiated. In these normal mixing effects, the zeroth Betti numbers β0(t) and first Betti numbers β1(t) begin vibrating about the mean value after t> T, which indicates the homogeneity of mixing is continuious, and non-homogeneity of mixing change in smooth. However, in parts of abnormal mixing effects, the first Betti numbers time series do not fit the normal distribustion, which shows the fitting curves of cumulative distribution and probability distribution deviate from each other. And the phenomenon that rapidly deviates from the average of the first Betti numbers time series shows that the non-homogeneity of mixing could quickly be changed. In order to study the characteristics of chaotic mixing effects further, the0-1test is introduced to analyse chaotic dynamics for the time series of the zeroth Betti number and the first Betti number, but the results show that the whole mixing process is chaotic after a sufficiently long mixing time, and at the same time, we get the effective quantitative of different mixing effects, however, different chaotic states have different values calculated by0-1test, which value should be between0and1, if it is close to1, it means the system is chaotic, if it is close to0, it shows that the system is non-chaotic. However, in this paper all of the Betti numbers time series which are caculated by0-1test methed are close to1, but the degree to close to1is different for the different mixing conditions. By calculating the poincare sections of Betti numbers in different mixing states, the result shows pieces of dense points with fractal structures, it means the mixing system is chaotic, and it can differentiate the normal and the abnormal mixing effects effectively by the feature of Poincare sections. If the slope of the largest lyapunov exponent caculated the by the method of Rosenstein is positive, which shows that the dynamic system is chaotic after fully mixing.Finally, this paper investigates the Zn-SiO2composite electrodeposition system, and one of the most common mixing ways which is electric-paddle stiring is applied to reseach the flow characteristics of the electrolyte. The distribustion of small particles and complex patterns formed by aggregating in the process of electrolyte mixing could be captured clearly by using digital image processing technology; in this paper, we propose the Betti numbers evaluation method and model for quantifying multiphase mixing effects to investigate the mixing effects of the composite electrolyte flow. By performance analysis of composite coating, it is verified that our evaluation method and model is feasibale and accurate, and provides an important reference for knowing and understanding the basic scientific issues of composite electrodeposition and optimization design of process.