Stability analysis of discrete population balance model for bubble growth and shrinkage,International Journal for Numerical Methods in Fluids

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Stability analysis of discrete population balance model for bubble growth and shrinkage
International Journal for Numerical Methods in Fluids ( IF 1.7 ) Pub Date : 2021-08-07 , DOI: 10.1002/fld.5036
Jiadong Li _{1,

2} , Yixiang Liao ₂ , Dirk Lucas ₂ , Ping Zhou ₁

Affiliation

The stability condition for solving the population balance equation (PBE) involving bubble growth and shrinkage within the Eulerian framework is proposed. The particle flux weighted average Courant number,

{\overline{C}}_{CFL}

, which reflects the propagation of particle state of the entire size classes on internal coordinates is first derived. Stability conditions of internal convection for PISO and PIMPLE algorithms are obtained by evaluating a series of tests concerning the constant bubble growth. The proposed stability conditions are then applied to simulate two kinds of laboratory experiments, that is, the bubble growth in stagnant liquid and condensing steam-water pipe flows. The results show that the stable PBE solutions hold for the cases using either PISO or PIMPLE algorithms combined with the corresponding stability condition. Meanwhile, the conservation of the zeroth and first moments of the number density function can be guaranteed when the stability condition is satisfied. In addition, the effect of heat transfer coefficient correlations is also discussed.

中文翻译：

泡沫增长和收缩的离散人口平衡模型稳定性分析

提出了在欧拉框架内求解涉及气泡增长和收缩的人口平衡方程（PBE）的稳定条件。粒子通量加权平均柯朗数，

{\overline{C}}_{节能灯}

，它反映了整个尺寸类的粒子状态在内部坐标上的传播。PISO 和 PIMPLE 算法的内部对流的稳定条件是通过评估一系列有关气泡恒定增长的测试获得的。然后应用所提出的稳定性条件来模拟两种实验室实验，即停滞液体中的气泡生长和冷凝蒸汽-水管流动。结果表明，稳定的 PBE 解决方案适用于使用 PISO 或 PIMPLE 算法结合相应的稳定性条件的情况。同时，在满足稳定性条件的情况下，可以保证数密度函数的零阶矩和一阶矩守恒。此外，还讨论了传热系数相关性的影响。

更新日期：2021-08-07

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