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Decarburization of Levitated Fe-Cr-C Droplets by Carbon Dioxide

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Abstract

Experiments have been conducted at 1873 K (1600 °C) to study the kinetics of decarburization of Fe-Cr-C levitated droplets containing 10, 17, and 20 wt pct Cr using argon–carbon dioxide gas mixtures containing up to 30 pct CO2, at flow rates of 100, 1000, 3000 and 12200 mL min−1. It was found that chromium did not have a strong influence on the kinetics of decarburization while showing only minor effects on the extent of carbon removal. The results indicate that, for high carbon concentrations in the melt, the decarburization rates were controlled by mass transfer in the gas phase. Conventional formulation of governing mass transport numbers did not adequately describe the experimental observations made in this work. The observed rates are consistently higher than the values predicted using either the Ranz–Marshall correlation or the Steinberger–Treybal equation. A new correlation has been proposed to express the decarburization kinetics of levitated droplets for gas-flows in the range of Reynolds numbers between 2 and 100. The experimentally-derived model was found to be in excellent agreement with rate data derived from studies conducted by other researchers using levitated droplets.

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Abbreviations

A :

Area of droplet surface (cm2)

Ar :

Archimedes number \( \left( { = \frac{Gr'}{{Re^{2} }}} \right) \)

C bulk :

Carbon concentration in bulk metal (wt pct)

C surface :

Carbon concentration at the gas–metal interface (wt pct)

C t :

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 p :

Diameter of the droplet (cm)

f :

Coefficient in Eq. [9]

Gr′:

Mean Grashof number (=Gr m + Gr H(Sc/Pr)0.5)

Gr m :

Grashof number for mass transfer \( \left( { = \frac{{\rho_{\text{g}} gd_{\text{p}}^{3} \left( {C_{\text{i}} - C_{\text{b}} } \right)}}{{\mu_{\text{g}}^{2} }}} \right) \)

Gr H :

Grashof number for heat transfer \( \left( { = \frac{{gd_{\text{p}}^{3} \left( {T_{\text{i}} - T_{\text{b}} } \right)}}{{T_{\text{f}} \mu_{\text{g}}^{2} }}} \right) \)

J i :

Flux of diffusion species i (mol cm−2 s−1)

k :

Thermal conductivity of gas (J cm−1 s−1 K−1)

k g :

Gas transfer coefficient (cm s−1)

k l :

Liquid transfer coefficient (cm s−1)

k x :

Mass transfer coefficient \( ({\text{mol}}\,{\text{cm}}^{ - 2} \,{\text{s}}^{ - 1} \,{\text{atm}}^{ - 1} ) \)

M :

Molecular weight of gas mixture \( ({\text{g}}\,{\text{mol}}^{ - 1} ) \)

M C :

Atomic weight of carbon \( ({\text{g}}\,{\text{mol}}^{ - 1} ) \)

m :

Coefficient in Eq. [9]

n :

Coefficient in Eq. [9]

P :

Total pressure (atm)

Pr :

Prandtl number \( \left( { = \frac{{\mu_{\text{g}} C_{\text{p}} }}{k}} \right) \)

R :

Gas constant (\( {\text{cm}}^{3} {\text{atm}}\,{\text{mol}}^{ - 1} \,{\text{K}}^{ - 1} \))

Ra :

Rayleigh number (=Gr′Sc)

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 f :

Film temperature (K) \( \left( { = \frac{{T_{\text{i}} + T_{\text{b}} }}{2}} \right) \)

t :

Time (s)

T E :

Effective temperature of gases (K) (=0.83T f)

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

γ :

Coefficient in Eq. [9]

β :

Coefficient in Eq. [9]

μ g :

Gas viscosity (g cm−1 s−1)

ρ :

Melt density (g cm−3)

ρ g :

Gas density (g cm−3)

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Acknowledgments

Appreciation is expressed to the Natural Sciences and Engineering Research Council of Canada who provided funding in support of this project.

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, University of Toronto, 184 College Street, Toronto, ON, M5S 3E4, Canada

    Paul Wu (Graduate Student), Yindong Yang (Senior Research Associate), Mansoor Barati (Associate Professor) & Alex McLean (Professor Emeritus)

Authors
  1. Paul Wu
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  2. Yindong Yang
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  3. Mansoor Barati
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Corresponding author

Correspondence to Paul Wu.

Additional information

Manuscript submitted December 19, 2013.

Appendix

Appendix

Assuming an ideal gas phase, the density is calculated from the relationship:

$$ \rho_{\text{g}} = \frac{MP}{RT}. $$

Data for viscosity, inter-diffusivity, heat capacity, and thermal conductivity are available from AspenONE Engineering Suite—Heat Exchanger Design.

$$ T_{\text{f}} = 1079\,{\text{K}}\left( {806\,^\circ {\text{C}}} \right);\quad D_{\text{AB}} = 1.520\,{\text{cm}}^{2} \,{\text{s}}^{ - 1} . $$

CO2 Mole 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

2

0.000452

0.000558

0.532

0.000460

6

0.000454

0.000561

0.560

0.000464

10

0.000456

0.000552

0.600

0.000461

15

0.000458

0.000560

0.636

0.000462

20

0.000460

0.000537

0.679

0.000464

25

0.000463

0.000529

0.717

0.000470

30

0.000465

0.000522

0.755

0.000482

$$ T_{\text{E}} = 896\,{\text{K}}\left( {623^\circ {\text{C}}} \right);\quad D_{\text{AB}} = 1.247\,{\text{cm}}^{2} \,{\text{s}}^{ - 1} . $$

CO2 Mole 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

10

0.000456

0.000552

0.594

0.000393

30

0.000465

0.000522

0.738

0.000411

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Wu, P., Yang, Y., Barati, M. et al. Decarburization of Levitated Fe-Cr-C Droplets by Carbon Dioxide. Metall Mater Trans B 45, 2211–2221 (2014). https://doi.org/10.1007/s11663-014-0126-8

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