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2007-14

The cell average technique for solving multi-dimensional aggregation population balance equation

by Kumar, J., Peglow, M., Warnecke, G. Heinrich, S..


Series: 2007-14, Preprints

MSC:
65R99 None of the above, but in this section
65M99 None of the above, but in this section

Abstract:
In this paper, the cell average discretization (J. Kumar et al., 2006, Chem. Eng. Sci.; 61, 3327-3342) is extended to solving multi-dimensional population balance equation. Similar to the one-dimensional case, the scheme is based on an exact prediction of certain moments of the population. The formulation is quite simple to implement, computationally less expensive than previous approaches and highly accurate. Numerical diffusion is a common problem with many numerical methods when applied on coarse grids. The presented technique nearly eliminates numerical diffusion and predicts four moments of the distribution function with high accuracy. The technique may be implemented on any type of grid. The accuracy of the scheme has been analyzed by comparing analytical and numerical solutions of some test problems. The numerical results are in excellent agreement with analytical results and show the ability to predict higher moments very precisely. Additionally, an extension of the proposed technique to higher dimensional problems is discussed.

Keywords:
Population balance; Discretization; Breakage; Particle; Cell average