液滴破碎模糊计算研究

On Applying Fuzzy Mathematical Theory to Computing Breakup of Droplets

利用模糊数学理论 ,选取液滴破碎过程影响参数 ,建立了指标特征矩阵 ,采用两级模糊模式识别模型来进行择优方案的选择 ,提出并建立了描述液滴破碎过程的模糊数学计算模型。利用模糊数学模型对不同工况下的 6个液滴破碎进行了理论计算 ,结果表明 ,液滴 3最易破碎 ,液滴 2最不易破碎。

Refs.1, 2, and 3 used mathematics other than fuzzy mathematical theory. We apply fuzzy mathematical theory to computing breakup of droplets, thus opening up a new way of understanding the process of breakup of droplets in high speed air flows. Section 1 discusses in much detail fuzzy mathematical model for breakup of droplets. Section 1 discusses six topics: (1) the establishment of an eigenmatrix X (subsection 1.2); (2) membership eigenmatrix R (subsection 1.3); (3) the selection of the proper weighted matrix(subsection 1.4); (4) the criterion for droplet breakup(subsection 1.5); (5)the physical meaning of model (subsection 1.6); (6) the function property of model (subsection 1.7). Section 2 gives a numerical example. The numerical values of u computed with eq.(14) for the six stochastically chosen droplets are: first droplet 0.072 647, second droplet 0.047 516, third droplet 0.826 475, fourth droplet 0.187 217, fifth droplet 0.679 958, sixth droplet 0.453 228. The closer u approaches 1, the easier it is for the droplet to break up. So the probability of breakup is biggest for the third droplet, and then the fifth droplet, the sixth droplet......in descending order.