New Accurate and Efficient Discrete Formulation for Reduced Tracer
Aggregation Population Balance Equation
Abstract
In this work, a new discrete formulation for a tracer aggregation
population balance equation is developed based on an assumption that the
particles properties are concentrated on the representative of the cell.
The new formulation is simpler, easy to code and can be easily adaptable
to any kind of grid. The proposed method is extended to solve a
mixed-suspension mixed-product removal (MSMPR) system in which
aggregation and nucleation are main mechanisms that effect the particles
properties. The performance of the new formulation is tested against the
cell average technique (Giri and Nagar, ESAIM-Math. Model. Num., 49(2),
349-372 (doi.org/10.1051/m2an/2014035)) for different analytically
tractable problems. The testing is conducted by taking into
consideration two bench marking cases, namely, batch and MSMPR systems
using both gelling and non gelling kernels. It is demonstrated that the
new scheme is computationally less expensive and predicts the numerical
results with high precision even on a coarser grid. For even a refined
grid, the new scheme tends to produce better results than the cell
average technique at a lesser computational time.