摘要
搅拌混合在工业生产中往往是最必不可少的工序,常用于冶金、造纸、食品加工制药、生物等领域,其中艾萨炉、奥斯麦特炉、Hismelt炉等都涉及搅拌混合,聚合反应器85%是搅拌混合设备,还有制药发酵过程几乎全部是搅拌混合过程。搅拌混合的目的是为了降低物料体系内部的非均匀性,能尽快地达到混合均匀,进而促进反应的进行。因此,如何获得多相混合均匀性以及非均匀性的有效量化,进一步提高搅拌效率,对于搅拌反应器的设计优化以及节能降耗具有重要的意义。
本文围绕搅拌槽内多相混合效果的评价,运用计算同调群、数字图像处理技术、混沌学以及统计学理论,对搅拌槽内多相混合效果的评价方法及应用开展了比较系统的研究,内容主要涉及多相混合的水动力学实验的设计、多相混合效果的贝蒂数评价方法及模型研究、多相混合效果的定性分析和定量分析以及该评价方法在Zn-SiO2复合电沉积中的应用研究。
本论文对搅拌混合效果评价的基本理论进行了综述。借鉴甲烷和氧化锌在熔融盐中反应的多相流混合模型,确定多相混合水动力学实验的设计方案,搭建了包括高速摄像机、透明搅拌槽、转子流量计、喷枪、氮气瓶在内的顶吹气体搅拌混合水力学实验平台,目的在于阐述并提出一种简单的多相流混合效果贝蒂数评价新方法,该方法可以同时实现混合均匀性及非均匀性的有效量化。通过实验研究不同的顶吹喷枪流量Q以及喷枪浸入深度l对混合效果的影响,结果表明：0维贝蒂数β0(t)随着时间的演化趋势为先增大后平稳变化,其拐点处对应的混合时间即最短混合均匀时间；随着喷枪流量Q的不断增大,其最短混合均匀时间呈减小趋势,当流量Q增大到1000L/h以后,最短混合均匀时间出现轻微波动,且变化不大；随着喷枪浸入深度l以及喷枪流量Q的不断增加,0维贝蒂数的平均值即混合均匀性程度波动较大,而1维贝蒂数β1(t)变化较为平稳,但是在一些非正常混合情况下也会迅速的偏离平均值,说明这种混合非均匀性也会影响整个混合过程的混合效果；同时构建了多相流混合效果评价模型,得出了获得较佳混合效果所需的条件：0维贝蒂数的平均值足够大,1维贝蒂数的平均值、流量的大小和0维贝蒂数的振幅要足够小,并且最短混合时间足够小,模型计算结果表明：最佳的混合效果条件与所用模型包括大小、形状等均有密切关系。
其次,对多相混合效果的定性特征进行了分析。研究了混合效果的统计学规律,通过计算不同搅拌条件下贝蒂数时间序列的柱状图,结果发现在所有的实验中其0维贝蒂数时间序列β0(t)和部分实验中的1维贝蒂数时间序列β1(t)近似符合正态分布；为了清晰的描述正态分布拟合的准确性,计算其累积分布函数图和概率分布图,根据曲线拟合的程度来判断混合效果的好坏。实验证明越好的混合效果其累积分布函数和概率分布函数中拟合曲线的拟合效果越好；计算1维贝蒂数时间序列的柱状图、累积分布图和概率分布图,也可以区分正常和非正常的混合效果。在这些正常混合效果之中,0维贝蒂数β0(t)和1维贝蒂数β1(t)在t>T后,它们的平均值平稳振荡,这表明混合均匀性是连续的,混合非均匀性变化平稳。然而,在部分非正常混合效果之中,1维贝蒂数时间序列不符合正态分布,其主要表现为累积分布和概率分布函数的拟合曲线相互背离,在1维贝蒂数时间序列中出现快速地偏离平均值的现象,这表明混合的非均匀性可以迅速地改变。为了进一步对多相混合效果的量化特征进行分析,引入0-1检验方法对0维和1维贝蒂数时间序列进行了混沌特征分析,结果发现经过足够长的混合时间之后,整个混合过程是混沌的,同时获得了不同混合效果的有效量化。尽管如此,不同的混沌状态对应于不同的0-1检验计算数值,该数值介于0-1之间,接近于1则代表系统是混沌状态,接近于0则代表系统是非混沌的,而本文0-1检验计算的所有贝蒂数序列均为接近于1,只是不同的混合工况接近于1的程度不相同；计算不同混合状况下贝蒂数序列的庞加莱截面图,计算结果为成片的密集点,说明该混合系统是混沌的,同时利用庞加莱截面图的特征还能有效地区分正常及非正常的混合效果；运用Rosenstein方法计算最大李雅普诺夫指数,计算得到的斜率为正的特征图说明充分混合之后的动力系统是混沌的。
最后,本文选择Zn-SiO2复合电沉积体系,以及最常用的搅拌方式——电动桨叶式搅拌来研究电解液的流动特性。利用数字图像处理技术清晰地捕捉到电解液搅拌过程中微小颗粒的分布和团聚所形成的复杂图样：运用本文提出的多相混合效果贝蒂数评价方法及模型深入地研究了该体系复合电解液的流动混合效果,通过镀层性能分析进一步验证了该方法和模型的可行性及准确性,为深入认识和理解复合电沉积基本科学问题及其工艺优化设计提供了重要参考。
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.
引文
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