Abstract
A local fixed pivot quadrature method of moments (LFPQMOM) is proposed for the solution of the population balance equation (PBE) for the aggregation and breakage process. First, the sectional representation for aggregation and breakage is presented. The continuous summation of the Dirac Delta function is adopted as the discrete form of the continuous particle size distribution in the local section as performed in short time Fourier transformation (STFT) and the moments in local sections are tracked successfully. Numerical simulation of benchmark test cases including aggregation, breakage, and aggregation breakage combined processes demonstrate that the new method could make good predictions for the moments along with particle size distribution without further assumption. The accuracy in the numerical results of the moments is comparable to or higher than the quadrature method of moment (QMOM) in most of the test cases. In theory, any number of moments can be tracked with the new method, but the computational expense can be relatively large due to many scalar equations that may be included.
Highlights
Determination of the interfacial area with high accuracy between different phases in a dispersed system is critical to the prediction of the flow behaviors and mass transfer
We focus our attention on the solution method for the population balance equation for tracking particle size distribution and its moment due to aggregation and breakage at a given location x
It is worth pointing out that, in traditional methods of moment (MOMs) such as quadrature method of moment (QMOM) [7] or fixed pivot quadrature method of moment (FPQMOM) [12], the assumption of continuous summation of the Dirac Delta function is adopted in the overall domain, the particle size distribution is lost in the simulation
Summary
Determination of the interfacial area with high accuracy between different phases in a dispersed system is critical to the prediction of the flow behaviors and mass transfer. Population balance equation (PBE)—as an essential tool to describe the multiphase system and capable of predicting the interfacial area by tracking the particle size distribution and describing the micro-behaviors that influence the particle size distribution of the disperse phase—has been widely used in scientific and engineering fields. Such an equation is rather complex, and the numerical method is the only choice in most cases. A promising numerical scheme—the sectional quadrature method of moment (SQMOM)—was proposed by Attarakih et al for solving the PBEs for aggregation and breakage processes [16]. Several benchmark test cases including pure aggregation, pure breakage, and aggregation and breakage combined processes are presented to validate the new method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
