CFD Simulations of Radiative Heat Transport in Open-Cell Foam Catalytic Reactors
Abstract
:1. Introduction
2. Results and Discussion
2.1. Model Verification
2.2. Quantification of Heat Flows and Temperature Distributions
2.2.1. Influence of the Wall Temperature and Solid Thermal Conductivity
2.2.2. Influence of the Superficial Velocity
2.2.3. Comparison with a Homogeneous Model
2.2.4. Influence of the Surface Emissivity
3. Materials and Methods
3.1. General Model and Meshing
3.2. Governing Equations and Thermal Radiation Modeling
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A. Geometrical Foam Properties
Parameter | Symbol | Value |
---|---|---|
pore count | 10 ppi | |
open porosity | ε0 | 0.77 |
specific surface area | SV | 521.3 m−1 |
cell diameter | dc | 5.76 ± 1.9 mm |
window diameter | dw | 3.3 ± 0.9 mm |
strut diameter | ds | 1.5 ± 0.5 mm |
Appendix B. Geometry for Verification
Appendix C. Analysis of P1 and fvDOM Radiation Models for Suitability in Open-Cell Foams
List of Symbols
Latin | |
cp | Isobaric heat capacity, J Kg−1 K−1 |
dc | Cell diameter, m |
ds | Strut diameter, m |
dw | Window diameter, m |
Erel | Relative error of heat flow, - |
I | Intensity, W m−2 sr−1 |
L | Cube dimensions, m |
Q | Heat flow, W |
QSF | Heat flow solid to fluid, W |
QSW | Heat flow solid to wall, W |
h | Specific enthalpy, J |
p | Pressure, Pa |
r | Position vector, - |
s | Direction vector, - |
S | Total heat source intensity, W |
Sv | Specific surface area, m−1 |
T | Temperature, K |
Tw | Wall temperature, K |
Tmax | Maximum temperature, K |
Tmean | Mean temperature, K |
U | Velocity, m s−1 |
v | Superficial velocity, m s−1 |
Greek | |
α | Degree of absorption, - |
γ | Degree of reflection, - |
τ | Degree of transmission, - |
Ω | Solid angle, sr |
κ | Absorption coefficient, m−1 |
σs | Scattering coefficient, m−1 |
ε0 | Open porosity, - |
ε | Surface emissivity, - |
μ | Dynamic viscosity, Pa s |
λ | Thermal conductivity, W m−1 K−1 |
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Property | Assumption | |
---|---|---|
Fluid dynamic viscosity | µ | Sutherland equation |
Fluid heat capacity | cp,f | Janaf model (OpenFOAM); |
polynomial (STAR-CCM+) | ||
Fluid thermal conductivity | λf | Eucken approximation (OpenFOAM); |
polynomial (STAR-CCM+) | ||
Fluid density | δf | ideal gas law |
Superficial velocity | v | const. (0.1–0.5 m s−1) |
Pore Reynolds number | const. (1–20) | |
Fluid absorption coefficient | κ | const. (10−9) |
Solid heat capacity | cp,s | const. (1000 J kg−1 K−1) |
Solid thermal conductivity | λs | const. (1–200 W m−1 K−1 [46]) |
Solid density | δs | const. (3950 kg m−3) |
Solid heat source | S | const. (total: 50 W; |
specific: 1.9 × 107 W m−3) | ||
Solid surface emissivity | ε | const. (0.1–1) |
Wall surface emissivity | εw | const. (0.65) |
Gravitational acceleration | - | neglected |
Radiation | - | fvDOM model (OpenFOAM); |
DOM model (STAR-CCM+) | ||
Turbulence | - | neglected |
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Sinn, C.; Kranz, F.; Wentrup, J.; Thöming, J.; Wehinger, G.D.; Pesch, G.R. CFD Simulations of Radiative Heat Transport in Open-Cell Foam Catalytic Reactors. Catalysts 2020, 10, 716. https://doi.org/10.3390/catal10060716
Sinn C, Kranz F, Wentrup J, Thöming J, Wehinger GD, Pesch GR. CFD Simulations of Radiative Heat Transport in Open-Cell Foam Catalytic Reactors. Catalysts. 2020; 10(6):716. https://doi.org/10.3390/catal10060716
Chicago/Turabian StyleSinn, Christoph, Felix Kranz, Jonas Wentrup, Jorg Thöming, Gregor D. Wehinger, and Georg R. Pesch. 2020. "CFD Simulations of Radiative Heat Transport in Open-Cell Foam Catalytic Reactors" Catalysts 10, no. 6: 716. https://doi.org/10.3390/catal10060716