Abstract
A multi-physics model has been developed to investigate the molybdenum and nickel distribution in large-scale Ti-0.3 wt.% Mo-0.8 wt.% Ni slab ingots obtained by electron beam cold hearth melting. Numerical methods are pivotal in revealing the distribution trends of molybdenum and nickel in slab ingot in different casting conditions. The distribution of molybdenum slightly changed between 0.28 and 0.32 wt.% in the solidified ingot. However, the sharp change in the nickel distribution (between 0.73 and 1.53 wt.%) was caused by the fluid velocity decrease along the flow direction, resulting from a weakened vortexing effect. Additionally, the increase of the casting speed or pouring temperature led to a deeper molten pool and evident vortexing effect. A potential relationship indicates the decrease of nickel segregation degree at higher pouring temperatures, or the casting speed decrease within the research scope.
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Abbreviations
- \(A_{{{\text{mushy}}}}\) :
-
Mushy zone constant
- \(A_{r}\) :
-
Pre-exponential factor (consistent units)
- \(a_{p}\) :
-
Cell matrix coefficient
- \(p\) :
-
Statics pressure, Pascal
- \(B_{T}\) :
-
Thermal expansion coefficient, 1/K
- \(C_{c,i}\) :
-
Solutal expansion coefficient, 1/wt.%
- \(\beta\) :
-
Liquid fraction
- \(C_{p}\) :
-
Specific heat, J/kg K
- \(D_{i,m,liq}\) :
-
Mass diffusion coefficient for species in the mixture, m2/s
- \(T\) :
-
Temperature, K
- \(\vec{Q}_{r}\) :
-
Source term
- \(\vec{g}\) :
-
Acceleration due to gravity, m/s2
- \(H\) :
-
Enthalpy, J/kg
- \(h\) :
-
Sensible enthalpy, J/kg
- \(h_{{{\text{ref}}}}\) :
-
Reference enthalpy, J/kg
- \({\Delta }H_{f}\) :
-
Pure solvent melting heat, J/kg
- \(k\) :
-
Thermal conductivity, K/m K
- \(K_{i}\) :
-
The partition coefficient of solute i
- \(K_{f,i}\) :
-
Forward rate constant for reaction
- \(L_{C}\) :
-
Latent heat of the material, J/kg
- \(Y_{{i,{\text{sol}}}}\) :
-
Locally averaged concentration of solute element i in solid phase, wt%
- \(m_{i}\) :
-
The slope of the liquidus surface with respect to Yi
- \(n\) :
-
Iteration number
- \(N_{t}\) :
-
Number of species
- \(\overline{{\overline{\tau }}}\) :
-
Stress tensor, N/m2
- \(\rho\) :
-
Density, kg/m3
- \(\sum\nolimits_{i} {}\) :
-
Sum based on solute element i
- \(T_{{{\text{ref}}}}\) :
-
Reference temperature, K
- \(T_{c}\) :
-
Cell temperature, K
- \(T^{*}\) :
-
Interface temperature, K
- \(T_{{{\text{melt}}}}\) :
-
Melting temperature, K
- \(R_{i}\) :
-
Reaction rate, kg/m2 s
- \(Y_{i}\) :
-
The mass fraction of solute i
- \(\Delta t\) :
-
Time step
- \( \overrightarrow {v} \) :
-
Cell velocity, m/s
- \( \overrightarrow {v}_{p}\) :
-
Pull velocity, m/s
- \(\vec{v}_{{{\text{liq}}}}\) :
-
Velocity of the liquid, m/s
- \(Y_{0}\) :
-
The initial mass fraction of solute i, wt%
- \(\lambda\) :
-
Relaxation factor with a default value, 0.9
- \(L\) :
-
Characteristic length, m
- \(V_{c}\) :
-
Cell volume, m3
- \(Y_{{i,{\text{liq}}}}\) :
-
Locally averaged concentration of solute element i in liquid phase, wt
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Acknowledgements
This work was supported by Major Science and Technology Projects of Yunnan Science and Technology Plan (No. 202002AB080001) and Science and Technology Major Project of Yunnan Province (No. 202202AG50007).
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Zhu, Z., Li, X., Zhou, R. et al. Numerical Simulation of Molybdenum and Nickel Distribution in Large-Scale Slab Ingots of Ti-0.3 wt.% Mo-0.8 wt.% Ni Alloys During Electron Beam Cold Hearth Melting. JOM 74, 3811–3820 (2022). https://doi.org/10.1007/s11837-022-05396-9
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DOI: https://doi.org/10.1007/s11837-022-05396-9