Effects of Mesh Generation on Modelling Aluminium Anode Baking Furnaces
Abstract
:1. Introduction
2. Related Works
3. Model Description
Standard κ–ε Turbulence Model
- ρ is the density of the fluid (SI units: kg/m3).
- μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/(m·s)).
- ν is the kinematic viscosity of the fluid (m2/s).
- ε is a small number added to avoid the division by zero.
- σk and σε are the turbulent Prandtl numbers for κ and ε.
- and the factor in front of the pressure term in the RANS equations are dropped. Then, if the true mean pressure field is sought, one has to take this into consideration.
- The default values of the model constants, have been determined from experiments with air and water for fundamental turbulent shear flows, including homogeneous shear flows and decaying isotropic grid turbulence. They have been found to work fairly well for a wide range of wall-bounded and free shear flows.
- Although the default values of the model constants are the standard ones, and the most widely accepted, one can change them (if needed).
4. Model Configurations
4.1. Geometry and Mesh
4.2. Simulations
4.3. Numerical Implementation
4.3.1. Finite Element Method in CFD
- It is a very general method,
- There is more facility to increment the element order,
- Physical fields may be reproduced more accurately,
- Physics and mathematics often require different type of functions for a phenomenon. Different phenomena can be represented at the same time with FEM,
- To reach more accuracy, increase order of polynomials and refine the mesh.
4.3.2. Theoretical Definition of FEM
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Test Using a Fourth Mesh
Appendix B. Wall Resolution from Different Isotropic Diffusion δ Parameters
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Authors | Year | Objectives | Combustion Model | Detailed Kinetics | Radiation Model |
---|---|---|---|---|---|
Ping. et al. | 2002 | Influence of the baffles on the flowing field | Non-reactive flow | Not included | Not included |
Severo et al. | 2005 | Developing a 3D CFD model for flue-wall design modification | EDM | Not included | P1 |
Ordronneau et al. | 2006 | Application of CFD simulation for crossover design off-gas cleaning system optimisation training purposes | Not specified | Not specified | Not specified |
Gregoire et al. | 2011 | Comparison of two modelling approaches to predict variability | Hot air jet approximation | Not specified | DO method |
Kocaefe et al. | 2013 | Different modelling approaches on anode baking furnace | Not mentioned | Not included | Not specified |
Baiteche et al. | 2015 | Effects of flue-wall deformation and employing different radiation models | Empirical kinetic expression | Not included | - P1 - Monte Carlo method |
Ghaui et al. | 2016 | Implementation of baffleless flue-wall technology | Not mentioned | Not included | Not specified |
Zaidani et al. | 2017 | Effects of flue-wall deformation | Non-reactive flow | Not included | Not specified |
Chaodong et al. | 2018 | Optimisation and development of the furnace structures, process parameters and firing control system | Not specified | Not specified | Not specified |
Nakate et al. | 2018 | Develop a mathematical 2D model to reduce NOx emissions considering turbulent flow, combustion model and radiation | EDM | - κ–ε - Spalart Allmaras | - P1 - DO |
Talice | 2018 | Develop a 2D model to analyse flow behaviour | Not used | Spalart Allmaras | Not used |
Nakate et al. | 2019 | Develop a 3D model to analyse flow behaviour | Not used | κ–ε | Not used |
Talice | 2019 | Develop a 3D model to analyse flow behaviour | Not used | κ–ε | Not used |
Nakate et al. | 2021 | Establish an analysis in 3D flow with a high rate of fuel injection | Energy equation | - Standard κ–ε - Realizable κ–ε | Not used |
Parameter | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 | Model 8 | Model 9 |
Fluid properties | |||||||||
Density (k/m3) | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 | 1.2 |
Dynamic viscosity (Pa·s) | 8.9 × 10−4 | 1.8 × 10−5 | 8.9 × 10−4 | 1.8 × 10−5 | 1.8 × 10−5 | 1.8 × 10−5 | 1.8 × 10−5 | 1.8 × 10−5 | 1.8 × 10−5 |
Initial values for Newton’s iteration | |||||||||
Ux (m/s) | 70 | 0 | 70 | 0 | 0 | 0 | 0 | 0 | 0 |
Uy (m/s) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Uz (m/s) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Pressure (Pa) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Boundary conditions | |||||||||
Wall | No slip | ||||||||
Inlet | Fully developed flow | ||||||||
Outlet | Pressure | ||||||||
Geometry and mesh | |||||||||
Geometry | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 |
Mesh | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 3 | 2 |
Mesh generator tool | cfM | cfM | cfM | cfM | cfM | cfM | COMS | COMS | cfM |
Artificial diffusion scheme | |||||||||
δ(u,p) | Off | Off | Off | Off | Off | 0.005 | 0.25 | Off | Off |
δ(κ,ε) | Off | Off | Off | Off | Off | Off | 0.25 | Off | Off |
Results used as initial value for the Newton Raphson method | |||||||||
Initial value | 0 | 0 | 0 | 0 | 0 | δ(u,p) = 0.01 | 0 | Model 7 | Model 8 |
Mesh | Mesh 1 | Mesh 2 | Mesh 3 |
---|---|---|---|
Generator | cfMesh | cfMesh | COMSOL |
Symmetry | No | Yes | Yes |
Length x-axis (m) | 5.5 | 5.5 | 5.5 |
Length y-axis (m) | 5.0 | 5.0 | 5.0 |
Length z-axis (m) | 0.54 | 0.27 | 0.27 |
Location of fuel inlet pipes (z-axis) (m) | 0.27 | 0.27 | 0.27 |
Cell shape | Cartesian | Cartesian | Tetrahedral |
Mesh | Number of Cells | Minimum Skewness | Average Skewness |
---|---|---|---|
Mesh 1 | 2,424,973 | 0.00 | 0.79 |
Mesh 2 | 545,694 | 0.23 | 0.86 |
Mesh 3 | 4,924,080 | 0.08 | 0.66 |
Model | Model 1 | Model 2 | Model 3 | Model 4 | Model 5 | Model 6 | Model 7 | Model 8 | Model 9 |
---|---|---|---|---|---|---|---|---|---|
Lowest error reached (u,p) | 10−3 | 10−3 | 10−3 | 10−2 | 10−1 | 10−3 | 10−3 | 10−3 | 10−2 |
Lowest error reached (κ,ε) | 10−3 | 10−3 | 10−3 | 10−2 | 10−3 | 10−3 | 10−3 | 10−3 | 10−2 |
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Libreros, J.; Trujillo, M. Effects of Mesh Generation on Modelling Aluminium Anode Baking Furnaces. Fluids 2021, 6, 140. https://doi.org/10.3390/fluids6040140
Libreros J, Trujillo M. Effects of Mesh Generation on Modelling Aluminium Anode Baking Furnaces. Fluids. 2021; 6(4):140. https://doi.org/10.3390/fluids6040140
Chicago/Turabian StyleLibreros, Jose, and Maria Trujillo. 2021. "Effects of Mesh Generation on Modelling Aluminium Anode Baking Furnaces" Fluids 6, no. 4: 140. https://doi.org/10.3390/fluids6040140