Droplet Formation and Dripping Behavior during the Electroslag Remelting Process with Two Series-Connected Electrodes
Abstract
:1. Introduction
2. Numerical Model
2.1. Mathematical Modeling
2.1.1. Electromagnetic Field Control Equation
2.1.2. Fluid Control Equation
2.1.3. Multiphase Flow
2.1.4. Governing Equation for Droplet
2.1.5. Boundary Condition
2.1.6. Calculation Strategy
3. Experimental Setup
4. Results and Discussion
4.1. Validation of Mathematical Model
4.2. Droplet Formation and Dripping Process
4.3. Velocity Field and Temperature Field
4.4. Variation of Electrical Parameters
4.5. Effects of Filling Rate on the Droplet Behavior
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
E | Electric field (V·m−1) |
H | Magnetic field intensity (A·m−1) |
J | Current density (A·m−2) |
B | Magnetic flux density (T) |
t | Time (s) |
ρ | Density of fluid (kg·m−3) |
v | Velocity (m·s−1) |
P | Pressure (Pa) |
μeff | Effective viscosity of the fluid (Pa·s) |
Floc | Electromagnetic force (N·m−3) |
μ0 | Vacuum permeability (H·m−1) |
Qj | Joule heat per unit volume (W·m−3) |
Electroconductibility (S−1·m−1) | |
U | Velocity of droplet (m·s−1) |
rd | Radius of droplet (m) |
qd | Density of droplet (kg·m−3) |
Cd | Resistance coefficient |
Conductivity of slag (S·m−1) | |
Cp | Heat capacity of liquid steel (J·kg·K−1) |
Tdp | Temperature of droplet (K) |
TL | Liquidus temperature (K) |
Tme | Melting point of electrode (K) |
I0 | Current (A) |
Qc | Heat of convection heat transfer (W·m−2·K−1) |
Qr | Heat transfer heat of the radiation (W·m−2·K−1) |
A | Heat exchange area (m2) |
h | Heat transfer coefficient (W·m−2·K−1) |
TB | Average temperature of slag/metal interface (K) |
CP,d | Heat capacity of the droplet (J·kg−1·K−1) |
CP,l | Liquid heat capacity of steel (J·kg−1·K−1) |
me | Melt rate (kg·s−1) |
Dm | Diameter of the mold (m) |
K | Filling rate |
Ts | Surface temperature of slag (K) |
re | Radius of electrode (m) |
R | Radius of mold (m) |
u | Melting rate of electrode (kg·s−1) |
L | Electrode filling rate (m·s−1) |
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Parameter | Value |
---|---|
Physical properties of slag | |
Density, kg·m−3 | 2850 |
Specific capacity, J·kg−1·K−1 | 1404 |
Thermal conductivity, W·m−1·K−1 | 10.45 |
Viscosity, kg·m−1·s−1 | 0.01 |
Emissivity | 0.6 |
Expansion coefficient, K−1 | 0.0001 |
Physical properties of steel | |
Density, kg·m−3 | 7200 |
Specific capacity, J·kg−1·K−1 | 502 |
Thermal conductivity, W·m−1·K−1 | 31.9 |
Steel solidus temperature, K | 1723 |
Steel liquidus temperature, K | 1693 |
Latent heat of solidification, J·kg−1 | 247,000 |
Process parameters | |
Immersion depth of electrode, m | 0.02 |
Mold diameter, m | 0.14 |
Length of electrode, m | 0.32 |
Voltage, V | 35 |
Height of slag, m | 0.07 |
Filling rate | 0.5, 0.6, 0.7, 0.8 |
Distance between the two electrodes, m | 0.0265 |
Parameter | Value |
---|---|
Length of electrode, m | 0.07 |
Inner diameter of beaker, m | 0.085 |
Resistance of resistor, Ω | 5 |
Depth of electrode immersion, m | 0.007 |
Height of slag, m | 0.056 |
Viscosity of wood alloy, kg·m−1·s−1 | 0.0042 |
Distance between the two electrodes, m | 0.001 |
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Tong, W.; Li, W.; Zang, X.; Li, H.; Jiang, Z.; Han, Y. Droplet Formation and Dripping Behavior during the Electroslag Remelting Process with Two Series-Connected Electrodes. Metals 2020, 10, 386. https://doi.org/10.3390/met10030386
Tong W, Li W, Zang X, Li H, Jiang Z, Han Y. Droplet Formation and Dripping Behavior during the Electroslag Remelting Process with Two Series-Connected Electrodes. Metals. 2020; 10(3):386. https://doi.org/10.3390/met10030386
Chicago/Turabian StyleTong, Wenjie, Wanming Li, Ximin Zang, Huabing Li, Zhouhua Jiang, and Yu Han. 2020. "Droplet Formation and Dripping Behavior during the Electroslag Remelting Process with Two Series-Connected Electrodes" Metals 10, no. 3: 386. https://doi.org/10.3390/met10030386