宽Re范围内气泡和液滴曳力系数的关联模型

A correlation model of drag coefficient for bubbles/droplets in a wide Reynolds number range

流粒(气泡或液滴)的曳力系数CD和上升/终端速度因有助于准确预测反应器内相含率分布、液相速度分布、流粒停留时间和传质速率而具有重要意义。但现有用于估算流粒CD的关联式大多分段且只在低雷诺数Re区间内有效,并难以同时准确预测不同实验体系和操作条件下的实验结果。针对这些不足,基于实验测量和理论分析,本工作提出了一个能够在整个Re范围内合理描述实验观测到的流粒CD演变规律的新数学关联式,并利用单组实验数据和编写的求解多维无约束线性优化问题的计算机程序确定了模型参数,且将新流粒CD关联式与现有经验模型、实验结果或三维数值模拟结果进行了对比。结果表明,新流粒CD关联式展现出优异的预测能力,能对不同实验体系(空气-水、空气-甘油-水、空气-甘油、甲苯-水、正丁醇-水、正辛醇-水等)、不同操作条件(气泡:0.1<Re<10^(4),10^(-11)<Mo<7;液滴:5<Re<2000,10^(-11)<Mo<10^(-6))下测量的流粒CD数据进行合理预测。另外,结合新流粒CD关联式和单流粒运动方程对流粒上升速度进行了预测,预测结果与不同体系中的实验测量数据之间呈现出较好的一致性。

It is of great significance to predict the drag coefficient CD and the rising velocity of fluid particles(i.e.bubbles or droplets)accurately because they are helpful to estimate the phase holdup distribution,liquid phase velocity distribution,fluid particle residual time and mass transfer rate in the reactor.However,most of the correlations in the literature to estimate CD are piecewise,only valid in the low Reynolds number(Re)range and difficult to be extended to different experimental systems.In the view of these shortcomings,based on the experimental and theoretical results,this work proposed a new mathematical correlation model which can describe CD evolution observed by experiments in a wide Re range,and complied a program to solve the multidimensional unconstrained linear optimization problem to determine the model parameters.The new fluid particle CD correlation showed a good prediction ability and reasonably predicted the fluid particle CD value measured by different researchers under different experimental systems(e.g.air-water,air-glycerol,air-glycerol-water,n-butanol-water,noctanol-water,toluene-water etc.)and different operating conditions(e.g.bubble:0.1<Re<10^(4),10^(-11)<Mo<7;droplet:5<Re<2000,10^(-11)<Mo<10^(-6)).In addition,the rising velocities of fluid particles were predicted by combining the new fluid particle CD correlation and single fluid particle motion equation.The predicted terminal velocity and rising velocity of fluid particles also were consistent with the results of different experimental systems.The above predictions presented that the new CD correlation model was universal,reasonable and reliable to some extent.