挑流泄洪雾化的水滴联合信息熵数学模型

Joint information entropy mathematical model for droplet formation in flood discharge atomization

当挑流水舌高速冲击下游水面时,在下游空间会形成大量的运动水滴,如何确定这些水滴粒径的分布已成为一个重要的科学问题。气象上各类降雨滴谱常用Gamma分布来拟合,在泄洪雾化水滴粒径分布的建模中,也多采用Gamma分布来模拟其滴谱分布,但是这种方法缺乏物理意义,而且计算的精度不高。为克服Gamma分布的不足,基于最大熵增方法,提出了一种在非平衡开放体系下的水滴宏观和微观的联合信息熵分布模型,并建立误差函数的方法对模型参数进行求解。计算结果表明,本文构建的联合分布模型的计算结果与实验数据吻合最好,在不同工况下,联合模型计算结果比Gamma、传统最大熵分布计算的结果决定系数分别高3.5%、25.3%,均方根误差分别低72.4%、79%。在不同的工况下,液滴平均直径之间存在等成正比关系,为泄洪雾化粒径分布的预测提供了理论基础。

When a high-speed water jet impacts the surface of downstream water,a large number of moving water droplets are generated in the downstream space.How to determine the size distribution of these water droplets has become an important scientific issue.In meteorology,various types of rainfall droplet spectra are often fitted using the Gamma distribution.Such a distribution is also frequently adopted in the modeling of droplet sizes in flood discharge atomization.However,this method lacks physical significance and its computational accuracy is limited.To overcome the shortcomings,this paper develops a joint information entropy distribution model of water droplets in a non-equilibrium open system based on the maximum entropy increase method,and formulates an error function method to solve the model parameters.The results show that in calculation of the droplet size probability density in jet flow discharge,this model has the best agreement with experimental data,compared with the Gamma distribution method or the traditional maximum entropy distributions.Under different operating conditions,the determination coefficient of its calculations is 3.5%and 25.3%higher than the other two methods respectively,and the root mean square error is 72.4%and 79.0%lower respectively;Under different operating conditions,there exists an equal proportional relationship between the average droplet diameters.This shows our new method would lay a theoretical basis for predicting the particle size distribution of flood discharge atomization.