Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique
Improved accuracy and convergence of discretized population balance for aggregation: The cell average technique
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DOI：
10.1016/j.ces.2005.12.014
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发表时间：
2006-05
影响因子：
4.7
通讯作者：
Jitendra Kumar;M. Peglow;G. Warnecke;S. Heinrich;L. Mörl
中科院分区：
文献类型：
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作者：
Jitendra Kumar;M. Peglow;G. Warnecke;S. Heinrich;L. Mörl
提出了一种新的凝聚方程离散方法。它与Kumar和Ramkrishna（1996 a.人口平衡方程的离散解法-Ⅰ。固定旋转技术。化学工程科学51，1311-1332）。离散化种群平衡的聚集问题的数值结果是一致的过度预测和发散的情况下，凝胶化核的凝胶点之前。目前的工作建立了一种新的技术，分配细胞内的粒子更精确。这是通过首先取细胞内新生粒子的平均值，然后将它们分配给相邻节点来实现的，这样预先选择的属性就可以被精确地保留下来。新技术保留了传统离散化方法的所有优点，并在预测颗粒尺寸分布（PSD）方面提供了显着的改进。此外，它被发现，该技术是一个强大的工具，计算胶凝问题。该技术的有效性示出了几个聚合问题的应用程序适当选择的聚合内核，包括物理相关的内核。
A new discretization method for aggregation equations is developed. It is compared to the fixed pivot technique proposed by Kumar and Ramkrishna (1996a. On the solution of population balance equations by discretization—I. A fixed pivot technique. Chemical Engineering Science 51, 1311–1332). The numerical results for aggregation problems by discretized population balances are consistently overpredicting and diverge before the gelling point in the case of a gelling kernel. The present work establishes a new technique which assigns the particles within the cells more precisely. This is achieved by taking first the average of the newborn particles within the cell and then assigning them to the neighboring nodes such that pre-chosen properties are exactly preserved. The new technique preserves all the advantages of the conventional discretized methods and provides a significant improvement in predicting the particle size distribution (PSD). In addition, it is found that the technique is a powerful tool for the computation of gelling problems. The effectiveness of the technique is illustrated by application to several aggregation problems for suitably selected aggregation kernels including physically relevant kernels.