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High order moment conserving method of classes in CFD code

  • Mohamed Ali Jama , Antonio Buffo , Wenli Zhao and Ville Alopaeus EMAIL logo
Published/Copyright: December 10, 2024
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Chemical Product and Process Modeling
From the journal Chemical Product and Process Modeling Volume 20 Issue 2

Abstract

Dispersed multiphase flows are widely present in the majority of chemical process industry equipment. For the purpose of design, optimization, and scale up of these industrial systems, robust, accurate and fast simulation methods are needed, especially when coupling computational fluid dynamics (CFD) with population balance models (PBM). In this work, the high-order moment conserving method of classes (HMMC) is implemented and tested within the commercial CFD software of ANSYS Fluent with two simple well-defined test cases and a realistic 3D simulation of rotating disc (RDC) extractor. Firstly, a zero-dimensional PBM with well-mixed assumption and no convection was solved for a single computational cell in Fluent to verify the implementation in comparison with a simple reactor model in MATLAB. Secondly, the convection was considered by solving a one-dimensional PBM for three computational cells side by side in Fluent and compared with an equivalent three staged reactor model in MATLAB. Eventually, realistic 3D RDC simulations were conducted to fully couple the HMMC and CFD in Fluent. The implementation of HMMC was compared to predictions with other state-of-the-art PBM solution methods, e.g., the quadrature method of moments (QMOM) and the fixed pivot technique (FPT) in Fluent and MATLAB platforms. The implementation of the HMMC in Fluent platform was straightforward with no additional challenges. The verification shows that the HMMC approach is robust and efficient for polydispersed multiphase CFD simulations.

Keywords: computational fluid dynamics; multiphase flow; method of classes; dispersed phase systems; liquid–liquid extraction; population balance model
Corresponding author: Ville Alopaeus, School of Chemical Engineering, Department of Chemical and Metallurgical Engineering, P.O. Box 16100, FI-00076 Aalto, Finland, E-mail:

Funding source: Academy of Finland.

Award Identifier / Grant number: Unassigned

  1. Research ethics: Ethical approval for this study was granted by Aalto University Research Ethics Committee, and all procedures were conducted in accordance with the ethical standards outlined in their guidelines.

  2. Informed consent: Informed consent was obtained from all individuals in this study.

  3. Author contributions: Mohamed Ali Jama implemented the models, carried out the validation, analyzed the results and wrote the paper. Zhao Wenli, Buffo Antonio and Alopaeus Ville assisted in developing the model and writing the paper.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: Authors state no conflict of interest.

  6. Research funding: The authors would like to acknowledge the financial support from the Academy of Finland.

  7. Data availability: The datasets are available from the corresponding author on reasonable request.

List of symbols

C 1–4

adjustable parameters for closure models [−]

d

droplet diameter, [m]

D col

column diameter, [m]

D R

stirrer diameter, [m]

D S

baffle inner diameter, [m]

f

volume fraction of particles belonging each size categories [−]

F

agglomeration rate, [m3 s−1]

g

breakage rate, [s−1]

H

compartment height, [m]

H C

compartment height, [m]

k

turbulent kinetic energy, [m2 s−2]

L

droplet diameter, [m]

m k

k-th moments, [m k−3]

n

number density function [#m−4]

N

agitation speed [RPM]

Q

gas flow rate, [m3 s−1]

t

time, [s]

U

time averaged velocity, [m s−1]

v, V

volume, [m3]

Y

droplet number density, [#m−4]

Greek letters

α

volume fraction, [s]

β

daughter particle size distribution: probability that a particle of size Li is born when Lj breaks, [m−1]

λ

internal coordinate (particle size), [m]

ξ

growth distribution: a table that determines the distribution to category of size

L i

due to growth of particle of size L j , [–]

χ

coalescence product distribution table, [–]

ρ

density, [kg m−3]

σ

surface tension, [N m−1]

ψ

distribution of primary nucleates, [–]

ϕ

volume fraction, [–]

ε

energy dissipation rate, [W kg−1]

μ

viscosity, [kg m−1 s−1]

λ

droplet diameter, [m]

η

dynamic viscosity, [kg m s−1]

Subscripts

M

mixture phase

d or 2

discrete phase

C or 1

continuous phase

Abbreviations

CFD

computational fluid dynamics

HMMC

high order moment conserving method classes

FPT

fixed pivot technique

QMOM

quadrature method of moments

CM

classes method (discrete model)

PBM

population balance model

UDF

user-defined functions

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Received: 2024-02-09
Accepted: 2024-10-23
Published Online: 2024-12-10

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/cppm-2024-0009
Keywords for this article
computational fluid dynamics; multiphase flow; method of classes; dispersed phase systems; liquid–liquid extraction; population balance model

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. CPPM special issue in honor of Professor Eugeny Kenig
  4. Review
  5. Capture and catalytic conversion of CO2 from marine and offshore applications – A review
  6. Research Articles
  7. Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure
  8. Application of CFD simulation to predict the fluid dynamics of tube columns with stacked packings for gas-liquid systems
  9. High order moment conserving method of classes in CFD code
  10. A framework for validating efficiency models of thermal separation columns with tray internals
  11. A systematic selection and decision matrix for energy-efficient intensified distillation technologies
  12. Capillary flow in corners slowed down by gravity and evaporation
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