Author Contributions
Conceptualization, C.L. and X.D.; methodology, X.Y.; software, C.L.; validation, H.L., C.D. and J.W.; formal analysis, C.L.; investigation, J.W.; resources, C.D.; data curation, H.L.; writing—original draft preparation, C.L.; writing—review and editing, X.D.; visualization, X.Y.; supervision, X.D.; project administration, X.Y.; funding acquisition, X.D. All authors have read and agreed to the published version of the manuscript.
Funding
This research was funded the National Key R&D Program of China (2017YFB0603801).
Institutional Review Board Statement
Not applicable.
Informed Consent Statement
Not applicable.
Data Availability Statement
Not applicable.
Conflicts of Interest
The authors declare no conflict of interest.
Nomenclature
As | Area (m2) | R | Molar gas constant (J/mol·K) |
Cp | Specific heat capacity (J/kg·K) | Ri | Rate of reaction i (mol/m3·s) |
Di | Mass diffusion coefficient (m2/s) | Re | Reynolds number (‒) |
Dsh | Diameter of kiln (m) | Sϕ,p | Source term for phase p (kg/m3·s) |
Ea,i | Activation energy of reaction i (J/kg·mol) | T | Temperature (K) |
Fgs | Drag force (N/m2) | vp | Velocity of phase p (m/s) |
Gr | Grashof number (‒) | Yi | Mole fraction of species i (‒) |
Hp | Enthalpy of phase p (J/mol) | Greek Symbols |
ΔHi | Enthalpy of reaction i (J/mol) | αs | Thermal diffusivity (m2/s) |
h | Heat transfer coefficient (W/m2·K) | εp | Volume fraction of phase p (‒) |
J | Radiation intensity (W/m2) | θ | Central angel (rad) |
k | Turbulence kinetic energy (J) | λp | Thermal conductivity (W/m·K) |
Ke,i | Equilibrium constant of reaction i (‒) | ρp | Density of phase p (kg/m3) |
Mi | Molecular weight of species i (kg/mol) | σ | Stefan-Boltzmann constant (W/m2·K4) |
P | Pressure (Pa) | Subscripts |
Pr | Prandtl number (‒) | g | Gas phase |
q | Heat flux (J/m2·s) | s | Solid phase |
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Figure 1.
Schematic diagram of the pre-reduction rotary kiln.
Figure 2.
Heat and mass transfer between freeboard region and bed region.
Figure 3.
Simplified geometric model of the rotary kiln.
Figure 4.
Computation mesh.
Figure 5.
Temperature distribution of the gas phase along the axial section.
Figure 6.
Temperature distribution of the solid phase within the bed cross-section.
Figure 7.
Temperature distribution of the cross-section along the axis of the rotary kiln.
Figure 8.
Composition distributions of the gas phase along the axial section.
Figure 9.
Average mole fraction of gas composition in the bed region along the axial section.
Figure 10.
Average mass fraction of solid composition in the bed region along the axial section.
Figure 11.
Average bed temperature along the axial section for different C/O mole ratios.
Figure 12.
Reduction potential along the axial section for different C/O mole ratios.
Figure 13.
Metallization rate along the axial section for different C/O mole ratio.
Figure 14.
Average bed temperature along the axial section for different fill degrees.
Figure 15.
Reduction potential along the axial section for different fill degree.
Figure 16.
Metallization rate along the axial section for different fill degrees.
Table 1.
Variables in Equation (1).
Phase | Eq. | ϕ | Γϕ | Sϕ |
---|
Gas | Mass | 1 | 0 | Sϕ,g |
Momentum | | 0 | |
Energy | Hg | λg/CP,g | |
Species i | Yi,g | ρg Di | |
Solid | Mass | 1 | 0 | Sϕ,s |
Momentum | | 0 | |
Energy | Hs | λs,eff/CP,s | |
Species j | Yj,s | ρsDj | |
Table 2.
Kinetic parameters of homogenous reactions [
20,
21].
Reaction | Ar (s−1) | Ea (J/kmol) | βr | Reaction Order |
---|
2CO + O2 = 2CO2 | 2.2 × 1012 | 1.7 × 108 | 0 | [CO][O2] |
2H2 + O2 = 2H2O | 6.8 × 1015 | 1.67 × 108 | −1 | [H2]0.25[O2]1.5 |
CO + H2O = CO2 + H2 | 2.75 × 109 | 8.4 × 107 | 0 | [CO][H2O] |
Table 3.
Kinetic parameters of heterogeneous reactions [
24].
Reactions | ki,0 (m·s−1) | Ea (J/mol) | Ke | Rate Expressions |
---|
C + CO2 = 2CO | 1.87 × 108 | 221,800 | exp (−20,765.92/T + 32.8) | Equation (9) |
C + H2O = CO + H2 | 6.05 × 105 | 172,700 | exp (−16,142.19/T + 28.16) | Equation (10) |
3Fe2O3 + CO = 2Fe3O4 + CO2 | 2700 | 113,859 | exp (5815.5/T + 5.5076) | Equation (7) |
3Fe2O3 + H2 = 2Fe3O4 + H2O | 160 | 92,000 | exp (2065/T + 8.102) | Equation (8) |
Fe3O4 + CO = 3FeO + CO2 | 23 | 71,100 | exp (−4685.22/T + 5.19) | Equation (7) |
Fe3O4 + H2 = 3FeO + H2O | 30 | 63,600 | exp (−1857.51 + 1.01) | Equation (8) |
FeO + CO = Fe + CO2 | 17 | 69,454 | exp (2376.46/T−2.82) | Equation (7) |
FeO + H2 = Fe + H2O | 30 | 63,600 | exp (−1857.51/T + 1.01) | Equation (8) |
Table 4.
Chemical composition of fuel gas.
Species | CO | CO2 | H2 | H2O | N2 |
---|
Mole fraction | 56.7 | 20.0 | 14.3 | 4.8 | 4.2 |
Table 5.
Chemical composition of raw material.
Species | Fe2O3 | FeO | Al2O3 | SiO2 | CaO | MgO | TiO2 | C | Vol | Ash |
---|
Mass fraction | 38.6 | 24.6 | 2.6 | 3.5 | 1.1 | 2.7 | 5.0 | 15.3 | 4.7 | 1.9 |
Table 6.
Comparison between measured and simulated results.
Parameters | Measured | Simulated | Relative Error |
---|
CO(%) | 19.4 | 20.2 | 4.3% |
CO2(%) | 24.2 | 22.9 | 5.1% |
H2(%) | 8.1 | 9.0 | 10.8% |
H2O(%) | 15.2 | 14.9 | 1.6% |
T(K) | 1023 | 1002 | 2.1% |
Metal(%) | 70.0 | 72.4 | 3.4% |
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