Abstract
The influence of thermal diffusion on the kinetics of decarburization of Fe-Cr-C droplets with CO2-Ar gas mixtures was investigated. With incorporation of the effect of thermal diffusion, a new correlation has been proposed to express the decarburization kinetics of levitated droplets for flows in the range of Reynolds number between 2 and 100. A thermal diffusion factor of 0.228 was evaluated for CO2-Ar gas mixtures at 1873 K (1600 °C).
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Abbreviations
- A :
-
Area of droplet surface (cm2)
- Ar:
-
Archimedes number \( \left({ = \frac{{{\text{Gr}}^{\prime}}}{{{\text{Re}}^{2} }}} \right) \)
- C :
-
Total molar concentration in gas phase (mol cm−3)
- C p :
-
Heat capacity of gas (J g−1 K−1)
- D AB :
-
Mutual diffusion coefficient in gas phase (cm2 s−1)
- D T :
-
Thermal diffusion coefficient (cm2 s−1)
- d p :
-
Diameter of the droplet (cm)
- Gr′:
-
Mean Grashof number \( \left( { = {\text{Gr}}_{\text{m}} + {\text{Gr}}_{\text{H}} \left( {{\text{Sc}}/{ \Pr }} \right)^{0.5} } \right) \)
- Grm :
-
Grashof number for mass transfer \( \left( { = \frac{{\rho_{\text{g}} gd_{\text{p}}^{3} \left( {C_{i} - C_{\text{b}} } \right)}}{{\mu_{\text{g}}^{2} }}} \right) \)
- GrH :
-
Grashof number for heat transfer \( \left( { = \frac{{gd_{\text{p}}^{3} \left( {T_{i} - T_{\text{b}} } \right)}}{{T_{\text{f}} \mu_{\text{g}}^{2} }}} \right) \)
- h :
-
Heat transfer coefficient (J cm−1 s−1 K−1)
- J i :
-
Flux of diffusion species i (m cm−2 s−1)
- k :
-
Thermal conductivity of gas (J cm−1 s−1 K−1)
- k T :
-
Thermal diffusion ratio
- m :
-
Coefficient in Eq. [11]
- n :
-
Coefficient in Eq. [11]
- \( {\text{Nu}} \) :
-
Nusselt number \( \left( { = \frac{{d_{\text{p}} h}}{k}} \right) \)
- P :
-
Total pressure (atm)
- Pr:
-
Prandtl number \( \left( { = \frac{{\mu_{\text{g}} C_{\text{p}} }}{k}} \right) \)
- R :
-
Gas constant (cm3 atm mol−1 K−1)
- r:
-
Radial distance from the droplet surface (cm)
- Re:
-
Reynolds number \( \left( { = \frac{{d_{\text{p}} v\rho_{\text{g}} }}{{\mu_{\text{g}} }}} \right) \)
- Sc:
-
Schmidt number \( \left( { = \frac{{\mu_{\text{g}} }}{{\rho_{\text{g}} D_{\text{AB}} }}} \right) \)
- Sh:
-
Sherwood number \( \left( { = \frac{{d_{\text{p}} k_{\text{g}} }}{{D_{\text{AB}} }}} \right) \)
- t :
-
Time (s)
- T E :
-
Effective temperature of gases (K) \( \left( { = 0.83\frac{{T_{i} + T_{\text{b}} }}{2}} \right) \)
- T f :
-
Film temperature of gases (K) \( \left( { = \frac{{T_{i} + T_{\text{b}} }}{2}} \right) \)
- T b :
-
Bulk gas temperature (K)
- T i :
-
Gas–metal interface temperature (K)
- v :
-
Relative velocity between gas and droplet (cm s−1)
- W :
-
Mass of the droplet (g)
- \( X_{{{\text{CO}}_{2} }}^{\text{b}} \) :
-
Mole fraction of CO2 in the bulk gas
- \( X_{{{\text{CO}}_{2} }}^{i} \) :
-
Mole fraction of CO2 on the gas–metal interface
- x i :
-
Mole fraction of component i
- α :
-
Binary thermal diffusion factor
- α i :
-
Thermal diffusion factor of component i
- β :
-
Coefficient in Eq. [11]
- σ SB :
-
Stefan–Boltzmann constant \( ( = 5.67037 \times 10^{ - 12} \,{\text{J}}\,{\text{cm}}^{ - 2} \,{\text{s}}^{ - 1} \,{\text{K}}^{ - 4} ) \)
- ɛ :
-
Emissivity of metal
- μ g :
-
Gas viscosity (g cm−1 s−1)
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Appreciation is expressed to the Natural Sciences and Engineering Research Council of Canada for provision of funding in support of this project.
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Manuscript submitted July 24, 2014.
Appendix
Appendix
Assuming an ideal gas phase, the density is calculated from the relationship:
Data for viscosity, inter-diffusivity, heat capacity, and thermal conductivity are available from AspenONE Engineering Suite – Heat Exchanger Design.
CO2 mol fraction | ρ g, Density at T f | μ g, Viscosity at T f | C p, Heat capacity at T f | k, Thermal conductivity of gas at T f |
|---|---|---|---|---|
T f = 1079 K (806 °C); D AB = 1.520 cm2 s−1 | ||||
2 | 4.52 × 10−4 | 5.58 × 10−4 | 0.532 | 4.60 × 10−4 |
6 | 4.54 × 10−4 | 5.61 × 10−4 | 0.560 | 4.64 × 10−4 |
10 | 4.56 × 10−4 | 5.52 × 10−4 | 0.600 | 4.61 × 10−4 |
15 | 4.58 × 10−4 | 5.60 × 10−4 | 0.636 | 4.62 × 10−4 |
20 | 4.60 × 10−4 | 5.37 × 10−4 | 0.679 | 4.64 × 10−4 |
25 | 4.63 × 10−4 | 5.29 × 10−4 | 0.717 | 4.70 × 10−4 |
30 | 4.65 × 10−4 | 5.22 × 10−4 | 0.755 | 4.82 × 10−4 |
CO2 mol fraction | ρ g, Density at T E | μ g, Viscosity at T E | C p, Heat capacity at T E | k, Thermal conductivity of gas at T E |
|---|---|---|---|---|
T E = 896 K (623 °C); D AB = 1.247 cm2 s−1 | ||||
10 | 5.47 × 10−4 | 4.90 × 10−4 | 0.594 | 3.93 × 10−4 |
30 | 5.58 × 10−4 | 4.62 × 10−4 | 0.738 | 4.11 × 10−4 |
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Wu, P., Yang, Y., Barati, M. et al. The Effect of Thermal Diffusion on Decarburization Kinetics. Metall Mater Trans B 45, 1974–1978 (2014). https://doi.org/10.1007/s11663-014-0211-z
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DOI: https://doi.org/10.1007/s11663-014-0211-z