Numerical Investigation and Optimization of Transpiration Cooling Plate Structures with Combined Particle Diameter
Abstract
:1. Introduction
2. Numerical Modeling and Validation
2.1. Geometric Models and Mathematical Models
2.2. Mesh Independence Verification
2.3. Numerical Method Validation
3. Analysis of Results and Discussion
3.1. Cooling Performance of Porous Plate Structure
3.2. Response Surface Methodology for Optimal Design
3.2.1. Parameter Setting
3.2.2. Response Surface Model Construction
3.3. Analysis of Optimization Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
Nomenclature | |||
Latin symbols | Greek symbols | ||
C | inertial coefficient | ρ | density, kg/m3 |
dp | particle diameter, m | ε | porosity |
E | total energy, J | μ | dynamic viscosity, Pa·s |
F | coolant injection rate | τ | stress, N |
h | height of hot end wall, m | η | cooling effectiveness |
J | mass diffusion flux, kg/(s·m2) | Subscript | |
k | thermal conductivity, W/(m·K) | ave | average |
K | permeability of porous media, m2 | c | coolant |
l | total length of hot end wall, m | eff | effective |
p | pressure, Pa | f | fluid |
T | temperature, K | s | solid |
U | velocity, m/s | w | wall |
Y | species mass fraction | ∞ | main stream |
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Boundary Conditions | Value | |
---|---|---|
Main Stream (air) | Temperature (T∞) | 500 K |
Velocity (V∞) | 20 m/s | |
Coolant (N2) | Temperature (Tc) | 300 K |
Mass Flow Rate (mc) | 30 g/s | |
Porous Media (Inconel-600) | Density | 8420 kg/m3 |
Thermal Conductivity | 20.615 W/(m·K) | |
Specific Heat | 460 J/(kg·K) |
Computational Domain | Governing Equations |
---|---|
Main Stream Channel and Cooling Chamber | Continuity equation: |
Momentum equation: | |
Energy equation: | |
Component equation: | |
Porous Media Region | Continuity equation: |
Momentum equation: , | |
Energy equation: |
Factor | Variable | Initial Value | Lower Limit | Upper Limit |
---|---|---|---|---|
dpA/μm | P1 | 40 | 40 | 200 |
εA | P2 | 0.3 | 0.2 | 0.6 |
h/mm | P3 | 5 | 5 | 9 |
lA/mm | P4 | 50 | 20 | 60 |
εB | P5 | 0.3 | 0.2 | 0.6 |
Initial Value | Optimal Value | ||
---|---|---|---|
P1−dpA/μm | 40 | 163.67 | |
P2−εA | 0.3 | 0.4671 | |
P3−h/mm | 5 | 9 | |
P4−lA/mm | 50 | 20 | |
P5−εB | 0.3 | 0.4627 | |
P6−ηave | Predictive value | 0.6738 | 0.7226 |
Simulated value | 0.6827 | 0.7238 | |
Error | 1.30% | 0.17% | |
P7−p/Pa | Predictive value | 39,755 | 3230 |
Simulated value | 37,824 | 3191 | |
Error | 5.11% | 1.22% |
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Wang, D.; Liu, Y.; Zhang, X.; Kong, M.; Liu, H. Numerical Investigation and Optimization of Transpiration Cooling Plate Structures with Combined Particle Diameter. Energies 2025, 18, 2950. https://doi.org/10.3390/en18112950
Wang D, Liu Y, Zhang X, Kong M, Liu H. Numerical Investigation and Optimization of Transpiration Cooling Plate Structures with Combined Particle Diameter. Energies. 2025; 18(11):2950. https://doi.org/10.3390/en18112950
Chicago/Turabian StyleWang, Dan, Yaxin Liu, Xiang Zhang, Mingliang Kong, and Hanchao Liu. 2025. "Numerical Investigation and Optimization of Transpiration Cooling Plate Structures with Combined Particle Diameter" Energies 18, no. 11: 2950. https://doi.org/10.3390/en18112950
APA StyleWang, D., Liu, Y., Zhang, X., Kong, M., & Liu, H. (2025). Numerical Investigation and Optimization of Transpiration Cooling Plate Structures with Combined Particle Diameter. Energies, 18(11), 2950. https://doi.org/10.3390/en18112950