(174h) Mass-Based Finite Volume Scheme for Aggregation, Growth and Nucleation Population Balance Equation

Mass-Based Finite Volume Scheme for
Aggregation, Growth and Nucleation Population Balance Equation

Mehakpreet Singh^a, Hamza
Y. Ismail^a, Themis Matsoukas^b,
Ahmad B. Albadarin^a,Gavin
Walker^a

^aDepartment
of Chemical Science, Bernal Institute, University of Limerick, Ireland,
e-mail: Mehakpreet.Singh@ul.ie

                                                                                                                                                             ^bDepartment of
Chemical Engineering, Pennsylvania State University, 158 Fenske Laboratory,
University Park, USA

Abstract

This work is focused on
developing new mass-based numerical method using the notion of Forestier and
Mancini [1] for solving a one-dimensional aggregation population balance
equation. The inherit issue of the existing finite volume schemes is that it
required very fine grid for predicting the number density function accurately
(Kumar et al. 2009). In addition to this, the sectional methods such as fixed
pivot technique and cell average technique are computationally very expensive
due to their complex formulations although highly accurate. It is observed that
the existing numerical scheme does not predict the certain required moments of
the number distribution functions accurately. In this present work, mass-based
finite volume is developed which leads to the accurate prediction of different
integral properties of number distribution functions. In
order to check the accuracy and efficiency, the mass-based formulation
is compared with the existing method for two kinds of benchmark kernels,
namely, analytically solvable and practical oriented kernels.  Moreover, the new mass-based and existed
finite volume schemes are extended to solve a simultaneous aggregation-growth
as well as aggregation-nucleation problems and are compared with the exact
results. The comparison reveals that the mass-based numerical methods compute
the number distribution functions as well as different order moments with
higher precision by consuming less computational time than the existing method.

Keywords:
Particle, Aggregation, Growth, Nucleation, Population Balances, Finite volume
Scheme.

References:

[1] Forestier-Coste, L., Mancini, S., 2012. A finite volume preserving
scheme on nonuniform meshes and for multidimensional coalescence. SIAM Journal on Scientific Computing 34
(6), B840–B860.