Synthetic PackedBed Generation for CFD Simulations: Blender vs. STARCCM+
Abstract
:1. Introduction
2. Methods
2.1. Packing Generation
2.1.1. Discrete Element Method—Soft Body Approach in STARCCM+
 Density (used for calculation of the equivalent particle mass) (Equation (8))
 Young’s modulus $E$ (Equation (6))
 Poisson ratio (calculation of equivalent Young’s modulus) (Equation (6))
 Coefficient of restitution $e$ (Equation (7))
 Static friction factor $\mu $ (Equations (9) and (11))
2.1.2. Blender—Rigid Body Approach in Blender
2.2. CFD
2.2.1. Governing Equations
2.2.2. Meshing and Solving
2.2.3. Local Porosity Determination
2.2.4. Local Velocity Profiles
3. Numerical Setup
4. Results
4.1. Overall Porosity
4.2. Spheres
4.3. Cylinders
4.4. Raschig Rings
4.5. Complex Particles
4.6. Simulation Time
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Latin Letters  
$A$  area  $\left({\mathrm{m}}^{2}\right)$ 
$d$  overlaps  $\left(\mathrm{m}\right)$ 
${d}_{\mathrm{p}}$  particle diameter  $\left(\mathrm{m}\right)$ 
$D$  tube diameter  $\left(\mathrm{m}\right)$ 
$\mathbf{D}$  deformation tensor  $()$ 
${e}_{\mathrm{N}}$  coefficient of restitution  $()$ 
${E}_{\mathrm{eq}}$  equivalent Young’s modulus  $\left(\mathrm{Pa}\right)$ 
$\mathbf{f}$  force (rigid body approach)  $\left(\mathrm{N}\right)$ 
$F$  force (soft body approach)  $\left(\mathrm{N}\right)$ 
${\mathbf{F}}_{\mathrm{b}}$  body force  $\left(\mathrm{N}\right)$ 
${\mathbf{F}}_{\mathrm{c}}$  contact force  $\left(\mathrm{N}\right)$ 
${\mathbf{F}}_{\mathrm{g}}$  gravity force  $\left(\mathrm{N}\right)$ 
${\mathbf{F}}_{\mathrm{s}}$  surface force  $\left(\mathrm{N}\right)$ 
$h$  height  $\left(\mathrm{m}\right)$ 
$I$  moment of inertia  $\left(\mathrm{kg}\cdot {\mathrm{m}}^{2}\right)$ 
$\mathbf{I}$  unit tensor  $()$ 
$K$  spring stiffness  $\left(\mathrm{kg}/{\mathrm{s}}^{2}\right)$ 
$m$  mass  $\left(\mathrm{kg}\right)$ 
${M}_{\mathrm{eq}}$  equivalent particle mass  $\left(\mathrm{kg}\right)$ 
$\mathbf{n}$  unit normal vector  $()$ 
$N$  tubetoparticlediameter ratio  $()$ 
$N$  damping  $\left(\mathrm{kg}/\mathrm{s}\right)$ 
${N}_{\mathrm{N}\mathrm{damp}}$  damping coefficient  $()$ 
$p$  pressure  $\left(\mathrm{Pa}\right)$ 
$R$  radius  $\left(\mathrm{m}\right)$ 
${R}^{2}$  coefficient of determination  $()$ 
$Re$  Reynolds number  $()$ 
${R}_{\mathrm{eq}}$  equivalent radius  $\left(\mathrm{m}\right)$ 
$r$  radius of radial position  $\left(\mathrm{m}\right)$ 
$\mathbf{t}$  unit normal vector  $()$ 
$t$  time  $\left(\mathrm{s}\right)$ 
$T$  stress tensor  $\left(\mathrm{Pa}\right)$ 
$v$  velocity  $\left(\mathrm{m}/\mathrm{s}\right)$ 
$\mathbf{v}$  velocity  $\left(\mathrm{m}/\mathrm{s}\right)$ 
$V$  volume  $\left({\mathrm{m}}^{3}\right)$ 
Greek Letter  
$\beta $  sliding speed  $\left(\mathrm{m}/\mathrm{s}\right)$ 
${\delta}_{\mathrm{BL}}$  Boundary layer thickness  $\left(\mathrm{m}\right)$ 
${\mathsf{\delta}}_{\mathrm{max}}$  maximum overlap  $\left(\mathrm{m}\right)$ 
$\epsilon $  porosity  $()$ 
$\eta $  dynamic viscosity  $\left(\mathrm{Pa}\cdot \mathrm{s}\right)$ 
$\mathsf{\mu}$  static friction coefficient  $()$ 
$\rho $  density  $\left(\mathrm{kg}/{\mathrm{m}}^{3}\right)$ 
$\mathsf{\tau}$  net moment  $\left(\mathrm{N}\cdot \mathrm{m}/\mathrm{rad}\right)$ 
$\omega $  angular velocity  $\left(\mathrm{rad}/\mathrm{s}\right)$ 
Subscripts  
$0$  inlet  
$\mathrm{Blender}$  data obtained by the use of Blender  
$\mathrm{B}\mathrm{Pellet}$  Blender object based pellet interaction  
$\mathrm{B}\mathrm{Container}$  Blender object based container interaction  
$\mathrm{Container}\mathrm{Pellet}$  Phase based containerpellet interaction  
$\mathrm{Cylinder}$  part: Cylinder  
$\mathrm{Cylinder}\text{}\mathrm{Plane}$  part: Cylinder Plane  
$\mathrm{DEM}$  Data obtained by the use of DEM  
$\mathrm{free}$  amount of free space or volume  
$\mathrm{Giese}$  experimental data taken from Giese et al. (1998)  
$\mathrm{Pellet}\mathrm{Pellet}$  phase based pellet interaction  
$\mathrm{n}$  normal direction  
$\mathrm{t}$  tangential direction  
$\mathrm{total}$  amount of total space or volume  
$\mathrm{p}$  particle  
$\mathrm{o}$  additional tangential direction  
$\mathrm{specific}$  specific radial velocity  
Abbreviations  
3D  3dimensional  
DEM  Discrete Element Method  
CAD  Computer Aided Design  
CFD  Computational Fluid Dynamics  
CT  Computer Tomography  
MRI  Magnetic Resonance Imaging  
STL  Standard Triangulation Language 
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CADGeometry  
Composite Particle of 100 Spheres  
Composite Maximum  560 spheres  449 spheres  543 spheres  441 spheres 
Size  Value 

Base Size  ${d}_{\mathrm{p}}$ 
Target Surface Size  $50\%\text{}\mathrm{of}\text{}\mathrm{Base}\text{}\mathrm{Size}$ 
Minimum Surface Size  $4\%\text{}\mathrm{of}\text{}\mathrm{Base}\text{}\mathrm{Size}$ 
Prism Layer Total Thickness  ${\delta}_{\mathrm{BL}}$(26) 
Method  DEM  Rigid Body 

Software 


Solver settings 



 

 
Friction 


Restitution 


Collision margin 


Damping 


Density 


 
Young’s modulus 


PoissonNumber 


Particle shape 


Source  Particle  Dimension  Boundary Conditions 

Giese et al. [30]  Sphere  ${d}_{\mathrm{p}}=8.6\mathrm{mm}$ $D=80\mathrm{mm}$  ${\mu}_{\mathrm{Pellet}\mathrm{Pellet}}={\mu}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.9$ ${e}_{\mathrm{Pellet}\mathrm{Pellet}}={e}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.67$ 
Cylinder  ${d}_{\mathrm{p}}=8\mathrm{mm}$ ${h}_{\mathrm{p}}=8\mathrm{mm}$ $D=80\mathrm{mm}$  
Raschig ring  ${d}_{\mathrm{outer}}=8\mathrm{mm}$ ${d}_{\mathrm{inner}}=6\text{}\mathrm{mm}$ ${h}_{\mathrm{p}}=8\mathrm{mm}$ $D=80\mathrm{mm}$  
Caulkin et al. [15]  Cylinder  ${d}_{\mathrm{p}}=3.42\mathrm{mm}$ ${h}_{\mathrm{p}}=3.46\mathrm{mm}$ $D=44.5\mathrm{mm}$  ${\mu}_{\mathrm{Pellet}\mathrm{Pellet}}={\mu}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.7$ ${e}_{\mathrm{Pellet}\mathrm{Pellet}}={e}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.7$ 
Raschig ring  ${d}_{\mathrm{outer}}=4.6\mathrm{mm}$ ${d}_{\mathrm{inner}}=2.5\text{}\mathrm{mm}$ ${h}_{\mathrm{p}}=5\mathrm{mm}$ ${D}_{\mathrm{top}}=28\mathrm{mm}$ ${D}_{\mathrm{bottom}}=24\mathrm{mm}$  ${\mu}_{\mathrm{Pellet}\mathrm{Pellet}}={\mu}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.9$ ${e}_{\mathrm{Pellet}\mathrm{Pellet}}={e}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.67$  
No reference  Complex Particles  ${d}_{\mathrm{p}}=10\mathrm{mm}$ ${r}_{\mathrm{inv}}=0.568\mathrm{mm}$ ${r}_{\mathrm{env}}=1\mathrm{mm}$ $D=80\mathrm{mm}$  ${\mu}_{\mathrm{Pellet}\mathrm{Pellet}}={\mu}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.7$ ${e}_{\mathrm{Pellet}\mathrm{Pellet}}={e}_{\mathrm{Cylinder}\mathrm{Pellet}}=0.7$ 
Source  Particle  Packing Generation  

Time Step  Solver Iterations  Number of Particles  
Giese et al. [30]  Sphere  $\Delta t=0.001\mathrm{s}$  $2$  $1000$ 
Cylinder  
Raschig Ring  
Caulkin et al. [15]  Cylinder  $\Delta t=0.001\mathrm{s}$  $2$  $1500$ 
Raschig Ring  $310$  
No reference  Complex Particles  $\Delta t=0.001\mathrm{s}$ Blender Mesh: $\Delta t=0.00025\mathrm{s}$  $2$ Blender Mesh: $10$  $1000$ 
Shape  ${\mathit{R}}^{2}$  

Blender  DEM  
Spheres  $0.92$  $0.91$ 
Cylinders  $0.41$  $0.29$ 
Raschig rings  $0.40$  ${0.22}^{*}$, $0.11{}^{+}$ 
Total  $0.87$  $0.79$ 
© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Flaischlen, S.; Wehinger, G.D. Synthetic PackedBed Generation for CFD Simulations: Blender vs. STARCCM+. ChemEngineering 2019, 3, 52. https://doi.org/10.3390/chemengineering3020052
Flaischlen S, Wehinger GD. Synthetic PackedBed Generation for CFD Simulations: Blender vs. STARCCM+. ChemEngineering. 2019; 3(2):52. https://doi.org/10.3390/chemengineering3020052
Chicago/Turabian StyleFlaischlen, Steffen, and Gregor D. Wehinger. 2019. "Synthetic PackedBed Generation for CFD Simulations: Blender vs. STARCCM+" ChemEngineering 3, no. 2: 52. https://doi.org/10.3390/chemengineering3020052