Population Balance Model (PBM) for Nucleation, ANSYS Fluent CFD Simulation Training


The present problem simulates the production process of Calcium-Oxalate based on the Population Balance Model (PBM) using ANSYS Fluent software.

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Project Description (PBM)

The present problem simulates the production process of Calcium-Oxalate based on the Population Balance Model (PBM) using ANSYS Fluent software. In this project, first, the calcium-oxalate production process is modeled, and then the PBM is analyzed using the production, growth, and displacement of production particles. The mechanism of the studied system is such that the flow of water carrying calcium and oxalate enters a chamber through two pipes; From one tube, only a mixture of water with calcium is injected, and from the other tube, only a stream of water is injected with oxalate. The two inlet streams are then mixed, and a chemical reaction occurs in which the combination of calcium and oxalate results in the production of calcium-oxalate. To define this simulation process in software, Multiphase and Species Transport models must be used.

Also, PBM, chemical reaction, and mass transfer should be activated. First, the Eulerian multiphase model defines a two-phase flow; The primary phase is a mixture of water, calcium, and oxalate. The secondary phase is calcium-oxalate resulting from a chemical reaction. A chemical reaction within a multiphase flow is then defined. Calcium and oxalate react with each other from the initial phase as a reactant and lead to the production of calcium-oxalate as a product. The rate of this reaction is defined based on Arrhenius, and the activation energy of the reaction is equal to 1e + 8 j.kg-1.mol-1. In addition to defining the chemical reaction, the process of mass transfer between materials must also be defined.

Project Description

Therefore, three stages of mass transfer are defined so that in these three stages of mass transfer, three substances, including water, calcium, and oxalate, can be converted to calcium-oxalate. Also, to define a mixture of water, calcium, and oxalate as the initial phase, the species transport model must be defined. After defining the process of conversion of primary phase materials to secondary phase and the occurrence of chemical reaction, it is possible to study the behavioral pattern of particles produced of the secondary phase. To study the behavior of produced particles, the population balance model (PBM) can be used to predict the density or population of particles in specific sizes.

When several particles are formed in an environment, various stages occur, including forming the initial particle nucleation, the growth of formed particles, the aggregation of several small particles together, and the breakage of a large particle into smaller particles. There are different models for defining the PBM in the software, which in this simulation, the discrete method is used. Using this method, several bins must be defined for different particle sizes to estimate the particle population or density in each size. It should be noted that the recognition of the number of categories and the definition range for categories is based on inductive reasoning and with several steps of simulation solution in the form of trial and error.

Project Description

In this simulation, 48 bins are used; So that the smallest size with a diameter of 5e-7 m is defined and the largest possible size for each particle up to a diameter of about 2.9345e-5 m. Also, in this simulation, it is assumed that aggregation and breakage do not occur, and only nucleation and growth processes occur. A UDF function is used to define the nucleation rate and growth rate.

Geometry & Mesh

We model the present model n three dimensions using Design Modeler software. The study model consists of a small rectangular cubic chamber to which two elbow tubes are connected. The chamber has a length, width, and thickness of 12 mm, 6 mm, and 2 mm, and the two inlet pipes have a circular cross-section with a diameter of 1.5 mm.

We carry out the model’s meshing using ANSYS Meshing software. The mesh type is unstructured. The element number is 112077. The following figures show the geometry and mesh.


PBM CFD Simulation

The following table represents a summary of the defining steps of the problem and its solution:

Viscous Laminar
Multiphase Model Eulerian
formulation implicit
number of eulerian phases 2 (primary phase & calcium oxalat)
Species Model Species Transport
Energy On
Boundary conditions
Inlet-Calcium Mass Flow Inlet
mass flow rate – praimary phase 1.663e-8 kg.s-1
temperature – praimary phase 300 K
calcium mass fraction – praimary phase 5e-5
oxalat mass fraction – praimary phase 0
mass flow rate – calcium-oxalat 0 kg.s-1
temperature – calcium-oxalat 300 K
Inlet-Oxalat Mass Flow Inlet
mass flow rate – praimary phase 1.663e-8 kg.s-1
Temperature – praimary phase 300 K
calcium mass fraction – praimary phase 0
oxalat mass fraction – praimary phase 5e-4
mass flow rate – calcium-oxalat 0 kg.s-1
temperature – calcium-oxalat 300 K
Outlet Pressure Outlet
gauge pressure 0 pascal
Walls Wall
wall motion stationary wall
heat flux 0 W.m-2
Pressure-Velocity Coupling Coupled
Pressure second order
momentum first order upwind
volume fraction first order upwind
energy first order upwind
primary-phase calcium first order upwind
primary-phase oxalat first order upwind
calcium-oxalat bin first order upwind
Initialization methods Standard
gauge pressure 0 Pascal
primary-phase velocity (x,y,z) 0 m.s-1
primary-phase calcium 0
primary-phase oxalat 0
primary-phase temperature 300 K
calcium-oxalat velocity (x,y,z) 0 m.s-1
calcium-oxalat volume fraction 0
calcium-oxalat temperature 300 K
calcium-oxalat bins fraction (0 to 47) 0


At the end of the solution process, we review the results. The results are presented as follows:

First, a two-dimensional contour is obtained related to the volume fraction of the primary phase (including water, calcium and oxalate) and the secondary phase (calcium-oxalate). These contours show that calcium-oxalate is formed by a chemical reaction and mass transfer from the primary to the secondary phase. The formation of the desired material occurs in the initial area of the chamber, which is the junction of two inlet pipes.


Then the table related to the sizes of each definition category (bin) is presented. There are 48 categories for particle size classification, starting at a minimum of 5e-7m at bin-47 and continuing to a maximum at bin-0. In addition, we represent the bar graph of number density in terms of the bin number. Number density represents the ratio of the number of particles per unit volume; That is, how many particles with the desired volume (according to the size of each bin) are within the desired area.



Finally, we obtain two-dimensional contours of the volume fraction of calcium-oxalate produced in different bins. The results show that from about bin-30 onwards, the amount of material produced becomes significant. This means that the volume of particles produced in the categories between bin-0 to bin-30 is imperceptible. Therefore, we can conclude that the produced particles are formed and grow in the range of smaller volumetric sizes (between bin-47 to bin-30) and are not noticeable in larger volumetric sizes.

You can obtain Geometry & Mesh file, and a comprehensive Training Movie which presents how to solve the problem and extract all desired results.


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