VMFL034

VMFL034
Particle Aggregation inside a Turbulent Stirred Tank

Overview

Reference	B. Wan, T.A. Ring, K. Dhanasekharan, J. Sanyal, "Comparison of Analytical Solutions for CMSMPR Crystallizer with QMOM Population Balance Modeling in Ansys Fluent". China Particuology, Vol. 3, pp. 213-218, 2005
Solver	Ansys Fluent
Physics/Models	Multi-phase, Population balance model, turbulent flow
Input File	`agglomeration.cas`
Project Files	Link to Project Files Download Page

Test Case

A 2-D approximation of a stirred tank is simulated in order to verify the population balance model that operates in conjunction with its multiphase calculations to predict the particle size distribution within the flow field. The flow rate at the inlet is equal to that at the outlet, allowing the mean residence time to be calculated from the inlet flow rate (velocity x inlet area) and the "volume" (box area x unit depth) of the box. To simulate the agitation in the tank the top and bottom walls are assumed to move in the direction of the outlet. The flow is turbulent, steady, and incompressible. Multi-phase, with QMOM population balance model is used for particle aggregation. The standard k-ε model is used for turbulence. Moments are solved on a frozen flow field.

Figure 91: Flow Domain

Material Properties	Geometry	Boundary Conditions
Density: 998.2 kg/m³ Viscosity: 0.00103 kg/m-s	Square box side = 0.1 m Inlet/Outlet openings = 0.02 m	Top wall velocity: 101 m/s Bottom wall velocity: 100 m/s Inlet velocity = 0.005 m/s Outlet gauge pressure = 0 Pa

Material Properties

Geometry

Boundary Conditions

Density: 998.2 kg/m³

Viscosity: 0.00103 kg/m-s

Square box side = 0.1 m

Inlet/Outlet openings = 0.02 m

Top wall velocity: 101 m/s

Bottom wall velocity: 100 m/s

Inlet velocity = 0.005 m/s

Outlet gauge pressure = 0 Pa

Analysis Assumptions and Modeling Notes

The results of the Ansys Fluent simulation are compared to steady a state analytical solution for the population balance in a stirred tank where aggregation takes place.

To optimize the calculations, the operations shown in the journal file below were performed. These steps must be followed to replicate the test case results.

rc VMFL034_aggregation.cas
solve set equations mixture flow yes ke yes mp no
solve set equations phase-2 moment-0 no moment-1 no moment-2 no moment-3 no moment-4 no moment-5 no
solve initialize initialize-flow
solve iterate 700
solve set equations mixture flow no ke no mp no
solve set equations phase-2 moment-0 yes moment-1 yes moment-2 yes moment-3 yes moment-4 yes moment-5 yes
solve patch phase-2 fluid () mp 1e-06
solve set under-relaxation phase-2 moment-0 0.9 moment-1 0.9 moment-2 0.9 moment-3 0.9 moment-4 0.9 moment-5 0.9
solve iterate 200
solve set under-relaxation phase-2 moment-0 1.0 moment-1 1.0 moment-2 1.0 moment-3 1.0 moment-4 1.0 moment-5 1.0
solve iterate 2000
report population-balance moments outlet () () 6 no

Results Comparison

In this table, moment of PBE for Ansys Fluent turbulent simulations is compared with analytical solution for aggregation alone at the outlet of the tank.

Table 27: Comparison of Moment of PBE

Moment	Target	Ansys Fluent	Ratio
m₀	0.132	0.132	1.000
m₁	0.225	0.226	1.004
m₂	0.547	0.548	1.002
m₃	1.910	1.910	1.000
m₄	9.073	9.133	1.007
m₅	53.797	53.816	1.000