Electric-Thermal Analysis of Power Supply Module in Graphitization Furnace
Abstract
:1. Introduction
2. Research Subject and Mathematical Model
2.1. Research Subject
2.2. Electric-Thermal-Fluid Coupling Process
2.3. Mathematical Model
- (1)
- Electric Field Governing Equation
- (2)
- Fluid Field Governing Equation
- (3)
- Thermal Field Governing Equation
3. Numerical Simulation and Validation
3.1. Mesh and Material Properties
3.2. Model Setup and Solving
3.2.1. Initial Conditions
- (1)
- Ambient temperature: The entire computational domain is initialized at an ambient temperature of 20 °C.
- (2)
- Fluid flow: The fluid domain is initialized with a velocity of 0 m/s and a gauge pressure of 0 Pa.
- (3)
- Electric potential: The entire solid domain is initialized with an electrical potential of 0 V.
3.2.2. Boundary Conditions
- (1)
- Thermal boundary conditions
- (2)
- Fluid Flow Boundary Conditions
- (3)
- Electrical Boundary Conditions
3.2.3. Contact Conditions
3.2.4. Solving Setup
3.3. Test Validation
4. Results and Discussion
4.1. End-Time Distribution
4.2. Temporal Variation of Temperature
4.3. Temporal Variation of Potential Differences
4.4. Heat Budget Analysis
4.5. Comparison with Previous Work
5. Conclusions and Future Work
5.1. Conclusions
- (1)
- Significant temperature differences and potential failure risks: The power transmission module exhibits notable temperature differences, with the highest temperature observed at the electrode block end face proximal to the furnace core and the lowest at the connector end face. Temperature gradient and current density analyses reveal elevated thermal stresses and ohmic heating at the bends of the splint plate, posing potential failure risks. Additionally, the temperature differences within the splint during graphitization are also pronounced, necessitating close monitoring to prevent thermal damage.
- (2)
- Resistance dominance and power savings: The electrode block accounts for a substantial portion of the total resistance within the power transmission module. Thus, maintaining relatively high temperatures, without compromising the splint plate, aids in keeping the total potential difference across the module at a relatively low level, thereby contributing to operational power savings.
- (3)
- Heat budget analysis and efficiency enhancement: The primary heat source for the power transmission module is thermal conduction from the furnace core through the electrode. Natural convection and forced convection via liquid cooling are the primary heat dissipation pathways. Optimizing the design of the cold plate and its liquid cooling channels, coupled with appropriate coolant flow rates and temperatures, is crucial for enhancing the energy efficiency of the graphitization process and ensuring stable operation of the power transmission clamp.
5.2. Future Work
6. Patent
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
J | [A/m3] | Current density |
Qj | [A/m3] | Current source |
σ | [S/m] | Electrical conductivity |
E | [V/m] | Electric field intensity |
φ | [V] | Electric potential |
V | [m/s] | Velocity vector |
ρl | [kg/m3] | Fluid density |
p | [Pa] | Pressure |
μ | [Pa·s] | Viscosity |
g | [m/s2] | Gravitational acceleration |
ρ | [kg/m3] | Density |
c | [J/(kg·K)] | Specific heat capacity |
T | [K] | Temperature |
t | [s] | Time |
λ | [W/(m·K)] | Thermal conductivity |
Sφ | [W/m3] | Heat source |
q | [W/m2] | Heat flux density |
h | [W/(m2·K)] | Convection heat transfer coefficient |
ΔT | [K] | Temperature difference |
L(T) | [W/(m·K)] or [S/m] | Thermal conductivity (or electrical conductivity) at temperature T |
T0 | [K] | Reference temperature |
L0 | [W/(m·K)] or [S/m] | Thermal conductivity (or electrical conductivity) at the reference temperature |
α | [K−1] | Temperature coefficient |
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Node Number | Element Number | Element Quality | Skewness | Orthogonal Quality | |||
---|---|---|---|---|---|---|---|
Average | Standard Deviation | Average | Standard Deviation | Average | Standard Deviation | ||
1,529,537 | 1,546,593 | 0.877 | 0.186 | 0.209 | 0.082 | 0.934 | 0.191 |
Material | Copper Alloy | Graphite | |
---|---|---|---|
Density (kg·m−3) | 8933 | 2300 | |
Specific heat capacity (J·kg−1·K−1) | 385 | 710 | |
Thermal conductivity | Reference value (W·m−1·K−1) | 390 | 680 |
Temperature coefficient (K−1) | −2.02 × 10−4 | 6.12 × 10−4 | |
Electric conductivity | Reference value (S·m−1) | 5.96 × 107 | 7.53 × 105 |
Temperature coefficient (K−1) | −8.10 × 10−4 | 6.12 × 10−4 |
Average Temperature | Total Current | End-Face Temperature of Electrode Block |
---|---|---|
Total | 0.848 | 0.999 |
Connector | 0.914 | 0.978 |
Cold plate | 0.883 | 0.991 |
Splint plate | 0.856 | 0.996 |
Electrode block | 0.847 | 0.999 |
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Xia, X.; Li, S.; Luo, D.; Chen, S.; Liu, J.; Yao, J.; Wu, L.; Zhang, X. Electric-Thermal Analysis of Power Supply Module in Graphitization Furnace. Energies 2024, 17, 4251. https://doi.org/10.3390/en17174251
Xia X, Li S, Luo D, Chen S, Liu J, Yao J, Wu L, Zhang X. Electric-Thermal Analysis of Power Supply Module in Graphitization Furnace. Energies. 2024; 17(17):4251. https://doi.org/10.3390/en17174251
Chicago/Turabian StyleXia, Xiangbin, Shijun Li, Derong Luo, Sen Chen, Jing Liu, Jiacheng Yao, Liren Wu, and Ximing Zhang. 2024. "Electric-Thermal Analysis of Power Supply Module in Graphitization Furnace" Energies 17, no. 17: 4251. https://doi.org/10.3390/en17174251
APA StyleXia, X., Li, S., Luo, D., Chen, S., Liu, J., Yao, J., Wu, L., & Zhang, X. (2024). Electric-Thermal Analysis of Power Supply Module in Graphitization Furnace. Energies, 17(17), 4251. https://doi.org/10.3390/en17174251