Abstract
A computational fluid dynamics model was developed to study momentum transfer from the plasma arc jet to the slag bath in a direct-current (DC) ilmenite smelting furnace. The arc was approximated with a steady-state turbulent gas jet that had a thrust equivalent to that of an arc. First, a sensitivity study was performed to understand the analogous turbulent gas jet chosen to represent the arc. Then, the turbulent gas jet representation was used to determine steady-state slag bath flow properties as a result of arc impingement. Lastly, to gauge the relative importance of arc impingement as a momentum source, the contributions of different momentum sources in a DC arc furnace were compared, including electromagnetic and buoyancy forces.
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Abbreviations
- A :
-
area [m2]
- \(A_{\mathrm {{F_{AT}}}}\) :
-
proportionality constant (1.663 × 10−7) [N A−2]
- B:
-
magnetic flux density [Wb m−2]
- \(d_{\mathrm {E}}\) :
-
diameter of electrode [m]
- \(d_{\mathrm {F}}\) :
-
diameter of furnace vessel [m]
- \(d_{\mathrm {N}}\) :
-
diameter of inlet jet nozzle [m]
- \(F_{\mathrm {AT}}\) :
-
arc thrust [N]
- \(F_{\mathrm {T}}\) :
-
thrust generated by a turbulent gas jet [N]
- \({\mathbf {g}}\) :
-
gravitational acceleration vector [m s−2]
- h :
-
heat transfer coefficient [W m−2 K−1]
- I :
-
arc current [A]
- \({{\mathbf {j}}}\) :
-
electric current density [A m−2]
- \(L_{\mathrm {A}}\) :
-
arc length [m]
- \(L_{\mathrm {E}}\) :
-
electrode length [m]
- p :
-
instantaneous pressure [Pa]
- q :
-
rate of heat transfer [W]
- \(r_{\mathrm {aaz}}\) :
-
radius of the arc attachment zone [m]
- \(r_{\mathrm {cs}}\) :
-
radius of the cathode spot [m]
- \(T_{\mathrm {fluid}}, T_{\mathrm {surface}}\) :
-
temperature [K]
- \({\mathbf {u}}\) :
-
velocity vector in Cartesian space [m s−1]
- \(U_i\) :
-
mean velocity component [m s−1]
- \(u_i\) :
-
fluctuating velocity component [m s−1]
- \(u_{\mathrm {G}}\) :
-
inlet velocity of gas jet [m s−1]
- μ:
-
dynamic viscosity [Pa s]
- \(\rho \) :
-
mass density [Kg m−3]
- \(\tau \) :
-
shear stress [N m−2]
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Acknowledgements
Authors would like to acknowledge the help provided by Dr Quinn Reynolds, Suzanne Roberts, and Dr Johan Heyns towards the completion of this work.
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Makgoale, T., Bogaers, A., Zietsman, J. et al. Momentum Transfer from Arc to Slag Bath in a DC Ilmenite Smelting Furnace: A Computational Analysis. JOM 73, 2682–2697 (2021). https://doi.org/10.1007/s11837-021-04792-x
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DOI: https://doi.org/10.1007/s11837-021-04792-x