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Article

Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation

by 1,2, 3, 1 and 4,5,*
1
School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2
Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian 116024, China
3
Mechanical Engineering College, Xi’an Shiyou University, Xi’an 710065, China
4
School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China
5
State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China
*
Author to whom correspondence should be addressed.
Processes 2018, 6(11), 209; https://doi.org/10.3390/pr6110209
Received: 16 September 2018 / Revised: 18 October 2018 / Accepted: 25 October 2018 / Published: 31 October 2018
(This article belongs to the Special Issue Recent Advances in Population Balance Modeling)
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. View Full-Text
Keywords: population balance equation; aggregation; breakage; local fixed pivot quadrature method of moment population balance equation; aggregation; breakage; local fixed pivot quadrature method of moment
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MDPI and ACS Style

Su, J.; Le, W.; Gu, Z.; Chen, C. Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation. Processes 2018, 6, 209. https://doi.org/10.3390/pr6110209

AMA Style

Su J, Le W, Gu Z, Chen C. Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation. Processes. 2018; 6(11):209. https://doi.org/10.3390/pr6110209

Chicago/Turabian Style

Su, Junwei, Wang Le, Zhaolin Gu, and Chungang Chen. 2018. "Local Fixed Pivot Quadrature Method of Moments for Solution of Population Balance Equation" Processes 6, no. 11: 209. https://doi.org/10.3390/pr6110209

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