Table of Contents
Using This Manual ........................................................................................................................................ v
1. The Contents of This Manual ................................................................................................................ v
2.The Contents of the FLUENT Manuals ................................................................................................... v
3.Typographical Conventions ................................................................................................................. vi
4. Mathematical Conventions ................................................................................................................ vii
5. Technical Support ............................................................................................................................. viii
1. Introduction ............................................................................................................................................ 1
1.1.The Discrete Method ......................................................................................................................... 1
1.2.The Inhomogeneous Discrete Method ............................................................................................... 1
1.3.The Standard Method of Moments .................................................................................................... 3
1.4. The Quadrature Method of Moments ................................................................................................ 4
2. Population Balance Model Theory .......................................................................................................... 5
2.1.The Particle State Vector .................................................................................................................... 5
2.2. The Population Balance Equation (PBE) ............................................................................................. 6
2.2.1. Particle Growth and Dissolution ............................................................................................... 6
2.2.2. Particle Birth and Death Due to Breakage and Aggregation ....................................................... 7
2.2.2.1. Breakage ......................................................................................................................... 7
2.2.2.2. Luo and Lehr Breakage Kernels ........................................................................................ 9
2.2.2.3. Ghadiri Breakage Kernels ................................................................................................. 9
2.2.2.4. Laakkonen Breakage Kernels .......................................................................................... 10
2.2.2.5. Parabolic PDF ................................................................................................................ 10
2.2.2.6. Generalized PDF ............................................................................................................ 11
2.2.2.7. Aggregation .................................................................................................................. 14
2.2.2.8. Luo Aggregation Kernel ................................................................................................. 15
2.2.2.9. Free Molecular Aggregation Kernel ................................................................................ 16
2.2.2.10. Turbulent Aggregation Kernel ...................................................................................... 16
2.2.3. Particle Birth by Nucleation .................................................................................................... 18
2.3. Solution Methods ........................................................................................................................... 18
2.3.1. The Discrete Method and the Inhomogeneous Discrete Method ............................................. 18
2.3.1.1. Numerical Method ......................................................................................................... 19
2.3.1.2. Breakage Formulations for the Discrete Method ............................................................. 21
2.3.2.The Standard Method of Moments (SMM) ............................................................................... 22
2.3.2.1. Numerical Method ......................................................................................................... 22
2.3.3.The Quadrature Method of Moments (QMOM) ........................................................................ 24
2.3.3.1. Numerical Method ......................................................................................................... 24
2.3.4.The Direct Quadrature Method of Moments (DQMOM) ............................................................ 25
2.3.4.1. Numerical Method ......................................................................................................... 25
2.4. Reconstructing the Particle Size Distribution from Moments ............................................................ 27
3. Using the ANSYS FLUENT Population Balance Model ........................................................................... 29
3.1. Population Balance Module Installation ........................................................................................... 29
3.2. Loading the Population Balance Module ......................................................................................... 29
3.3. Population Balance Model Setup ..................................................................................................... 30
3.3.1. Enabling the Population Balance Model .................................................................................. 30
3.3.1.1. Generated DQMOM Values ............................................................................................ 37
3.3.2. Defining Population Balance Boundary Conditions ................................................................. 41
3.3.3. Specifying Population Balance Solution Controls .................................................................... 42
3.3.4. Coupling With Fluid Dynamics ................................................................................................ 43
3.3.5. Specifying Interphase Mass Transfer Due to Nucleation and Growth ........................................ 44
4. Postprocessing for the Population Balance Model ............................................................................... 49
4.1. Population Balance Solution Variables ............................................................................................. 49
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