Mass-based finite volume scheme for aggregation, growth and nucleation population balance equation

Abstract

In this paper, a new mass-based numerical method is developed using the notion of Forestier-Coste & Mancini (Forestier-Coste & Mancini 2012, SIAM J. Sci. Comput. 34 , B840–B860. ( doi:10.1137/110847998 )) for solving a one-dimensional aggregation population balance equation. The existing scheme requires a large number of grids to predict both moments and number density function accurately, making it computationally very expensive. Therefore, a mass-based finite volume is developed which leads to the accurate prediction of different integral properties of number distribution functions using fewer grids. The new mass-based and existing finite volume schemes are extended to solve simultaneous aggregation-growth and aggregation-nucleation problems. 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. The comparison reveals that the mass-based method computes both number distribution functions and moments more accurately and efficiently than the existing method.

Characterization of Simultaneous Evolution of Size and Composition Distributions Using Generalized Aggregation Population Balance Equation

“…. , u p max ] T is replaced with ∞ in the second integral of PBE (1). Thus, the original PBE (1) takes the following form:…”

“…Population balance equations (PBEs) describe the behavior of particle properties' changes due to phenomena such as nucleation, growth, aggregation and breakage [1]. Many applications of PBEs can be found in the area of chemical engineering [2], depolymerization [3,4], waste water treatment [5], bubble columns [6], physics [7] and pharmaceutical sciences [8][9][10][11][12], where these mechanisms have a significant impact on the particle properties in the system.…”

Solving the population balance equation for non-inertial particles dynamics using probability density function and neural networks: Application to a sooting flame

“…6 A large variety of methods for simulating the time evolution of PSD have been discussed in the literature and applied with success, including advanced numerical strategies proposed recently to address the issues mentioned above. [7][8][9][10][11][12][13] However for many of these approaches, securing accuracy in the PSD shape prediction goes with a large computing effort, jeopardising the systematic application of the most precise methods to three-dimensional and unsteady simulations for virtual prototyping of real systems. Advanced methods for solving the PSD have been applied to canonical problems featuring low or moderate Reynolds numbers studied with direct numerical simulation (DNS), [14][15][16] while simplified approaches are usually developed to deal with complex three-dimensional flows, specifically in the context of particulate emissions from burners and com-2 This is the author's peer reviewed, accepted manuscript.…”

Finite volume approach for fragmentation equation and its mathematical analysis

“…However, the aforementioned issues were also addressed by developing highly efficient and accurate finite volume schemes [6,8,21,38,39,41] which are highly efficient and accurate. Furthermore, these schemes are straightforward to extend to solve problems involving higher-dimensional population balances [9,35,36,40,42].…”